摘要:

Faraday Discuss. Chem. SOC., 1986,82, 1-12 Preferential Population of Magnetic Sublevels of Photodissociated Atoms Photodissociation of Alkali-metal Dimers and the Effect of Magnetic Field Hajime Kat6 Department of Chemistry, Faculty of Science, Kobe Uniuersity, Nada-ku, Kobe 657, Japan By applying an external magnetic field, we have determined the population of the magnetic sublevels of photodissociated atoms from the intensities of atomic fluorescence lines split by the Zeeman effect. A preferential popula- tion of the magnetic sublevels of the atomic fragment Na(3 2P3/2), which arises from the direct photodissociation through the D 'II (continuum) state of the NaK molecule, has been observed. The results are explained by assuming the separability of electronic and nuclear motion during the dissoci- ation.The observed results could be rationalized by the sum of the photodis- sociation amplitudes caused by excitation of the P, Q and R branches. The population of the magnetic sublevels of Rb(5 *P3/2) atoms produced by predissociation of the C 'nu state of the Rb2 molecule by the repulsive molecular state c 'E: has been determined from the Zeeman spectra of the emission Rb(5 2P3/2 --* 5 'S;;). The observed results are interpreted by including the spin-orbit coupling between an excited level of the C 'nu state and levels of the c 'X: state and the effect of the external magnetic field. The fluorescence of excited fragments which arise from photodissociation has been found to give a detailed picture of photodissociation dynamics.The degree of polariz- ation was shown to be related to an anisotropic spatial distribution of dissociation products and a preferential population of the magnetic sublevels of the excited frag- ments.' Rules for determining what type of atomic states results from dissociation of a given molecular electronic state were derived by Wigner and Witmer: and worked out by M~lliken.~ Singer et aL4 studied the photodissociation of a diatomic molecule by considering the correlation of angular momentum on the basis of quantum mechanics and presented the polarization ratio for various electronic coupling schemes. Vigue et al.' also presented a quantum-mechanical treatment of photodissociation and fluores- cence from the fragment and calculated the polarization ratio. In the calculation of the differential fluorescence cross-section in both ref.(4) and ( 5 ) a quantum interference between the photodissociations through different excitations was taken into account. It will be shown in this article that the observed fluorescence spectra of the fragments should be interpreted as the superposition of the photodissociation amplitudes of individual excitations. By applying an external magnetic field, we have determined the population of the magnetic sublevels of the photodissociated atoms directly from the intensities of the fluorescence lines split by the Zeeman effect. The relative strengths of the Zeeman lines P3/2-2S7\, which are expected for the fluorescence of atoms distributed equally over the magnetic sublevels,6 are shown in fig.1. The polarization ratio of the fluorescence in the absence of an external magnetic field should be the same as the one in the presence of the field if the electric vector of the exciting light is parallel to the external magnetic field (the principle of spectroscopic stability).7i8 We consider, throughout this article, 1 2 m2 Magnetic Sublevels of Photodissociated Atoms H = O m 312 112 -1 /2 - 3 1 2 112 -1 / 2 4 4 1 3 3 1 Fig. 1. Allowed transitions [full lines polarized perpendicular (a) and broken lines polarized parallel (T) to the magnetic field] and strengths of the Zeeman lines 2Pjm/2-2S;;, which are expected for atoms equally distributed over magnetic sublevels. The expected line patterns for observation perpendicular to the magnetic field are shown.Their relative strengths are indicated both by the lengths of the lines and by the numbers. this optical disposition keeping the electric vector of the exciting light parallel to the external magnetic field. First, the polarization and Zeeman spectra of the sodium D2 line, emitted following excitation of the NaK molecule, are reported. Secondly, the population of the magnetic sublevels of the Rb(5 2P3"/2) atom, produced by predissociation of the C 'nu state of the Rb2 molecule by the repulsive molecular state c 'Z;, has been determined, and the results are reported. The observed results are analysed theoretically and the population of the magnetic sublevels of the photodissociated atoms is discussed. Experimental A plane-polarized laser beam was propagated along the x-axis with its electric vector E pointing along the z-axis.The direction of the external magnetic field coincides with the z-axis. A fluorescence detector was placed along the y-axis. The intensity IT( = 111) of light polarized along the z-axis (parallel to the electric vector of the incident light) and the intensity I,( = IL) of light polarized along the x-axis (perpendicular to the electric vector of the incident light) were observed separately through the polarization analyser followed by a polarization scrambler. The experimental apparatus for the measurement of fluorescence was the same as in previous report^.^'^^ We devoted great care to the elimination of self-reversal of the atomic emission. The laser beam passed close to the cell window. The diameter of the beam was 0.5 mm and we estimate that the fluorescence collecting lens collected all radiation from within ca.1 mm diameter of the sampling point. The vapour pressure was kept as low asH. Kat6 3 A ( a ) (b) - - 16974 16973 16974 16973 16975 16972 16975 16 972 wavenumber/cm-' Fig.2. Observed spectra of the sodium D2 line polarized along ( a ) the z-axis (I,) and (b) the x-axis ( I , ) for an external magnetic field strength (A) H = 0 and (B) H = 1.55 T. possible within the sensitivity limit of our fluorescence detector. The temperature of the cell was maintained ca. 10 K above the temperature of the reservoir in order to prevent condensation on the cell window. Potassium metal, which was 99.95% pure and contained sodium as a 0.05% impurity, was used in the study of the NaK molecule.The partial pressures of K and K2 in the cell at 500 K were ca. 2 x and 3 x Torr,? respectively, and that of NaK was estimated at <2 x lo-' Torr. When the sample was irradiated by the Ar+ laser line at 4765 A, the resonance fluorescence of only the NaK molecule was observed. Rubidium-85 metal was obtained by the reduction of 85RbCl (Oak Ridge National Laboratory, 99.78% 85RbC1, 0.22% of 87RbC1). The partial pressures of "Rb and 85Rb2 in the cell used to excite the 85Rb2 molecule at 400 K were 1 x lop3 and 5 x lop7 Torr, respectively. The absence of self-reversal was confirmed by observing that the spectral lineshapes did not change when the vapour pressure was reduced by a factor of 10. Direct Photodissociation Photodissociation of NaK and Fluorescence of the Na D2 Line When a mixture of sodium and potassium was irradiated by the 4765 A (20 981 cm-') line of an Ar' laser, fluorescence series attributed to the NaK molecule and the atomic D lines were ob~erved.~~"-'~ The D2 line Na(3 2P3/2 -P 3 'SIl2) was observed to be polarized in the absence of the external magnetic field, and the degree of polarization, given by was 0.10 * 0.02.By applying an external magnetic field, the line intensity of the fluores- cence from each of the magnetic sublevels Na(3 2P" ) could be observed separately as shown in fig. 2. The intensity of the transition Na(3 P3/* -P 3 "S:{:) was equal to that of the transition Na(3 2P132/2 -+ 3 2Sl/i2), yet different from the intensities of the transi- tions Na(3 'P:{: -3 'ST$) and Na(3 2PT/:/2 -+ 3 'S:::) which were observed to be of the same magnitude.The ratio of intensity of the transition Na(3 'P:{! -+ 3 S{/12) to that of the transition Na(3 'P:$ -+ 3 'S:$ was observed to be 1 : 2, which is different from the 1:3 ratio expected for atoms distributed equally over the magnetic sublevels 3/?2 3 / 2 (fig. 1). f'l Torr = 101 325/760 Pa.4 Magnetic Sublevels of Photodissociated Atoms At short and long internuclear distances, the D ‘II state is expected to be at a higher energy than the d 3111 state.” Hence, the D ‘II (continuum) state will be correlated mainly with the separated atoms Na(3 25/2) + K(4 2S1/2). The most likely source of the sodium D2 emission is therefore ‘direct photodissociation’ of NaK through the excitation to the D ‘J3 (continuum) state: NaK(X ‘Z+; v > 10) + hv ---* NaK(D ‘n; continuum) + Na(3 2P3/2) + K(4 2S1/2).(2) Theory of Fluorescence of Photodissociated Atoms and Discussion We consider here the atomic fluorescence which arises from a direct photodissociation following an optical excitation from a level of the ‘C state to a continuum of the ‘II state. The hamiltonian for a diatomic molecule can be written in the form H”= He,+ H, (3) where He, is the vibrational-electronic part and H, is the rotational part of the hamil- tonian. The eigenfunctions and eigenvalues of H” can be obtained by solving the secular equation composed of the matrix for H” in terms of the basis set IA)lSZ)lu)lJRM), where [A) is the electronic orbital part, I SZ) is the electronic spin part, I u) is the vibrational part and IJRM) is the rotational part.The values L and S are quantum numbers of the total electronic orbital angular momentum (L) and electronic spin angular momentum (S), and A and Z represent their projection along the molecular axis, respectively. We use the functions 1A)I SE)l u ) expressed in molecule-fixed coordinates. The rotational part (JRM) is expressed in laboratory-fixed coordinates, where J and M specify the total angular momentum and its projection along the laboratory-fixed z-axis, respectively, and iR = A+Z. The eigenfunctions for levels of the ‘Z+ and ‘II are expressed as ]‘Z+VJM) = lO+)lOO)l U)JJOM) (4) l’n;UJM)= (I1)lOO)lv)lJlM)zt I-l)lOO)lU)lJ- 1M))IJZ. ( 5 ) and The matrix elements of the electric dipole moment along the laboratory-fixed R, component can be calculated as” ( A’S’Z’v‘J’fi’M’lpR, IASEvJR M ) = 1 (-) ’-‘(A’S’Z’U’I~,., IASZU)( -)”-”[ (2J’ + 1)(2J + 1)]’’2 t =o,* 1 where the last two factors within parentheses are the Wigner 3 - j symbols, and pr, is the molecule-fixed rr component of an electric dipole moment p.For excitation by plane-polarized light with its electric vector along the z-axis, the non-vanishing transition moments for the transition ‘Z+-’rI are: ( J + Z ) ( J + M + 1)(J- M + 1) ( (J+ 1)(2J+ 1)(2J+3) (‘Z+v’’JMlpzl’lIev‘J+ 1M) = -pI ( J - 1)(J+ M)(J - M ) ( J(2J+ 1)(2J- 1) (‘Z+~’’JMIppl1nev‘J - 1 M ) = (7) where pl = (OOOu”Jp,.+,l- 100~‘) = (OOOU”~~,.-~~~OOU’).H. Kat6 5 Table 1. Algebraic formulae of MA[’II(?uJM)-’PG2] m MA[’II( ~ U J M ) - ~ P G ~ ] M A [ ‘ I I ( ~ U J M ) - ~ P ~ , I J ( J + 1)(2J2+2J - 3 ) * (2J - 1)(2J+3)M + (2J2+ 2J+ 3)M2 4J(J+ 1)(2J- 1)(2J+3) J ( J + 1) * M - M’ 4J(J+1) *3/2 J ( J + l)(10J2+ 10J-3)*(2J- 1)(2J+3)M-3(2J2+2J+3)M2 J ( J + l)* M + 3 M 2 *1/2 12J(J+ 1)(2J- 1)(2J+3) 12J(J+ 1 ) We have studied the rules for determining what type of atomic state with a definite electronic angular momentum j k and its projection mk along the z-axis, where k ( = a or 6 ) refers to the two atoms, results from a given dissociative state of a diatomic molecule.“ If a molecule in a definite state dissociates adiabatically into atoms in a specified fine-structure state I C k j k m k ) , the molecular basis functions can be written as x C 1 C (Jj-Mm(R-M+m) Llalh A a A b j o J h m a m h x (4 -aln(RO)(jlnj,j,Ih,AbsC) x ( ~ , ~ b ~ , ~ , l ~ ~ ) ( ~ , ~ b m ~ m b l j m > l c ~ ~ m , ) l C b j b m b ) .(8) Substitution of eqn (8) into the eigenfunction of a molecular state yields the eigenfunction expanded in terms of the atomic wavefunctions Ic&m,) and Icbjbmb). The square of the coefficient integrated over Euler angles (a, /3 and y ) gives the probability that the adiabatic dissociation of a molecule in the state expressed by the eigenfunction leads to the two atoms expressed by Ic&rn,) and Ic&mb). An NaK molecule excited to the D ‘II(continuum) state dissociates into two atoms Na(3 2P3/2) + K(4 2S1/2). We observed the emission of the total photofragments. The population of the photofragment Na(3 2P3”/2) could be observed by the emission Na(3 ’P3”/’ + 3 ’S;’;), but the accompanying K(4 2S;2) atom could not be detected since it does not emit any photon.The squares of the coefficients of (Na3’Pj= 3/2m)lK 4 ’Sj = 1/2m = 1/2) and INa 3 ’pj = 3/2m)(K 4 ’Sj = 1/2m = -1/2), integrated over Euler angles for the spherical functions and over the internuclear distance for the vibrational wavefunctions, are summed. The sum gives the probability of producing the atoms Na(3 2P,”/2) through the dissociation via the molecular state D ‘II(;vJM) expressed by eqn (9, and this is denoted by the symbol MA[’II(;vJM) - 3 2P,”/2]. The algebraic formulae are listed in table 1. The probability of producing a 3 2P,”/2 atom following the excitation ‘II(;v’J‘M’) + ‘Z+( v”JM) is proportional to: P [ ’ ~ ’ ( v ’ ‘ J M ) - ’ ~ ( ~ u ’ J ‘ M ) - ~ 2P,”/2] = 1(1x+~”~~ICL,11n;~f~’~)12~~[1n(;~r~r~)-3 ’P,”/,].(9) The summation of the photodissociation amplitude P over the quantum numbers M = J, J - 1 . . . - J is equivalent to averaging over all orientations of the molecule. The resulting algebraic formulae are listed in table 2. A direct photodissociation takes place following the excitation from a stable lower state to a continuous upper state. Even when excited by a laser line of a narrow linewidth, P, Q and R excitations from a particular rotational level can take place simultaneously for the transition ‘II( continuum) + ‘C+. The vibrational wavefunction of the dissociative continuum is normalized with respect to energy. l4 We cannot distinguish experimentally whether the dissociated atoms are produced through excitation of the P, Q or R branch.6 Magnetic Sublevels of Photodissociated Atoms Table 2.Algebraic formulae of C-,’= P[’Z’( u”JM) - ‘II(;v’J’M) - 3 2PQ2]/(2J + 1) in units of P w ’ l v ’ ) 1 2 m *3/2 * 1/2 (6J3 + 20J2 + 17J + 2)/60(J + 1)(2J + 1)2 (22J3+80J2+89J+34)/180(J+ 1)(2J+ 1)2 -J m c P[’~+(v”JM)-’n(fu’JM) -2P52]/(2J+ 1 ) M = J *3/2 *1/2 (2J2+2J+ 1)/60J(J+ 1 ) ( 14J2 + 14J - 3)/ 180J( J + 1) *3/2 *1/2 (6J3 - 2J2 - 5J + 1)/60J(2J + 1)2 (22J3 - 14J2 - 5 J - 3)/ 180J(2J + 1)2 However, interference effects for production of dissociated atoms by these excitations do not occur because the vibrational wavefunctions of the continuum excited by the P, Q and R branches are approximately orthogonal to each other. The probability of producing the Na(3 2P3”/2) atom following the excitation ‘II(continuum) + ‘Z through P, Q and R branches is then given by -J C {P[’Z+(v”JM)-’II(ev‘J+ 1M) -2P3m/2J+P[L~+(t)”JM)-LII(f2r’JM)-2P3m/2J M = J +P[’Z+(v”JM) -‘II(eu’J- 1M)-2P3m/2J}/(2J+ 1).(10) If we assume that the Franck-Condon factors of the P, Q and R branches for excitation from a particular rotational level are of the same magnitude, the ratios of producing the Na(3 ’Pz;:), Na(3 ”Pi::), Na(3 2P;/:/2) and Na(3 2PT,?/2) atoms are calculated to be 10J4 + 20J3 + 12J2 + 2J + 1 50J4 + 100.1~ + 64J2 + 14J - 3 30J(J+ 1)(2J+ 1)2 - 90J(J+ 1)(2J+ 1)2 ’ 50J4+ 100J3+64J2+14J-3 10J4+20J3+12J2+2J+1 (11) 90J(J+ 1)(2J+ 1)2 30J(J+ 1)(2J+ 1)2 using eqn (10) and the results in table 2. temperature T is approximately: The rotational-vibrational level distribution function of the ground state X’Z+ at a Be F(v,J)=-(2J+l) exp[-B,J(J+l)/kTI[l-exp(-w,/kT)] exp(-oev/kT) (12) kT where Be and o, are the rotational and vibrational constants and k is Boltzmann’s constant.This distribution function goes through a maximum at CQ. J = 43 for NaK at 500 K. Hence, the fine-structure states of the dissociated atom Na(3 2P3”/2) are expected to be populated in the ratio of 3 : 5 : 5 : 3 for m = 3/2, 1/2, -1/2 and -3/2 [from eqn (1 1 )H. Kat; 7 at large J]. The transition probabilities of the cr-polarized emission from the magnetic sublevels of m = 1/2,3/2, -3/2 and -1/2, which are in the order of high to low transition energies, are in the ratio of 1:3:3: 1 as shown in fig. 1 and those of the wpolarized emission from the magnetic sublevels of m=-1/2 and 1/2 are in the ratio of 4:4.Therefore, the line intensities of the a- polarized emission of the photodissociated atom Na(3 2P,"/2) of m = 1/2,3/2, -3/2 and -1/2 are expected to be in the ratio of 5 : 9: 9: 5 and those of the wpolarized emission of Na(3 'PZ2) of m = -1/2 and 1/2 are expected to be in the ratio of 20: 20. These results are in good agreement with the observed Zeeman spectra shown in fig. 2. In the absence of the external magnetic field, the value of I,,./I, is expected to be 10/7, hence the degree of polarization P is 3/17, which is close to the observed value 0.10 f 0.02. Let us now consider the quantum interference effects in the resonance fluorescence. The total rate R(a, 6 ) at which photons of polarization a are absorbed and photons of polarization 6 are re-emitted in the resonance fluorescence process (iJ") --* (eJ) + (fJ') is proportional to: 15-18 (eM, I er a liM")( iM"I er ale M2)(eM21 er 6 ( f M')( f M'I er 61 eM,) LreM,M2- i ( E e M l - EeM2)/ h1 R ( a , b ) = c M", M' M l M 2 (13) where M" and M' denote the magnetic sublevels of the initial state i and the final state f, respectively, and those of the excited state e are denoted by M, and M2.Eqn (13) provides a quantum-mechanical description of the interference effects which occur when two or more of the excited states are close enough together so that: reMlM2' (EeM1 -EeM2)/ (14) where r e M l M 2 = ( r e M 1 + r e M 2 ) / 2 and r e M , ( n = 1,2) is the spontaneous decay rate of the excited state eM,.The summation over all magnetic sublevels is equivalent to averaging over all orientations of the molecule. We observed the atomic fluorescence Na(3 2 P 3 / 2 + 3 2S1/2) which arises from a direct photodissociation following the optical excitation D 'II +- X 'X+ of the NaK molecule. Let us assume that the final state of the two atoms separated after the photoemission is expressed by the eigenfunction of the X 'C+ state expanded in terms of the atomic wavefunctions according to eqn (8): 1 I'Z'VJM) = lu) - YJM(PCf)(INa 3 2Si4)IK4 'si-f) 4 2 4 -"a3 2Si-$)(K42S$))/fi. (15) Then, the total rates of a-polarized emission Na(3 2P::$ + 3 2ST/i2), Na(3 P 3 / 2 + 3 'S;;;), Na(3 'PY7i2 + 3 2SF/i2) and Na(3 2PT/:/2 + 3 'S:$) are calcu- lated to be in the ratio of 17:9:9: 17 and those of the .rr-polarized emission Na(3 2P:;f+ 3 'S::;) and Na(3 2Py//2+ 3 2S;/:/2) are calculated to be in the ratio of 68 : 68.Accordingly, the value of I,,./ I, in the absence of the external magnetic field is expected to be 34/ 13, hence the degree of polarization P is 21/47. This result is coincident with the one calculated by Singer et aZ.,4 but this is different from the observed value of P = 0.10*0.02. The wavefunction of the final state IfM') in eqn (13) must be the eigenfunction of the same hamiltonian as the one for the molecular states X 'X+ and D 'n. However, it is not possible to represent the final state of the dissociated atoms after the photo- emission as the eigenfunction of the hamiltonian of the molecular state. Hence eqn (13), which takes into account a quantum interference between the photodissociation ampli- tude through the different excitation, is not appropriate to describe the rate of atomic 2 3/28 Magnetic Sublevels of Photodissociated Atoms fluorescence, which arises from the photodissociation following an optical excitation of a molecule.As shown above [see eqn (lo)], the observed fluorescence of the photofrag- ment should be interpreted as the superposition of the photodissociation amplitudes of individual excitations. Predissociation Predissociation of Rb2 and Fluorescence of the Rb D2 Line Predissociation of Rb, was observed when a rubidium vapour was irradiated by the Ar+ laser. When rubidium vapour in a cell was ir~-adiated,'~-~l the fluorescence of the Rb, molecule as well as the atomic D2 line Rb(5 ,P3/2 --+ 5 ,SlI2) were observed, whereas the D1 line Rb(5 ,P1/, ---* 5 2S1/2) was very weak.Feldman and Zare22 measured the fluores- cence resulting from the irradiation of a nozzle beam of rubidium using the 4765 A laser line. Under such collision-free conditions only the molecular fluorescence of the C 'nu + X 'Z: transition and the atomic 0, line were observed. Breford and Enge1ke2' excited Rb, in a supersonic beam using a dye laser. They concluded that the predissoci- ation of the C 'nu state is caused through the c 'Z: state, which correlates with the separated atoms Rb( 5 P3/2) + Rb( 5 2S1/2). We irradiated a cell containing isotopically pure rubidium-85 using the 4765 A line of the Ar+ laser and observed the molecular fluorescence of "Rb2 C 'nu --* X 'Zg and the atomic D2 line; again the D1 line was very weak.Three molecular fluorescence series were observed prominently and were tentatively assigned as those originating from the excitations C 'nu( v' = 3, J' = 44) + X 'Xi( v'' = 0, J"= 45), C 'nu( v' = 3, J' = 49)4-X1Z~(v"=O,J"=49) and C 'II,(u'=3, J'=54)+-X1Zi(v"=0, J"=53). The spectrum of the molecular fluorescence was similar to the one reported by Tam and Happer.,' Significant magnetic-field effects on one of the molecular fluorescence series were observed; part of the spectrum is shown in fig. 3. The intensity of the molecular fluorescence originating from the excitation C 'nu( v' = 3, J' = 54) + X 'Xi( v" = 0, J" = 53) was observed to decrease significantly when the external magnetic field was applied, whereas the intensity of the atomic D2 line at 1.55 T was about twice that at 0 T.Hence, the excited level C 'nu( v' = 3, J'= 54) is considered to be most strongly coupled to the predissociation through the c 'Z: state. The observed Zeeman spectra of the D2 line Rb(5 2P,"/2 --* 5 :Sz>) are shown in fig. 4. We estimated from the intensities of the lines Rb(5 ,P3"/,--* 5 SIj2) at 1.55 T and the transition probabilities from fig. 1 that the population of the magnetic sublevels rn = 3/2, 1/2, -1/2 and -3/2 of the photodissociated atoms Rb(52P,"12) are in the ratio of 0.28:0.32:0.25:0.15. The 0, line in the absence of the external magnetic field was slightly polarized, and the degree of polarization was 0.05 f 0.03.These observations are discussed below. Theory of Predissociation through the Perturbation between 'nu and '2; and Discussion We consider here the population of magnetic sublevels of the predissociated atoms Rb(5 ,P3"/,) arising through the perturbation between the C 'II, and c 'E: states follow- ing the excitation C 'nu (v' = 3, J' = 54) +- X 'Xi( v" = 0, J" = 53) of Rb,. The transition moment for the excitation C 'nu( v'JM) +- X '2f( v"J - 1M) by plane-polarized light with its electric vector along the z-axis is expressed as: (J+ 1)(J+ M)(J- M) ( J(2J- 1)(2J+ 1) ('Z+V''J - lMIpZ('IIev'JM) = -pL The perturbation, which causes the predissociation of the C 'nu state through the c 'Z: state, is spin-orbit coupling Hso. The transition probability per unit time betweenH.Kat6 9 P R Q R L I 1 I I I 20140 20160 20140 20160 wavenumber/cm-’ Fig. 3. Part of the fluorescence spectrum of 85Rb2 excited by the 4765 A line of the Ar+ laser for external magnetic field strengths ( a ) H = 0 and ( b ) H = 1.55 T. Shown on the plots are the P branch of the fluorescence originating from the excitation C ‘nu( u’ = 3, J’ = 54) t X ‘Xi( U” = 0, J”= 53), the R branch of the fluorescence originating from the excitation C ‘nu( v’ = 3, J’ = 44) *- X ‘mi( v” = 0, J” = 45) and the Q branch of the fluorescence originating from the excitation C ‘nu( v‘ = 3, J’ = 49) t X ‘Xi( v’ = 0, J”= 49) overlapped with the Rand P branch of fluorescence lines originating the two excitations mentioned above. - I 12815 12817 12815 12817 wavenumber/cm-‘ Fig.4.Observed spectra of the rubidium D2 line ( a ) polarized along the z-axis (I,) and (b) polarized along the x-axis ( I - ) for an external magnetic field strength H = 1.55 T.10 Magnetic Sublevels of Photodissociated Atoms Table 3. Algebraic formulae of MA[3Xc+( uN = JJM)-2P3m/2] m MA[3X+( vN = JJM)-2P3m/2] 312 J 2 ( J + 1)’- J ( J + l)M + ( J 2 + J - 3)M’ + 3M3 J ( J + 1)(2J+3)(2J- 1) J ( J + 1)(5J2+ 5J - 6) + ( 17J2+ 17J - 6 ) M - 3(J2+J - 3)M2 - 54M3 3J(J+ 1)(2J+3)(2J- 1 ) J ( J + 1 )( 5J2 + 5J - 6) - ( 17J2 + 17J - 6)M - 3(J2 + J - 3)M2 + 54M3 3J(J+ 1)(2J+3)(2J- 1 ) 112 -112 -312 J2( J + 1)2 + J ( J + l)M + ( J’ + J - 3)M2 - 3 M 3 J ( J + 1)(2J+3)(2J- 1 ) a discrete state i and a continuous state { j } is given by first-order perturbation theory as:24 The non-vanishing matrix element between wavefunctions of ‘n( eu’JM) and 31;+ is (18) where (0’1 u ) is the overlap integral between the vibrational wavefunctions v’ and v and f is the coupling constant. The molecular levels 3X+( vN = JJ * 1 M ) and 3Z+( vN = JJM), which are degenerate in the absence of an external magnetic field, split into three levels I; (vN = JME,) of E, = 2)4&, o and - 2 p ., ~ in the presence of a magnetic field H.” Then the non-vanishing matrix elements of H,, are (111ev’JMIHso131;+vN = JJM) = (v’lu)5/2 3 + M (0‘1 4 5 [4J(J+ 1)y2 (’IIev’JM]Hso13Z+vN = JME, = 0) = - The eigenfunction for the level 3Z+( vN = JJM) is expressed as I ~ Z + ~ N = JJM) = ( l o + ) p i ) l v ) p i M ) - lo+)li - i)lv)lJ - ~ M ) ) / J Z . (20) lv) in eqn (20) is the vibrational wavefunction of the dissociative continuum for the c ’X: state, which is repulsive.A Rb, molecule in the c ’I;: state dissociates into two atoms Rb( 5 2S1/2) + Rb(5 ,P3/2). Substitution of eqn (8) into eqn (20) yields the eigen- function expanded in terms of the atomic function ISim‘) and IPgm). The square of the coefficient integrated over Euler angles gives the probability that the adiabatic dissociation of a molecule in the state c3Z:(vN=JJM) leads to the two atoms Rb(5 ‘ST;) + Rb(5 ,P3”/,). Fluorescence from all these photofragments could be observed in the present experiments. We determined the population of Rb(5 ,P,”/,) by observing the emission Rb(5 ,P,”l, -+ 5 ’SF,), but we did not detect the accompanying Rb(5 ’S$) atom since it does not emit a photon.The squares of the coefficients of ISz)lP$m) and IS$-i)IP$m) are integrated over Euler angles and are summed. This gives the probability of producing an Rb(5 ’P&) atom through dissociation via the molecular state c ’X:( uN = JJM). The sum is denoted by the symbol MA[3Z+( vN = JJM) - ’P,”/,]. The algebraic formulae are listed in table 3. The probabilities of produc- ing an Rb( 5 ’P,”/,) atom through dissociation via the molecular state c ’X:( uN = JME,)H. Kat6 11 Table 4. Algebraic formulae of I-,”= PA[ ‘Z+( v”J - 1 M ) - ‘n( ~ u ’ J M ) - ~ Z + ( vN = JJM or MEz)- P3/2]/(J + 1) in units of p:12)( u’I u)I2/60 2 m -J m C PA[’Z+(u”J- lM)-’n(ev’JM)-3ZC+(vN= JJM)-2P,”/2]/(J+ 1) M = J *3/2 *1/2 (3J2-2J+ 1)/J(2J- 1) ( llJ2 -4J -3)/3J(2J - 1) *2pBH *3/2 *2pBH *1/2 *2pu,H r1/2 *2pBH 7312 0 *3/2 0 * 1/2 ( 16J2 - 5J + 3)/ 14J(2J - 1 ) (24J2 -4J - 13)/21J(2J - 1 ) ( 16J2 - 5J + 3)/42J(2J - 1) 0 ( 5J2 - 9 J + 4)/ 14J(2J - 1 ) (13J2- lSJ+2)/42J(2J- 1 ) are given in table 1 of ref.(10) and we shall denote these by the symbol MA[’Z+( uN = The probability of producing an Rb( 5 ’ P z 2 ) atom via the molecular state c ’Z:( uN = JJM) following the excitation C ‘nu( eu’JM) + X ‘Z+( u”J - 1M) and through the perturbation between the levels of C ‘nu( eu‘JM) and c X:( uN = JJM) is proportional to the following: l(’X+uff~ - ~ M ~ I - L ~ I ’ ~ ~ ~ ’ J M ) J ~ ~ ( ~ ~ ~ ~ ‘ J M ~ ~ ~ ~ ~ ~ z + ~ N = JJM)J~ JME,) - 2P3”/2]. H x MA[3Xt( VN = JJM) - 2P3”/2]. (21) Let us express this factor as PA[ ‘2+( u”J - 1M) - ‘II( eu’JM) - ’X+( uN = JJM) - 2P3”i2].When the intensity of laser radiation is uniform over the Zeeman splitting of the C ‘I&,( eu’JM) + X ‘2;( u”J - 1M) transition, the probability of producing an Rb(5 2P3”/2) atom is given by summing the factors PA over the quantum numbers M .= J . . . - J. The algebraic formulae of -J c PA[’Z+(~”J- 1 ~ ) - ‘II(~~’JM)--~z+(~N = JJM) -2~3”/21/(2~+ 1 ) (22) M = J are listed in table 4. The corresponding formulae in the presence of the external magnetic field are also listed in table 4. The population of Rb(5 2P,”/2) atoms produced by predissociation through the molecular state c ’EL( uN = 54, J = 54) following the excitation C ‘nu( eu’ = 3, J = 54) +- X ‘Z:( u” = 0, J” = 53) are calculated to be in the ratio of 0.224 : 0.276 : 0.276 : 0.224 for rn = 3/2 : 1/2 : -1/2 : -3/2, from table 4.Then, the polarization ratio of the atomic emission Rb(5 2 P 3 / 2 + 5 2S1/2) in the absence of a magnetic field is expected to be 0.075, which is good agreement with the observed value of P = 0.05 f 0.03. In the presence of the external magnetic field, the population of the magnetic sublevels of the photodissociated atom depends on the Zeeman sublevels of E, = 0, *2pBH of the ’Z+ state (see table 4) through which the excited molecules dissociate. The probability of the predissociation depends on the Zeeman energy E, and can be very sensitive to12 Magnetic Sublevels of Photodissociated Atoms the level energy near the level crossing. If the magnitude of I<u’lu)12 is taken to be the same for all the perturbation matrix elements between the level C ‘nu( u’ = 3, J = 54) and the levels c ’Z:( vN = 54E,) with E, = 2pBH, 0 and -2pBH, the dissociated atoms Rb( 5 2P3”/2) are calculated to be populated in the ratio of 0.224 : 0.276 : 0.276 : 0.224 for m = 3/2: 1/2: -1/2: -3/2, from table 4.This ratio is coincident with the one in the absence of a magnetic field. However, the observed results at H = 1.55 T (fig. 4) show that the photodissociated Rb( 5 2P5‘2) atoms are populated preferentially in the magnetic sublevels in the ratio 0.28 : 0.32 : 0.25 : 0.15 for rn = 3/2 : 1/2 : -1/2 : -3/2. The observed population of Rb( 5 2P,”/2) could result from the Franck-Condon factors between the C ‘II,(v’= 3, J ’ = 54) and the c ’Z;(vIV = 54Ez) levels, which could decrease with the energies Ez = 2pBH, 0 and -2pBH.This decrease in Franck-Condon factor with decreasing E, leads us to suspect that the adiabatic potential curve of the c 3Z+( vN = 54Ez) state may cross the outer side of the potential curve of the C ‘II,(J = 54) state below the C *nu( v’ = 3, J’ = 54) level. If we assume that the ratio of the Franck-Condon factors at 1.55T to be 4:3:2 for ](u’=3 of C1II,(J’=54))v of c3Tt(N=54, E,= -2pBH))I2, we can calculate the population ratio of the atomic sublevels Rb(5 2P:2) to be 0.282:0.314:0.237:0.167 for m=3/2: 1/2:-1/2:-3/2. This is in good accord with the observed results, and the observed pattern of the atomic emission in fig. 4 can be explained. Therefore, the preferential population of magnetic sublevels of the photodissociated atoms Rb(5 ’P3”/,) in the presence of the external magnetic field can be attributed to the Zeeman splitting of the c 3T:(vNE,) level and the resulting depen- dence of the perturbation amplitude I( C ‘nu( v’JM)I H,,Ic ’5?( vNEZ))l2 on Ez.The author thanks the Ministry of Education, Science and Culture of Japan for a Grant-in-aid for scientific research no. 60470014 and is very grateful to Dr Peter Hackett for useful comments. 2PBH))l2: l(U‘=31U Of C 3Z+( N =54, Ez =O))l’: ](V‘=31U Of C 3X+(N= 54, Ez = References 1 R. J. Van Brunt and R. N. Zare, J. Chem. Phys., 1968,48, 4304. 2 E. Wigner and E. E. Witmer, 2. Phys., 1928, 51, 859. 3 R. S. Mulliken, Reu. Mod. Phys., 1932, 4, 1. 4 S. J. Singer, K. F. Freed and Y. B. Band, J. Chem. Phys., 1983,79, 6060. 5 J. ViguC, J. A. Beswick and M. Broyer, J. Phys., 1983,44, 1225. 6 E. U. Condon and G. H. Shortley, The Theory ofAtomic Spectra (Cambridge University Press, London, 7 W. Heisenberg, 2. Phys., 1925, 31, 617. 8 P. P. Feofilov, The Physical Basis of Polarized Emission (Consultants Bureau, New York, 1961). 9 H. Kate, M. Baba and I. Hanazaki, J. Chem. Phys., 1984, 80, 3936. 1951). 10 H. Kat8 and K. Onomichi, J. Chem. Phys., 1985, 82, 1642. 1 1 H. Kat8 and C. Noda, J. Chem. Phys., 1980, 73, 4940. 12 G. Alzetta, A. Kopystynska and L. Moi, Nuovo Cimento Lett., 1973, 6, 677. 13 C. Noda and H. Kat6, Chem. Phys. Lett., 1982, 86, 415. 14 R. A. Buckingham, in Quantum Theory I. Elements, ed. D. R. Bates (Academic Press, New York, 1961), 15 G. Breit, Rev. Mod. Phys., 1933, 5, 91. 16 P. A. Franken, Phys. Rev., 1961, 121, 508. 17 M. E. Rose and R. L. Carovillano, Phys. Rev., 1961, 122, 1185. 18 R. N. Zare, J. Chem. Phys., 1966, 45, 4510. 19 J. M. Brom Jr and H. P. Broida, J. Chem. Phys., 1974, 61, 982. 20 A. C. Tam and W. Happer, J. Chem. Phys., 1976, 64, 4337. 21 E. W. Rothe, U. Krause and R. Diiren, J. Chem. Phys., 1980, 72, 5145. 22 D. L. Feldman and R. N. Zare, Chem. Phys., 1976, 15, 415. 23 E. J. Breford and F. Engelke, Chem. Phys. Lett., 1980, 75, 132. 24 I. Kovacs, Rotational Structure in the Spectra of Diatomic Molecules (Adam Hilger, London, 1969), p. chap. 4, pp. 147-170. 216. Received 12th May, 1986

ISSN:0301-7249    

DOI:10.1039/DC9868200001

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1986, 82, 13-24 Product Correlations in Photofragment Dynamics Gregory E. Hall, Natarajan Sivakumar, Rachel Ogorzalek, Gunjit Chawla, Hans-Peter Haerri? and Paul L. Houston* Department of Chemistry, Cornell University, Ithaca, New York 14853, U.S.A. Itamar Burak School of Chemistry, Sackler Faculty of Science, Tel-Aviv University, Tel-Aviv, Israel John W. Hepburn Centre for Molecular Beams and Laser Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada Correlations between either scalar or vector quantities measured in the study of photodissociation dynamics can serve to provide a very detailed picture of the dissociative event. This article discusses the use of Doppler profile and time-of-flight spectroscopy to learn about the correlation between the separate internal energies of two recoiling fragments, to study the way in which the internal energy distribution of a fragment varies with its recoil direction and to determine the angle between a photofragment's recoil velocity direction and its rotation vector.Two new techniques are introduced. High-voltage switching of the potential applied to a time-of-flight mass spectrometer is used to map the velocity distribution of photofragments onto their arrival time distribution. Probing of photofragments by polarized light with sub-Doppler resolution is used to determine the degree of angular correlation between their rotation vector and their recoil velocity vector. The sophistication with which the dynamics of photodissociation events can be probed has increased significantly in the past few years.Measurement of the internal distribution of photofragments (electronic, vibrational, rotational, lambda doublet, fine structure etc.) has become almost determination of the recoil speed distribution by time-of-flight 13925,26 or Doppler techniques22 has blossomed and even measurement of vector properties, such as the direction of a fragment's recoil 13,25,26 or the orientation of its rotation ~ e c t o r ~ ~ ~ ~ ' ~ ~ " with respect to the electric vector of the dissociation source, has become more widely employed. While the collection of measurements concerning these parts of the dissociation event is certainly impressive, one may nonetheless ask whether the whole picture might not be more than the sum of its parts. Could the dissociation event be brought into even better focus by considering the correlations between measurable parameters? As we shall see, there is often as much information in these correlations as in all the parts by themselves. What type of correlations might we expect? Correlations between two scalar proper- ties include those, for example, between the vibrational and rotational energy or between the electronic and vibrational-rotational energy of a particular fragment.Such correla- tions are routinely measured in the course of determining the internal energy for the selected fragment. A more important scalar-scalar correlation is that between, say, the internal energy of a fragment and its recoil speed. Knowledge of the speed of a state-selected fragment allows one to determine the internal energy of the unobserved fragment (assuming there are only two) and often to infer its state (e.g.when the unobserved fragment is an atom in one of two electronic states). Vector-scalar correla- tions are also important. Knowledge of the direction of recoil for a state-selected t Present address: Ciba-Geigy, R. and A. Research Facility, WFM 185.003, CH-1701 Fribourg, Switzerland. 1314 Correlations in Photodissociation fragment with respect to the electric vector of the photolysis source allows one to decompose the overall spatial anisotropy into components for individual internal levels. A bimodal rotational distribution, for example, might be found to display different anisotropy parameters for its high- and low-J components, perhaps indicating that two surfaces are involved.Finally, we can consider vector-vector correlations. An example is the correlation between the recoil velocity vector of a diatomic fragment and its rotation vector. If these vectors were found to be perpendicular, one might infer that dissociation took place from a planar intermediate, whereas if they were found to be parallel one might infer that dissociation involved a torsional mode. Thus, knowledge of the correlations between observables in a photodissociation can lead to a much more detailed picture of the process than might be gained from the observables by themselves. This paper is devoted to examination of such correlations. The relationship between the internal energy and the recoil speed will be used to decide whether a given CO( u, J) product of OCS dissociation is produced in coincidence with S('D) or S(3P).The correlation between the internal energy and the recoil direction will be used to show that OCS and CD31 dissociate on a time scale short compared to rotation and to show that dissociation of the former molecule probably involves more than one excited surface. Finally, the angular correlation between the recoil velocity vector and the angular momentum vector of the CO product in the photolysis of OCS and glyoxal will be used to show that these molecules dissociate from a planar configuration. Experimental Two different experimental arrangements were used in these studies. In each case the sample was prepared by nozzle expansion and photolysed with one of several available laser sources.Products were detected in one case by laser-induced fluorescence and in the other by multiphoton ionization. For studies of OCS and glyoxal, a pulsed nozzle source without collimation was used to prepare the sample and a tunable vacuum- ultraviolet laser was employed to probe the CO photo fragments by laser-induced fluores- cence. For studies of methyl iodide, a well collimated molecular beam was used to prepare the sample and multiphoton ionization using a time-of-flight mass spectrometer was employed for detection of the I and CD3 products. Each of the systems is described in greater detail below. OCS and Glyoxal Studies Photolysis of OCS and glyoxal was performed in a pulsed supersonic jet apparatus similar to that described el~ewhere.~~ Mixtures were prepared by flowing helium over OCS or glyoxal, which was held in a trap at a specified temperature.The seeded gas was then expanded from a total pressure of 1300Torrt through a 0.5 mm diameter pinhole using a pulsed nozzle assembly (Newport). A KrCl excimer laser (Lumonics TE861-4) or an Nd:YAG pumped dye laser/wavelength extension package (Quanta Ray, DCR-2A, PDL-1, WEX) was used to generate the 222 nm light for dissociation of OCS. An excimer pumped dye laser (Lambda Physik EMG-101, FL2001E) was used to excite glyoxal on the 8; band of its first excited singlet state. In both cases, the laser intersected the molecular jet ca. 1.25 cm from the nozzle source. The CO(X 'Z, v, J) product of either dissociation was probed by laser-induced fluorescence using a tunable vacuum-ultraviolet source based on four-wave mixing in magnesium v a p o ~ r .~ ~ The V.U.V. source has been described in detail in recent studies of the photodissociation of g l y ~ x a l ~ ~ and OCS35 and is very similar to that used previously for detection of Br and C0.36-41 t 1 Tom = 101 325/760 Pa.G. E. Hall et al. 15 The molecular jet, the dissociation laser, and the V.U.V. source propagated in mutually orthogonal directions for the studies of OCS, while for studies of glyoxal the dissociation and V.U.V. sources were propagated in antiparallel directions perpendicular to the molecular jet. Fluorescence from CO was detected at 45" from the probe laser and 90" from the jet by an EMR solar-blind photomultiplier tube (5416-09-17).A second solar-blind photomultiplier (EM1 G-26E3 14LF) detected a reflection of the tunable V.U.V. light; its signal was used to normalize the spectra of CO for variations in the probe laser intensity. CDJ Studies Photolysis of CD31 was performed in an apparatus consisting of a pulsed supersonic nozzle source, two skimmers and a standard time-of-flight mass ~pectrometer.~~ Its design is similar to systems described previously43 and will be reported in detail else- where.'"' Methyl iodide was dissociated using the 266nm output of a quadrupled ND:YAG laser (Quanta-Ray DCR-l), whose linear polarization could be rotated with a waveplate. Two-photon resonant/ three-photon ionization of the I and CD, fragments was induced with a doubled Nd:YAG pumped dye laser (Quanta-Ray, DCNA, PDL-1).The relevant experimental conditions are as follows: source pressure, 8% CD31 in 1900 Torr helium; source temperatures, 298 K; molecular beam diameter at laser intersection, 1.6 mm; beam velocity 11 80 m s-'; flight tube length, 105 cm; extraction field, 500 V/2.54 cm; acceleration field, 1500 V/ 1.27 cm; dye laser wavelength, 334-310 nm (DCM); dye laser energy/pulsewidth, 1 mJ/ 10 ns; photolysis energy/pulsewidth, 5 mJ/ 10 ns. The photolysis and probe lasers were made to intersect each other and the molecular beam at a location 8 mm upstream from the centre line of the mass spectrometer and were timed so that ionization was induced <50 ns after photolysis. The extraction and acceleration voltages were held at ground potential during the photolysis and for an adjustable time delay, r d , thereafter.During this delay the ionized fragments recoil with the velocity imparted by the dissociation. Following the delay Td, voltages were applied to the grids of the time-of-flight mass spectrometer during a switching time of ca. 0.05 ps. This voltage caused the ionized photofragments to accelerate toward the detector, where their arrival time was a sensitive function of their position and velocity at the time Td. Thus, the shape of the appropriate mass-spectral peak in the time-of-flight distribution provided information concerning the recoil velocity of photofragments in the particular state to which the ionization laser was tuned?' Results and Discussion Correlation between Internal Energies of Two Photofragments Dissociation of OCS at 222 nm can result in two possible sets of products: ocs + CO(u, J ) + S ( , P ) + CO(u,J)+S('D). Ca.19 880 cm-' of energy is available to recoil and CO internal excitation in the former case, while only 10640cm-' is available in the latter case. Direct monitoring of the S( ' D ) and S ( , P ) atoms by V.U.V. laser-induced fl~orescence~'~~ has shown that the S( ' D ) branching fraction is 0.85. The CO product is formed almost exclusively in the o = 0 level, with a rotational distribution shown in fig. 1. It is tempting to speculate that the smaller peak at higher J in the rotational distribution corresponds to those CO fragments produced in coincidence with the less probable S(,P) channel and that the larger peak at lower J corresponds to the dominant S('D) channel.Indeed, such a hypothesis was16 Correlations in Photodissociation I 2 5 - h 10 1 0- i3 0 0 A Q a 0 b 0 8 0 0 0 35 45 55 65 75 rotational level ( J ) Fig. 1. Rotational distribution of CO( u = 0) produced in the 222 nm photodissociation of OCS. A, 0,O indicate measurements on P-, Q-, and R-branch transitions, respectively. Note that there are two peaks in the distribution, one near J = 56 and one near J = 65. Since the peak areas are roughly in the 85/15 ratio, corresponding to S('D)/S(3P), one might expect that the peak near J = 56 corresponds to CO( = 0) produced in coincidence with S('D), while that near J = 65 corresponds to CO( u = 0) produced in coincidence with S(3P). Analysis of the Doppler profile of the individual rotational lines can confirm or disprove this hypothesis. proposed by us in an earlier p~blication.~~ It is possible to test this hypothesis by measuring the Doppler profiles of individual CO rotational lines, e.g. J = 56 and J = 66, which are near the maxima of the two peaks.If all the CO were produced in coincidence with S( ' D ) , for example, then the Doppler linewidth of the J = 66 line would be narrower than that of the J = 5 6 line, since this product would have a slightly higher internal energy (by 2375 cm-') with correspondingly less energy for recoil. On the other hand, if CO(J = 66) were produced in coincidence with S(3P), while CO(J = 56) were produced in coincidence with S('D), there would be 10 640-2375 = 8265 cm-' more energy avail- able for recoil of CO(J=66) than for CO(J=56); i.e.the Doppler width of the CO(J=66) would be broader than that for CO(J=56). The data, shown in fig. 2, demonstrate clearly that both CO molecules are produced in coincidence with S('D). Thus, it is possible through measurements of the magnitude of the recoil velocity to determine the correlation between the internal energies of the two photofragments. Correlation between the Internal Energy of a Photofragment and its Recoil Direction Similar correlations are possible between scalar and vector quantities, for example between the internal energy of a photofragment and its recoil direction. Consider the photodissociation by linearly polarized light of a molecule into two fragments. It is well known that the probability of finding the recoil velocity vector for the fragments at an angle of 0 with respect to the polarization vector of the dissociating light can be described by the function 1 +/3P2(cos @).47i48 A value of p is derived from the Doppler profile of a single internal energy state of the fragments, measured with a tunable probleG.E. Hall et al. 17 I 1 1 1 -0.50 -0.25 0.00 0.25 0.50 detuning/ cm-’ Fig. 2. Doppler profiles of the CO( v = 0, J = 56) ( a ) and CO( v = 0, J = 66) ( b ) produced in the 222 nm photodissociation of OCS. Q-branch transitions were used and the circularly polarized probe laser propagated in a direction perpendicular to both the electric vector and the propagation direction of the linearly polarized photolysis laser.The Doppler width of the J = 6 6 line is narrower than that for the J = 56 line, so it cannot be the case that J = 66 is produced in coincidence with S(3P), while J = 56 is produced in coincidence with S(’D). In fact, the widths and shapes for both lines are in very good agreement with those predicted (smooth curves) if both fragments are produced in coincidence with S( * D ) . laser propagating perpendic2larly to the direction of the dissociation laser and at an angle 8’ with respect to the E vector of the dissociation laser. For fragments of sharply defined kinetic energy rnvi/2, the probability of finding a recoil velocity vector at an angle x with respect to the probe beam propagation direction is given by49 mx7 8’)K 5 d 4 W X , 8‘, 4 ) (1) where wx7 87 4 ) = [1 +PP,(COS 811 cos 8 = cos 8’ cos x +sin 8’ sin x cos 4 ( 2 ) (3) with and 4 is the azimuthal angle of o about the probe direction as measured from the plane containing the probe direction and the polarization vector of the dissociation laser.The result of integration over + is4’ D(X, el) oc 2 T [ 1 + pp2(c0S x) P,(CO~ 8’11 (4) where the component of the velocity responsible for the Doppler detuning is vocosx. If the fragment has no angular momentum or if J is uncorrelated with 0 Doppler lineshapes can be analysed simply with eqn (4) to determine p. In this way, the angular18 Correlations in Photodissociation I 1 1 1 d -0.50 -0.25 0.00 0.25 0.50 detuning/cm-' Fig. 3. Q-branch Doppler profiles for the CO(v = 0, J = 66) ( a ) , CO(v = 0, J = 57) (b), and CO( u = 0, J = 46) ( c ) products of 222 nm OCS photodissociation.The circularly polarized probe laser propagated in a direction perpendicular to that of the photolysis laser, but parallel to its polarization vector. The recoil velocity distribution is characterized by p = 1.8 for J = 66, p = 0.7 for J = 57, and p = -0.5 for J = 46. The change in p with J suggests that more than one dissociative potential surface is involved. distribution of product recoils may be measured for a particular internal energy level of the fragment. By combining such correlated measurements for many internal energy levels one can separate the internal energy distribution into component parts having similar recoil velocity distributions. The discovery of more than one component may imply that the dissociation involves more than one excited surface.The OCS photodissociation offers an example of the correlation between internal energy and fragment recoil direction. Fig. 3 displays the Q-branch Doppler profiles for three CO(u = 0, J) lines (J = 66, 57, 46) following dissociation of OCS with linearly polarized light aligned parallel to the propagation direction of the circularly polarized probe laser. The profile at the highest J shows a pronounced dip in the centre, indicative of excitation via a near-parallel OCS transition followed by prompt fragmentation. However, as lower rotational values of J are probed, the Doppler profile shifts to oneG. E. Hall et al. 19 22 .o 22.5 23 .O arrival time/ps Fig. 4. Arrival time distribution of the I+ ion from multiphoton ionization of I* following 266 nm dissociation of CD31 with light polarized parallel ( a ) or perpendicular ( b ) to the acceleration axis of the time-of-flight mass spectrometer.which is more peaked at the centre frequency, indicative of a more perpendicular transition in the OCS. One way to summarize these results qualitatively is to note that the recoil velocity distribution changes with the rotational level of the photofragment from a nearly cos2 8 distribution at high J to a more sin2 8 distribution at lower J. An alternative description is that the rotational distribution of the CO product varies strongly with the recoil angle used for detection: the rotational distribution observed along the direction of the electric vector of the photolysis light is peaked at high J, while that observed perpendicular to the direction of the electric vector is peaked at lower J.Since in addition to this correlation between internal energy level and recoil direction, there is a strong correlation between recoil direction and angular momentum vector (see below), we will postpone for the moment a more quantitative description. offers a second example of the correlation between internal energy and fragment recoil velocity. In this experiment the CD3, I and I* fragments were probed by multiphoton ionization using the pulsed extraction technique described earlier. Fig. 4 displays the arrival time spectrum of the I' ion produced by multiphoton ionization of I* at 31 1.4 nm following photolysis of CD31 with 266nm light polarized either parallel or perpendicular to the centre line of the time-of-flight mass spectrometer.Because the CD31 dipole moment is parallel to the symmetry axis, and because the dissociation is rapid compared to the CD31 rotational period, the CD3 and I or I* fragments recoil predominantly along the polarization axis of the dissociation laser. Ionization of the state-selected fragment occurs immediately following the photolysis pulse (within 50 ns), and the concentration of ions is low enough that space-charge effects can be ignored. Thus, while the field is held at zero, the ions recoil with the velocity distribution imparted by the dissociation. When the field is switched on after the delay Td, the ions are accelerated toward the detector, where their arrival time is a measure of their position and velocity at Td.For The 266 nm photodissociation of CD31 to yield CD3 + I, I* (I* =20 Correlations in Photodissocia tion the ‘parallel’ geometry, the products which have recoiled forward and backward along the polarization vector have different velocities and positions along the field direction and thus arrive at the detector at different times. For the ‘perpendicular’ geometry, on the other hand, both sets of products have the same velocity and position along the field direction and thus reach the detector at the same time. Detailed analysis of the arrival time distribution can be used to obtain the velocity distribution of the state-selected fragment. Preliminary analysis suggests that the I* fragment recoils with an anisotropic distribution characterized by p = 2.0.Although the analysis of the corresponding data for the I fragment is complicated by the relative strength of the I+ signal caused by the probe laser alone, the results also indicate a high degree of anisotropy for the I fragment. For the particular time-of-flight tube employed in these experiments (105 cm) it was not possible to image all of the CD3 fragments. In principle, however, with a shorter flight tube it should be possible with this technique to measure the velocity distribution of CD3 fragments in a selected vibrational and rotational level. Correlation between a Photofragment’s Velocity and Angular Momentum Vectors Correlations between vector quantities can also yield important information about the photodissociation process, as shown by consideration of an example when the two vectors u and J , describing the recoil velocity and the angular momentum of a product, respectively, have an angular correlation.Suppose that the fragment with angular momentum J is a symmetric-top molecule and let the projection of J onto u be described by a distribution P(M,). If there is an angular correlation between u and J, then the projection of J onto u will produce a non-statistical population of Mu levels. E.g. if J is constrained to be perpendicular to u, then P ( Mu = 0) = 1 and all other probabilities are zero. Now suppose that the molecule is probed by laser-induced fluorescence with light propagating along an axis z which makes an angle x with u. The projection of P(Mu) onto z to give P’(MJ) will produce a distribution of M, values that depends on the angle x, i.e.one that changes with the velocity probed by the Doppler technique. To pursue the above example, if J is perpendicular to u, then molecules moving with u parallel to z will have only M, = 0, while those moving with u perpendicular to z will have a broad distribution of MJ values. Since polarized light will interact differently with different Mj distributions, the actual LIF Doppler profile will be different from that predicted by eqn (4). The change in the Doppler profile caused by the u-J correlation will depend on several factors: the polarization characteristics of the probing light, the angle and polarization acceptance of the detector and the nature of the absorption and fluorescence transitions.Measurement of the Doppler profile as these factors are varied can be used to uncover the degree of u-J angular correlation. The detailed mathematical relationship between the Doppler profile and the degree of u-J correlation has been treated elsewhere50i51 so we will concentrate here on some applications. Consider again, for example, the dissociation of OCS at 222 nm. Conserva- tiop of angular momentum for this dissociation gives the following relation: where L is the orbital angular momentum of the half collision. Since the OCS is dissociated from very low rotational levels (Jocs=O) and since Jco is so large that JhY = 1 and Js = 2 can be ignored, we find that L = -J Because L must be perpendicular to u, it follows that J is perpendicular to u.The lower row of panels in fig. 5 displays the experimental data (dots) and the convolution of the laser linewidth (0.14 cm-’ f.w.h.m.) with the Doppler profiles predic- ted by with an anisotropy parameter of p = 0.6 (solid lines). The upper row of panels shows the convoluted profiles expected in the absence of any u-J correlation-0.5 0.0 0.5 0.0 0.5 0.0 -0.5 0.0 0.5 detuning/cm-' Fig. 5. Experimental and calculated data for the Q( 59) and P( 59) lines of CO produced in the photodissociation of OCS and probed by laser-induced fluorescence on the CO A 'II 4- X 'X transition using circularly polarized light. The dissociation and LIF probe lasers were orthogonal. Upper row: Doppler profiles expected in the absence of v-J correlation (solid lines); the Gaussian laser linewidth is shown in the dashed curve.Bottom row: Experimental profiles (dots) and profiles calculated for v l J (%olid curves). From left to right the panels show the Q( 59) line with the electric vector of the dissoci%ting light E aligned perpendicular to the propagation vzctor of the probe light z ( e l = 90°), the Q(59) line with El(< ( O ' = O'), the third panel is for the P(59) line with E L 2 (O'=90°) and the last panel is for the P(59) line with Ell2 ( 6 ' = 0'). Calculations were made with values of p=O.6 for the recoil anisotropy, 0.14cm-' for the f.w.h.m. laser linewidth, and 1232ms-' for the recoil velocity, as determined by energy and momentum conservation.22 Correlations in Photodissociation -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 detuning/cm-' Fig. 6.Calculated and experimental profiles for CO produced in the photodissociation of glyoxal. Top row: calculation assuming a Boltzmann distribution of CO speeds and assuming u l J . Middle row: calculation assuming a Boltzmann distribution of CO speeds and assuming ullJ. In each of the top two rows the left panel is for an R- or P-branch transition. Bottom row: experimental data for Q(41) and P(41) transitions. for /3 = 0.6. The laser linewidth is given as the dotted line in the first panel. It is clear from the figure that lineshapes in the presence of u-J angular correlation (solid lines, bottom row) are qualitatively different from those when there is no correlation (solid lines, top row), and that there are differences in the lineshapes depending on the transition probed and the angle 6'.An attempt to fit these data without including the effect of u - J correlation would lead to different apparent values of /3 for different 6', as well as incorrect total linewidths. Inclusion o'f the u - J correlation is necessary to obtain reasonable fits to the data. As a second example, consider the dissociation of the planar glyoxal molecule (trans-CHOCHO) to give CO and a variety of possible other products: CHOCHO + CO+H,CO + 2CO+H, -+ CO+CHOH. In the case of OCS it was possible to predict beforehand that J is perpendicular to u, but in the dissociation of a molecule with more than three atoms such a prediction is not feasible. However, there are two interesting limits that can be considered.If the glyoxal retains its planar configuration throughout the dissociation, we would expect that the CO would rotate in the plane and that J would be perpendicular to u. On the other hand, if the dissociation is accompanied by substantial out-of-plane bending and if it is primarly this torsional motion that leads to the rotational excitation of the CO, then one would expect J to be aligned more nearly parallel to u.G. E. Hall et al. 23 Analysis of the Doppler profiles allows one to distinguish between these two cases. In general, as we have seen above, the Doppler profile will contain information concern- ing both the distribution of recoil velocities and the correlation of J and u. Fragmentation in glyoxal is caused by predissociation of the first-excited singlet level on a time scale (ca.1 ps) which is extremely long compared to the parent molecule’s rotational period. It is expected, therefore, that the distribution of recoil velocities will be essentially isotropic. Thus, the Doppler profile of the CO is determined simply by the u-J correlation and by the distribution of recoil speeds. In the limiting case of a single recoil speed for a given internal state and for the counterpropagating photolysis/ probe configuration employed, the predicted51 Doppler profiles of the CO A + X lines are as follows. (a) For Q lines with the u l J constraint as well as for P or R lines with the u IJJ constraint, a relative minimum occurs at the centre frequency. (b) For P or R lines with the u llJ constraint as well as for Q lines with the u l J constraint, a relative maximum occurs at the centre frequency.Of course, because there are several possible unprobed products ( H2C0, H2, CHOH) and because these may each have a distribution of internal energies, the recoil speed of the CO will not be sharp. The composite Doppler profile of CO molecules for a particular rotational transition will be an integral over the speed distribution of a speed-dependent profile function, whose shape for the particular transition is described above. E g . , a Boltzmann distribution of speeds would give rise to the composite profiles illustrated in the top two rows of fig. 6, depending on whether v is aligned perpendicular or parallel to J. The actual data, shown in the bottom row of fig.6, clearly indicate that the predominant orientation of J is perpendicular to u. Thus, by careful analysis of the Doppler profile, it is possible to determine whether the transition state in a photodissociation is planar or non-planar. Using similar techniques, Dubs et aZ.52 have recently inferred a planar transition state in the photodissociation of (CH3)*NN0. Conclusion The application of advanced laser-based techniques to the study of molecular photodis- sociation can yield correlations between scalar and/ or vector properties. Often, these correlations provide a much more detailed picture of the photodissociation than the scalar or vector properties taken alone. Specific correlations between the internal energy levels in the departing fragments, between the internal energy of a fragment and its recoil direction and between the recoil velocity vector and the rotational angular momentum vector have been demonstrated.It seems likely that such correlations will play an increasingly important role in studies of molecular photodissociation. This work was supported by the U.S. National Science Foundation (CHE-8314146) and the U.S. Air Force Office of Scientific Research (F49620-83-K-0012). The research employed lasers funded through the U.S. Department of Defense Instrumentation programme (DAAG29-84G-0076) and the Dow Chemical Foundation. J.W.H. gratefully acknowledges support from NSERC (Canada) and NATO (grant no. 637/83). The partial financial support of H-P.H. by the Swiss National Science Foundation is also gratefully acknowledged.References 1 P. Andersen, G. S. Ondrey, B. Titze and E. W. Rothe, J. Chem. Phys., 1984,80, 2548. 2 P. Andresen, G. S. Ondrky and B. Titze, Phys. Rev. Lett., 1983, 50, 486. 3 P. Andresen and E. W. Rothe, Chem. Phys. Lett., 1982, 86, 270. 4 P. Andresen and E. W. Rothe, J. Chem. Phys., 1983 78,989. 5 M. P. Docker, A. Hodgson and J. P. Simons, Mol. Phys., to be published. 6 A. Hodgson, J. P. Simons, M. N. R. Ashfold, J. M. Bayley and R. N. Dixon, Chem. Phys. Lett., 1984, 107, 1.24 Correlations in Photodissociation 7 A. Hodgson, J. P. Simons, M. N. R. Ashfold, J. M. Bayley and R. N. Dixon, Mol. Phys., 1985,54, 351. 8 J. P. Simons and A. J. Smith, Chem. Phys. Lett., 1983, 97, 1. 9 J. P. Simons, A. J. Smith and R. N. Dixon, J. Chem. Soc., Faraday Trans.2, 1984, 80, 1489. 10 R. Vasudev, R. N. Zare and R. N. Dixon, Chem. Phys. Lett., 1983,96,399; J. Chem. Phys., 1984,80,4863. 11 G. E. Hall, N. Sivakumar and P. L. Houston, J. Chem. Phys., 1986, 84, 2120. 12 R. J. Donovan and J. Konstantatos, J. Photochem., 1972, 1, 7 5 . 13 J. H. Ling and K. R. Wilson, J. Chem. Phys., 1975, 63, 101. 14 M. J. Sabety-Dzvonik and R. J. Cody, J. Chem. Phys., 1977, 66, 125. 15 A. P. Baronavski and J. R. McDonald, Chem. Phys. Lett., 1977,45, 172. 16 S. T. Amimoto, J. R. Wiesenfeld and R. H. Young, Chem. Phys. Lett., 1979, 65, 402. 17 W. M. Pitts and A. P. Baronavski, Chem. Phys. Lett., 1980, 71, 395. 18 A. P. Baronavski, Chem. Phys., 1982, 66, 217. 19 W. Krieger, J. Hager and J. Pfab, Chem. Phys. Lett., 1982, 85, 69. 20 W. H. Fisher, T.Carrington, S. V. Filseth, C. M. Sadowski and C. H. Dugan, Chem. Phys., 1983,82,443. 21 I. Nadler, H. Reisler and C. Wittig, Chem. Phys. Let?., 1984, 103, 451. 22 I. Nadler, D. Mahgerefteh, H. Reisler and C. Wittig, J. Chem. Phys., 1985, 82, 3885. 23 W. J. Marinelli, N. Sivakumar and P. L. Houston, J. Phys. Chem., 1984,88, 6685. 24 J. V. V. Kasper and G. C. Pimentel, Appf. Phys. Lett., 1964, 5, 231. 25 S. J. Riley and K. R. Wilson, Faraday Discuss. Chem. Soc., 1972, 53, 132. 26 M. J. Dzvonik and S. C. Yang, Rev. Sci. Instrum., 1974, 45, 750. 27 S. L. Baughcum and S. R. Leone, J. Chem. Phys., 1980, 72, 6531. 28 R. K. Sparks, K. Shobatake, L. R. Carlson and Y. T. Lee, J. Chem. Phys., 1981, 75, 3838. 29 H. W. Hermann and S. R. Leone, J. Chem. Phys., 1982,76,4759.30 G. N. A. van Veen, T. Bailer, A. E. de Vries and N. J. A. van Veen, Chem. Phys., 1984,87, 405. 31 M. D. Barry and P. A. Gorry, Mof. Phys., 1984, 52, 461. 32 R. D. Bower, R. W. Jones and P. L. Houston, J. Chem. Phys., 1983, 79, 2799. 33 S. C. Wallace and G. Zdasiuk, Appl. Phys. Lett., 1976, 28, 449. 34 J. W. Hepburn, N. Sivakumar and P. L. Houston, in Laser Techniques in the Extreme Ultraviolet, ed. 35 N. Sivakumar, I. Burak, W-Y. Cheung, P. L. Houston and J. W. Hepburn, J. Phys. Chem., 1985,89,3609. 36 J. W. Hepburn, D. Klimek, K. Liu, J. C. Polanyi and S. C. Wallace, J. Chem. Phys., 1978, 69, 431 1. 37 J. W. Hepburn, D. Klimek, K. Liu, R. G. Macdonald, F. J. Northrup and J. C. Polanyi, J. Chem. Phys., 38 J. W. Hepburn, K. Liu, R. G. Macdonald, F. J. Northrup and J. C. Polanyi, J. Chem. Phys., 1981, 75, 39 J. W. Hepburn, F. J. Northrup, G. L. Ogram, J. M. Williamson and J. C. Polanyi, Chem. Phys. Lett., 40 P. Ho and A. V. Smith, Chem. Phys. Lett., 1982,90, 407. 41 D. J. Bamford, S. V. Filseth, M. F. Foltz, J. W. Hepburn and C. B. Moore, J. Chem. Phys., 1985,82,3032. 42 W. C. Wiley and I. H. McLaren, Rev. Sci. Instrum., 1955, 26, 1150. 43 T. G. Dietz, M. A, Duncan, M. G. Liverman and R. E. Smalley, J. Chem. Phys., 1980,73,4816. 44 H-P. Haem, R. Ogorzalek and P. L. Houston, in preparation. 45 G. E. Hall, H-P. Haerri, R. Ogorzalek and P. L. Houston, in preparation. 46 N. Sivakumar, G. E. Hall, P. L. Houston, J. W. Hepburn and I. Burak, in preparation. 47 R. N. Zare and D. R. Herschbach, IEEE Proc. Nutf Aerosp. Electron. Con$, 1963, 51, 173. 48 S. Yang and R. Bersohn, J. Chem. Phys., 1974, 61, 4400. 49 R. Schmiedl, H. Dugan, W. Meier and K. H. Welge, 2. Phys., 1982, A403, 137. 50 G. E. Hall, N. Sivakumar, P. L. Houston and I. Burak, Phys. Rev. Lett., 1986, 56, 1671. 51 G. E. Hall, N. Sivakumar, P. L. Houston and I. Burak, in preparation. 52 M. Dubs, U. Bruhlman and J. R. Huber, J. Chem. Phys., 1986, 84, 3106. S. E. Harris and T. B. Lucatorto (AIP Conf. Proc. No. 119, 1984), pp. 126-134. 1981, 74, 6226. 3353. 1982, 85, 227. Received 19th May, 1986

ISSN:0301-7249    

DOI:10.1039/DC9868200013

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1986, 82, 25-36 Photodissociation Dynamics of H202 at 248 nm Photofragment Quantum-state Distributions and Vector Correlations Michael P. Docker, Andrew Hodgson and John P. Simons" Department of Chemistry, University of Nottingham, Nottingham NG7 2RD Photodissociation of H202 at 248 nm produces vibrationally and rotationally cold OH(X 211) fragments (f, < 3%, fR = 1 lyo), the bulk of the energy release going into product translational excitation. The OH fragment translational anisotropy was studied by Doppler spectroscopy, identifying the dissociative state as a ' A state. The translational anisotropy is high, p being close to its limiting value of - 1, indicating a prompt dissociation. Doppler profiles were found to be sensitive to the polarisation of the probed transition and to the probe/photolysis geometry, indicating a correlation between JOH and V,, , fragment rotation being aligned along the recoil direction.Fragment rotation is predominantly generated by torsion about the 0-0 axis, either from breaking of the v4 torsional mode or due to a torsional dependence to the first excited ' A potential. The photodissociation of simple triatomic or polyatomic molecules has long been recognised as a particularly simple dynamic process which is amenable to both detailed experimental study'72 and theoretical c a l ~ u l a t i o n . ~ ~ ~ Much of the experimental effort on such systems has centred on the determination of nascent (diatomic) fragment internal- state energy distributions P ( v, J ) by resolving the photofragment fluorescence at fixed excitation wavelengths.172 While detailed product state distributions often illuminate qualitatively the general dynamical features of the dissociation process and may be compared directly with the results of classical or quantum scattering calc~lations,~'~ provided realistic ab initio or model potential surfaces exist, the energy-release data nevertheless provide only a limited view of the dissociation event.More recently, experimentalists have begun to look in detail at the angular momentum disposal during dissociation and how the initial alignment of the photoexcited molecule6-* is retained or modified during the dissociation step9"' by observing the fragment rotational align- ment Ag) using polarisation spectroscopy.The theory of population and alignment measurements by photofragment fluorescence or laser-induced fluorescence (LI F) has been clearly described in a number of paper^.^'-'^ Other studies have examined the translational energy distribution and anisotropy of the dissociating fragments by angular scattering and time-of-flight measurements. l5 As in the rotational alignment measure- ments, these experiments may reveal the symmetry of the parent excited state, whilst any decrease in fragment anisotropy due to parent molecular rotation gives information on the timescale of the dissociation process. 15-'7 The application of fragment anisotropy or alignment measurements is restricted, at least in practice, to molecules which dissociate on a timescale much shorter than rotation, because at longer times the correlation of the parent molecular frame to the laboratory frame (i.e.to the photolysis beam polarisa- tion axis E ~ ) becomes too weak to provide measurable fragment rotational alignment (correlation of J to E ~ ) or translational anisotropy (correlation of recoil velocity u to E ~ ) . This is the case when a predissociated level is used to state-sslect the parent molecular quantum number, e.g. in the case of OH(A *Z+) from H20( C 'B1) which has no detectable alignment." 2526 Pho todissocia t ion Dynamics of H202 The use of LIF as a probe of fragment internal level population and allows- a very detailed examination of ground-state fragments [ e.g. OH(X 211) from H20(A 1B,)].20 Moreover if the fragment centre-of-mass recoil velocity is large, or the parent Doppler motion and probe laser linewidth small, it becomes possible to examine the fragment angular recoil and velocity distribution by Doppler spectroscopy.21 This has been reported as a function of fragment internal level for OH and CN from the photodissociation of HON022 and ICN,23 providing an extremely thorough description of the fragmentation.However, by selecting a particular fragment recoil velocity com- ponent vk, along the probe beam axis, the dipolar symmetry of the excitation process is destroyed.'4922 The LIF intensity is dependent on the rotational alignment of the probed sample and hence the Doppler lineshapes become sensitive not only to the anisotropy in the recoil velocity u but also to the alignment of J as a function of vk (the recoil velocity along the probe beam direction k,) and hence to the correlation between fragment recoil velocity u and angular momentum J.Such a correlation is inevitable if the fragments display a bulk rotational and translational anisotropy in the laboratory frame, but is perhaps more fundamental, being independent of the correlation between the molecular and laboratory frame. The correlation between u and J may be observed through the alignment dependence of the Doppler profiles, by varying the probe polarisa- tion geometry or the polarisation of the transition (i.e. AJ = 0 or *1)24725 and can be observed (at least in principle) even when parent molecular rotation has destroyed the memory of the initial geometry ( i e . the correlation to E,,).This potentially allows the vector correlation_ to be studied for fragments from rotationally selected predissociated levels [ e.g. H20( C or where the dissociation proceeds via a long-lived 'complex' (e.g. NCN02') provided only that the Doppler shift can be made large compared to experimental linewidths ( i. e. parent motion and probe linewidths) .24 Probe polarisaton-dependent Doppler lineshapes, indicative of a mutual correlation between u and J have been observed for OH(X 211) and NO(X ' g ) fragments from the photodissociation of H20224 and (CH3)2NN025 as well as in 0CS2* where (trivially) uco must lie perpendicular to Jco. The theory of the vector correlation between u and J and the analysis of the Doppler profiles has been elegantly described by D i ~ o n .~ ~ Hydrogen peroxide provides a good prototype system for examining this correlationz4 since the OH(X 'n) fragments are produced with a comparatively narrow spread of rotational excitation3' and hence of recoil velocities, unlike the rather more complex case of dimethyl nifr~samine.~~ Experimental Hydrogen peroxide (80% w/w, courtesy of Interox Ltd, was flowed continuously through an LIF cell at 0.5-50 mTorrt (H20-H202), being allowed to passivate the vessel prior to the experiment. The photolysis source was a KrF excimer laser (<3 mJ) at 248 nm, which could be polarised using a quartz Rochon polariser. The OH(X 'II) fragment was detected by LIF on the (0,O) band of the A 2X+-X 211 transition near 310 nm, careful baffling of the probe-laser beam ensuring negligible interference from scattered light.The probe beam was supplied by a frequency-doubled dye laser (305 < A < 315 nm, bandwidth ca. 0.25 cm-' broadband or ca. 0.07 cm-' with an intracavity etalon) pumped by the KrF excimer laser. The probe beam was spatially smaller than the photolysis beam and was delayed by 10ns at the centre of the cell. The probe laser power was maintained as low as practicable by attenuating the pump laser power and the LIF signals were proportional to probe laser power. The fluorescence was recorded, using an unpolarised detection system incorporating a photomultiplier tube (EM1 9558QB), looking along the probe beam polarisation axis ( E ~ ) , fig. 1.The photolysis t 1 Torr = 101 325/760 Pa.M. P. Docker, A.Hodgson and J. P. Simons 27 D 4 t D t D t Fig. 1. Geometries used for the photolysis (kp, E ~ ) and probe beam ( k , , E , ) polarisation E and propagation k directions. Cases ( a ) and (c) are equivalent ( E~ I k,, E~ 11 E , ) and excitation with an unpolarised laser and collinear detection (fig. 2) is equivalent to case (a)+case ( b ) . The detector D is directed along the probe-beam polarisation axis E , and detects all polarisations. beam could be polarised with E~ 11 or 1 to E, in either the collinear ( k , 11 k,) or crossed- beam geometry ( k , I ka), geometries ( a ) and (c) being equivalent (fig. 1). The probe laser power and fluorescence signal were monitored simultaneously and analysed by a microcomputer, allowing the fluorescence to be normalised to probe-laser power and the line-profiles to be integrated digitally to obtain reliable spectral intensities free from lineshape eff e ~ t s .~ ~ Results and Discussion Excitation at 248 nm overlaps the weak long wavelength tail of the first U.V. absorption continuum of H202. The absorption contour is smooth with no evidence of any vibrational structure, indicative of a prompt dissociation. The first excited state, predicted to be 'A, arises from the promotion of an electron from one of the 4b(n) lone-pair orbitals on the oxygen atoms to the 7b( a*) 0-0 antibonding orbital.31 OH( X ) linewidths dependent on probe laser propagation direction were observed by Ondrey et aL3' suggesting this assignment at 248 nm, but indicating that the transition is probably mixed at shorter wavelengths (193 nm where the absorption is considerably more intense) in agreement with the prediction of a ' B state [5a(n) -+ 7 b ( a * ) ] in this region.31 Excitation in the long-wavelength tail of the absorption is likely to involve hot-band excitation, primarily of the v4 torsional mode ( v4 = 254 cm-' 32-34) ca.10% of the ground-state population being in v4 = 1 at 300 K. Product State Distribution The LIF spectrum of the OH(X 'II) fragment, recorded using an unpolarised photolysis laser with a collinear probe geometry, is shown in fig. 2(a). Under these conditions the bulk alignment A:: of the OH(X 'II) fragment can be determined by selecting the polarisation of the detected signal using a polariser in front of the detector. This gave the low value IAgLI < 0.06, which was confirmed by selecting instead the polarisation axis to give AgL = 0.11 [see later discussion (the alignment for the unpolarised case Ab:L = -$Agz)].'5 The hexadecapole moment AY' is zero for a dipole-induced process provided the recoil velocity is not selected." The population distribution shown in28 Photodissociation Dynamics of H202 9 15 R2 1 1 5 1 A.. ! 307 308 309 A /nm a 0 a 0 a 0 a 1000 2000 3000 - E,/ cm - ’ Fig.2. ( a ) OH (A-X) LIF spectrum recorded on the (0,O) band near 308 nm with an unpolarised photolysis laser and a pressure (H20 + H202) = 10 mTorr. The spectrum is recorded digitally and normalised to the probe-laser pulse energy, the photolysis power being constant within 10%. (b) Population distributions in the form of a Boltzmann plot for rotational levels of the Fl(211,,2) (a) and F2(2114) (0) substates, obtained from the unpolarised data with no correction for rotational alignment.The two substates are populated equally. fig. 2 ( b ) was therefore taken directly from the P, R branch data with no correction for alignment. It shows a maximum near N” = 8 with levels up to N”= 15 significantly populated, the higher levels with N”> 9 follow an approximately Boltzmann form, fig. 2 ( h ) , and there is a slight population inversion for lower N” levels. The P, R branches probe the II’, A-doublet, which for high rotation has the unpaired electron in a p~ orbital aligned in the plane of rotation, Q branch lines probe the other n- component which has the unpaired electron in a p n orbital 11 to J.36,37 The A-doubletM.P. Docker, A. Hodgson and J. P. Simons 29 population ratios It-/ II’( fig. 3) were obtained both from the population-distribution data corrected for product alignment and directly from measurements of relative P and Q branch intensities for different photolysis beam polarisation geometries [cases ( a ) and ( b ) fig. 13. The ratio is near 1 at low N”, where the II+ and IT levels are mixed,36937 but reaches 2 at high N”. For high N” the A-doublet ratio therefore gives information about the alignment of_the unpaired PT orbital 11 or I to J.36737 While for many simple systems, such as H20(A 1Bl)20 or HONO (A the interpretation of the A-doublet ratio is straightforward, in the case of H202 a direct dissociation following 4b(n) -+ 7b( a*) promotion will give two OH fragments, one with the unpaired T electron in an orbital directed along the 0-0 axis and the other in an orbital directed I to the OOH plane.For either an axial torsion model leading to J parallel to the 0-0 axis, i e . J)I u, or a repulsive model of the angular momentum release, leading to J 1 u, one fragment will be II+ and the other II-, giving a A-doublet ratio of ca. 1. Thus no simple dynamical picture can be inferred from the observed A-doublet ratio, contributions to the excited state from other excitations3’ presumably influencing the observed A-doublet ratio. The total energy available for partitioning into fragment internal excitation is 280 f 3 kJ m ~ l - ’ , ~ ’ , ~ * of which an average of 11% or 15 kJ mol-’ per OH appears as product rotational excitation.Since negligible population was observed in 0’’ = 1, indicating an approximately constant OH bond length during dissociation, the remaining 89% of the energy release must appear as translation of the two OH fragments, the dissociation dynamics being dominated by the direct repulsion along the 0-0 axis.30 The OH product rotation resulting from this impulse may be estimated to be fR = 6% ,15 while a similar amount could be attributed to the zero-point motion of the bending modes v2, v4 and v6, which would also generate fragment rotation following 0-0 bond rupture. Excitation of hot bands (primarily the v4 OH torsion) would increase this figure slightly; clearly the two mechanisms for generating rotation are adequate to explain the observed rotational energy disposal, but the more sensitive indicator of the dissociation dynamics is the disposal of rotational (and orbital) angular momentum.OH Rotational Alignment The relative P, R and Q branch intensities are sensitive both to the rotational alignment of the OH fragments and to the relative A-doublet populations. The two quantities can be separated by measuring the relative P/Q branch intensities recorded in the two photolysis geometries a and b ( i e . the collinear geometry with cp 11 or I to c , ) . This allows the A-doublet population ratio to be eliminated between the two geometries to give the bulk alignment, averaged over recoil velocity A?: and hence the A-doublet ratios (fig. 3). The degree of rotational alignment was small, Ah:; = 0.11 f 0.05 compared to the high-J limits of 4/5 b AFL b - 2 / 5 , corresponding to fragment rotation parallel or perpendicular to the transition moment.Translational anisotropy measurements show that the transition moment lies along the C2 axis, hence the bulk alignment measurements indicate that OH fragment rotation has a small preferential alignment along the C2 axis. Any variation in A?: with N” is small (4 < N” < 14) and within the experimental scatter. Fragment Translational Anisotropy As described earlier, the Doppler profiles of the OH(X ’II) fragments are sensitive not only to the fragment translational velocity distribution but also to the correlation between u and J. The situation is simplified if the probed transition does not show any alignment dependence [ e.g.the R2( 1) line], the lineshape is then determined solely by the fragment recoil anisotropy parameter p and the recoil velocity distribution W( The profile obtained for the R2(1) line with k, I cp is shown in fig. 4. For this geometry the profile30 Photodissociation Dynamics of H,O, 0 ' O O O I . i 0 5 10 15 N Fig. 3. A-doublet ratio n-/II', where for high J the I T level has the unpaired electron in a p orbital parallel to J and is probed by Q branch lines, whereas the II+ level has the unpaired electron in an orbital perpendicular to J and is probed by P or R branch lines.36 The F,(O) and F 2 ( 0 ) A -doublet ratios are similar within experimental error. I 0.5 Q Or5 A u/ cm-' Fig. 4. Line profile for the R,(1) line with k, I ep.The simulation employs an energy release ET = 23 440 cm-' and an anisotropy parameter p = -1, the limiting value for perpendicular recoil.M. P. Docker, A. Hodgson and J. P. Simons 31 shows a splitting which is a sensitive measure of the anisotropy parameter. The solid line shows the calculated profile S(Av), for a single fragment recoil velocity u22*39 with an angle x between cp and k,, S(AY) = l/AvD[l + P P ~ ( A Y / A Y D ) P ~ ( C O S x)] A v AvD S(Av) = 0 A v > AvD where Av is the Doppler shift from the line centre vo, AvD= vov/c, P2(x) is the second Legendre polynomial P2(x) = (3x2- 1)/2 and p is the anisotropy parameter being +2 or -1 in the limit of fast dissociation parallel or perpendicular to the parent absorption dipole.The calculated profile was convoluted with a Gaussian to account for the parent H202 Doppler motion (A vD = 0.069 cm-') and the probe laser linewidth (A v = 0.07 cm-'), obtained from measurement of thermal OH line profiles and consistent with a linewidth at the fundamental laser frequency of <0.04cm-'. The simulation of fig. 4 used an energy release into translation ET of 23 440 cm-', (the excess energy at 248 nm plus a contribution of 550 cm-' from parent rotation and vibration3'), and an anisotropy parameter p = - 1, (the limiting value for fragment recoil perpendicular to the absorption dipole). The assumption of a single-fragment recoil velocity ( ZI = 4.06 x lo3 m s-l) is acceptable since the energy spread of the fragments would only be 5.5% if the rotation of the two fragments (i.e.Ny and N;) is uncorrelated and any correlation between Nr and N i might be expected to reduce this spread. It will not, however, be such a good approximation for high N" levels where ET is significantly lower ( ER =: 4500 cm-' for N"= 15) and correlation between Nr and N ; is more important. The magnitude of p, indistinguishable from the limiting value of -1, implies that the transition moment is perpendicular to the fragment recoil direction, i.e. the 0-0 axis. This identifies the excited state as purely 'A, with the transition moment lying along the C2 axis; if the excited state were ' B the transition moment would lie in the perpendicular plane and recent calculations indicate a transition moment with a large component along the 0-0 axis.31 The absence of any decrease in the observed transla- tional anisotropy due to rotation of the parent molecule indicates a very fast dissociation and allows a limit to be placed on the lifetime of the excited 'A state.For a dissociation which takes place faster than parent rotation [i.e. (or)2<< 1 where r is the lifetime and o is the angular velocity] the reduction in translational alignment is given by a factor (1 + w 2 r 2 ) / ( 1 + 4 02r2).16 Assuming a Boltzmann rotational population distribution in the excited state allows an estimate of CORMS = 4.96 x 10l2 rad s-' and from the simulated profiles for R2( 1) p < -0.9 giving a limit of r < 40 fs for the dissociation to OH( N" = l), cf: the 0-0 stretching period in the ground state of 37 fs, the timescale for a 'quarter vibration' from classical turning point to the potential minimum being 9 fs.The 0-0 stretching coordinate of the excited 'A state must therefore be steep and directly dissociative, giving a rapid dissociation. Polarisation and N" Dependence of the Doppler Profiles: Correlation between Fig. 5 shows the profile of the P1(2) line ( J " = 1.5) which, like the R2 branch, is not blended with satellites at low Nn.40 The profile shows a Doppler splitting when k, I cp, as for R2(l), but the exact profile is dependent on the choice of photolysis beam polarisation axis cp 11 or 1 to E,, cases ( a ) and (6) (fig. 1). For cp I E, [case (b)] the line profile [fig. 5 ( b ) ] shows a contrast to the central dip of 0.37, corresponding to an anisotropy parameter p = -1, whereas for E~ 11 E, [case (a), fig.5(a)] the dip is enhanced to 0.43, corresponding to an observed anisotropy parameter PeR = - 1.2. In the absence of a correlation between JOH and uOH the two geometries should be equivalent, with the Doppler profile depending only on p and x, the angle between k, and E~ (90 O here). and JOH32 Photodissociation Dynamics of H202 I 1 I -0.5 0 0.5 -0.5 0 0.5 A u/cm-' . . I I I I I I r I 1 I 0 1.0 0 1.0 A vlcm-' Fig. 5. Line profiles for the P1(2) line with E~ I k, and E~ (1 &,(a) or ep 1 E, (b) [cases ( a ) and (b), fig. 13. The simulations employ an energy release of 23 440 cm-', the thermodynamics limit, and an effective anisotropy parameter29 PeR = -1.2 and -1. Fig. 5( c) and (d) show the line profiles for Q,(4) and its satellite QP12(4) with cp 11 E, (c) or E~ I E, (d).Note that the parent and satellite are not drawn to the same scale. Furthermore a value PeE = - 1.2 for the translational anisotropy is physically unreason- able and can only occur if the line profile is 'distorted' by the correlation of tlOH to JOH, giving an alignment Ah:: (uk) which varies across the Doppler profile. Since Q-branch lines show the opposite dependence on the fragment alignment they should show an increase in the observed value of Pefi. This is shown for the Q,(4) line and its satellite QP21(4) both of which originate from the same level [fig. 5(c) and ( d ) ] and display an opposite effect, the Q-branch line having a reduced contrast to the central dip. A similar dependence of line profile on rotational branch is observed for all N" (e.g.N" = 10, fig. 6), the Q branch always displaying a reduced anisotropy compared to the P or RM, P. Docker, A. Hodgson and J. P. Simons 33 i i 1 I . - - 0.5 0 015 - 0.5 0 OI5 Av/cm-’ Fig. 6. Doppler profiles for the ( a ) Ql(lO) and ( b ) P1(lO) lines of OH(X 211). The solid lines show a simulation using eqn (6) with p = -1 and the angle between uOH and JOH, 8’= 42” ( u2 = 0.33). The energy released into translation of the two OH fragments, which determines the width of the profile, was modelled as E, = 21 500 cm-’, very close to the energy release for N”= 1 (23 440 cm-’) less the rotational energy of N ” = 10 (2020 cm-’). branches. This may be explained qualitatively, by considering only the L.I.F.excitation if the fragment rotation JOH is aligned preferentially along the recoil axis uOH. In the high-J limit the transition moment for a Q-branch line is aligned along J, while that for a P- or R-branch line lies perpendicular to J. 14936941 For an unpolarised photolysis beam [ i e . cases ( a ) plus ( b ) ] the fragment rotation will have a positive alignment of JOH about k, for the wings of the transition ( u 11 k,) and a negative alignment for the line centre ( u I k,). This implies a negative alignment of JOH to E,, the probe-beam polarisation axis, for fragments contributing to the wings of the profile and a weak, positive alignment to E, at the line centre. Thus Q-branch lines will tend to be enhanced for Au = 0 and reduced for Av = AuD, while P- and R-branches show the reverse behaviour, in agreement with the experimental results.The large decrease in splitting for Q-branch lines with E~ 1 E, [case ( b ) ] rather than cp 11 E, [case ( a ) ] is consistent with this picture. As N” is increased the Q-branch lines show a decreased splitting, which disappears entirely for the profile with E 1 E,, while the P- and R-branch lines retain their split Doppler profile (fig. 6). Dixon’ has discussed the analysis of Doppler profiles for the case of a single recoil velocity v, where u and J are correlated, allowing the coefficients of the various bipolar moments to be obtained from the values of Pefl for different branches and excitation geometries. Analysis of the OH lineshapes in terms of these coefficients will be discussed el~ewhere,~~ for the present we consider only the qualitative features of the lineshapes and discuss how a simple model of the dissociation fits the results.In general the classical distribution of JOH in a molecule-fixed frame will be non- axially symmetric, 1~14,29 therefore JOH will be correlated in this case with both the C2 axis (the transition moment) and the 0-0 axis (the fragment recoil axis uOH). We have shown above that the fragment angular momentum JOH is aligned along the recoil velocity uOH and so it is interesting to observe how closely a simple model, which considers in the classical high4 limit only the correlation of JOH to the recoil axis uOH, can explain the experimental data. Such a model is reasonable provided the OH groups rotate significantly about the 0-0 axis during dissociation and have a strong correlation34 Photodissociation Dynamics of H,O, of JOH to uOH, giving an axially symmetric distribution of JOH about uOH.Then, for a racemic mixture of H202, the distribution of JOH about uOH may be expanded in terms of the axially symmetric Legendre polynomials Pn(cos 8'), where 8' is the angle between JOH and uOH (the 0-0 axis) I @ ' ) =C a,Pn (COS 8') n where a, = 1, an = (2n + l)(Pn (cos 8'))43 and an = 0 for n odd (since the distribution for a racemic mixture will be symmetric with respect to 8' = 90 "). For the general case of a probe beam k, at an arbitrary angle to 2, the symmetry axis of the exciting light (cp for a polarised beam, k, for an unpolarised beam), the alignment AF) ( v k ) and hence the line profile can be obtained by integration over the fragment angular recoil distribu- tion.However the line profiles are particularly simple when the probe beam propagation direction k, lies along 2. Then for a single fragment recoil velocity vOH and a recoil angle 8 between uOH and k, = 2 we obtain, using the spherical harmonic addition theorem: 43 (Pn(JOH z)) = (pn(JOH uOH))Pn(uOH z, (3) (4) a n P, (COS e) -- - (2n + 1 ) where the angular recoil velocity distribution is given by7*' I ( e ) = [i +~P,(COS e)p,(cos XI] ( 5 ) x being the angle between cp and k, = 2. The LIF intensity (in the classical, high J limit) is sensitive to terms (Pn(JoH - 2)) with n = 0, 2 and 411 and hence the observed LIF intensity may be written analytically in terms of 8, u2 and a4 to give the dependence of the line profile (Au/AvD = cos 8 = x) on the correlation of JOH to uOH; (6) where Ag) = 2( P2(&H Z ) ) , AC) = (P4( JOH 2)) and t('), t ( 2 ) and t ( 4 ) depend on AJ for the transition and the experimental geometry," t(*) and t ( 4 ) having opposite signs for P-, R- and Q-branch lines.The line profiles are primarily dependent on p and a2, the P4(x) term being small and were simulated by choosing a particular recoil angle 8' between JOH and uOH. Simulations of the P- and Q-branch lineshapes obtained in this way are shown in fig. 6, assuming that p, the translational anisotropy parameter, remains fixed at the same value determined for R2( l), p = - 1. Choosing a2 positive (Le. 8'< 54.7') gives the correct dependence of lineshape on rotational branch, confirming the alignment of JOH along the fragment recoil velocity.The assumption of an axially symmetric distribution of JOH about uOH can be seen to be inadequate when the bulk alignment of JOH is considered. The bulk alignment is given by S( x) = [ 1 + pP2( x) P2 (cos x)]( t(') + t(2)AF) + t'4'Ar') AgL = 2(P2(JOH 2)) = 2(P2(JOH ' uOH))(P2(%H ' 2)) (7) Eqn (8) shows how the bulk alignment Af! (referenced to cp = 2, i.e. x = 0") depends on P and the recoil angle between JOH and uOH, thus for a parallel transition the alignment lies between -2/5 and +4/5 for JOH I uOH and JOH 11 vOH, respectively, whilst for a perpendicular transition the corresponding limits are 1/5 and -2/5. If a2 is positive then the model predicts a negative alignment Agi, whereas in fact we measure AgL= 4-0.1 1 f 0.05, and a positive alignment of JOH cannot be reconciled to a positve correlation of JOH to uOH in this model.The discrepancy arises because JOH is not axially distributedM. P. Docker, A. Hodgson and J. P. Simons 35 about uOH, retaining a memory of the initial torsion angle and the position of the C2 axis. In order to explain the OH Doppler lineshapes it is therefore necessary to use the generalised description of D i ~ o n ' ~ in terms of the bipolar moments of the distribution. Discussion The correlation of JOH along uOH observed here for photodissociation of H202 at 248 nm may be contrasted with recent studies on the photodissociation of (CH3)2NN0,25 OCS28 and HON0,22 where J (fragment) was found to be perpendicular to u.For a triatomic photodissociation provided J (fragment) >> J (parent), so that fragment rotation is generated by the repulsion with the atom, J must lie perpendicular to u and correspond- ingly simple Doppler-recoil profiles have recently been reported for OCS.28 In the case of ( CH3)2NN0, photodissociation generates rotationally, translationally and vibra- tionally excited NO ( X 'II) fragment^,^^ which consequently have a broad spread of recoil velocities W(u). The Doppler profiles and bulk alignments are consistent with a correlation of JNo perpendicular to uNO, the NO fragment rotation being generated by the repulsion along the N-N bond, causing a torque about the NO centre of mass. When the fragment is an OH radical the axis of the impulse is necessarily closer to the OH centre of mass, hence giving only a low rotational excitation.In the dissociation of HONO the OH fragment rotation JOH was found to align perpendicular to the molecular plane at high N", attributed to rotational excitation from breaking of the HON in plane bending mode v3? rotational excitation from the impulse being less important (the energy release was 10290cm-' for HONO dissociation at 369nm, compared to 23 440 cm-' for photodissociation of H202 at 248 nm). Since p = -0.8 for OH from HONO, JOH will presumably tend to lie perpendicular to t)OH,29 similar to the correlation of J perpendicular to u in OCS and (CHJ'NNO caused by the torque on the recoiling fragment. For H202 there are three possible sources of fragment rotational excitation (neglecting parent rotation which is small) ( a ) recoil torque about the OH centre of mass, (6) breaking of the v2, v4 and v6 bending modes and (c) an azimuthal dependence on the OH torsion angle in the excited 'A state. OH rotational excitation from the recoil impulse may be estimated asfK == 6%, but will align JOH I uOH, contrary to that observed.Similarly the zero-point motion of the v2 and v6 modes can generate 330cm-' per OH rotational excitation ( ER = 1290 cm-' per OH from experiment) but again this will tend to give JOH I uOH. The two remaining sources of OH rotational excitation JOH 11 uOH are from the parent torsional bending motion and from a torsional dependence to the upper-state potential. The torsional mode v4 has a frequency of 254cm-' and the zero-point motion will contribute only ca.30cm-' per OH rotational excitation. As noted earlier the excitation may involve hot bands of v4, but the low frequency of this mode and the reduced fraction of energy going to product rotation in higher quanta (the molecule spending more of its time at the classical turning points) makes it difficult to attribute the correlation of JOH along uOH entirely to this source. Instead we attribute the product rotational excitation to a torsional motion on the excited ' A surface, genrating fragment rotation parallel to the 0-0 axis, i.e. JOH 11 uOH. Since the dissociation is prompt ( T < 40 fs, i.e. the surface is steeply repulsive) this would require a large depen- dence of the potential on torsion angle.Removal of an electron from the 46(n) lone-pair orbital may be expected to reduce lone pair repulsion increasing the torsion angle but no calculations have been published on the torsional dependence to the ' A potential (although some have been referred to44 which indicate a strong torsional dependence). This study illustrates clearly how Doppler-LIF probing of the nascent photofrag- ments, from photodissociation of a small polyatomic molecule, may provide a very detailed picture of the fragment motion and hence insight into the photofragmentation dynamics. Information may be gained from the scalar properties, such as fragment36 Pho todissocia tion Dynamics of H202 rotational and vibrational energy distributions (and hence for H202 the translational energy distribution), from the correlation between rotation NY and N: in the two OH fragments [if W(v) can be measured as a function of N”], from the vector properties such as the bulk rotational alignment A?)( N”) and translational anisotropy p ( o”, N”) and finally from the correlation between fragment translation 0 and rotation J.In particular it is to be expected that the study of vector correlations both in p h o t o d i s s ~ c i a t i o n ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ and in scattering will greatly help in elucidat- ing the dynamics of these systems. We are grateful to the S.E.R.C. for support of this work and for a Research Fellowship to A.H., and to R. N. Dixon for sending us ref. (29) prior to publication. References 1 S. R. Leone, Adv. Chem.Phys., 1982,50,255. 2 J. P. Simons, J. Phys. Chern., 1984,88, 1287. 3 M. Shapiro and R. Bersohn, Annu. Rev. Phys. Chem., 1982, 33, 409. 4 G. G. Baht-Kurti and M. Shapiro, Adv. Chem. Phys., 1985, 60, 403. 5 R. Schinke, J. Phys. Chern., 1986,90, 1742. 6 R. Bersohn and S. H. Lin, Adv. Chem. Phys., 1969, 16, 67. 7 R. N. Zare, Mol. Photochem., 1972, 4, 1. 8 R. N. Zare and D. R. Herschbach, Proc. IEEE., 1963, 51, 173. 9 T. Nagata, T. Kondow, K. Kuchitsu, G. W. Loge and R. N. Zare, Mol. Phys., 1983, 50, 49. 10 M. T. Macpherson, J. P. Simons and R. N. Zare, Mol. Phys., 1979, 38, 2049. 11 C. H. Greene and R. N. Zare, J. Chern. Phys., 1983, 78,674. 12 C. H. Greene and R. N. Zare, Annu. Rev. Phys. Chern., 1982,33, 119. 13 R. Altkorn and R. N. Zare, Annu. Rev. Phys. Chem., 1984, 35,265.14 D. A. Case, G. M. McClelland and D. R. Herschbach, Mol. Phys., 1978, 35, 541 15 G. E. Busch and K. R. Wilson, J. Chern. Phys., 1972, 56, 3626; 3638. 16 C. Jonah, J. Chern. Phys., 1971, 55, 1915. 17 S-c. Yang and R. Bersohn, J. Chem. Phys., 1974,61, 4400. 18 A. Hodgson, J. P. Simons, M. N. R. Ashfold, J. M. Bayley and R. N. Dixon, Mol. Php., 1985,54, 351; 19 J. L. Kinsey, Annu. Rev. Phys. Chem., 1977, 28, 349. 20 P. Andresen, G. S. Ondrey, B. Titze and E. W. Rothe, J. Chem. Phys., 1984,80, 2543. 21 J. L. Kinsey, J. Chern. Phys., 1977, 66, 2560. 22 R. Vasudev, R. N. Zare and R. N. Dixon, J. Chem. Phys., 1984, 80, 4863; Chem. Phys. Left., 1983,96, 23 I. Nadler, D. Magherefteh, H. Reisler and C. Wittig, J. Chem. Phys., 1985, 82, 3885. 24 M. P. Docker, A. Hodgson and J. P. Simons, Chern. Phys. Lett., 1986, 128, 264. 25 M. Dubs, U. Briihlmann and J. R. Huber, J. Chem. Phys., 1986,84, 3106. 26 M. P. Docker, A. Hodgson and J. P. Simons, Mol. Phys., 1986, 57, 129. 27 C. X. W. Qian, M. Noble, I. Nadler, H. Reisler and C. Wittig, J. Chem. Phys., 1985, 83, 5573. 28 G. E. Hall, N. Sivakumar, P. L. Houston and I. Burak, f i y s . Rev. Left., 1986, 56, 1671. 29 R. N. Dixon, J. Chem. Phys., 1986, 85, 1866. 30 G. Ondrey, N. van Veen and R. Bersohn, J. Chem. Phys., 1983,78, 3732. 31 C. Chevaldonnet, H. Cardy and A. Dargelos, Chern. Phys., 1986, 102, 5 5 . 32 P. A. Gigukre and T. K. K. Srinivasan, J. Mol. Spectrosc., 1977, 66, 168. 33 P. A. Giguhe and K. B. Harvey, J. Mol. Spectrosc., 1959, 3, 36. 34 R. H. Hunt, R. A. Leacock, C. W. Peters and K. T. Hecht, J. Chern. Phys., 1965,42, 1931. 35 J. P. Simons, A. J. Smith and R. N. Dixon, J. Chem. SOC., Faraday Trans. 2, 1984, 80, 1489. 36 M. H. Alexander and P. J. Dagdigian, J. Chern. Phys., 1984, 80, 4325. 37 P. Andresen and E. W. Rothe, J. Chern. Phys., 1985, 82, 3634. 38 H. Okabe, Photochemistry of Small Molecules (Wiley, New York, 1978). 39 R. Schmiedl, H. Dugan, W. Meier and K. H. Welge, Z Phys., 1982, A304, 137. 40 G. H. Dieke and H. M. Crosswhite, J. Quanf. Specfrosc. Radiat. Transfer, 1962, 2, 97. 41 M. P. Sinha, C. D. Caldwell and R. N. Zare, J. Chem. Phys., 1974, 61, 491. 42 M. P. Docker, A. Hodgson and J. P. Simons, to be published. 43 J. D. Barnwell, J. G. Loeser and D. R. Herschbach, J. Phys. Chem., 1983, 87, 2781. 44 H. Golzenleuchter, K-H. Gericke, F. J. Comes and P. F. Linde, Chern. Phys., 1984, 89, 93. 45 D. A. Case and D. R. Herschbach, Mol. Phys., 1975, 30, 1537. Chern. Phys. Lett., 1984, 107, 1. 399. Received 17 July, 1986

ISSN:0301-7249    

DOI:10.1039/DC9868200025

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

GENERAL DISCUSSION Prof. R. N. Zare (Stanford University, USA) said: Can Prof. Kat6 give us any additional information about how the strong magnetic field he uses might affect his conclusions about the photodissociation dynamics of NaK and Rb2? Are angular momentum uncoupling effects important? Prof. H. Kat6 (Kobe University, Japan) said: The effect of nuclear spin on the degree of polarization should be considered in the absence of an external magnetic field or at small magnetic field.' However, if the magnetic field is high enough to uncouple the electronic angular momentum J and the nuclear-spin angular momentum I, the spatial quantization of these vectors takes place independently of each other ( Paschen-Back effect for hyperfine structure2). The magnetic hyperfine structure constant AJ is 1011.9 MHz for "Rb(5 2S1/2), 25.029 MHz for 85Rb(5 2P3/2), 885.82 MHz for 23Na(3 2S1,2) and 18.65 MHz for 23Na(3 2P3/2).3 Hence, the effect of the hyperfine interaction on the polarization can be neglected in magnetic fields as strong as 1.55 T.1 C. H. Greene and R. N. Zare, Annu. Reu. Phys. Chem., 1982, 33, 119. 2 P. P. Feofilov, The Physical Basis of Polarized Emission (Consultants Bureau, New York, 1961). 3 A. Corney, Atomic and Laser Spectroscopy (Oxford University Press, Oxford, 1977). Prof. K. F. Freed (University of Chicago, USA) said: Prof. Kat6 has presented a series of fascinating experiments studying the external magnetic field dependence of the atomic sublevel populations in photodissociation. The experiments exhibit orienta- tion (difference between up and down components of angular momentum along the magnetic field) in Rb2 but none in NaK.Both are 'L'n transitions. Our previously published papers only consider the high-energy axial recoil limit in which the results are dependent on the nature of the initial and final electronic states only.'.2 Our paper in this meeting3 presents some calculations of orientation for the CH+ photodissociation in the low-energy regime. The near-threshold low-energy orientations and alignments can differ considerably from the high-energy-limited values appropriate to the axial recoil limit.'y2 It would, therefore, be of interest to consider further experiments with wavelength control to study the energy dependence of the orientation phenomena. Our calculations have also included the depolarizing effects of the hyperfine interactions and it is necessary to incorporate these corrections in comparing theory and experiment. 1 S.J. Singer, Y. B. Band and K. F. Freed, J Chem. Phys., 1984, 81, 3064. 2 S. J. Singer, Y. B. Band and K. F. Freed, Adv. Chem. Phys., 1985, 61, 1. 3 C. J. Williams, K. F. Freed, S. J. Slinger and Y. B. Band, Faraday Discuss. Chem. Soc., 1986, 82, 51. Mr C. J. Williams (University of Chicago, USA) said: Prof. Kat6 has measured a polarization ratio of P = 0.10 * 0.02 for the Na (3 2P3/2 --* 3 2S1/2) fluorescence resulting from the direct photodissociation of the NaK molecule after exciting the optically allowed X 'X+ -+ D 'n transition. This is compared to the polarization ratio (P = 21/47) predicted in the high-energy axial recoil limit for this photodissociation by Singer et aZ.' Discrepancies between these two numbers may arise from several sources.First, the magnetic field introduces additional anisotropy and lifts the degeneracy of the magnetic sublevels. Consequently, the frame transformation and recoil limit of Singer et al.' may be inappropriate when these extra anisotropies are not included in the calculations. Secondly, Prof. Kat6 earlier told me that the excess kinetic energy in the X '2+- D 'II dissociation of NaK is currently unknown, and thus it is possible that the recoil limit has not been attained in the experiments. Singer et find that the 3738 General Discussion high-energy axial recoil limit may not be reached until the excess fragment kinetic energy is orders of magnitude larger than the fragment spin-orbit splittings.If this is the case in NaK, full dynamical calculations of the polarization ratio P are required. This feature is already illustrated by our previous calculations, but the additional dynamical effects due to the presence of the magnetic field remain to be studied theoretically. 1 S. J. Singer, K. F. Freed and Y. B. Band, J. Chem. Phys. 1983, 79, 6060. 2 S. J. Singer, K. F. Freed and Y. B. Band, J. Chem. Phys., 1984, 81, 3091. Prof. H. Kat6 (Kobe University, Japan) (communicated): The polarization ratio of P = 0.1Ost 0.02 was observed in the absence of the external magnetic field, as in my paper [above eqn (l)]. In our experiment, molecules in thermal equilibrium were irradiated.Hence, molecules populated in many rovibrational levels of the ground electronic state can be excited simultaneously to the dissociative continuum. We need a device to excite molecules from a single level to the dissociative continuum in order to make the analysis clear. Dr G. G. Baht-Kurti (University ofBristo2) and Dr M. Shapiro ( Weizmann Institute, Israel) said: The paper of Hall et al. discusses the measurement of correlations between various fragment attributes in photodissociation processes. One of the primary objectives in studying any photodissociation process is to learn about the underlying molecular features such as the potential-energy surface and the transition dipole moment function. The purpose of measuring the various correlations discussed in the paper of Hall et al.is to gain additional detailed knowledge of the system in order to further our search for these molecular quantities. The experimental observables, including all the correla- tions discussed, are related to the fundamental molecular quantities through the detailed differential photodissociation cross-section. In a previous paper’ we have discussed the relationship of this cross-section to the molecular quantities for a triatomic system, and have derived specific cross-sections for various types of experiments by performing suitable averages over the cross-section for the most detailed possible process. The cross-sections have been expressed in such a way as to isolate the irreducible dynamics of the photofragmentation process from the unavoidable angular and angular momentum algebra.Our analysis of the formal expressions led us in particular to propose that experiments in which the velocity, angular direction and mi states of photofragments were measured would yield much more information on the underlying molecular dynamics than had till then been available. In the language of the paper of Hall et al. this corresponds to the measurement of the correlation between the photofragment velocity and fragment angular momentum vector. Such correlations have also been considered in the work of Dixor2 1 G. G. Balint-Kurti and M. Shapiro, Chem. Phys., 1981, 61, 137. 2 R. N. Dixon, J. Chem. Phys., 1986, 85, 1866. Dr M. A. O’Halloran (Argonne National Laboratory, USA) said: In experiments performed at Stanford University with Prof.Zare, we also have observed the effects of velocity-angular momentum correlations on the polarization dependence of the laser- induced fluorescence probe of the CN fragment produced in the photodissociation of ICN at 249 nm. In a slightly different formalism from those presented in the papers discussed today, the intensity of the LIF signal may be expressed as’ I = CS d r ’ & ( k d , k,, k, q : a ) o ( k d , k,, k ; Ji, J,, J f ) . kd, ka, k 4 In this equation, dr) are the multipole moments of the angular momentum distribution, E(kd, k,, k, q ; a) are factors dependent on the experimental geometry (a), and o ( k d , k,, k ; Ji , J,, Jf) depend only on the particular probe transition Ji --* J, --* Jf.-0.1 1 -o.4 -0.5 t T 39 Fig.1. Rotational alignment, db2), plotted against rotational quantum number, N", determined from polarizations measured in the two experimental configurations: I( (detector 1) photolysis laser polarization) and I (detector I photolysis laser polarization). 0, PI[; 0, PI. When the angular momentum distribution is created by a cylindrically symmetric dipole process, such as photodissociation, it may possess only moments with k = 0,2 and q = 0, that is to say: dip'.. 1 and If this is the case, then it is sufficient to measure the LIF intensity for only two different geometries in order to determine the alignment, dr). In our experiment, a measurement of the LIF intensity at two different angles of the probe laser polarization is used to determine the alignment of the CN fragment produced in photodissociation of ICN.When we performed our experiment, we measured the polarization response of the LIF probe in two experimental configurations designated 11 or I, according to whether the detector is parallel or perpendicular to the direction of polarization of the photolysis laser. If there were only two moments dp) and dr), we should be able to invert the two sets of polarization data to obtain the same values for the alignment. What we observed, however, as shown in fig. 1, was that there was a small but systematic discrepancy between the alignments determined for the two experimental configurations. We found an explanation for this observation in the correlation between the velocity and the angular momentum of the CN photofragment.Since the probe laser line was narrower than the Doppler width of the transition, we were not observing the entire CN population, but rather those molecules with particular velocity projections on the probe direction. If the direction of the angular momentum vector is correlated with the direction of the velocity, then we do not observe the entire cylindrically symmetric, dipole-created angular momentum distribution, ,but rather a subset with reflection40 General Discussion 1.0 0.5 0.0 fraction Doppler width 0.0 0.5 1.0 0.0 0.5 1.0 1.0 1 0.0 0.5 0 . 0 3 V 0.06 6.0 2.5 - 1.0 fraction Doppler width Fig. 2. Moments of the angular momentum distribution, dy), integrated over various fractions of the Doppler width, for a arallel transition and for u l J The higher moments are normalized to ( a ) df), ( b ) dr), ( c ) dy); ( d ) dc); ( e ) (f> 103dy).symmetry through the plane containing the probe laser and the polarization vector of the photolysis laser. The LIF intensity is then sensitive to moments with k = 0,2, 4 and q = even. Using the expressions of Prof. Dixon,* I calculated the values of these moments, integrated over various fractions of the Doppler width, for the case of a parallel transition with t, I J (fig. 2). When the entire Doppler profile is integrated, dr’ and dr) approach their limiting values and the higher moments go to zero. However, our probe laser is ca. 0.7 of the Doppler width, and there is still some contribution from the higher moments, which may explain our experimental observations.What this calculation also suggests is that if the laser is further narrowed with an intracavity etalon, the polarization response of the probe should be even more sensitive to the velocity-angular momentum correlation. The technique of measuring the polariz- ation response across the Doppler profile would be fundamentally the same as the technique of measuring the shape of the Doppler profile (the LIF intensity across the Doppler profile). The advantage of measuring a polarization, however, is that it is a quantity which can be normalized on a shot-to-shot basis if the polarization of the probe laser is rotated rapidly, and thus it can be less sensitive to changes in sample pressure or laser power. 1 C. H. Greene and R. N. Zare, J. Chem. Phys., 1983, 78, 6741.2 R. N. Dixon, J. Chem. Phys., 1986, 85, 1866. Dr P. A. Gorry ( University ufManchester) said: A considerable weight is being placed on the p parameter and the dynamical information that can be obtained from it. However, measured p values arise from an amalgamation of several effects, all of which must be allowed for if detailed dynamical information is to be obtained. In general, a measured p value results from a convolution of the initially prepared orientations over rotational velocities, dissociation lifetime and fragment relativeGeneral Discussion 41 velocities.' These effects are particularly important at low dissociation velocities where even the sign of p may be changed.2 In predissociating states the lifetime may be different for each J level requiring a knowledge of each individual lifetime to calculate the correct averaging over rotational velocity.Furthermore, vibrational motions may significantly alter the p value since vibrational motion perpendicular to the dissociation axis appears as a transverse component to the separation ~ e l o c i t y . ~ In addition to such legitimate averaging effects there are several experimental pitfalls to be avoided. First, one must be certain that only one electronic transition is involved, since overlapping transitions with different p values can easily be misinterpreted as dynamical effects. Shapiro has recently shown4 that coherent summation of states of differing p values occurs, rendering the decomposition of the /3 parameter impossible. Finally, great care must be taken to ensure that no saturation is occurring in the photodissociation since this also decreases the measured p value.' 1 S.C. Yang and R. Bersohn, J. Chem. Phys., 1974, 61, 4400. 2 R. N. Zare, Mol. Photochem., 1972, 4, 1. 3 G. E. Busch and K. R. Wilsor J. Chem. Phys., 1972, 56, 3638. 4 M. Shapiro, J. Phys. Chem., 1986,90, 3644. 5 J. H. Ling and K. R. Wilson, J. Chem. Phys., 1976, 65, 881. Dr K-H. Gericke (Frankfurt-am-Main, West Germany) said: In the first three papers at this Discussion the vector correlation between the translational and rotational motion of a photofragment has been mentioned and qualitatively established by Doppler spectroscopy. We wish to report on an experiment concerning the photodecomposition of hydrogen peroxide,'.2 where for the first time all vector correlations between p (transition dipole moment in the parent), u (product recoil velocity) and J (product rotation) are determined quantitatively by the use of bipolar moments, recently intro- duced by D i ~ o n .~ H202 has been photodissociated at a wavelength of 266nm and the OH fragments completely characterized by Doppler and polarisation spectroscopy using the laser- induced fluorescence technique at six different excitation-detection geometries. The entire internal state distribution (vibration, rotation, spin and A components), trans- lational energy, angular distribution and vector correlations between p( H202), u( OH) and J(OH) are measured. The OH fragments are formed exclusively in the X 2113j2,1/2 ground state with 90% of the available energy, E,, = 248 kJ mol-' being released as OH recoil translation.The internal motion of OH is vibrationally cold ( fr < 0.002), while the rotational excitation (fr = 0.1) can be described by a Boltzmann distribution with a temperature parameter of Trot = 1530 f 150 K for higher J. The two spin states are found to be populated nearly statistically. The n- component of the A doublet shows a higher population than the I'I' component and this inversion increases with increasing OH rotation. The various vector correlations are analysed and evaluated in terms of the four bipolar moments pi(02), pi(20), p:(22) and pi(22) by observation of more than 200 Doppler lineshapes. The observed profiles of recoil Doppler-broadened spectral lines are strongly dependent on the nature of the transition (see fig. 3), the excitation-detection geometry and the relative polarisations of the photolysing and analysing laser light.However, the line intensities show only a minor dependence on geometry and polarisa- tion. Therefore, the OH fragments are only weakly aligned [ &j2) = $:(02) G 0.11 for all rotational states N(0H) [fig. 4(d)]. The bipolar moment pi( 20) corresponds to the conventiordly defined spatial anisotropy parameter p = 2p;(20) and is found to be negative, pi(20) = -0.36 [fig. 4(a)]. Thus the angular distribution peaks in the direction perpendicular to the electric vector of the dissociating laser light (nearly a sin2 8 distribution). Since the transition moment is perpendicular to the product recoil direction, 2.e.the 0-0 axis, the excited electronic42 1.0 0.8 Genera I Discussion 0.2 0.0 309.85 309.86 309.87 309.88 309.89 wavelength/ nm Fig. 3. Doppler profile of the Ql(lO) main line ( a ) and the accompanying 4P21(10) satellite line ( b ) . The origin of both lines is the same quantum state. The different shape is mainly caused by a strong and positive v(OH), J ( 0 H ) correlation, indicating a more parallel orientation of J ( 0 H ) to v(0H). state at 266 nm in H202 is of ' A symmetry. Deviation from the limiting value of #3 = -1 is caused, for an ' A -+ ' A transition, by internal motion of H202. The lifetime T of the excited The moment /3:(22), which describes the correlation between the translational and rotational moment of the fragment, is positive and increases with increasing J ( 0 H ) [fig.4(b)], showing a bias towards v ( 0 H ) and J ( 0 H ) being parallel to one another. The influence on the observed Doppler profiles associated with pg(22) depends only on the branch of the excitation transition and is completely independent of beam geometries and polarisation. Thus p:(22) may be a measure of the dynamics of predissociating states where all other vector correlations are smeared out in the frame of observation. We observe a low positive value of pG(22) [fig. 4(c)] which describes the mutual correlation of the photoproduct translational and rotational vectors [ u( OH), J ( OH)] and of the transition dipole vector [p(H202)] in the parent molecule. The determination of the vector correlations in the photodissociation of H,02 at 266 nm allows an analysis of the expectation values of the J ( 0 H ) components.When we define a coordinate system with p(H202) being parallel to the z-axis and u(OH)(x- axis) perpendicular to p(H202) then the expectation value of ( J : ) should be very small. The OH product rotation is generated by the bending vibration and by the torsional mode in hydrogen peroxide, where the origin of the expectation value ( J : ) =: 450 cm-' are the bending modes of roughly planar H202 with the H atoms in trans position, while the expectation value of ( J i ) == 600 cm-' generated by the internal torsional rotation of H202, either directly from excitation into the-initial level, or from the torque provided by the strong angular dependence of the AIA[ (4a)*( 5 ~ ) ~ ( 4 b ) ' ( 5b)'I state potential surface.' A state should be of the order of T S 60 fs. The overall rotational distribution function P( J ) is then given byGeneral Discussion 43 0 / - / / & I I I I I I I I , - 0.8 0.4 0.3 0.2 0.1 0 I 1 I I 1 1 1 I I 1 0.2 1 fdJ r I-- -I--- 3 5 7 9 NOH Fig. 4. Bipolar moments ( a ) pi(02), ( b ) p;(22), ( c ) pi(20), ( d ) pi(22) as a function of NOH. The anisotropy parameter pi(02) corresponds to the alignment parameter AL2), pi(O2) =i The conventionally defined anisotropy parameter p is proportional to the bipolar moment &20), pg(20) = ip. Its large negative value indicates that the OH fragments are ejected essentially perpendicular to the transition dipole moment p( H202). The increasing positive value of &22) with increasing rotation of the fragment indicates a more parallel orientation of J ( 0 H ) to tr(0H).The bipolar moment pi( 22) describes the correlation of the translational and rotational motion of OH and of the transition dipole moment p(H202). The short-dashed curve stems from calculations on the basis of a semiclassical dynamical model.' The observed scalar and vectorial properties can be qualitatively described by a semi- classical dynamical model. 1 K-H. Gericke, S. Klee, F. J. Comes and R. N. Dixon, J. Chem. Phys., 1986,85, 4463. 2 S. Nee, K-H. Gericke and F. J. Comes, J. Chem. Phys., 1986, 85, 40. 3 R. N. Dixon, J. Chem. Phys., 1986, 85, 1866. Prof. F. J. Comes ( Frankfurt-am-Main, West Germany) said: The photodissociation of H202 at the wavelengths 266 and 248 nm obviously shows that there is only one upper state, A 'A, which is excited.This situation may change if an exciting radiation of shorter wavelength, e.g., 193 nm is used. There exists already a measurement at that wavelength' from which it follows that the population of the rotational levels, P ( J ) , in the vibrationless state of OH is non- Boltzmann, but with P( J ) / (2J + 1 ) decreasing monotonically. No vibrational excitation was found. Recently we have repeated the photofragmentation of H202 at 193 nm with the important result that the earlier measurements are strongly influenced by rotational relaxation.' Under the experimental conditions of Ondrey et al.' the same distribution44 Genera 1 Discussion 0 0 0 0 o o 0 0 0 0 - 0% .0 0 O 0 0 0 0 0 0 0 B Fig. 5. Rotational state distribution of OH fragments from the photolysis of H202 at 193 nm. Contributions from the two spin states are given by squares from the 2113/2 and by circles for the 2 h / 2 . was found again but at much lower pressures (5 mTorr) and shorter delay times between pump and probe laser (50 ns) the rotational state distribution changed, showing that now at low J the population was strongly reduced (fig. 5). The rotational state distribution is strongly inverted with P( J ) / (2J + 1 ) now increas- ing for J I 12. Also lineshapes were measured, from which Peff parameters could be extracted. As an example the lineshape of Ql(lO) transition is shown (fig. 6). So far no alignment has been considered, for it is estimated to be small under the experimental conditions.The asymmetry parameter Peff = +0.35 (obtained from a fitting procedure) is slightly more positive than the one found when using 266 nm as the excitation wavelength. The positive value may indicate that besides the 'A-state the 'B-state is also excited at 193 nm. The Doppler shift shows that the OH fragments carry a translational energy of 185 kJ mol-' each, which is ca. 84% of the available energy. As no vibrational excitation is involved in the photofragmentation process, Doppler measurements of the OH in a specific rotational state may allow to determine the rotational energy of the other fragment which is coincidently formed in the photofragmentation. 1 G. Ondrey, N. van Veen and R. Bersohn, J. Chem. Phys., 1983, 78, 3732.2 A. U. Grunewald, K-H. Gericke and F. J. Comes, Chem. Phys. Lett., 1986, 132, 121. Prof. R. N. Dixon (University of Bristol) said: The papers by Hall et aZ. and by Docker et al. both describe experiments which demonstrate the existence of a vector correlation between the angular momentum and the angular distribution of translational momentum of a photoproduct. In the interpretation of such experiments it is important to separate those aspects of the observables which derive from the chosen geometrical arrangement of the experiment from those which are associated with the anisotropy of the intramolecular forces which operate during the dissociation, and which are of prime interest.General Discussion 45 1.0 0.8 x U 3 0.4 E Y .- 0.2 0 309.845 309.8 55 309 865 wavelength/nm 309.875 Fig. 6.Doppler lineshape of Q1( 10) transition of the (0,O) band of OH (X 'n). &= +0.35 is obtained by deconvolution with a 300 K thermal motion of H202 (A v = 0.069 cm-') and a Gaussian laser profile (Av, = 0.1 cm-'). Laser beams are counter-propagated and linearly polarized parallel to each other with the E vector parallel to the direction of observation. One approach to this separation has been described in a recent publication,' in which the vector correlation is described by a set of bipolar moments. For a single product J value and translational wavevector k a fundamental description of the pair angular distribution function will be by a density matrix p ( k J ) . The observables are related to one or more moments of this distribution defined by where the bipolar tensor operator is given by2 and n( k, k2K) is a renormalisation constant chosen to obtain simple numerical ranges for the dimensionless moment^.^ One manifestation of this vector coupling concerns the profiles of photofragment spectral lines which are broadened by the Doppler shift of fast recoil, as in both the papers under discussion.These profiles are sensitive to both the propagation directions and polarisations of all photons that are involved in detecting a fragment spectrum. In the case of laser-induced fluorescence detection following photofragmentation with linearly polarised light the most general line profile involves bipolar moments with 0 = 0, K = 0 and 2, k, = 0, 2, 4 and 6, and k2 = 0, 2 and 4, and can be represented by46 General Discussion where P,, is a Legendre polynomial, xD is the fractional Doppler shift from line centre (8v/AvD) and the g,, are linear combinations of the bipolar moments with geometry- dependent coefficients.Eqn (3) provides a method of analysis of line profiles, from which one or more non-zero moments can be determined,’ thereby providing a method of interpreting experimental data to deduce the form of the pair density matrix and the underlying photofragmentation dynamics. This approach has been used in connection with the 266 nm photolysis of hydrogen per~xide.~ A possible disadvantage of an analysis through moments is that (in principle) nine non-zero moments contribute to the line profiles with LIF detection. Limited resolution and signal-to-noise ratios, and a finite velocity spread, may militate against determining all of these.The most fruitful approach to interpretation will, therefore, probably be a combination of moment analysis and forward calculation from a dynamical model. A One important aspect of this analysis is that the bipolar moment p,0(22) = ( P2( 6 J ) ) is overall isotropic and is, therefore, independent of the frame of reference. Con- sequently, there may still be detectable u/J correlation between product motions even for weakly predissociated parent states, for which the memory of the initial excitation will be lost through extensive rotation before dissociation. This will particularly be the case when the weak predissociation involves a slow radiationless transition to a final state with an initially well defined geometry, from which rapid dissociation occurs on a repulsive surface.The angular distribution of u is probed by the propagation direction of the analysing light, and J by its electric vector, and these two are fixed at right-angles by the transverse nature of light. Thus the influence of p:(22) on a line profile is independent of the experimental geometry, but is in general of opposite sign for Q-branch transitions compared with P or R transitions. A comparison between different branches therefore provides a method of testing for u / J correlation. 1 R. N. Dixon, J. Chem. Phys., 1986, 85, 1866. 2 D. M. Brink and G. R. Satchler, Angular Mommenturn (Clarendon Press, Oxford, 2nd edn, 1968). 3 See C. H. Greene and R.N. Zare, Annu. Rev. Phys. Chem., 1982, 33, 119 for a discussion of tensor 4 K-H. Gericke, S. Klee, F. J. Comes and R. N. Dixon, J. Chem. Phys., 1986, 85, 4463. operators and multipole moments. Prof. J. C . Polanyi (University of Toronto) said: Surprise has been expressed that correlation between product velocity, u’, and rotation, J’, can be-as we heard it expressed-‘maintained’ despite lingering of the dissociating molecule in an electroni- cally excited state that ultimately predissociates. The correlation is likely, however, to be due to the fact that u’ and J‘ have a common origin, namely the repulsion along the direction of what was previously a bond and has, as a consequence of predissociation, become an anti-bond. The source of the bulk of u‘ and J’, according to this view, lies in an event that occurs as the photoproducts separate, consequently the prior lifetime of the photo-excited species has no bearing on the extent of the correlation.This type of correlation has been extensively explored for product excitation in what are termed ‘repulsive’ chemical reactions, for which a major portion of the energy release occurs as the reaction products separate.’ Photolysis, since it resembles the second half of a chemical reaction, is pre-eminently (though not exclusively) a repulsive event. In the simple case A*BC (the dot represents the repulsion) the apportionment of recoil energy between u’ and J’ can be calculated from the distance by which the point of a plication of the force is removed from the centre-of-mass of the molecular fragment BC!3 The u’J‘ correlation arises from the fact that there is a limited range of ‘transition- state geometries’ for the labile AOBC, and a correspondingly restricted range of values for the torque.The correlation is interesting to the extent that it sheds light on the range of ‘transition-state geometries’. The reaction-dynamicist must contend not only with aGeneral Discussion 47 substantial range of intermediate geometries, but also with the presence in the transition state of angular momentum that derives from energetic reagents. In photodissociation, averaging over these quantities is less severe since the energy of the transition state is that of a stable molecule at normal temperatures. The averaging can be further sup- pressed if the range of energies and geometries that lead to dissociation is reduced by the existence of a localised inter-system crossing.This suggests that the most advantageous case for v’J’ correlation is the one that occasioned this comment, namely the case of photo-excitation to an excited state which, following a delay for exploration of the available phase space, passes through a narrow ‘gateway’ onto a repulsive potential that leads (from a restricted region of phase-space) to the explosion into photofragments. 1 N. H. Hijazi and J. C. Polanyi, J. Chem. Phys., 1975, 63, 2249. 2 P. J. Kuntz, M. H. Mok and J. C. Polanyi, J. Chem. Phys., 1969, 50, 4623. 3 M. G. Prisant, C. T. Rettner and R. N. Zare, J. Chem. Phys., 1984, 81, 2699. Prof. P. L. Houston (Cornell University) said: An alternative theory for relating the degree of correlation between angular momentum and velocity vectors has been presented by Hall et al.’ Consider the case when the Doppler profile is measured with light propagating along a Z-axis which makes an angle 8’ with respect to the electric vector of the linearly polarized dissociating light.The Doppler profile of molecules moving in a direction specified by the polar angle x and the azimuthal angle 4 with respect to the propagation direction will depend (1) on the number of fragments recoiling into this angle and (2) on their M, distribution on the Z-axis, taken here to be the direction of propagation. Molecules recoiling at polar and azimuthal angles x and 4 with respect to the direction of propagation will make a specified polar angle, 8, with respect to the electric vector of the dissociating light. The angle 8 is related to the angles 8’, x and 4 by the condition cos 8 = cos 8‘ cos x +sin 8‘ sin x sin 4 ( 1 ) where 4 is measured from the plane containing the probe direction and the polarization vector of the dissociation laser. In order to calculate the Doppler profile, we need to ascertain the M, distribution on the Z-axis of propagation, but the correlation between o and J is most conveniently described in the molecular frame using v as the axis of quantization. We define the probabilities for projections M, of J onto v to be the diagonal elements of a density matrix p ( 8 ) .The density matrices corresponding to the two basis sets M,, and M, are related by a unitary transformation:2 (2) P ’ ( X , 8’, 4) = rm-4, x, 4)1-1P(wm-4, x, +)I where p( 8) describes the distribution of projections of J onto v, and p’( x, 6’, 4) contains diagonal elements, describing the probabilities for projections of J onto 2, and off- diagonal elements, describing the coherences.The intensity of laser-induced fluorescence for molecules described by the matrix p’ is given by3,4 I(x, 8‘) - I d4W(x, 8’, 4) Tr A F (3 1 where W( x, 8‘, 4) = [ 1 + pP2(cos 8)] gives the probability of recoil into a given direction, and the matrices A and F describe the absorption and fluorescence steps, respectively. The matrices AFg and FFg are given by A zM = C (J’ K ’ M I Q, I JKM, ‘) p ’( MJ ‘ M, ) (JKMJ I Q,I J‘ K ’ M ’) (4)48 General Discussion where the summation is over MJr, MJ from -J to J, and IJKM) are the symmetric-top wavefunctions.For linear polarization the @ matrices occurring in the absorption or fluorescence steps can each be described as a sum: where F = X , Y, 2 are the laboratory coordinates, g = x, y, z are the molecular co- ordinates, and the coefficients A F are the projections of the electric vector onto the laboratory coordinates, while the coefficients A, are the projections of the dipole moment onto the molecular coordinates. The elements aFg are the direction cosine matrices, listed el~ewhere.~ I ( x , O r ) in eqn (3) gives the intensity of laser-induced fluorescence as a function of Doppler detuning, x, for any particular relative angle 8’ between the polarization vector of the dissociation laser and the probing direction. In response to a question by Professor J.P. Simons as to why we looked for any correlations in glyoxal, I would like to comment as follows. The vibrational-rotational distribution of the CO product from glyoxal was particularly uninformative as to which dissociation channels might be responsible for the observed product. The CO was produced entirely in u = 1 and with a rotational distribution stretching from J < 10 to J > 60. The distribution showed no structure which might have been interpreted as being due to the three possible channels: H2C0 + CO, HCOH + CO and H,+ 2CO. We measured the Doppler profiles of individual rotational lines in order to see which channels contributed at each product J level.At first, before our spectral resolution was improved to 0.16 cm-’, we noticed the curious effect that all of the Q-lines appeared to be broader than the corresponding P- or R-lines. With improved resolution, we discovered that the Q lines all had ‘dips’ in the centre, whereas the P- and R-lines did not. That this effect is due to the correlation between u and J is demonstrated in the paper; a more complete account will be published shortly.‘ The widths of the rotational lines provided evidence that most of the population in the highest rotational levels was produced by the H2C0 + CO channel. 1 G. E. Hall, I. Burak, N. Sivakumar and P. L. Houston, Phys. Rev. Lett., 1986, 56, 1671. 2 A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, 1957), p.61. 3 The procedure used here follows the notes for the 1980 Baker Lectures, Cornell University, R. N. Zare, 4 G. Breit and I. S. Lowen, Phys. Rev., 1934, 46, 590. 5 P. C . Cross, R. M. Hainer and G. W. King, J. Chem. Phys., 1944, 12, 210. 6 I. Burak, J. W. Hepburn, N. Sivakumar, G. E. Hall, G. Chawla and P. L. Houston, State-to-State personal communication; see also R. N. Zare, J. Chem. Phys., 1966, 45, 4510. Photodissociation Dynamics of trans-Glyoxal, J. Chem. Phys., accepted for publication. Dr G. E. Hall (Cornell Uniuersity) said: As a summary of our paper, I make the following comments. Photofragmentation of molecules with more than three atoms can lead to photo- fragment Doppler lineshapes that are substantially harder to analyse than from triatomic parent molecules. The Doppler lineshapes can be considered to be determined by three photofragment properties. First is the distribution of kinetic energies of the spectro- scopically selected photofragment. Second is the angular distribution of the fragments relative to the polarization axis of the dissociating light. The added complication of angular distributions that are different for different kinetic energies, corresponding to different internal states of the unmeasured fragment, cannot be ruled out in general. Finally, the Doppler lineshapes will be affected by the anisotropy of J, described by the correlations between J, v and J, p. Without some special simplification, this is too much information to extract uniquely from measured lineshapes.General Discussion 49 In the case of OCS, we know the kinetic energy distribution is sharp and we know the correlation between J and u. We can extract p and test the analysis procedure. In the case of glyoxal, the slow predissociation and rotationally unresolved excitation ensures isotropic fragmentation velocities. Here, qualitative features of the J, u correla- tion can be deduced, even with a broad velocity distribution. In the case of H202, the small degree of internal excitation of the OH fragments makes the kinetic energy distribution sharp enough to extract detailed vector correlations.

ISSN:0301-7249    

DOI:10.1039/DC9868200037

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1986,82, 51-66 Non-adiabatic Effects on the Photodissociation of Diatomic Molecules to Open-shell Atoms Resonances, Polarizations and Angular Distributions for the CH+ Model Systems Carl J. Williams* and Karl F. Freed The James Franck Institute and the Department of Chemistry, The University of Chicago, Chicago, Illinois 6063 7, U. S. A. Sherwin J. Singer? A T & T Bell Laboratories, Murray Hill, New Jersey 07974-2070, U.S.A. Yehuda B. Band Ben Gurion University of Negev, Beer-Sheva, Israel The theory of the photodissociation of diatomic molecules to open-shell atoms is applied to the near-threshold dissociation of CH+. Close-coupled calculations for the photodissociation cross-section and various anisotropy parameters exhibit a wealth of structure in conformity with our previous theoretical predictions that non-adiabatic interactions between molecular states, approaching the same atomic term limit, lead to the emergence of resonance features in the spectra.Some of these features are associated with Feshbach and shape resonances on states that carry no oscillator strength in zeroth order. The particular quantities evaluated are the total photodis- sociation cross-sections for the production of individual C+(2P3/2, states from selected initial CH+ levels and the fragment angular distribution, orientation and alignment. Certain resonances are more pronounced in the anisotropy parameters than in the total cross-section, indicating further that their measurement would aid in the experimental assignment of resonances in photodissociation.The calculations provide a qualitative understanding of the complexity of the available experimental data for the photodissociation of CH+. Photodissociation dynamics provides a wealth of information concerning the nature of the contributing molecular electronic potential surfaces. 1-4 Special interest exists for low-energy photodissociation of molecules to open-shell fragment^'.^ because systems producing open-shell fragments have several nearly degenerate asymptotic electronic potential surfaces and therefore present the possibility of interesting non-adiabatic effects. Strong non-adiabatic couplings occur in these molecules at intermediate fragment separations because the small non-adiabatic interactions become larger in this region than the spacings between the nearly degenerate electronic potential surfaces.’ Previous calculations show that this situation often leads to interesting qualitative effects.Similarly, the intersection of electronic potential surfaces leads to a frequently studied predissociation problem, where again the weak non-adiabatic couplings become impor- tant because they connect nearly degenerate intersecting electronic states. t Permanent address: Department of Chemistry, Ohio State University, Columbus, Ohio 43210, U.S.A. 5152 Non-adiabatic E8ects in CH+ Photodissociation The non-adiabatic interactions arise by virtue of spin-orbit, Coriolis and hyperfine interactions. The magnitudes of these three types of interactions are dependent on the atomic quantum numbers of the final fragments, the reduced mass of the system etc.The interaction which is dominant may vary between molecules and even for different dissociation channels in a single molecule. Regardless of the nature of the coupling mechanism, the near-degeneracy of several fragment asymptotic states and their non- adiabatic coupling imply that near-threshold photodissociation probes the structure of the potential surfaces and their couplings. Several previous theoretical analyses’75 and computation^^-^ have shown that this type of near-threshold photodissociation results in the emergence of resonances which occur solely due to non-adiabatic interactions. The resonances appear in the photodis- sociation cross-sections and in the angular distributions of photofragments and of fluorescence from electronically excited fragments.The orientation and alignment of open-shell fragments provide additional probes of the resonances8910-12 and even more detailed information is, in principle, available from coincidence measurements of frag- ments and their fluorescence. The resonance structure is most easily interpreted when only a single or a few non-adiabatic resonances are present, when one or a few initial states are involved or when resonant two-photon experiments select an intermediate state to be dissociated by the second photon. Some molecular systems dissociating to open-shell fragments have been predicted by us to exhibit extremely complicated resonance ~tructure.~” The calculations indicate why an accurate determination of fragment kinetic energy would be helpful in understanding experiments for these complicated photodissociation spectra.Calculations also show that the non-adiabatic effects in the production of open-shell fragments often persist to energies over two orders of magnitude larger than the asymptotic fragment fine-structure splittings. This non-adiabaticity is particularly notice- able in predicted non-statistical branching ratios for the production of atomic fragment fine-structure states. Here we review the full multichannel quantum theory of photodissociation of diatomics to atomic fragments with fine structure. The theory is illustrated by multichan- nel calculations for the model system Calculations are provided of the anisotropy parameters for the production of photofrag- ments, of parameters related to the alignment and orientation of the C+ fragment, of branching ratios and of total and partial photodissociation cross-sections.Our interest lies in determining whether these quantities provide independent sources of information which could be combined to aid in the interpretation of experimental data for CH+ or similar diatomic dissociations. We present the motivation for study of CH+ and a general review of the theory of diatomic photodissociation to atomic fragments with fine structure. The final two sections present our results and conclusions. Motivation Low-energy atom-atom scattering is sensitive to the long-range intermolecular forces, the attractive regions of the potentials and the non-adiabatic interactions between different electronic potential curves approaching the same atomic term limit.Thus, the inversion of these scattering data should permit, in principle, the determination of these potentials and couplings. However, crossed-beam scattering experiments between pairs of open-shell atoms are currently not feasible and, even if they were, the scattering data bury the information in averages over impact parameters and averages over reactant kinetic energies. The half-collision of photodissociation dynamics probes the sameC. J. Williams et al. 53 regions of electronic potential curves and the non-adiabatic couplings; however, the possibility in photodissociation of selecting a single or small number of intial (or intermediate) bound states implies precise control of the total energy of the system and its angular momentum (effectively an impact parameter selection).Moreover, the use of polarised light in the photodissociation process introduces anisotropy into the diatomic system to provide the possibility for extracting additional information from the polariz- ation of the atomic fragments. Thus, photodissociation, in principle, provides more detailed (i.e. less averaged) data than can be obtained in current cross-beam scattering experiments. The diatomic molecule dissociation to open-shell fragments is the simplest system where non-adiabatic coupling between nearly degenerate electronic surfaces affects the direct photodissociation process. The cylindrical symmetry and the lack of internal (vibration-rotation) degrees of freedom for the atomic fragments make the diatomic dissociation theoretically simpler to treat than that of polyatomic systems.Because these diatomic dissociations already present major theoretical and conceptual difficulties, we have developed a full quantum theory to treat their photodissociation dynamics 13-15 and have predicted novel effects such as non-adiabatic resonances, non-statistical branch- ing ratios, structure in the energy dependence of angular distributions etc. The predicted non-adiabatic resonances are of two types. The first involves non- adiabatic shape resonances, arising from tunnelling through a centrifugal barrier on an electronic surface other than the optically pumped surface. Feshbach resonances are associated with the formation of a 'bound' state on an electronic surface, which is energetically closed asymptotically.When this electronic surface correlates with an upper fine-structure state, then Feshbach resonances formed on it may decay through non-adiabatic coupling to electronic surfaces which correlate to lower fine-structure states. Our previous theory shows that the non-adiabatic couplings enable the observa- tion of some of these resonances and thereby provide a method of studying near-threshold 'dark' electronic states, which are not radiatively coupled in zeroth order to the initial (or intermediate) bound electronic state. The theory has been illustrated for the direct dissociation of CH', NaH and Na2 6-9 and for the predissociation of OH.'6 Both NaH and OH show that the branching ratio for production of fine-structure fragments may remain non-statistical at excess energies greater than two orders of magnitude larger than the atomic spin-orbit splittings.'*16 This paper focuses upon low-energy calculations for the photodissociation of CH+ and discusses the dynamical effects leading to the immense and complicated structure in this system. CH+ provides an ideal model system for illustrating non-adiabatic effects in photodis- sociation because of the moderate spin-orbit splitting of the C+(2 ' P ) fragment (64 cm-'), the relatively small reduced mass leading to moderately strong Coriolis coupling and a maximal number of bound states since all electronic potential curves support bound states (fig. 1). Even the primarily repulsive c 3C+ potential has bound states because of the attractive long-range ion-atom interaction in this state.The previously studied NaH and Na, have a small Na(3 ' P ) atom splitting (17 cm-') and hence do not support as many 'quasibqund' states in the energy region between the two fine-structure components of the Na(3 - P ) atomic state. Further, the NaH B '11 and c 'Z' states are purely repulsive and thus serve to simplify the photodissociation dynamics of this diatomic system. The large reduced mass and the resulting weak Coriolis coupling of Na2 combine with the existence of a barrier in the B 'nu potential at large internuclear separations to make the Na, system behave more adiabati~ally.~ Additional impetus for theoretically studying the CH+ system comes from previous and continuing photodissociation experiments for this molecule using optical 17-19 and infrared2' excitation.A small fraction of the large number of experimentally observed resonances in the optical region have been assigned to shape resonances on the A 'll54 Non-adiabatic Eflects in CH' Photodissociation 1 - 0- 2 5 -1 e g -2- \ h M - - .- c) U a -3 - -4 - Fig. 1. Diagonalized potentials, including Coriolis and spin-orbit interactions, for the CH+ states which dissociate to the C+(2 2 P ) and H( 1 ' S ) atomic term limit. The potentials are displayed at intermediate nuclear separations on the right-hand side with an expanded energy scale to show the existence of a small well in the c3X+ electronic state and to exhibit the correlations of the fully diagonalized potential with the two fine structure states of C+.Many of the low J resonances in CH+ arise from 'quasibound vibrational states' on potential curves which approach the energetically closed C'(2P3/2) limit, but which decay through couplings to states correlating with the energetically open C'( fine-structure state. electronic No Feshbach resonances, lying in the region between the two fine-structure components of the C'('PP> states, have yet been assigned in the experi- mental spectra, although predictions of A 'II and other resonances in this region have been made.6.7 Preliminary6 and subsequent7 calculations for CH+ demonstrate that the inclusion of non-adiabatic couplings provides a sufficient number of resonances to explain the larger than previously expected number of resonances which is observed experi- mentally.An analysis of the complicated resonance structure of the theoretically calculated photodissociation spectrum7 of CH+ shows that many rules of diatomic spectroscopy can be applied to analyse such spectra. The complexity of the computed spectra arises, in part, because the asymptotic non-adiabatic couplings essentially eliminate all elec- tronic selection rules (including spin) in the photodissociation ~pectra.~ Owing to this complexity, the experimental analysis of fragment kinetic energy would be extremely helpful in assigning photodissociation resonances in experimental spectra, where several different initial states may be involved. Attempts at relating individual resonances in our calculations on CH+ to experi- mentally observed features are complicated by a lack of experimental information of the initial rotational and vibrational states involved, by uncertainty in the correct dissociation energy for CH+ and by a lack of experimental information on fragment kinetic energies.This last feature presents problems in relating the experimental photon energy scale to our natural theoretical energy scale given by fragment kinetic energy. Additional impediments are the large number of computed and experimentally observedC. J. Williams et al. 55 resonances, the fact that some computed resonances are very narrow and finally the inherent inaccuracies of the adiabatic Born-Oppenheimer ( ABO) potential curves used in our calculations. Small changes in the electronic potential curves or their positions relative to one other would lead to significant shifts in computed positions of certain resonances, their couplings and mutual interferences. Our calculations of the angular distributions and of the fragment polarizations for CH+ photodissociation show that these types of measurements provide additional probes of the complicated dynamics that may arise in the near-threshold photodissociation of diatomics to open-shell atomic fragments.Measurements of fragment polarizations are currently unavailable experimentally for CH+ , but experiments on Na221 have measured the polarization of the Na( 3 ’ P ) fragment. Several photodissociation experiments on a1 kali-metal dimers have studied photodissociation in a magnetic field, which lifts the degeneracy of the magnetic sublevels of the fragment fine-structure states.22 Further experiments on CH+ with initial state selectively and the determination of fragment angular distribution and polarization would be most interesting since the theoretical simulation of CHt photodissociation exhibits many novel features which in experiments probably could only be interpreted by combining such a battery of measurements with detailed theoretical analysis.Review of Theory The primary advancements made by our full quantum theory of dissociation to open-shell atoms involve the complete inclusion of non-adiabatic couplings, the treatment of all the coupled angular momenta and the analysis of the proper asymptotic scattering states. The theory utilizes two molecular basis sets which provide a zeroth-order description of the ‘half-collision’ dynamics in the molecular and the asymptotic regions, respectively.In addition, we introduce a transformation TB between these two basis sets, such that TB is independent of internuclear separation ( r ) . Elsewhere, the general theory of diatomic photodissociation is described along with a treatment of resonant two-photon dissociation processes and an analysis of the angular distribution and polarization of photo fr agmen t s . 4- Below a brief overview of this theory is presented. Basis Functions The first basis set is a space fixed (SF) basis set derived from one Hund’s coupling case basis. Here a case ( a ) basis IASE) is chosen, where S is the total spin of the system and A and C are the projections of electronic and spin angular momenta onto the diatomic internuclear axis.The latter axis is termed the body fixed (BF) z-axis. Since all couplings are included in our calculations, it is possible to adopt any of the Hund’s case coupling schemes according to which basis in zeroth order is most advantageous. The BF Hund’s case ( a ) basis provides a zeroth-order SF basis IJMASEp) of inversion symmetry p as where DLn(apO) are the Wigner rotation matrices, J is the total angular momentum of the system, LR = A+E is the projection of the total angular momentum along the internuclear axis and M is the projection of the total angular momentum along the SF z-axis. The quantity u is zero unless the electronic state is of E- symmetry, in which case it takes the value 1.Thus the parity of the basis set I JA4ASX.p) is given by ( - )”.56 Non-adiabatic Eflects in CH’ Photodissociation The second basis set IJMjZjJb) is called an ‘atomic’ basis set because this molecular basis set has the special property that as r + co the individual basis functions become a product of atomic fine-structure states I jam,) I jbrnb) and a spherical harmonic y r c ~ (31, which describes rotation of the atomic fragments about their centre of mass. The quantum numbers j , and j b are the electronic angular momentum quantum numbers of fragment a and b, respectively, with projection rn, and mb onto the SF z-axis; Z is the angular momentum quantum number for rotation about the centre of mass; p is the quantum number associated with projection of 1 onto the SF z-axis; j = j a + j b is the total fragment electronic angular momentum; and J is the total angular momentum quantum number resulting from J = j + 1.It is important to note that at arbitrary internuclear separations the basis set (JMjZjJb) cannot be written as a product of atomic fine-structure states, but is a linear combination of ABO electronic states. Hence, the ‘atomic’ basis set is defined to have the limiting form: lJMjGdb)= c )jmjdb)~P(;)(JMIilrnp), r -+ ( 3 4 mP where (jrnjdb) is given by The parity of I JkfjQ&) is ( - ) %+Ib where 2, and 2, are the electronic orbital angular- momentum quantum numbers of the fragments with j , = 1, + s, and with s, the spin angular momentum operator for fragment a.The basis 1 JMASXp) properly describes the zeroth-order dynamics in the molecular region since it diagonalizes the electronic Hamiltonian without the small relativistic and Coriolis interactions and radial derivative couplings between states of the same symmetry. The ‘atomic’ basis I JMjZjJb), on the other hand, appropriately describes the dynamics in the asymptotic region since it contains the proper boundary conditions for the production of atomic fragments in specific fragment states. The ‘atomic’ basis thus diagonalizes the total Hamiltonian for r -+ a. The transformation TB between these two bases is derived by recognizing that at infinite internuclear separation the Hund’s case ( a ) electronic states can be rewritten as IASx) = I z a A a ) 1 zbAb) I sx)(AaAb IA), O0 (4) AaAb where A, and Ab are the quantum numbers for the projections of the total electronic orbital angular momenta 1, and lb of the fragments onto the internuclear axis.The spins are taken to remain coupled. Eqn (4) is simplified when one fragment is produced in an S state (i.e. either Z, or lb = 0). Assuming 2b = 0, the sum in eqn (4) reduces to a single term because (&Ab IA) = aAnA. In most cases the coefficient &Ab 111) must be evaluated at some large, but finite internuclear separation r. The r-independent trans for- mation matrix T, is then determined by substituting eqn (4) into eqn (2) and by examining how eqn (3) projects onto this basis. Thus, a linear combination of the ‘atomic’ basis functions IJMjG, jb) is found to possess the same asymptotic form as obtained by substituting eqn (4) into eqn (2).[The details are described in ref. (1) and (14).] Because T B is obtained from the r + 00 form of the two basis sets, TB is independent of r and can be used at all internuclear separations to transform the Hund’s case basis to a molecular basis which has the appropriate asymptotic boundary conditions. Continuum Wavefunction and Hamiltonian The full Hamiltonian X(r) can be written asC. J. Williams et al. 57 where Xelec( r) is the electronic Hamiltonian, T,,,( r) is the nuclear kinetic energy operator, and Xre,(r) is the relativistic Hamiltonian, which is taken for simplicity to be the spin-orbit Hamiltonian Xso(r). In general, hyperfine and spin-spin interactions are added to Yeerel( r), but this complicates the angular momentum algebra for the derivation of the basis transformation TB and introduces, in principle, additional channels in the close-coupling calculations. The nuclear kinetic energy operator is composed of radial and angular parts as: - f i 2 1 a2 fi2 2p r a r 2 2pr TnUc(r) =- - - r + y Z2.The Hund’s case ( a ) basis diagonalizes Xelec(r) with energy eigenvalues that are the adiabatic BO electronic curves. The off -diagonal elements of the orbital angular momen- tum operator Z2 in this basis are the Coriolis coupling elements. At large r the atomic basis diagonalizes the full Hamiltonain X( r) since the electronic Hamiltonain Yeelec( r ) tends to zero. The operator Xso( r ) is diagonal at r + 00 in the atomic basis with diagonal matrix elements given by the atomic spin-orbit splittings of the fragment states; the radial part of T,,,( r ) in this basis becomes a constant matrix for r + 00 and the operator f 2 is diagonal since 1 is a good quantum number in our ‘atomic’ basis for r + 00. The scattering wavefunction I kfjpzdbrnb-)) is a solution of the Schrodinger equation: [ E - %?I 1 kfj,m, jbmb-)) = 0 (7) in which the full Hamiltonian X for dissociative motion includes all non-adiabatic couplings and electronic curves which are needed to describe the dissociative dynamics.The scattering wavefunction 1 k&m&mL-)) can be expanded in terms of energy-normal- ized continuum wavefunctions 1 EJMjZjJL-’) of total angular momentum J through the standard partial wave expansion I kfjamdbmi-)) = I EJMjGaL-’)(JM Ijlmp)(jm Ijdbm,mb)i’Y$(L). (8) Jjlrnp In practice, the close-coupled equation (7) is solved for a given value of J to obtain the spherical wavefunction I EJMjZjJL-’) defined in eqn (8).The spherical wavefunction 1 EJMjZjJL-’) has the property that outgoing flux is in the channels labelled by j , 1, j , and j b and incoming flux is in all other channels. Transition Amplitudes and Differential Cross-sections? The spherical continuum wavefunction I EJMjljQb-’) is used to calculate the photodissoci- ation or ‘half-collision’ amplitude (EJMjZjdL-) 1 E x I JoMOqO) that describes the transition amplitude between the initial bound state and the dissociative continuum wavefunction with all non-adiabatic interactions between electronic states incorporated in the con- tinuum wavefunction.The radiation field is assumed to be weak so that the transition between the ground and dissociative states can be described by first-order perturbation theory. The ground-state wavefunction 1 JOMoqo) has initial angular momentum Jo with the electric dipole selection rule specifying the final angular momentum as J = Jo, Jo * 1 for the dissociative wavefunction. Mo is the projection of Jo onto the SF z-axis; qo collects all other quantum numbers necessary to characterize the initial state and includes the vibrational quantum number vo, as well as the electronic quantum numbers A, S and 2. t The basic notation of this section follows that of ref. (1). The partial cross-sections are those defined in ref. (16). which are not identical with those of ref.(1). The difference in partial cross-sections from ref. (1) is a result of the inclusion of circularly polarized light which cannot be written in terms of a spherical harmonics [see eqn (9) and ref. (16)]. The main result of this change is that many of the anisotropy parameters of ref, (1) have slightly different algebraic forms in terms of the partial cross-sections.58 Non-adiabatic Efects in CH+ Photodissociation The photodissociation amplitude can be factored using the Wigner- Eckart theorem to separate the dependence on M,, M and the polarization indices q as (EJMjQJL-)I 6 XIJoMoTo)=C ( J M J 1&qkfO)&zT(4Qab IJoTo) (9) 4 where the T(J~Z~&IJ~T,) are called reduced transition amplitudes. The sum in eqn (9) can be removed if the incident light is in a state of pure polarization. For linearly polarized light it is convenient to choose the SF z-axis along the polarization vector of the incident light, while for circularly polarized light the SF z-axis is taken as parallel to the direction of propagation of the incident beam.Our general theory of diatomic photodissociation to open-shell atoms enables us to calculate the double-differential cross-section: where k^ is the direction of the receding fragments in the SF coordinate system and ZS is the polarization vector, relative to the SF z-axis, of the emitted light from an excited photofragment or of the polarization vector of a probe laser for one of the photo- fragments. The C ? : K ~ Q ~ ; K ~ Q ~ are coefficients that are found through rather complicated angular momentum algebra1~15~16 to be proportional to a bilinear sum of reduced transition amplitudes T( Jjljajb I J , ~ , ) and their complex conjugates T*(J'j'l'j& I J ~ ~ ~ ) .Here CKQ(O, 4 ) is a renormalized spherical harmonic23 given in terms of the usual spherical harmonics Y K Q ( 8,4) by and 4 K s Q s ( E I i ) is the photon polarization density matrix in spherical coordinates, as defined by 0 m 0 n t ~ ~ to be The alignment and orientation of atomic fragments, along with various polarization ratios, can be expressed as simple algebraic expressions in terms of these the partial cross-sections GKsQs;KDQD. When the polarization of final fragment states is not deter- mined or when all spontaneously emitted light is collected, regardless of its polarization, then the differential cross-section for detection of atomic fragments reduces to Similarly, by integrating eqn (10) over all fragment angles k^ we obtain the differential cross-section for the polarization of atomic fragments as The total or integral cross-section is within a constant factor Gm;oo and is related to a linear superposition of I T( 4Q& I J , T ~ ) 1'.Anisotropy Parameters The partial differential cross-section for fragments [eqn (13)] light polarized in the z-direction, can be written in terms of PD as produced by dissociating the anisotropy parameter d a - ( 6) = go[ 1 + k^ 2^)] dokC. J. Williams et al. 59 where P2(k^* z^) is the second Legendre polynomial and 2 r u 0 is the integral photodissociation cross-section.In a similar fashion, an anisotropy parameter Ps for the angular distribution of fluorescence is defined as The familiar polarization ratio, where Ill and I* are the intensities of the spontaneously emitted (or probed) light polarized parallel and perpendicular to the original linearly polarized radiation, is related to P s by p=-. 3Ps 4+Ps This parameter Ps is proportional to the alignment A, of the fragments as defined where the average is over the states of the emitting fragment. If right- and left-circularly polarized light are used for the dissociation and probing of fragments, it is possible to measure an additional anisotropy parameter which is related to the orientation Oo as given by Because final fragment states with j = have A. = 0 but Oo not necessarily vanishing, the orientation Oo may be useful to analyse the structure in cross-sections when the fragment states have j = $.The circularly polarized photodissociation ratio is defined by where I, and I, are the intensities of right- and left-circularly polarized light emitted from excited photofragments or used in the probing of photofragments. Pc is, in general, a complicated function of both the orientation and the alignment. In a recent paper16 it is shown that a judicious choice of angles makes Pc become proportional to the orientation only. The required angle is the ‘magic angle’ OM with respect to the SF z-axis at which the second Legendre polynomial P2(0) vanishes. At this angle we have which is simply proportional to Oo.60 Non-adiabatic Eflects in CH+ Photodissociation Results and Discussion In this section we present selected calculations for the CH+ model system of eqn (1).The theory of the last section is applied with fragments a and b taken to be C'('P) and H(2S), respectively. This implies Z, = Zc+ = 1, s, = sc+ = with j , =jc+ = {$, i} for the two fine-structure states of the C+ ion. The Hamiltonian [eqn (5)] in the atomic basis can be rewritten as where TB is the basis transformation from our 'atomic' to the molecular Hund's case ( a ) basis, and VABo( r ) is a diagonal matrix of electronic potential curves.? The matrix 'Xso is diagonal in the atomic basis with eigenvalues given by the asymptotic spin-orbit splitting of the C' fragment, while f 2 is diagonal in this basis with matrix elements equal to the eigenvalues of ( J - j ) 2 at infinite separaton.The approximation of replacing the Coriolis and spin-orbit interaction matrices by their r -+ ~0 form is common in scattering t h e ~ r y ~ ~ - ~ ' and is invoked because the required electronic matrix elements for CH+ are currently not available. These approximations can be qualitatively justified in scattering dynamics by noting that the non-adiabatic couplings become important in CH+ only as the coupled potential surfaces become nearly degenerate. However, this arises in CH+ at intermediate r and is, hence, in the region where the coupling elements must begin to approach their r + co values. The Schrodinger equation (7) is solved numerically at energy E to obtain the spherical continuum wavefunction I EJMjljc+jC)) as defined in eqn (8).The photodissociation or reduced transition amplitude of eqn (9) is evaluated simultaneously to give the amplitude for first-order electric dipole transitions from an initial bound state of angular momentum Jo to a final continuum state of angular momentum J. Experimental spectra implicitly contain a sum over all possible final states and an average over the initial states present. On the other hand, theoretical total cross-sections may be evaluated for the hypothetical transition from a given initial state to a selected final J state, with the observable cross-section obtained as a sum of these 'partial' cross-sections. Because interference effects between states of different J may contribute and be important, the calculation of angular distributions and isotropy parameters requires the inclusion of all final J = Jo, Jo f 1 states.Close-coupled calculations for the three observable quantities, the integral photofrag- ment cross-section 6oo;oo, the asymmetry parameter pD governing the angular distribution [eqn ( l s a ) ] of photofragments, and the orientation parameter fc( 0,) of eqn (19) for production of oriented photofragments, are shown in fig. 2-4 for the X 'C+ -+ A 'I1 transition in CH'. These three observables are displayed as a function of the final fine-structure state of the C+ fragment and of the excess dissociation energy, where the zero of energy is taken as the barycentre of the C'(2P) fine-structure fragment states. This choice fixes C+(2P1/2) as having an energy of -42 cm-' and C+(2P3,2) with an energy of 21.3 cm-'.Fig. 2 presents results of calculations for the principal perpendicular transition X *C+( Y = 0, Jo = 3) + A ' l l ( J ) where Cf(2P1/2) fragments are produced. Fig. 5 displays individual final J contributions to the X *Z+( Y = 0, Jo = 3) -+ A ' l l ( J ) transi- tion. Although such cross-sections cannot be observed experimentally, they are a convenient theoretical tool for understanding and analysing the dynamics of the half- collision as is evident through the greater detail available from fig. 5 than fig. 2. Fig. 3 and 4 provide additional calculations of 6oo;oo, PD and Pc( 6,) for Jo = 6 and Jo = 11, respectively. Note that these figures provide the first multichannel calculations for PC( e,>.t A description of the ABO potentials, transition dipole functions and Coriolis and spin-orbit coupling elements for CH' is given in ref. (7) and references therein.C. J. Williams et al. 61 3 - C 0 5 2 - N 2 1 - 0- 1 I I I I 1 -1 -45 -30 -15 0 15 30 45 energy/cm-' Fig. 2. ( a ) The anisotropy parameters pD (-) and Pc(6,) (- - -) and ( b ) the integral photodissociation cross-sections for the X 'Z+( v = 0, Jo = 3) + A 'n(J = J o , Jo f 1) photodissoci- ation of CH+ to C+(2P1,2) using right-hand circularly polarized light. The orientation parameter Pc(6,) for the C'('P,,,) fragments is computed assuming that the C'('P,,,) fragments are excited to the C+(,D) state with right-hand circularly polarized light. Although both anisotropy parameters show structure, it is interesting to note the structure in pD which is not apparent in the integral cross-section.All of the observables in fig. 2-5 exhibit a wealth of structure for the near-threshold dissociation of CH'. The resonances of fig. 5 have previously been assigned on the basis of a series of multichannel calculation^.^ To make assignments in ref. (7) individual electronic potentials were modified by adding or subtracting a small square well onto the bottom of these potentials, leading to shifts in certain resonance positions. The information from such calculations is combined with various calculations on the same surfaces, where different transitions, such as a 3132 + c 'X:, are excited to aid in the assignment of the resonances [see ref. (7) for a more thorough discussion of the assignments].Comparison of fig. 2 and 5 then allows the assignment of the major features in fig. 2 for the integral cross-section. Similarly, comparison of fig. 5 with the anisotropy parameter pD of fig. 2 shows that many of the features of pD can be related to resonances of a particular final J which are not necessarily apparent in the predicted integral cross-section in fig. 2. Some resonances, however, are more pronounced in pD and, therefore, pD provides additional dynamical information which may be useful when applied to actual experimental data to aid in untangling the different final J contributions to the integral cross-section. The parameter Pc( 0,) also has some struc- ture, but not to the extent of PD in the calculations presented herein.The very low translational energy region for Jo = 6 and Jo = 11 is displayed in fig. 3 and 4 and has similar behaviour to that of Jo = 3. Once again, p,, exhibits additional structure, which is not apparent in the integral cross-section c?oo;oo, but which can often62 Non-ad ia ba tic Eflects in C H + Pho tod issocia tion 4- 3 - 0 0 b" 2 - 1 - 0- -2 - 1 - t 1 I I I I . ,-1 energy/cm-' -45 -30 -15 0 15 30 45 Fig. 3. As for fig. 2, but for the X 'X+( v = 0, Jo = 6) + A 'n(J = Jo, Jof 1) transition. Of special interest is the unresolved structure in pD near threshold and the structure at 10 cm-'.C. J. Williams et al. 63 I I 1 I -45 -30 -15 0 15 30 45 energy/cm-' Fig. 5. Total cross-sections for the 'idealized' experiment in which the final angular momentum state can be selected.The production of C'('P,!,) fragments in the X 'X+( v = 0, Jo = 3) + A 'n( J) transition with J = (a)& (b)3 and (c)4. In pnnciple, anisotropy parameters may be calculated for these state-to-state transitions, but unlike the linear additivity of the integral cross-sections, interference between different final J states may play an important role in the anisotropy parameter. Comparison of the anisotropy parameter pD of fig. 2 with structure in the individual cross-sections shown above helps to explain some of the additional structure in pD, which is not evident in the integral cross-section of fig. 2. be related to features that exist in the partial cross-sections computed for a selected final angular momentum J. Fig. 6 presents the three basic quantities for the production of C+('P3,2) fragments from Jo= 11. The anisotropy parameter ps is displayed instead of the parameter Pc(8,).Note that Ps is not relevant for the production of C'('P,/,) fragments, since it is identically zero for j , < 1. Finally, fig. 7 presents calculations for the a 3112( Y = 10, Jo = 6 ) + c 'XT ( J ) transition. Comparison of fig. 3 and 7 shows the difference in structure that emerges when different transitions are pumped. It is important to realize that the same continuum wavefunctions are involved in fig. 3 and 7. The differences in structure are primarily a result of the difference in the component of the continuum wavefunction which receives the flux in the transition. Apart from possible resonance just above threshold to the C+('Pll2) state, the strongest features in the X 'Z+( v = 0, Jo = 6) + A ' n ( J ) transition integral cross-section of fig.3 are A 'II and a 3112 resonances, while the strongest resonances in the a 'n2( Y = 10, Jo = 6 ) + c 3 X + ( J ) transition of fig. 7 are primarily c 'Z: and c 'Z; resonances. Conclusions Two previous papers7 demonstrate that many of the rules of diatomic spectroscopy can be applied to explain the structure in the predicted low-energy photodissociation spectra64 Non-adiabatic Efects in CH+ Photodissociation 1: ;o 3b - Lo i o $0 ;o - 80 . i o lob-' energy / cm - ' Fig. 6. ( a ) The anisotropy parameters pD (-) and ps (- - -) for production of C'(2P3,2) fragments in the X 'Z+( v = 5, Jo = 11) + A 'n(J = Jo, Jof 1 ) transition and ( b ) the integral cross- section.At even higher angular momenta additional structure emerges in the anisotropy parameters and cross-sections for production of C'(2P3,2) fragments.6 of CH+. The increased number of resonances over those previously expected arises because of the breakdown of electronic selection rules due to asymptotic non-adiabatic couplings. The resonances may, however, be assigned effective vibrational quantum numbers and rotational constants. One problem in unravelling the total cross-section is that many of the resonances, which are apparent in the hypothetical state-to-state cross-sections, are washed out in the integral cross-section, where there is a coherent sum over final angular momenta J = JO, Jo * 1. This occurs because of different Franck- Condon factors for the P-, Q- and R-branch transitions, as well as because there are several resonances with different final J lying in the same energy region. Anisotropy parameters, such as pD, may be helpful in unravelling some of the 'hidden' dynamics in systems like CH+ because the contributing resonances often enter into pD with different weights than in the total cross-section.The structure present in an anisotropy parameter may either point to resonances which are not apparent from the integral cross-section or to interference effects between resonances. Other anisotropy parameters like ps and Pc( 6,) may provide further dynamical information. In addition, measurements of fragment kinetic energy can be useful in analysing resonances when several initial states are i n ~ o l v e d .~ Finally, the use of two-photon resonant dissociation introduces additional anisotropy into the dissociation of diatomic systems 178~15 and provides additional structure in the anisotropy parameters along with new anisotropy parameters such as (T00;40 y D = 7 . goo; 00C. J. Williams et al. 65 9r I l2 I I I -45 -30 -15 0 15 energy/cm-' Fig. 7. (a) Examples of pD (-) and PC(OM) (- - -) for production of C+(2P1,2) fragments in the a 3112( Y = 10, Jo = 6 ) + c 3Z+(J = Jo, Jo* 1) transition. The above structure should be com- pared with that of fig. 3. Although the same continuum states are involved in both fig. 3 and 7, different components of the continuum are receiving the flux in the two cases. The narrow resonances near threshold are noticeable in both figures.The other resonances in the integral cross-section (b) are primarily due to the c 'El state, while fig. 3 has the resonances basically of A 'II and a 3112 character. The quantity yD is similar to PD, but is the coefficient of the fourth Legendre polynomial in an expansion like eqn (15a). The model calculations presented here are intended to demonstrate the observability of interesting near-threshold structure caused by non- adiabatic interactions in the photodissociation of diatomic systems to open-shell frag- ments. Our calculations suggest the importance of the measurement of anisotropy parameters to help untangle experiments spectra on these complicated systems. The full quantum theory of diatomic photodissociation thus predicts many novel features in the near-threshold dissociation of diatomics.This theory is the first to include the angular recoupling algebra necessary to describe both the internal angular momentum of the parent molecule and that of the fragments produced in the half-collision. (See also the recent work on triatomic photodissociation.28) New experiments, such as the dissociation of diatomics in magnetic fields,22 may provide additional information, beyond that described in this paper, on the near-threshold dissociation of diatomics to atoms with fine structure. This research was supported, in part, by NSF Grant CHE 83-17098 and the U.S.-Isreal Binational Science Foundation.66 Non-adiabatic Efects in CHi Photodissociation References 1 S. J.Singer, K. F. Freed and Y. B. Band, Adu. Chem. Phys., 1985, 61, 1. 2 J. T. Moseley, Adv. Chem. Phys., 1985, 60, 245. 3 S. R. Leone, Adv. Chem. Phys., 1982, 50, 225. 4 M. Shapiro and R. Bersohn, Annu. Rev. Phys. Chem., 1982, 33, 409. 5 Y. B. Band, K. F. Freed and D. J. Kouri, Chem. Phys. Lett., 1981,79,233; Y. B. Band and K. F. Freed, 6 S. J. Singer, K. F. Freed and Y. B. Band, Chem. Phys. Lett., 1984, 105, 158. 7 C. J. Williams and K. F. Freed, Chem. Phys. Lett., 1986, 127, 360; C. J. Williams and K. F. Freed, J. 8 S. J. Singer, Y. B. Band and K. F. Freed, Chem. Phys. Lett., 1982, 91, 12; S. J. Singer, K. F. Freed and 9 W. S. Struve, S. J. Singer and K. F. Freed, Chem. Phys. Lett., 1984, 110, 588. Chem. Phys. Lett., 1981, 79, 238. Chem. Phys., in press. Y. B. Band, J. Chem. Phys., 1984, 81, 3091. 10 Y. B. Band, K. F. Freed and S. J. Singer, J. Chem. Phys., 1986, 84, 3762. 11 U. Fano and J. M. Macek, Rev. Mod. Phys., 1973,45, 553. 12 C. M. Greene and R. N. Zare, Annu. Rev. Phys. Chem., 1982, 33, 89; C. M. Greene and R. N. Zare, 13 S. J. Singer, K. F. Freed and Y. B. Band, J. Chem. Phys., 1983, 79, 6060. 14 S. J. Singer, K. F. Freed and Y. B. Band, J. Chem. Phys., 1984,81, 3964. 15 S. J. Singer, K. F. Freed and Y. B. Band, J. Chem. Phys., 1986,84, 3762. 16 S. Lee, C. J. Williams and K. F. Freed, Chem. Phys. Lett., 1986, in press. 17 P. C. Cosby, H. Helm and J. T. Moseley, Astrophys. J., 1980, 235, 52. 18 H. Helm, P. C. Cosby, M. M. Graff and J. T. Mosley, Phys. Rev. A, 1982, 25, 304. 19 P. J. Sane, J. M. Walmsley and C. J. Whitham, J. Chem. SOC., Faruday Trans. 2, 1986, 82, 1243. 20 A. Carrington, J. Buttenshaw, R. A. Kennedy and T. P. Softley, Mol. Phys., 1982, 45, 747. 21 G. Geber and R. Moller, Phys. Rev. Left., 1985,55,814; E. W. Rothe, U. Krause and R. Duren, Chem. 22 H. Kato, Faruday Discuss. Chem. SOC., 1986,82, 000; H. Kato and K. Onomichi, J. Chem. Phys., 1985, 23 D. M. Brink and G. R. Satchler, Angular Momentum (Clarendon Press, Oxford, 2nd edn, 1968). 24 A. Omont, Prog. Quantum Electron., 1977, 5, 69. 25 J. C. Gay and W. B. Schneider, 2. Phys. A, 1976, 278, 211 and references therein. 26 J. M. Launay and E. Roueff, J. Phys. B, 1977, 10, 879; F. H. Mies, Phys. Rev. A, 1973, 7, 942; J. C. 27 J. H. Van Vleck, Phys. Rev., 1929,33,467. 28 G. G. Balint-Kurti, J. Chem. Phys., 1986,84, 443. J. Chem. Phys., 1984,48, 4304. Phys. Lett., 1980, 72, 100. 82, 1642; H. Kato, M. Baba and I. Hanazaki, J. Chem. Phys., 1984,80, 3936. Weisheit and N. F. Lane, Phys. Rev. A, 1971, 4, 171. Received 19th May, 1986

ISSN:0301-7249    

DOI:10.1039/DC9868200051

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

Faraday Discuss. Chem. Soc., 1986,82, 67-78 High-resolution Laser Photofragment Spectroscopy of Molecular Ions Peter J. Sarre,* Jon M. Walmsley and Christopher J. Whitham Department of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD High-resolution laser photofragment spectra of CH+ and SiH' have been recorded by the detection of C+ and Si+ ions using a fast-ion-beam apparatus. Information on near-threshold dissociation is obtained by the observation of transitions to predissociated (quasibound) levels, some of which exhibit predissociation lifetime-broadening and nuclear hyperfine splittings. Measurement of the centre-of-mass kinetic energy release and the photofrag- ment angular distribution is also described. The predissociation mechanisms for three rotationally quasibound levels of the A 'II state of CH+ are investigated through analysis of lifetime- broadening of rotational lines of the A 'II-X 'X+ electronic transition.Comparison is made with the results of a calculation of the tunnelling and radial contributions to the predissociation rates. The first predissociation spectra of SiH+ are reported and transitions to two levels which lie only ca. 80 cm-' above the dissociation limit are discussed in detail. Evidence is found for non-adiabatic interactions near to dissoci- ation. It is proposed that 'near-threshold' photofragment spectra of CH+ observed in the 18 350-19 600 cm-' region arise from transitions between triplet levels near to the C'(2P)+H(2S) dissociation limit and a shallow (bound) triplet state which correlates to the C('P) + H+ limit.Radiative decay to the continuum and near-threshold levels above the C'('P) + H(2S) limit yields low-energy C+ ions. The experiments described in this paper form part of a growing interest in probing the region of internuclear separation between the atomic and molecular limits and in the role of non-adiabatic interactions near to dissociation. Detailed information can be obtained through the detection of resonances (shape, Feshbach) in the molecular photodissociation cross-section. Novel effects, including multichannel resonances, have been predicted to be present in near-threshold photodissociation spectra of molecules which dissociate into atoms which possess electronic angular momentum.'-3 We have chosen to study CH' and SiH+ as model examples of molecules which fragment into open-shell atoms, i.e. C'('P) + H(2S) or Sif(2P) + H(2S), and which are likely to show evidence of non-adiabatic interactions in their photodissociation spectra.In practice this is achieved by tunable laser photodissociation of a mass-selected ion beam and detection of the photofragment ions.4 The principal aim of this work is to obtain information on the role of resonances and non-adiabatic interactions in chemical reactions, collisions and photodissociation through the study of CH+ and SiH+. However, an additional motivation for the experiments is provided by the importance of these two ions and their component atoms in astrophysics. The abundance of CH+ is not satisfactorily explained by simple models of interstellar cloud ~hemistry.~ For many years the radiative association reaction C'(2Pl,2)+H(2S) + CH'" + CH+(X 'X+)+hv ( 1 ) 6768 Photofragment Spectroscopy of Molecular Ions has been suggested as a likely CH+ formation route,6 but even the most recent calculation' of the rate, including shape and other resonances, does not fully remove the discrepancy between the observed and calculated CH+ density.This has led to the consideration of other formation mechanisms, including the endothermic reaction of C+ with H2 to form CHf.' The importance of orbiting and other resonances in enhancing the radiative association rate is known,7 but close-coupled calculations indicate that not all contribut- ing resonances have yet been taken into account and could increase the CH' formation rate.''2 In due course a full interpretation of resonances observed in a photodissociation experiment [the reverse of reaction (l)] should allow an accurate determination of the association rate and its temperature dependence.The SiH+ ion has not been detected so far in interstellar clouds. Emission arising from the transition between the 'P3/2 and 2Pl/z fine-structure states in both C+ and Si+ has been detected from interstellar sources. In both cases the upper 'P3/* state is believed to be populated in collisions between the atomic ions in their 'PlI2 states and atomic hydrogen. The non-adiabatic collision of C+ and Si+ with atomic hydrogen, followed by photon emission, provides an important cooling mechanism in some interstellar regions.9y10 Finally, we note that the rates of photodissociation of CH+ and SiH+ in the interstellar medium are clearly influenced by the existence of near-threshold resonances.' ' In principle laser photo fragment spectroscopy4 in fast ion beams can provide detailed information of relevance to radiative association, non-adiabatic collisions and photodissociation cross-sections.In part this has already been a~hieved.~." However, high-quality ab initio calculations and fully coupled calculations of photofragmentation cross-sections are also essential and complementary to experimental work. In this paper we describe progress towards a full understanding of photodissociation resonances in CH+ and SiH+. Following sections on experimental aspects and the theoretical back- ground to the predissociation of near-threshold levels, three experimental studies are described.The relative importance of different dissociation mechanisms in three rota- tionally quasibound levels of the A 'TI state of CH+ is assessed through measurement of line-broadening in photodissociation spectra of 12CH+ and 13CH+. Secondly, the detection of resonances in photodissociation spectra of SiH+ is described. Finally, a new interpretation of apparent near-threshold photodissociation resonances in CH+ is proposed. Experimental Details of the operation of our ion-beam apparatus (fig. 1) have already been published.'* In outline, CH+ (SiH') ions are formed from CH4 (SiH4) in an electron-impact ion source and are extracted by a high positive accelerating potential, usually 4.5 kV for CH+ and 3.5 kV for SiH+.A small electromagnet permits selection of a pure beam of a single mass-to-charge ratio. The ion beam is subjected to focussing and deflection immediately prior to, and following, the magnetic sector and travels in free-flight over a 0.4 m pathlength towards the entrance slit of an electrostatic (energy) analyser (ESA). Photofragment ions are formed by coaxial irradiation of the parent ion beam and are detected with an electron multiplier. The ESA is a 15 in (0.381 m) radius, 90 O sector instrument and serves both as a coarse 'mass' selector and as a high-quality analyser of the photofragment translational energy. At present the energy resolution is limited by the energy spread in the parent ion beam. The laser beam is amplitude-modulated at a frequency of 3 kHz with a mechanical chopper, and phase-sensitive detection is employed in order to discriminate against fragment ions which arise from collision- induced and unimolecular decomposition of the parent cations.The ion-beam energy spread also determines the spectroscopic resolution of the experiment, corresponding to ca. 100 MHz for CHf and ca. 40 MHz for SiH+ at a laser wavenumber of 17 000 cm-'. This narrow Doppler width arises from the effect of kinematic compression in fast-ionI , electron lock-in amplifier -I- -1- ion monitor I plate (osci lloscope) entrance slit = I= source voltage Fig. 1. Schematic diagram of the fast-ion-beam apparatus. Photofragmentation of CH+ to form C+ is shown. The laser radiation is provided by a Coherent CR-699-29 C.W.single-mode dye laser pumped by an Innova-20 argon-ion laser. For this work Rhodamine -B, -6G and -1 10 dyes were used and an output power of up to 950 mW was achieved at the peak of Rhodamine-6G when pumped with 6 W of 514.5 nm radiation. Experimental and Theoretical Background Experimental Information A wide range of experimental data may be obtained from fast-ion-beam laser photofrag- ment spectro~copy.~ The transition frequencies provide information on the potential- energy curves of the electronic states. "3 The narrow Doppler width allows measurement of predissociation lifetimes when the level is sufficiently short-lived to cause broadening of the lines. For Doppler-limited or slightly broadened lines, the high resolution allows observation of nuclear hyperfine splittings in appropriate cases."J* (This is extremely valuable as it provides information on the electronic wavefunction and can give an indication of the type of level involved in a transition.) The high laser power enables saturation of transitions to be achieved and often causes power-broadening of the lines. However, partially forbidden transitions exhibit power-broadening to a lesser extent and so this effect can be used to give a qualitative indication of the oscillator strength associated with a line in the spectrum and assist in assignment. Information is also obtained from measurement of the translational energy and angular distribution of the photofragments. An amplification factor arises in the transfor- mation from a centre-of-mass energy release into the laboratory frame and consequently very small energy releases can be measured." The energy analyser is also sensitive to70 Photofragment Spectroscopy of Molecular Ions I,,,,,,, 1 2 3 4 internuclear separation/ A Fig.2. Potential-energy curves for CH+ [adapted from curves given in ref. (15)]. A similar set of curves holds for SiH+.20,21 -10 - E -20- 2 -30- 5 \ Do E -40 -50 - - -60 - 3 -70 - / 1 I I I 3 L 5 - 80 internuclear separation/ A Fig. 3. Correlation of molecular and atomic states including spin-orbit coupling [adapted from ref. (22) and (23)]. The fine structure splitting in C+ is 63.4 cm-’. the angular distribution of the photofragments. This can provide confirmation of the spectroscopic assignments and an example is given later for SiH+.Finally, we note that the CH+ and SiHf ions possess a high degree of electronic, vibrational and rotational excitation. This is a highly desirable aspect of the experiment as it allows study of regions of the potential-energy surfaces of molecular ions which are not readily investigated by other techniques.P. J. Sarre, J. M. Walmsley and C. J. Whitham 71 Predissociation of Near-threshold Levels We discuss here principally the theory of predissociation as applied to CH+, but all general comments apply equally to SiH+. Potential-energy curves for CH+ are shown in fig. 2. Shape resonances exist for electronic states in which a centrifugal barrier arises in the potential-energy curve, and examples of these have been detected in spectra involving the 11116*18 and 311'7 states.Centrifugally bound levels of the A 'II state may predissociate by tunnelling through the barrier and also by rotational and radial coup- ling.24 The rotational-electronic coupling occurs with the X 'X+ state but only operates for the e25 lambda-doublet component of each J level of the 'II state because of the selection rules on J and parity. Radial coupling arises through the effect of the nuclear kinetic energy operator on states with a= 1 ('II, , '111) which are mixed by spin-orbit coupling. Levels of the 'II state which lie between the fine-structure dissociation limits (see fig. 3) are predissociated by radial and rotational coupling only. Graff et al. have calculated the contributions of all of these mechanisms to the linewidths in the A 'H-X 'Z+ predissociation spectrum, and full details of the theoretical approach are given in their paper.24 For levels which are very near to dissociation where the non-adiabatic interactions are of most importance, a fully coupled calculation is required.Extensive calculations have been performed for CH+ and it is predicted that multichannel resonances should be observed in the near-threshold photodissociation Shape Resonances of the A 'II State of CH+ Four molecular electronic states, 'Z+, 3Xf, 'II and 311 correlate with the C'('P) + H(2S) dissociation limit of CH+, as shown in fig. 2. Transitions between the A 'II and X 'X+ states involving u ' d 4 and u " d 3 have been observed in emission at high resolution, and molecular parameters for these states have been obtained.'" Limited experimental information is available on the a 311 state from a study of the b 3XC--a 311 tran~ition,~' but the location of this state with respect to the C'('P) + H(2S) dissociation limit is not known.The c 'Z+ state is calculated to be repulsive apart from a long-range van der Waals minimum (see fig. 3) but has not been detected experimentally. For sufficiently high values of J, the A 'II state supports narrow quasibound rotational levels (shape resonances). Transitions to these levels from the X 'X+ state have been recorded by laser photofragment spectroscopy by the detection of C+ fragment In a notable study, Helm et a1.16 assigned over fifty transitions involving 32 levels of the A 'II state and obtained an improved potential for this state.Subsequently, we recorded many of these resonances at high resolution.'8 Our work provided support for the earlier assign- ments16 through the observation of additional predicted16 weak resonances and the measurement of predissociation linewidths. We have recently recorded a number of lines at high resolution in the corresponding spectra of 13CH+ and CD+ which also fall within the expected accuracy of the predictions based on the A 'II potential.16 Details of these results will be reported in a future publication. A calculation by Graff et al. has shown that in addition to the tunnelling contribution, radial and rotational couplings can be ~ignificant.~~ In order to determine the relative contributions of these dissociation mechanisms, we have made a study of the predissoci- ation of three quasibound levels of 12CH+ and 13CH+ which exhibit lifetime broadening" (see fig.4). The linewidth measurements for transitions involving u = 0, J = 35; u = 1, J = 33 and u = 2, J = 31 are given in table 1. The radial contribution to the predissociation rates for these levels has been calculated by Graff28 using the method described in ref. (24) and a refined version of a 'II potential due to Helm.29 The tunnelling contribution was calculated by us using the same potential and a computer program of LeRoya3* From the results in table 1 it is clear that for the highest lying level, u = 0, J = 35, the tunnelling contribution is dominant, while for the72 Photo fragmen t Spectroscopy of Molecular Ions 200c 150C - I E n 3 1000 5 ; Q) 500 0 -500 internuclear separation/ A Fig.4. Potential-energy curves and energy levels for ( a ) u = 0, J = 35, ( b ) u = 1, J = 33 and (c) u = 2, J = 31 of the A 'n state of CH+. The A 'II rotationless potential is a modified version28 of a potential derived by Helm.29 Table 1. a Calculated and measured predissociation linewidths (in GHz) for the levels u = 0 , J=35; u = 1, J = 3 3 and u = 2 , J = 3 1 of '*CH+ and 13CH+ J' isotope 0 35 "C H+ 4.3(0.4) 5.5(0.5) 4.0 0.3 4.3 13CH+ 2.6( 0.2) 3.3(0.2) 2.0 0.2 2.2 1 33 "CH' 4.5 (0.5) 6.0( 1 ) 1.4 1.6 3 .O 13CH+ 2.5(0.5) 3.4(0.5) 0.7 0.8 1.5 2 31 12CH+ 2.0(0.5) - 1.0 0.9 1.9 I3CH+ 1 h(0.3) - 0.4 0.5 0.9 a The wavenumbers of the lines from which the linewidth measurements were made will be published elsewhere.la quoted. other two levels both tunnelling and radial contributions are important. This is the case for both isotopic forms of CH+. The overall agreement between theory and experiment is satisfactory and the predicted reduction in linewidth between 12CH+ and 13CH+ is confirmed by experiment. The calculation of linewidths is very sensitive to the form of the potential and the agreement between theory and experiment is perhaps better than might reasonably be expected. The contribution of rotational-electronic coupling to the linewidths is in principle readily assessed because only the e component is affected. For two of the levels the linewidth of the f component is found to be greater than for the e component. This is in the opposite sense to that expected on the basis of rotational-electronic coupling.However, it has been pointed that when rotationallyP. J. Sarre, J. M. Wcrlmsley and C. J. Whitham 73 Table 2. Vacuum wavenumbers of the transitions to the level(s) d= 1, J'= 17 of the A 'n state of SiH+ ~~ 18 285.440 e 18 518.915 - 18 047.849 - e 16 234.65 1 16 691.642 (1,3) J'= 17 + f (1,4) J'= 17 + f 16 465.008 adiabatic potentials are employed, the tunnelling lifetime for the e level can be longer than for theflevel because of the contribution of the Coriolis term to the potential-energy barrier. Given the importance of the tunnelling mechanism for these levels, it seems probable that this is the origin of the different widths for the e and f levels. We are currently attempting to obtain rotationally adiabatic potential energy curves by inversion of experimental data on 12CH+, 13CH+ and CD+.This should allow a fuller comparison of our results with theory. Near-threshold Dissociation in SiH+ We have recorded the first laser photofragment spectra of the SiH' ion by detection of Si+ ions. In many respects the electronic structure of the SiH+ ion is very similar to that of CH', the most notable differences being the comparative of the A 'n and a 311 wells and the larger fine-structure splitting of 287 cm-' in Si'. Optical emission spectra of the A '11-X '2' system have been reported by Douglas and Lutz" and by Carlson et al.33 Using RKR potentials derived from these data,34 we have employed the program of LeRoy3O to calculate the energies of the bound and quasibound levels of the two states.The dissociation energy of the A 'I3 state is quoted33 as 1230*210 cm-', which is very much lower than for the equivalent state of CH+. As emission has been recorded involving levels up to and including v' = 3, J' = 633 only a short extrapolation between the known rotational levels and the quasibound levels is required. The assignment of the photofragment resonances has been achieved by combining a wide range of experimental and theoretical information including the observed and predicted transition frequencies, calculated oscillator strengths, predissociation linewidths and kinetic energy releases. We describe here in detail transitions from the X 'X+ state to the two lambda-doublet components of the v' = 1, J' = 17 level of the A 'II state and the predissociation of these levels, The measured transition frequencies are given in table 2 and are all in good agreement with the predictions based on the potentials described.We have also succeeded in recording two of the corresponding lines in 29SiH+. Profiles of three of the lines are shown in fig. 5. Calculation of the line strengths for these transitions using a published transition showed that lines of the 1-3 and 1-4 bands involving the two levels with v ' = 1, J'= 17 are expected to be among the strongest in the spectrum, and this is found to be the case. Further confirmation of the assignment is obtained from energy analysis of the photofragments. For a AJ = 0 ( Q ) transition the Si' fragments are ejected preferentially along the ion-beam axis, while for AJ = *1 (R, P) lines the scattering occurs perpendicularly to the beam direction.This difference is illustrated in fig. 6 where the effect on the angular distribu- tions for AJ = 0 and AJ = +1 excitation is clear. The centre-of-mass kinetic energy release for the v ' = 1, J'= 17 level is measured from the f.w.h.m. to be lO(5) meV which is equivalent to 80(40) cm-'. We cannot determine if this measurement is with respect to the upper or lower fine-structure dissociation limit, but we believe from the following74 Photofragment Spectroscopy of Molecular Ions 18528.39 18528.42 1 18057.07 18057.10 18057.13 wavenumber/cm-' 18294.806 18294.816 Fig. 5. Profiles of ( a ) R(16), (6) Q(17) and (c) P(18) lines of the 1-3 band of the A 'II-X 'X,+ system of SiH+.The P and R lines are broad owing to rotational coupling to the X 'Z+ state and the Q line shows a nuclear hyperfine splitting of 150(20) MHz. The wavenumber scale is not corrected for the Doppler shift. I I 3550 3535 1 I 3550 3535 laboratory energy/eV Fig. 6. Kinetic energy release profiles for excitation of ( a ) R( 16) (AJ = +1) and ( b ) Q( 17) (AJ = 0) lines of the 1-3 band of the A 'II-X 'E+ system of SiH+. arguments that the level lies just above the lower limit. Transitions to the e and f components have markedly different spectroscopic linewidths, 550( 100) MHz and 70(20) MHz, respectively, and this arises because only the e component can interact with the X 'Z+ state. The rotational-electronic coupling operator, which also gives rise to the lambda-doublet splitting of the 'II energy levels, does not operate for the f component.As the X 'X+ state correlates with the lower 2P,/2 limit, this strong coupling to the ground electronic state combined with the low energy release leads us to conclude that the level is ca. 80cm-' above the Si'(2P,,2)+H(2S) limit. Unexpectedly, the 'f' component (Q line), shows a doublet splitting of 150*20 MHz. This splitting must arise from proton nuclear hyperfine structure. For a pure 'I2 level any splitting will beP. J. Sarre, J. M. Walmsley and C. J. Whitham 75 17804.63 0 17804.640 17804.650 wavenumber/cm-' Fig. 7. One of a number of transitions detected in the photofragment spectrum of SiH+ which exhibit large proton nuclear hyperfine splittings (in this case ca. 425 MHz).The wavenumber scale is not corrected for the Doppler shift. negligible and we infer that this level is mixed with a nearby triplet level. We have used the results of ab initio calculations of the a 311 state by Hirst21 in the LeRoy program3' and find that energy levels of the 311 state of appropriate J and parity do exist in the same energy region. In due course it should be possible to identify the perturbing levels directly in the spectrum. We have recorded a number of transitions to levels with very large nuclear hyperfine splittings and low energy releases, one example of which is given in fig. 7. This transition must involve a triplet level (mixed slightly with the 'II state) in order to give a hyperfine splitting as large as 425 MHz, and the level may be described as a 'multichannel' resonance.Additional Transitions in CH+ Apart from the relatively well understood transitions to quasibound 'II levels, 16,18 numerous additional resonances have been found in the ~ l t r a v i o l e t , ~ ~ visible 16-18 and infrared17 spectral regions. In each case essentially the same type of ion-beam apparatus was employed. We consider here only those transitions which are known to give rise to photofragment C+ ions with low kinetic energy release. In the ultraviolet region near 350 nm,35 37 lines were observed in short Doppler-tuned segments of the spectrum, only four of which have been assigned to transitions from the X '.C+ state to 'II quasibound levels.16 The extra resonances were attributed tenta- tively to transitions from X 'Z+ levels to near-threshold levels of the a 311 state.35 However, it has also been ~uggested'~ that these lines originate from pumping the (0,O) band of the 6 3E--a 311 system.Radiative decay of the 6 3C- levels into the continuum and quasibound levels just above the dissociation limit yields C+ fragment ions which are detected.76 Photofragment Spectroscopy of Molecular Ions 18690.50 18691-00 1 8691.50 18692.00 wavenumber/cm-' Fig. 8. A 2 cm-' section of the CH+ spectrum near 18 691 cm-'. Many lines exhibit hyperfine splittings in the range 500-600 MHz. Laser excitation of all the lines in this spectrum gives rise to C+ fragment ions with less than 25 meV energy. [Reproduced from ref. (18) with permission.] In the infrared predissociation spectrum 87 transitions between 875 and 1095 cm-' have been detected." The majority of the resonances have been attributed to vibration- rotation transitions within the a 'I3 state involving J = 20 to 40 and v = 7 to 12.Perhaps the most puzzling part of the laser photofragment spectrum of CH+ was discovered by Helm et a1.l6 and consists of a large number of lines extending from ca. 18 350 cm-' to at least 19 600 cm-'. A surprising observation is that laser excitation in most of these lines generates C+ ions with less than ca. 25 meV kinetic energy. In an earlier study," we recorded part of this region at Doppler-limited resolution and found that many of the lines exhibit nuclear hyperfine splittings, usually in the range 500- 600 MHz (see fig.8). This is attributable to a Fermi-contact interaction at the proton nucleus and indicates that at least one of the states involved in this transition has substantial triplet character. The high value of the splitting implies that the level is near to dissociation'8 and led us to conclude that these transitions probably arise from excitation between levels of the X 'Z+ state and near-threshold levels of the a 31T state." Transitions of this type in CH+, in which non-adiabatic interactions near dissociation play an important role, have been considered in detail by Williams and Freed in their multichannel treatment.2 While it is likely that some multichannel resonances are present in the CH' spectrum, we propose here a different origin for the wealth of lines in the 18 350-19 600 cm-' region.The key to the interpretation is the recognition that this spectral region includes the separation (in wavenumbers) between the C'('P) + H(2S) and C('P) + H+ dissoci- ation limits of 18 858 cm-', i.e. the difference in the ionisation potentials of carbon and hydrogen. It is well established from the infrared experiments17 that levels of the a 'II state are populated up to the dissociation limit and it is likely that the van der Waals (ion-induced-dipole) well of the c 'C+ state (see fig. 3) is also populated. Therefore laser excitation of CH+ ions from levels which lie just below the C'('P)+H(2S) dissociation limit to higher-lying electronic states is possible. Inspection of fig. 2 shows that two electronic states, b 31;- and d 'II, correlate to the C('P) + H' dissociation limit.The d 311 state is repulsive for R62.5 .$, but possesses a potential well at long range (not shown in fig. 2) caused principally by ion-induced-dipole (R-4) and charge- quadrupole ( R-3) interactions. It has a calculated well-depth of ca. 700 ~ m - ' . ~ ~ Excita- tion from near-threshold levels of the a 311 state and/or the c 3Z+ state, to the bound levels of the shallow d 'll state necessarily occurs at photon energies close to the energy separation of the two dissociation limits, i.e. near 18 858 cm-'. This wavenumber lies approximately in the middle of the observed spectrum. Neglecting any contribution due to excitation from metastable levels lying above the C'('P) + H('S) dissociation limit, the long-wavelength cut-off in the spectrum is determined by the well-depth in the d 'I3 state.Ignoring the d 311 zero-point energy, the cut-off is predicted at ca. 18 158 cm-', which is in reasonable agreement with the observed cut-off in the spectrum at ca. 18 350 cm-'. The short-wavelength extent of the spectrum is determinedP. J. Sarre, J. M. Walmsley and C. J. Whitham 77 by the intensity of the transitions from vibrational levels which lie progressively deeper into the a 'II well and for which the outer turning point of the vibrational motion moves to shorter internuclear separations. Calculation of the Franck-Condon factors for the d 311-a 'II transition using ab initio potential-energy curves indicates that the intensity decays to shorter wavelengths and is negligible at 20000cm-'.We propose that, following excitation, the d 311 state decays radiatively into continuum and quasibound levels which lie just above the threshold for dissociation into C'(2P)+H(2S). Con- sequently, excitation in all spectroscopic lines yields low-energy C' ions (see fig. 8). A proportion of the radiative decay is to bound levels and is not detected. A number of observations support this proposal. Apart from the absolute wavelength and extent of the spectrum, which match the expectations based on the a6 initio potentials, the observation of large nuclear hyperfine splittings indicates that at least one state is a triplet state and that the levels of this state are very close to dissociation." Triplet levels near to the C'('P) + H(2S) limit possess this characteristic but the Fermi- contact interaction at the proton for the d 311 state will be very small as this state correlates to C('P) + H+.Consequently, large hyperfine splittings in some of the branches of the d 311-a 'I3 and d 'H-c 'E+ electronic spectra are expected. The Franck-Condon factors for these transitions are calculated to be favourable, and as this is a charge-transfer transition it is likely to be strong. Lines of 13CH+ and CD+ are also found in the same spectral region as expected. We have not been able to find additional lines (apart from transitions to 'II shape resonances) in the regions 22 450-24 150 cm-' (scanned broad- band) or 16 500-18 200 cm-' (scanned single-mode), although coverage of this second region is not complete. Given that the ions are 'hot', other vibrational bands would be expected if the electronic spectrum involved the inner parts of the potential-energy wells.Finally, we note that the proposed interpretation of the CH+ spectrum has many characteristics in common with charge-transfer spectra observed, for example, in A full spectroscopic analysis of the lines near 18 858 cm-' is in progress. If these proposals are confirmed, it appears that this may be a fairly general approach to the study of molecular ions near to dissociation. A particularly interesting aspect is the possibility of studying the bound levels of an excited electronic state by the detection of ions formed following radiative decay (C' in this case), while the quasibound levels of the upper state can be interrogated by the detection of the other fragment ion (H+) which arises from tunnelling and other predissociation mechanisms.H ~ N ~ + 3 7 3 8 Conclusion It is clear that so far only a partial understanding of near-threshold behaviour in CH+ and SiH+ has been achieved. In particular, no definitive examples of multichannel resonances in CH+ have yet been identified. In SiH+ the spectrum is very much clearer and there is a good prospect of a complete analysis and assignment of all types of resonances in the near future. We have proposed a new explanation for the numerous additional 'resonances' found in the visible spectrum of CH+. If our interpretation proves to be correct following a full spectroscopic assignment, similar transitions are likely to be detectable in other ions by the same method. We suggest that this would open up a promising route for the study of long-range interactions in molecular ions.We are very grateful to Dr M. M. Graff for recalculating the radial contribution to the CH+ linewidths and extending the calculation to 13CH+ and for sending us the results on three of the levels prior to publication. We also thank Dr M. Larsson for RKR potentials for SiH+ and Dr D. M. Hirst for providing the a6 initio potentials for SiH+ before publication. Technical assistance from Mr N. Barnes has been much appreciated. 1278 Photofragment Spectroscopy of Molecular Ions We are grateful to the Research Corporation trust for a research grant and to the S.E.R.C. for equipment grants and studentships to J.M.W.and C.J.W. References 1 S. J. Singer, K. F. Freed and Y. B. Band, Adv. Chem. Phys., 1985, 61, 1 and references therein; Chem. 2 C. J. Williams and K. F. Freed, Chem. Phys. Lett., 1986, 127, 360; J. Chem Phys., 1986,85, 2699. 3 C. J. Williams, K. F. Freed, S. J. Singer and Y . B. Band, Faraday Discuss. Chem. SOC., 1986, 82, 000. 4 J. T. Moseley, J. Phys. Chem., 1982,86, 3282; Adv. Chem. Phys., 1985,60, 245. 5 For a recent overview of the problem see D. L. Lambert and A. C. Danks, Astrophys. J., 1986,303,401. 6 See for example A. Dalgarno, in Atomic Processes and Applications, ed. P. G. Burke and B. L. Moiseiwitch 7 M. M. Graff, J. T. Moseley and E. Roueff, Astrophys. J., 1983, 269, 796. 8 M. Elitzur and W. D. Watson, Astrophys. J., 1978, 222, L141. 9 J. M. Launay and E.Roueff, J. Phys. B, 1977, 10, 879 and references therein. Phys. Lett., 1984, 105, 158. (North Holland, Amsterdam, 1976), chap. 5 . 10 M. R. Haas, D. J. Hollenbach and E. F. Erickson, Astrophys. J., 1986, 301, L57. 11 M. M. Graff and J. T. Moseley, Chem. Phys. Lett., 1984, 105, 163. 12 C. P. Edwards, C. S. Maclean and P. J. Sarre, Mol. Phys., 1984, 52, 1453. 13 S. L. Kaufman, Opt. Commun., 1976, 17, 309. 14 C. P. Edwards, C. S. Maclean and P. J. Sarre, J. Mol. Struct., 1982, 79, 125. 15 H. Helm, in Physics ofEIectronic and Atomic Collisions, ed. J. Eichler, I. V. Hertel and N. Stolterfoht, 16 H. Helm, P. C. Cosby, M. M. Graff and J. T. Moseley, Phys. Rev. A, 1982, 25, 304. 17 A. Carrington, J. Buttenshaw, R. A. Kennedy and T. P. Softley, Mol. Phys., 1982,45,747; A. Carrington 18 P. J. Sarre, J. M. Walmsley and C. J. Whitham, J. Chem. SOC., Faraday Trans. 2, 1986, 82, 1243. 19 R. G. Cooks, J. H. Beynon, R. M. Caprioli and G. R. Lester, in Metastable Ions (Elsevier, Amsterdam, 20 P. J. Bruna and S. D. Peyerimhoff, BulL SOC. Chim. Belg., 1983,92, 525. 21 D. M. Hirst, Chem Phys. Lett., 1986, 128, 504. 22 M. M. Graff, J. T. Moseley and E. Roueff, Astrophys. J., 1983, 269, 796. 23 J. F. Bazet, C. Harel, R. McCarroll and A. Riera, Astron. Astrophys., 1975, 43, 223. 24 M. M. Graff, J. T. Moseley, J. Durup and E. Roueff, J. Chem. Phys., 1983, 78, 2355. 25 J. M. Brown, J. T. Hougen, K-P. Huber, J. W. C. Johns, I. Kopp, H. Lefebvre-Brion, A. J. Meter, D. A. 26 A. Carrington and D. A. Ramsay, Phys. Scr., 1982, 25, 272 and references therein. 27 M. Carre, Physica, 1969, 41, 63. 28 M. M. Graff, personal communication. 29 H. Helm, see ref. (6) of J. Chem. Phys., 1983, 78, 2355. 30 R. J. LeRoy, University of Waterloo Chemical Physics Research Report No. CP-110. 31 H. Helm, P. C. Cosby, R. P. Saxon and D. L. Huestis, J. Chem. Phys., 1982,76, 2516. 32 A. E. Douglas and B. L. Lutz, Can. J. Phys., 1970,48, 248. 33 T. A. Carlson, J. Copley, N. Duric, N. Elander, P. Erman, M. Larsson and M. Lyyra, Astron. Astrophys., 34 M. Larsson, personal communication. 35 P. C. Cosby, H. Helm and J. T. Moseley, Astrophys. J., 1980, 235, 52. 36 B. Levy, J. Ridard and E. Le Coarer, Chem. Phys., 1985, 92, 295. 37 Y. Tanaka, K. Yoshino and D. E. Freeman, J. Chem. Phys., 1975, 62, 4484. 38 I. Dabrowski and G. Herzberg, J. Mol. Spectrosc., 1978, 73, 183. (North Holland, Amsterdam, 1984), p. 275. and T. P. Softley, Chem. Phys., 1986, 106, 315. 1973). Ramsay, J. Rostas and R. N. Zare, J. Mol. Spectrosc., 1975, 55, 500. 1980, 83, 238. Received 18th June, 1986

ISSN:0301-7249    

DOI:10.1039/DC9868200067

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1986,82, 79-88 Photodissociation Dynamics of ICN Unequal Population of the CN X2Z+ Fine-structure Components H. Joswig, Maureen A. O'Halloran and Richard N. Zare Department of Chemistry, Stanford University, Stanford, California 94305, U.S. A. Mark S. Child Department of Theoretical Chemistry, Oxford University, 1 South Parks Road, Oxford OX1 3QZ Photolysis of ICN at 281.5, 266 and 249 nm produces CN X '2+ fragments in which the population of the F,(J"= N''+;) and F2(J"= "'-4) fine- structure components vary markedly as a function of d', N" and dissociation wavelength. Population differences favour either F1 or F2, and can be > 2: 1. A model is proposed to explain this behaviour, in which out-of-plane, spin-dependent forces cause the electron spin on CN to have a preferred orientation with respect to rotation of the CN fragment.The strong N" dependence of the F,/F2 ratio is attributed to interference between different dissociation channels, probably enhanced by various curve crossings. 1. Introduction Internal state distributions of photofragments are often a sensitive probe of the dynamics which characterize a specific photodissociation process. Perhaps the best known examples involve the distributions of rotational and vibrational energy in the fragments, from which mechanisms for partitioning of the excess energy of dissociation can be deduced. A more subtle example is the unequal population of the nearly degenerate A-doublet levels of a 'II molecular fragment, such as those produced in the photodissoci- ation of NH3192, H20334 and HON0.596 In these cases the population difference of the A-doublet states can be interpreted in terms of the geometrical arrangement of the v-electron lobe relative to the rotation of the fragment.The case of a 2C molecule is even more interesting. Each rotational level, N, is split by coupling of the spin of an unpaired electron to rotation to form the two components, Fl and F2, characterized by total angular momentum J = N + i and J = N -$, respectively. There is no geometrical reason to expect a difference between the populations of the two levels other than that given by the 2J + 1 statistical weighting factor. Nonetheless, Wittig and have recently reported an unequal population of the F1 and F2 components of the CN X 'Z+ fragment produced in the photodissociation of the ICN and BrCN at 266 nm.In these cases the explanation for the population difference must involve the complicated electronic structure of the molecules, rather than simple geometrical arguments. Several excited states, leasing asymptotically to the two different exit channels which produce I(2P3/2) or I*(2Pl/,), are known" to be involved in the photodissociation of the ICN. In addition, measurements of the alignment and the angular distribution of the CN fragments suggest a strong mixing of the states i n v ~ l v e d . ~ ~ " - ' ~ In this paper we present detailed experimental results concerning the anomalous population of the spin-rotation states in the CN X 2Z+ fragment produced in the photodissociation of ICN.Three different photolysis wavelengths (249, 266 and 281.5 nm) are used, covering different portions of the so-called A absorption continuum of ICN. According to the results of Pitts and Baronavski,1° the photodissociation 7980 Photodissociation Dynamics of ICN dynamics should be sensitive to the contributions of different electronic states to the A absorption continuum as the wavelength is changed. A model is presented to explain the preferential population of the Fl and F2 components for a 2C photofragment and the observed variation of population differences as a function of the final rotational quantum number N. 2. Experimental ICN (Eastman-Kodak) was purified by resublimation and its vapour was made to flow slowly through a vacuum chamber, typically at pressures of 5-20mTorr. The ICN molecules were photodissociated by U.V.laser pulses at 249, 266 or 281.5 nm, and the CN X 'Z+ fragments were then detected via laser-induced fluorescence by a probe dye laser tuned through the CN B21;+-X2X+ transition. The two laser beams entered the chamber collinearly and anti-parallel, and fluorescence was collected with a lens normal to the propagation direction of both lasers and imaged onto a photomultiplier tube (RCA 7326). Light baffles and a filter act to suppress scattered light. The photomultiplier signal was processed by a boxcar integrator (EG&G PAR, models 162 and 165) and displayed on a chart recorder. Several laser systems were used to generate the different photodissociation wavelengths. An excimer laser (Lumonics TE 861) with a KrF gas mixture provide a photolysis wavelength of 249 nm.Light of 266 nm was provided by the fourth harmonic of an Nd:YAG laser (Quanta Ray DCR-1, HG-2). For 281.5 nm, the frequency-doubled output of an Nd:YAG pumped dye laser (Quantel 581C) was employed. In each case the dissocation pulses were 10ns long, and the output was unfocused and limited to 5-20 mJ per pulse. The excimer laser at 249 nm is also used to pump a probe dye laser (Lambda Physik FL2002E), which was operated at low power (without the second amplification stage) in order to avoid saturation effects. The bandwidth of the laser was ca. 0.2 cm-', and could be narrowed to ca. 0.04cm-' by use of an intracavity etalon. Scanning was accomplished by a combination of angle and pressure tuning.The delay between the pump and probe lasers could range from 0 to 400ns; in all cases, the delay and the ICN pressure were chosen to establish collision-free conditions, so that it was the nascent CN X 'Z+ fragment distribution that was being determined. The signals were confirmed to be linear with respect to ICN pressure and to dissociation and probe laser powers. In a separate experiment the polarization dependendence of the signals was mea~ured.'~ It should be emphasized that the polarization dependence of the signals was the same for the Fl and F2 components, and the signal difference reflects a population difference and not an alignment effect. 3. Results We observe unequal populations of the Fl and F2 components in the CN X 2Z+ fragment for all the vibrational levels v'' = 0, 1 , 2 examined. In the lower vibrational levels v" = 0 , l , however, a considerable amount of the excess energy is channelled into translation, leading to Doppler broadening of the lines and prohibiting the resolution of the spin-rotation components at lower N".Wittig et aL9 have used a different experimental technique based on lineshape measurements in two geometries and a lineshape fitting procedure in order to overcome this problem. We concentrate here on the vibrational state 0'' = 2, for which it is possible to resolve directly the Fl and F2 components over a large range of N". Fig. 1 shows a 'low resolution' scan of a portion of the CN B 2Z+-X 'Z+ (0,2) band. Although the two spin-rotation components are not completely resolved, it is obvious that the Fl and F2 levels are unequally populated.Fig. 2 shows a 'high-resolution' scanH. Joswig, M. A. O'Halloran, R. N. Zare and M. S. Child 81 90 4579 wavelength/A Fig. 1. Portion of the CN B 'X+ - X 2Z+ (0,2) fluorescence excitation spectrum following photoly- sis of ICN at 249 nm. Unequally populated Fl and F2 components are observed for high N". u/cm-' Fig. 2. High-resolution fluorescence excitation spectrum of the P(48) line shown in fig. 1. The shaded area represents the fluorescence signal; the background fringes are produced by a monitor etalon (Av = 0.61 cm-'). The probe laser bandwidth is ca. 0.04 cm-'. over the P(48) line. Here, the Fl and F2 levels are resolved and the difference in population can be clearly determined.The relative populations for the two fine-structure components have been determined from such 'high-resolution' scans for as many rotational elvels as could be resolved for each of the different dissociation energies.82 Ph o todissocia t io n Dynamics of I C N L 20 40 N 60 Fig. 3. The fine-structure difference function f( N”) us. N” for photolysis of ICN at ( a ) 249, ( b ) 266 and ( c ) 281.5 nm. Representative error bars are indicated. In fig. 3 we plot the quantity f“”) = [ n ( F , ) - n(F2)1/Cn(F,)+ n(F2)I ( 1 ) where n(F,,,) represents the population in the F, or F2 levels, respectively, for the same values of N”. f ( N ” ) is shown as a function of final CN rotational quantum number, N”, for the three different dissociation wavelengths. f( N”) exhibits a strong N” depen- dence with an oscillatory behaviour, favouring Fl over F2 for certain N”, where for other values of N“, F2 is dominant.For each dissociation wavelength, the highest observed levels, NLax, is close to the highest value allowed by conservation of energy. Hence the shifts of N&ax by 15 units from fig. 3(a) to ( b ) and by 23 units from fig. 3(a) to (c) are accounted for by the change in excitation wavelengths. The function f ( N ” ) thus seems to depend principally on Nkax - N”, so that the above shifts bring the three diagrams essentially into coincidence when f( N“) is plotted on a scale linear with N”. In the following section we offer a model to account qualitatively for the existence of the spin-rotation population differences and for their variation with dissociation energy and N”.4. Theory Fig. 4 introduces the angular momenta involved, defined for nearly separated fragments: j , the total electronic angular momentum of the iodine atom ( j = 4 or $); S the electronic spin of the CN radical (S=i); N, the rotational angular momentum of CN ( N = 0,1,2,. . .); and 1 the orbital angular momentum of the recoiling fragments ( Z = 0, 1 , 2 , . . .). Because the torque produced in ICN photodissociation is directed nearlyH. Joswig, M. A. O'Halloran, R. N. Zare and M. S. Child 83 N Fig. 4 W + M I 2 4 \ I. Angular momenta describing the dissociation of ICN. in the ICN plane, N points almost perpendicular to this plane and passes through the CN centre of mass. We assume that when the fragments are close together, spin-orbit interaction causes j and S to be coupled strongly to form the resultant J 1 2 = j + S .Moreover, we suppose that J12 is quantized with respect to the axis passing from the I atom through the CN centre of mass, giving rise to well defined components A12 E M12. On the same axis, which we take as the z axis in the molecular frame, N makes the projection MN, where MN<< N. Quantization along the I-C axis would be more realistic, but this would severely complicate what follows, and the I-C vector would still lie on average along the z axis. One might also argue that the orbital part of j should be at least partially quenched in the molecular region, but the following argument would still hold with j replaced by the electron spin on I, provided spin-orbit coupling was strong enough to cause the appearance of states with well defined M12.The Hamiltonian consistent with fig. 4 may be written as H = Ho+ 12/2pR2 (2) where p is the reduced mass of the CN and I fragments, R is their separation and Ho is assumed to have eigenstates I(jS)J12N; M12MN)= I M12, MN), Le. CN is already rotating freely. Let us denote the total angular momentum of the excited ICN molecule as JT= 1 + N + J l , . We can restrict the discussion to rotationally cold ICN (JT=O), since it is known that the rotation of the parent ICN has negligible effect on the distribution of rotational energy in the CN fragment. Then I+N+J=O (3) HI= N*J12/pR2 (4) and upon substituting - ( N + J , , ) for 1 in eqn (2) it is seen that a coupling term is obtained.The term H' is treated as a perturbation to Ho, and taken to be the non-adiabatic coupling term operating at a curve crossing between two potential-energy surfaces to cause the state I M12, M N ) to develop amplitudes p* in the channels I M12 * 1, MN 7 l ) , respectively.In essence, the N * J12 coupling term represents forces not directed in the I-CN scattering plane, and these forces cause non-adiabatic transitions between different potential curves denoted by M12. Propagation of the excited state on the different potential-energy surfaces then give rise in the asymptotic region to the final superposition state: where the phases c $ ~ arise from the evolution along the potential curves associated with different MI2 values. Since N is related to 1 through eqn (3), the centrifugal contribution84 Ph o tod issocia tion Dynamics of IC N Table 1.Non-zero coefficients C(J12, M12 ; J, mi, MJ) in the limits N >> 0, MN << N to #v might be expected to vary with N even if the amplitudes pv were relatively insensitive to N. Also important is the fact that trajectories that lead to different final values of N will sample different portions of the potential-energy surface. We have concentrated here on the coupling term No J12 and neglected other coupling terms (such as Coriolis terms that arise, for example, if JT is non-zero). However, the main point is the presence of the above discussed non-adiabatic transitions and the form of the final superposition state [eqn ( S ) ] , regardless of the specific form of the coupling terms. It remains to decompose the final state If) into the detectable asymptotic states I j ( SN)J; mjMJ) with S recoupled to N to form the resultant J.Straightforward angular momentum algebra shows that I ( j S V l 2 ~ ; M ~ ~ M N ) = C (jsmjMS 1 ~ 1 2 ~ 1 2 ) I jmJ) I ~ M S ) I N M N ) = C = 1 [(2J12+ 1)(2J+ 1)]'/"( - 1 ) N - J + M 1 2 + M J m,, MS C (jSmjMs I J~~M~~)(SNMSMN I JM,) I j ( s W ~ ; mjM,) (6) m~pMS J,'J J, MJ, m, Since S = 4, the sum in eqn ( 6 ) is limited for fixed j and .Il2 to two terms with ( mj, M,) equal to ( M12 ++, MN -;) or ( M12 -4, MN +$) for each of the possible values of J = N + ; or J = N-4. Table 1 collects the coefficients for the different I(jS)J,,N; M12MN) appearing on the right-hand side of eqn (6) in the limits N >> 0 and N >> MN.The most important feature of these coefficients for the present discussion is that the relative signs of the two entries for given J12 and N differ according to whether J = N +; or J = N -4. The quantity experimentally measured is the probability for the CN fragment to be in one of two J levels for a given value of N. This is given by and it is readily verified by use of table 1 that the ratio of spin-rotation component populations is P(F1) P(N, J = N + $ ) P(F,) - P(N, J = N - + ) -- where x+ = 2J*2p; + ( 4 2 - M12 + 1 )p? + ( J , 2 + Ml2 + 1 1 P: (9)H. Joswig, M. A. O'Halloran, R. N. Zare and M. S. Child 85 A* = [J12(J12+ 1 ) - M12(M12f 1)11'2 (11) and the upper and lower signs in eqn (8) and (1 1) apply for J12 = j + and JI2 = j - 4, respectively.In the limits p: << p i and pp = 1, the factors X , becomes 2 j + 1. Inspection of eqn (8)-(11) shows that the population ratio is independent of the sign of M12, provided only that transitions from M12 to M12+ 1 occur with equal facility as transitions from - M12 to - M12- 1. Eqn (8) also shows that the departure of the spin-rotation population ratio P ( Fl)/ P( F2) from unity increases as the value of JI2 becomes larger and that of MI2 smaller, owing mathematically to the A, factors in eqn (8) and physically to the larger projection of ..Il2 onto N (see fig. 4). Conversely, A, = A- = 0 for J12 = 0. Thus one would not expect a population preference to appear in the F,, F2 fine-structure components of a 'Z photofragment unless the companion photofragment has j # 0 and strong spin-orbit interaction causes j to be quantized along the separation axis. For example, one would anticipate no preference in the direction of the spin, relative to either rotation or orbital angular momentum, in either pair of photofragments for photodissociation of HCN or CH,CN, but it might occur in the photodissociation of CH31 or HI., As long as there is more than one surface correlating asymptotically to the same experimentally observable final state, there is the possibility of interference between the different pathways.The exact phase difference accumulated on the different possible paths will depend on both the particular trajectories followed and upon the distribution of probability between the different possible paths.The potential-energy surface that describes the interaction between the department fragments is a multidimensional surface. Even for the simple case of scattering between an atom and a rigid rotor, the potential energy still depends upon both the distance, R, between the two fragments and the angle, 8, between the axis of the diatom and the coordinate R. Which trajectories are followed on the potential-energy surfaces, and hence the differences in accumulated phase, will be dependent upon both the linear velocity, dR/dt, i.e. upon the excess energy, and upon the angular velocity, d8/dt, i e . upon the rotational energy. Moreover, the crossings between these surfaces will not be single points, but rather seams, and the curve-crossing probability will vary depending on the difference in slope between the surfaces at different points along the seam and upon the velocity (excess energy) of the fragments.Thus the presence of a population difference which varies with both dissoci- ation energy and with the final rotational state of the CN fragment can be easily understood. 5. Model Calculation To complete this treatment, we calculate the spin-rotation population ratio using a simple semiclassical approach. The phase difference #o - #* are evaluated by integrating the momentum along the classical trajectory, so that &, = lim ( k - k") dR R-Pm I where the radial (R) and angular (8) components of k = p / A are obtained by running a trajectory over the effective potential Vu( R, 8) + I( I + 1) R2/2pR2 + BN( N + 1).In the calculation of k" the potential Vu(R, 8) is omitted. The potentials are taken from Marinelli et all4 where we assign Vo = V, and V* = V, . They obtained these potentials by fitting them to match the ICN absorption spectrum and the rotational distributions of the CN fragment produced following photodissociation of ICN at several photolysis wavelengths. Classical trajectories with initial conditions reflecting cold ICN are run86 Photodissociation Dynamics of ICN 0-4 - 0.2 P 2 0.0 7 -0.2 20 40 60 -0.4 N" Fig. 5. Calculated fine structure difference function f( N") us. N" for photolysis of ICN at 249 nm, based on potential surfaces of Marinelli et aL14 on these surfaces, and phases are accumulated after passing through a curve crossing between the two potential-energy surfaces.The parameters in eqn (8)-(11) are taken to be j = ; , J12=2, and M12=0. With M12 = 0, there is no difference between the M12 = +1 and M12 = -1 coupling, and A, = A-, p+=p- and #+=#-. We use the values po=0.94 and p+=p-=O.25, and B = 1.8563 cm-'. Fig. 5 shows results of this calculation, displayed in the same way as the experimental data in fig. 3, namely, as f( N") us. N". The model is considered to be only qualitatively correct: the full average over different excited states, e.g. the intercontinuum coupling between different vibrational levels, has not been taken into account. The calculations do show, however, that a relatively small curve crossing probability is sufficient to give spin-rotation population differences of the same order of magnitude as observed.Moreover, the accumulated phase changes with N" in such a manner as to cause a reversal of this preference. An even simpler model can be adopted in which the curve crossing is assumed to occur at a distance, R, beyond the range of significant coupling between radial and angular motion. The phase terms then reduce to one-dimensional integrals, so that +u = R+CO lim IR: (s [ E - BN( N + 1) - V, ( R )] - I( I + 1 )/ R2 (13) These integrals diverge as R + a, but the differences between them remain constant provided .that the Vu( R ) have the same asymptotic limit. Calculations have been made using two curves; V,(R), taken as the collinear section through the surface V, of Marinelli et aI.,14 V, = vim+ 1.53 x lo8 cm-' exp (-3.5k'R) (14) and V - ( R ) , taken in the Morse form, V-( R ) = vim + D, {exp [ - 10 A-'( R - Re)] - 2 exp [ - 5 A-'( R - R , ) ] } (15) because it proved impossible to obtain sufficiently rapid variation in the relative popula- tion function, f (N"), with a, purely repulsive potential.The parameters adopted were D, = 2706 cp-', Re = 3.622 A, and Kim = 3031 cm-', which gives a curve crossing at R, = 3.475 A. These parameters were chosen to fit the experimental data at 249 nm, subject to the constraint that the crossing point R, be classically accessible at the highestH. Joswig, M. A. O’Halloran, R. N. Zare and M. S. Child 87 -o.2 t I I 20 40 60 N” Fig. 6. Calculated fine-structure difference function f ( N ” ) us. N” for photolysis of ICN at (a) 249, (b) 266 and ( c ) 281.5 nm. One-dimensional potential-energy functions are used.Open circles represent values of N” for which f( N”) was measured. observed value of N”, NAaX = 47, at lowest dissociation energy, when A = 281.5 nm. The parameters of eqn (9) and (13)-( 15) were J I 2 = 2, MI2 = 0, p+ = 0, p - = 0.5 and po = 0.97. The continuous curves in fig. 6 cover the experimentally observed range indicated in fig. 3, and it is seen that the data for A = 249 nm are indeed well reproduced, at least for N”> 40. It is also interesting to observe that in the dashed extensions, which cover all classsically allowed values. at R = R,, the three curves begin to reproduce the translational superimposition evident in the experimental data. Moreover, this appears to be no accident relating to the choice of excitation energy, because phase differences at the non-integer cutoff values of N” = NAax are almost identical; 4 - +o = 38.7, 38.9 and 38.8 for A = 249, 266 and 281.5 nm, respectively.This remarkable result can be understood to some extent by noting that where E( R ) = 0 . 3 k-( R) + ko( R)], because the second integral is dominated by the region R =r R,, where k(R)+O as N”+ Nkax, and because the R dependence of k ( R ) is dominated in this region by variations in the V,(R), rather than variations in the term Z(Z+1)/R2 in eqn (13). If this behaviour carries over to more realistic situations with several coupled degrees of freedom, it suggests that the seam between the surfaces is close to the Franck-Condon88 Photodissociation Dynamics of ICN region, i.e. the region directly above the potential-energy well of the bound parent molecule, so that the maximum N” value observed is also the maximum value classically allowed. The spin-rotation component preference, f( N”), is thus shown to be a sensitive measure of the complex photodissociation dynamics that occur when more than one potential surface interacts. This work was supported by the U.S. National Science Foundation under NSF PHY-85- 06668. H.J. thanks the Deutsche Forschungsgemeinschaft for a postdoctoral fellowship. References 1 F. Alberti and A. E. Douglas, Chem. Phys., 1978, 34, 399. 2 A. M. Quinton and J. P. Simons, Chem. Phys. Lett., 1981,81, 214. 3 P. Andresen and E. W. Rothe, Chem. Phys., 1983, 78, 989. 4 P. Andresen, G. S . Ondrey, B. Titze and E. W. Rothe, J. Chem. Phys., 1984, 80, 2548. 5 R. Vasudev, R. N. Zare and R. N. Dixon, Chem. Phys. Lett., 1985,96, 399. 6 R. Vasudev, R. N. Zare and R. N. Dixon, J. Chem. Phys., 1984, 80, 10. 7 I. Nadler, H. Reisler and C. Wittig, Chem. Phys. Lett., 1984, 103, 451. 8 F. Shokoohi, S. Hay and C. Wittig, Chem. Phys. Lett., 1984, 110, 1. 9 I. Nadler, D. Mahgerefteh, H. Reisler and C. Wittig, J. Chem. Phys., 1985, 82, 3885. 10 W. M. Pitts and A. P. Baronavski, Chem. Phys. Lett., 1980, 71, 395. 11 J. H. Ling and K. R. Wilson, X Chem. Phys., 1975, 63, 101. 12 G. E. Hall, N. Sivakumar and P. L. Houston, to be published. 13 M. A. O’Halloran, H. Joswig and R. N. Zare, unpublished work. 14 W. J. Marinelli, N. Sivakumar and P. L. Houston, J. Phys. Chem., 1984, 88, 6685. Received 13th May, 1986

ISSN:0301-7249    

DOI:10.1039/DC9868200079

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

GENERAL DISCUSSION Dr G. G. Balint-Kurti (University of Bristol) said: The paper of Williams, Freed, Singer and Band discusses the many resonances which are expected to be observable in the photodissociation of diatomic molecules in near-threshold regions. In most cases the peak of the photon absorption cross-section for a diatomic molecule is well above the threshold region and leads to open-shell atomic fragments with considerable relative kinetic energy. I would like to note that even for such processes interesting dynamical effects q a y be observed. We have studied in particular the photodissociation of HC1 via its A 'II + X 'X+ absorption.' The interesting feature here is the branching ratio for producing the different levels of the Cl atom [i.e. the Cl(2P3/2)/Cl(2P1,2) ratio].In our paper we show that this ratio is not statistical and varies with photon frequency. Photodissociation from initially excited vibrational levels of HCl leads to an oscillatory absorption cross-section which maps out the nodal structure of the initial vibrational state.2 More surprisingly, we find that this oscillatory structure is also present in the Cl(2P3,2)/Cl( 2Pl,2) branching ratio. The non-statistical behaviour of the branching ratio is an entirely dynamical effect and has its origins in the same non-adiabatic coupling phenomena as give rise to the resonances discussed in the paper of Williams et al. 1 S. C. Givertz and G. G. Baht-Kurti, J. Chem. SOC., Furuduy Trans. 2, 1986, 82, 1231. 2 M. S. Child and M. Shapiro, MoI. Phys., 1983 48, 111.Prof. K. F. Freed (University of Chicago, USA) said: The oscillatory branching ratio found by Dr Baht-Kurti is quite new and interesting. Our earlier calculations had indicated that the effects of non-adiabatic coupling persist to rather high kinetic energies. For instance, we find that branching ratios in the NaH molecule' do not approach their high-energy axial recoil limit until kinetic energies at least one order of magnitude larger than the atomic spin-orbit splitting. The high-energy asymptotic limit is never attained for the Na, molecule2 at energies for which the photodissociation cross-section is non-negligible. I should also emphasize that the high-energy axial recoil limit branching ratios are not necessarily predicted to be statistical when both of the atoms are not in S states.1 S. J. Singer, K. F. Freed and Y. B. Band, J. Chem. Phys., 1984 81, 3091. 2 W. S. Sturve, S. J. Singer and K. F. Freed, Chem. Phys. Lett., 1984, 110, 588. 3 S. J. Singer, Y. B. Band and K. F. Freed, J. Chem. Phys., 1984, 81, 3064; Adu. Chem. Phys., 1985 61, 1. Mr C. J. Williams (University of Chicago, USA) said: One interesting aspect of our equation for the photodissociation cross-section is that all the dynamical information describing the photodissociation or predissociation process is carried in the reduced transition amplitude elements T. The CJ are primarily angular coefficients depending on the quantum numbers, polarization indices and the independent angles describing the experimental set-up. The reduced transition amplitudes are functions only of the initial and final quantum numbers and not of angles, polarization indices or projections of quantum numbers.Thus, once we have done the hard work and have calculated all the reduced transition amplitudes T for a given dynamical system, it is straightforward to evaluate cross-sections, polarizations etc. for any imaginable experiment on the system by taking the apppropriate bilinear sum described in eqn (1). 8990 General Discussion Table 1. Linewidths for the 'II( v = 0, J = 35) resonances (in GHz) multichannel calculation expt" r (tunnelling) 'rIe 16.3 ln' 5.1 4.3 (0.4) 1 .o 5.5 (0.5) 2.4 ~~ " Experimental results of P. Sarre and C . Whitman. Tunnelling rates are obtained from single-channel calculations employing diagnonalized potentials that include spin-orbit and Coriolis contributions.Dr M. S. Child (Oxford University) said: Can either of the sets of authors comment on the failure to observe any of the coupled channel resonances so nicely predicted by the Chicago group? Could it be that the predissociation is too slow for convenient observation, perhaps because the predissociation lifetime is long compared with that for fluorescence or long compared with the flight time in the apparatus? Dr P. J. Sarre ( University of Nottingham) said: The predissociation lifetimes associ- ated with the calculated resonances vary over many orders of magnitude. In our experiment it is possible to observe transitions to levels with lifetimes lying in the range between ca. 1 ps and 1 ps, so it is unlikely that the predissociation lifetime is a problem.The failure to observe multichannel resonances in CH+ is most likely due to a variety of factors which affect the sensitivity in the experiment, and include the ion-beam intensity and the vibrational and rotational population distribution. Laser excitation to the relatively weak 'multichannel resonances' from the more highly populated lower-lying vibrational levels of the ground state (using a laser operating in the ultraviolet) may enhance the sensitivity sufficiently to allow their detection. Mr C. J. Williams (University of Chicago, USA) said: I have spent the past two weeks with Dr Sarre and collaborators working on relating our calculations with experimentally observed resonances and would like to report on our progress.We have performed calculations for the 'I: -+ '17( v = 0, J = 35) transition which confirm the existence of two resonances that have previously been assigned by Helms et al. The P- and R-branch transitions 'E( v = 0, Jo = 34,36) + 'rI( v = 0, J = 35) contain a '17 resonance which is the e-lambda doubling component, while the f-component appears in the Q-branch transition 'C( vo = 0, Jo = 35) -+ 'It( v = 0, J = 35). The two reson- ances are experimentally separated by ca. 20 cm-' and we calculate a separation of ca. 15 cm-', with the e-component higher than the f-component in both cases. Table 1 presents the experimental and calculated linewidths for these two resonances. The highest-energy e-component resonance is experimentally narrower than the f- component.As noted by Dr Sarre, this arises because the angular barrier for the e-resonance is higher than that for the f-resonance, producing a larger area under the centrifugal barrier. The multichannel calculations predict a resonance linewidth almost four times the experimental value for the e-component, while predicting the correct width (within experimental error) for the f-componenet. This result is probably due to an overestima- tion of the Coriolis interaction by our asymptotic approximation for these coupling elements. The effect is more important for the e-component because the parity block containing the 'He state also contains the 'C0 state which may be strongly (predissocia- tively) coupled to the I l l e state by Coriolis interactions. On the other hand, the f-component lacks an electronic state of the appropriate parity to which it can dissocia- tively couple through Coriolis interactions in first-order perturbation theory.The over- estimation of the Coriolis interaction emerges because the shape barrier for J = 35 occurs at a short internuclear separation where our asymptotic approximation becomes invalidGeneral Discussion 91 and the predissociation rate is overestimated. In order to confirm this hypothesis, we plan to perform further calculations in conjuction with Sarre and Whitham. One independent confirmation of the above hypothesis is obtained from more approximate calculations as follows: single-channel resonance widths are readily com- puted using the diagonalized electronic potentials, where the Coriolis and spin-orbit interactions are included. The tunnelling lifetimes are evaluated in the correct order, but the calculations omit possible predissociative mechanisms from spin-orbit and Coriolis interactions which would serve to shorten the lifetimes.Another means of confirming the overestimation of Coriolis couplings involves measuring the branching ratio for production of C’(’P) fragments from the dissociation of the resonance state. The calculated branching ratio [C’(’P,,,) : C+(’P1/,)] for the e-components is 1.2, while it is 3.0 for the f-component. If our calculations overestimate the Coriolis interaction, then the experimental e-component branching ratio is expected to be larger than 1.2 as follows : the ‘Z state is produced by the Coriolis coupling of the ‘II e-component and strongly correlates to the Cf(’Pl12) atomic term limit.If our Coriolis interaction is too large, more C’(’P,,,) fragment would be predicted than is observed. At present no experimental measurements exist for the C’( ’ P ) branching ratios. Hopefully, further collaboration between the Freed and Sarre groups will unravel the fascinating non-adiabaticity in diatomic systems, assign some of the non-adiabatic resonances and enhance our understanding of the dissociation mechanisms for these strongly coupled systems. Finally, I would like briefly to mention how measurements of anisotropy parameters may aid in the analysis of experimental photodissociation spectra like CH+. As discussed in our paper and more thoroughly in ref. (7), one difficulty in unravelling the low-energy photodissociation spectrum appears because the total cross-section has a coherent sum over all possible final J states produced in the photodissociation from an initial state of total angular momentum Jo (i.e.J = Jo, Jo* 1 all contribute). We can separate the different final J contributions theoretically, but this is impossible in experiments. When J is high, the large differences in resonance energies for J = Jo, Jo* 1 and the formation of narrower resonances make this overlapping largely disappear. On the other hand, at low J the J = Jo, Jo* 1 resonances often overlap, severely complicating the spectrum. Fig. 2 of our paper presents the X ‘Z+( v = 0, Jo = 3) + A ‘ r I ( J ) transition, where there is a great deal of structure that appears in the anisotropy parameter Po in the energy region from 15-25 cm-’.More structure is present in pD than in the total cross-section for this transition. Comparison of the structure in pD of fig. 2 with the individual final J contributions to the total cross-section (fig. 5 ) shows that much of the structure in pD is related to individual resonances in the different final J contributions. Hence, structure present in the anisotropy parameters but absent in the total cross-section may generally reflect ‘washed out’ or ‘lost structure’ in the total cross-section owing to overlap or interference of the J = Jo and Jo* 1 and Jof 1 contributions. Dr P. J. Sarre (University of Nottingharn) said: In the close-coupled calculations described by Williams et al.the dependence of the spin-orbit and Coriolis coupling on internuclear distance is not included and the matrix elements of the operators are replaced by their asymptotic values. Can the authors comment on the validity of this approximation? Dr M. S . Child (Oxford University) said: On the question of the validity of asymptotic values of the spin-orbit coupling constant and the electronic Coriolis matrix element it is pertinent to note that the angular momentum recoupling gives rise to non-adiabatic transition of the Demkov type,’ characterized by adiabatic curves with an asymptotic splitting A, which diverge exponentially say a Aexp ( - a R ) , as R decreases. The non-adiabatic transition zone is known to occur in such cases at internuclear separation92 General Discussion around R = -C1 In (A/A).2-4 It should be a simple matter to estimate this radius from the potential curves employed in the paper.1 Yu N. Demkov, Sou. Phys. J.E.T.P. 1964, 18, 138. 2 D.S.F. Crothers, J. Phys. B, 1973, 6, 1418. 3 E. E. Nikitin, Adu. Quantum Chem., 1970, 5, 135. 4 M. S. Child, in Atom-Molecule Collisions, ed. R. B. Bernstein (Plenum Press, New York 1979), pp. 427-465. Mr C. J. Williams ( University of Chicago, USA) said: We realize that our asymptotic approximations for the spin-orbit and Coriolis coupling elements are only appropriate under limiting circumstances. Our approximations should be reasonable for low total angular momenta J because the different electronic states become strongly coupled at low J only at intermediate internuclear separations R, where the different electronic surfaces become nearly degenerate. At these intermediate internuclear separations, both the Coriolis and spin-orbit coupling elements must begin to approach their asymptotic values, and we expect our asymptotic approximation to be reasonable.As already mentioned in the discussion, our calculated Coriolis coupling interaction between 'C and 'II' appears too large for J = 35. We conclude this because our calculated II (0 = 0, J = 3 5 ) resonance has a half-width four times the experimentally observed value, whereas we agree with the experimental width for the 'nf( v = 0, J = 3 5 ) resonance state. In the former case the *IIe state can couple to the state by first-order Coriolis coupling. On the other hand, the 'JJf state resonance has negligible first-order Coriolis interactions since the '& state is of the wrong parity dissociatively to couple to *IIf.This failure of our model in prediciting the appropriate Coriolis coupling for J = 3 5 is not surprising, as the centrifugal barrier for higher J becomes shifted into small inter- nuclear separations where our asymptotic approximation is expected to be poor for J = 35. The Demkov-type analysis is not applicable in our calculations for several reasons: the Demkov method requires knowledge of both the asymptotic splittings as well as the splittings in the region where the non-adiabatic couplings are assumed to be important. In the absence of the spin-orbit interaction, the ABO electronic potential curves are all degenerate asymptotically and a Demkov treatment is not appropriate.Some of the aymptotic degeneracy of the ABO electronic potentials can be lifted as shown in fig. 1 of our paper by diagonalizing the total potential 1 e written in a Hund's case (a) molecular representation. This basis has VABo( R ) diagonal; the matrices I( I + 1 ) and HsA0. are the diagonal Coriolis and spin-orbit coupling elements in our 'atomic-like' molecular basis, and T is our frame transformation from the 'atomic' to the Hund's case (a) basis. A Demkov analysis could not be attempted for transitions between states correlating to different atomic fine-structure states of the C+ atom, but such a treatment uses our asymptotic approximation for the coupling elements in partially lifting the degeneracy of the electronic states. The coupling between electronic states, corre1at:ng to the same atomic fine-structure state, can still not be treated by the Demkov method.This coupling between asymptotically degenerate electronic states remains important in our calculations since it helps to explain the existence of resonances with partial 3112 character when excitation is nominally to the 'II electronic state. The Demkov method could only be applied in this case if the molecule were in the presence of a magnetic field to lift the degeneracy of the magnetic sublevels of the atomic fine-structure states, but the problem of obtaining the correct coupling elements, of course, remains.General Discussion 93 One additional problem with the Demkov method is that it apparently does not deal with possible coherence effects between several electronic states when there exists an envelope of nearly degenerate electronic curves in a localized region in space, as for CH+ at intermediate internuclear separations.If the exact couplings were known and our asymptotic approximation were not required to lift the degeneracy of the zeroth-order ABO curves, then perhaps a Demkov type method could be developed for this problem. However, given the exact couplings the multichannel treatments are likewise exact. In lieu of a general theoretical treatment for the appropriate functional form of these non-adiabatic couplings as a function of R, we appeal to those who perform a6 initio calculations to evaluate both the diagonal and off-diagonal values of these Coriolis and spin-orbit coupling elements.Dr M. S. Child (Oxford University) said: My intention in citing the Demkov method was to suggest a test whereby the authors could assess the validity of their use of the asymptotic spin-orbit coupling and electronic Coriolis interactions. This test, which in retrospect applies only to the spin-orbit coupling, is simply to compare the Demkov transition radius with the distance at which significant perturbations to the atomic wavefunctions are expected. Any attempt to replace the close-coupled calculations by a Demkov-based model would be much more ambitious. Mr Williams outlines a possible approach, starting from his V,,,,,(R) matrix, but restricted by the omission of Coriolis terms not included in the frame transformation.The latter omission seems to be the major difficulty. The problem that the Demkov formula, as normally encountered, gives a transition probabil- ity rather than a probability amplitude is not an essential one; I feel sure that the necessary phase information for the problem could be included in a manner similar to that which has proved successful for curve-crossing resonances.' 1 See M. S. Child, in Semiclassical Methods in Molecular Scattering and Spectroscopy, ed. M. S. Child (Reidel, Dortrecht, 1980). Prof. J. N. Murrell (University of Sussex) said: Can the type of measurements described in your paper determine the long-range form of the interatomic potential? For CH+ and SiHf the potential should contain leading terms varying as R-4 and R-6 and the question of how these are damped when there is a small amount of overlap between orbitals is a matter of considerable interest. Dr P.J. Sarre (University of Nottingham) said: In principle it should be possible to obtain information on the long-range form of the potential, but as only two (or possibly three) quasibound levels of the A 'n state can be observed for a given value of u, this is not likely to be achieved readily. A more promising probe of the long-range behaviour is via the spectroscopic analysis of transitions to states with long-range minima, such as described in our paper. Mr C. J. Williams ( University of Chicago, USA) said: One thing that has been omitted from the discussion of near-threshold dissociation of diatomic molecules is the motiva- tion for such studies.The low-energy resonance structure contains information concern- ing the non-adiabatic couplings and the long-range and attractive portions of the electronic potential-energy curves. Information on the long-range tails of these electronic curves is difficult to obtain from both experiments and accurate ab initio calculations. The near-threshold dissociation provides a sensitive probe of electronic structure in the intermediate or recoupling region of the electronic curves, if the structure obtained from such data can be suitable inverted. Additionally, the destruction of electronic selection rules by strong non-adiabatic couplings implies that near-threshold photodissociation also allows the probing of 'dark' states which are not radiatively coupled to the ground electronic state and which are thus difficult to study spectroscopically.94 General Discussion Dr D.M. Hirst (University of Warwick) said: We have been making ab initio calculations for SiH+ and CH* in order to provide potential-energy curves which can be used by Sarre et al. in the interpretation of the laser photofragment spectra of these ions. Full details of the calculations for SiH' have been published elsewhere' so only a brief summary of the results will be given. For the X 'E+ state we obtain very good agreement between experimental spectroscopic constants and those derived from calcu- lated vibration-rotation levels obtained using our potential-energy curve in the nuclear Schrodinger equation. For example, we obtain an o, value of 2155.35 cm-' and a Bo value of 7.6786cm-'.These can be compared with the experimental values of 2157.15 cm-' and 7.6576 cm-', respectively. Clearly our calculations are yielding a potential-energy curve which has the correct shape in the equilibrium region. It is less easy to reproduce exactly the experimental dissociation energy and for Do we obtain a value of 3.097 eV compared with the experimental value of 3.22 f 0.03 eV.2 We, therefore, expect our results for the a 'II state state to be reasonable predictions of the experimental parameters. The potential well in the A 'II state is very shallow and the accurate calculation of the potential-energy curve for this state is a severe challenge to theory. Our calculations underestimate the well-depth for this state, giving a value of ca.730 cm-' compared with the experimental estimate of 1230*210 cm-' for Do.' It is expected that expansion of the basis set to include f-functions will lead to improved values of the calculated dissociation energies. There have been many ab initio calculations of potential-energy curves for CH+,'-'' but there has been no recent comprehensive treatment of all the states that may be of importance in the work of Sarre et al. In general, relatively few points have been calculated in regions of large internuclear separation and it is these regions which are of particular importance in the photofragmentation. Therefore, we have undertaken a comprehensive set of calculations for the X 'C+, A 'n, a 'n, 6 'E-, c 'E+ and d 311 states of CH' using an extensive basis set: C (12s8p2d) contracted to [9s6p2dI7 H (7s2p 1 d ) uncontracted. Molecular orbitals have been obtained from complete active space MC-SCF (CASSCF) calculations for the states in question using an active space consisting of the orbitals 2 a 3 a 4 a l ~ ~ l T,,.The potential-energy curves were obtained in CI calculations in which the configuration lists were obtained by generating all single and double excitations with respect to the configurations used in the CASSCF calcula- tions. This resulted in configuration lists of the order of 10000. The calculations were made using the GAMESS (generalized atomic and molecular electronic structure system) suite of programs12 implemented on the FPS-164 computer at the Daresbury Laboratory.Work is still in progress on the d 'II state. The calculated potential-energy curves for the other states are shown in fig. 1 and calculated spectroscopic constants for the X 'E+, A 'II, a 311 and b 'X- states are compared with experimental data in table 2. Excellent agreement with experiment" is obtained for the X 'X+ state, indicating that the calcula- tions are providing an accurate description s f the potential well of this state. Comparison with experiment is more difficult for the A 'n state since this state is perturbed by the a 311 state and it was not possible to fit either the observed vibrational intervals or the rotational constants to the usual power series expansion in (27 + l/2).'' However, our Bo value is in very satisfactory agreement with experiment and our AG values are closer to experiment than those quoted by Larsson and Siegbahn.* Our calculations underesti- mate the dissociation energies for these states.Some preliminary calculations have been made for the X 'E+ state with additional sp functions located at the mid-point of the CH bond and suggest that an improvement of 0.069 eV can be achieved. It is expected that the inclusion of a set off-functions on carbon will result in improved values for the calculated dissociation energies. 1 D. M. Hirst, Chern. Phys. Lett., 1986, 128, 504. 2 T. A. Carlson, J. Copley, N. DuriC, N. Elander, P. Erman, M. Larsson and M. Lyyra, Astron. Astrophys., 1980, 83, 238.General Discussion 95 Fig. 1. Ab -37.4 - -37.5 - -37.6 - E, -37.7 - -37.8 - -37.9 - -38.0 - I I I I I I I 1 J 1 2 3 4 5 6 7 8 9 10 R l a , initio potential-energy curves for the X 'Z+, A 'n, a 311, b 3Z- and c 3E+ states of CH+.3 4 5 6 7 8 9 10 11 12 13 14 I S. Green, P. S. Bagus, B. Liu, A. D. McLean and M. Yoshimine, Phys. Rev. A, 1972, 5, 1614. P. Rosmus and W. Meyer, J. Chem. Phys., 1977, 66, 13. I. Kusunoki, S. Sakai, S. Kato and K. Morokuma, J. Chem. Phys., 1980, 72, 6813. R. P. Saxon, K. Kirby and B. Liu, J. Chem. Phys., 1980, 73, 1873. R. P. Saxon and B. Liu, J. Chem. Phys., 1983, 78, 1344. M. Larsson and P. E. M. Siegbahn, Chem. Phys., 1983, 76, 175. B. Levy, J Ridard and E. Le Coarer, Chem. Phys., 1985,92, 295. J. Gerratt, J. C. Manley and M. Raimondi, J. Chem. Phys., 1985, 82, 2014. F. R. Ornellas and F. B. C. Machado, J. Mol. Struct.(Themhem), 1985, 120, 149. M. F. Guest and J. Kendrick, GAMESS, Part 1. An Introductory Guide, S.E.R.C. Daresbury Laboratory, Daresbury, Warrington, 1986. A. Carrington and D. A. Ramsay, Phys. Scr., 1982, 25, 272. M. Carre, Physica, 1969, 41, 63. Table 2. Calculated and experimental spectroscopic constants for CH+ (experimental values in parentheses) x 'E+ A 'n a 3n 3Z- we/ cm- ' w,x,/cm-' Bo/ cm-' Be/ cm-' a,/cm-' AG1/2/~m-1 AG3/2/cm-' Do/ eV 2859.20 (2857.558) 58.72 (59.3192) 13.9302 (13.9302) 14.1713 (14.1766) 0.485 (0.4939) 2741.76 (2739.658) 2624.32 (2623.048) 3.958 (4.080) 1783.94 2694.90 2064.41 1 16.28 79.41 58.06 11.2138 (11.4227) 13.7405 (13.7469) 11.4448 (11.436) 14.0522 (14.048) 11.7189 (11.705) 0.623 (0.603) 0.548 (0.538) 1551.38 (1641.272) 2536.08 1948.29 (1939) 1318.82 (1433.282) 23 77.26 1832.18 0.956 (1.159) 2.788 1.74296 General Discussion Prof.S. A. Rice (University of Chicago, USA) said: The paper by Prof. Zare and his coworkers describes the influence of spin-rotation coupling on the population of diff erent fine-structure components of the CN product from the direct photodissociation ICN --* I+CN(X ,E+). It is interesting to note that spin-rotation coupling can also influence the rate of predissociation of a polyatomic molecule, one example being C1O2(,A2) -+ ClO+O. Michielsen et al.’ have shown that for this reaction: (i) the rate of predissociation is weakly dependent (in some ranges of N and K almost independent) of the state of rotation of the initially excited molecule; (ii) the rate of predissociation depends on the spin state prepared, being greater for the Fl(J = N + 1/2) state than for the F,(J = N - 1/2) state; (iii) for vl < 3 the rate of predissociation from the states (v,OO) is independent of v l , but for v1 > 3 the rate increases with v1 ; (iv) the bending mode is a promoting mode for the prediss~ciation.~-~ Enough is known about C102* that these observations considerably restrict the possible mechanisms for the predissociation. Michielsen et al.argue that spin-orbit coupling is the dominant interaction between the prepared *A2 state and the intermediate manifold in this indirect predissociation. They show, by studying several coupling mechanisms consistent with the indirect predissociation, that the observed differences in the rates of predissociation of F‘, and F2 states must be a consequence of spin-rotation induced mixing of these states.That is, the spin-rotation interaction mixes the nominally pure spin Fy and Fi levels producing new states. In the two-state approximation, retaining only diagonal terms in N and K, the rates of predissociation from Fl and F2 states are shown to be different, as found experimentally. All of the qualitivative features of the rotational state dependence exhibited in the experimental data are reproduced. However, because of simplifications in the analysis, the predicted ratio of predissociation rates is only in semi-quantitative agreement with the observed ratio. These two examples, i.e. predissociation of C10, and direct photodissociation of ICN, show how very small couplings in either the reactant or one of the products can markedly influence a dynamical process.They are important as illustrations of the persistence of interference effects at energies for which the density of final states is large. 1 S. Michielsen, A. J. Merer, S. A. Rice, F. A. Novak, K. F. Freed and Y. Hamada, J. Chem. Phys., 1981 2 J. B. Coon, J. Chem. Phys., 1946, 14, 665. 3 N. Bosco and S. K. Dogra, Proc. R. Soc. London, Ser. A, 1971, 29, 323. 4 I. P. Fischer, Trans. Furuduy Soc., 1967, 63, 684. 5 J. C. D. Brand, R. W. Redding and A. W. Richardson, J. Mol. Spectrosc., 1970, 34, 339. 6 R. F. Curl, K. Abe, J. Bissinger, C. Bennett and K. Tittel, J. Mol. Spectrosc., 1973, 48, 339. 7 P. A. McDonald and K. K. Innes, Chem. Phys. Leu., 1978, 59, 562. 8 Y.Hamada, A. J. Merer, S. Michielsen and S. A. Rice, J. Mol. Spectrosc., 1981, 86, 449. 74, 3089. Mr D. Baugh and Prof. C. Wittig (University of Southern California, USA) said: When the phenomenon of CN spin-polarization was first observed in our laboratories, CN was produced by the 266 nm photodissociation of ICN. At that time we pondered two questions, which we would like Dr Child to consider in light of his model calculations. ( a ) Does the strength of the spin-orbit interaction of X in XCN compounds affect the degree of polarization More specifically, how important is spin-orbit coupling in the excited ICN complex as compared to spin-other orbit (J12 = L12), spin-spin ( J , , = S12) or both ( J , , = S,, + L12)?General Discussion 97 ( b ) How would the 2-dependence of spin-orbit coupling in X manifest itself when X is varied, i.e. X = H, C1, Br, I etc.? Finally, your treatment shows that the ratio P ( F , ) / P ( F2) strongly depends on the magnitude of J12.The 266 nm photolysis of ICN produces both I*(J12 = 1/2) and I(J12=3/2),l and shows, albeit only over a limited range of N”, that the departure of this ratio from unity is greater for the I* channel than the I channel, which appears to be inconsistent with your results. 1 I. Nadler, D. Mahgerefteh, H. Reisler and C. Wittig, J. Chem. Phys., 1985, 82, 3885. Dr M. S . Child (Oxford University) said: In considering the amplitude of fluctuations in the relative Fl and F2 populations for other members of the XCN series, our model indicates that two factors must be taken into account.The spin-orbit coupling in the molecular region must be strong enough to couple the spin to the molecular axis. In broad terms this means that the spin-orbit splitting must be large compared with the rotational energy separations 2BJ, which measure the rate of rotation of the axis. It seems likely that this condition will be satisfied for all the halogen cyanides, because even for fluorine the atomic spin-orbit splitting of 404cm-’ is at least two orders of magnitude larger than 2BJ. HCN is, however, quite different because the spin-orbit splitting is only 0.4cm-I and this is why we expect only a statistical CN fine-structure distribution from the photodissociation of this molecule. The second important factor affecting the amplitude of fluctuations in fig. 3-5 of our paper, is the probability amplitude p+ or p - for the Coriolis-induced non-adiabatic transition. It is important to emphasise that it is this amplitude which occurs in eqn (8), not the transition probability; thus p+ = 0.1 even when the transition probability is as small as 0.01. The factors affecting this amplitude in a Landau-Zener theory are the strength of the Coriolis coupling dependent on N and the rotational constant, the local classical velocity and the rate of divergence between the interacting potential curves. Our model attributes the Coriolis term predominantly to the CN radical; hence the first of the above factors would differ very little from one member of the XCN to another. The other two factors depend, however, on the shapes of the potential-energy surfaces, which are difficult to assess without detailed calculation. The final comment by Mr Baugh and Prof. Wittig concerning the spin polarisation in the I and I* channels overlooks the fact that while J12, which differs between the two channels explicitly appears in our eqn (8)-( 1 l ) , there are other relevant factors that do not. In particular, the potential curves relevant to I+CN and I*+CN, and any curve-crossings they encounter will be quite different. Hence the transition amplitudes po and p* can be assumed to differ quite widely, and the effects of such differences can outweigh the influence of J12. All this points to the great value of the spin-perturbation measurement as a source of information on the potential surfaces responsible for the p hotodissociation.

ISSN:0301-7249    

DOI:10.1039/DC9868200089

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1986,82,99-110 Hydrogen-atom Photofragment Spectroscopy Photodissociation Dynamics of H20 in the 6-2 Absorption Band H. Joachim Krautwald, Ludger Schnieder and Karl H. Welge* Fakultaet fur Physik, Universitat Bielefeld, Bielefeld, Federal Republic of Germany Michael N. R. Ashfold School of Chemistry, University of Bristol, Bristol BS8 1 TS The photofragmentation dynamics of H20 molec$es following vacuum ultraviolet laser excitation at wavelengths within the B 'A1-X ' A , absorption band have been investigated using a novel form of photofragment transla- tional spectroscopy. Analysis of the nascent H atom time-of-flight spectra confirms the importance of the dissociation channel leading to ground-state H+OH products. In addition, it reveals that the OH(X) fragments are formed predominantly in their zero-point vibrational level with a highly excited, inverted rotational-state population distribution. A consideration of the topology of the various potential-energy surfaces sampled by the H20 molecules during this electronically non-adiabatic dissociation process sug- gests a likely explanation for this observed pattern of energy disposal.The past few years have witnessed continued improvement in the detail and sophistication being applied to studies of the dynamics of molecular photofragmentation processes. 172 The water molecule has long been popular as an (albeit complicated) model triatomic system, and aspects of its photodissociation behaviour have been revealed by a variety of e ~ p e r i m e n t a l ~ - ~ ~ and t h e ~ r e t i c a l ~ ~ - ~ ~ techniques.The recent classic studies of Andresen and coworkers, 13-16 supported by dynamical calculations from Schinke et aL,31-33 have done quch to clarify our picture of H20 photodissociation from its first excited singlet state ( A ' B 1 ) . Even so, experimental studies may still be hampered by the fact that excited-state predissociation precludes the use of laser-induced fluorescence (LIF) detection methods for quantitative population measurements of OH( X ) fragments carrying even moderate rotational and/ or vibrational e ~ c i t a t i o n . ~ ~ The complexities @crease manyfold at shorter excitation wavelengths. The second excited singlet state ( B ' A , ) has a very contorted potential-energy surface with a deep well in the HO-H dissociation coordinate resulting from a conical intersection with the ground-state Depending upon the Erecise excitation wavelength, photoabsorption may result in direct population of the B state, or in population of one of the more stable Rydeerg s_tates22v36-39 which can then predissociate via radiationless transition to either the A or B states.22 Four spin-allowed fragmentation channels have been identified for H 2 0 following excitation at wavelengths below 129 nm.These and their associated thermochemical thresholds are listed below:40 /H+OH(X *n) Do< 5.118 eV (1) H,+ o(' D ) H +OH( A 2Ec+) Do d 7.00 eV Do d 9.05 eV H20 + hv LH + H+ o ( ~ P ) Do d 9.61 eV. (4) Quantum-yield measurements have been reported for channels (2) and (4) following excitation of H20 at 121.67 and 123.6 nm,6 whilst several groups have provided estimates of the relative importance of channels ( 1 ) and (3).9-'2 All conclude that dissociation 99100 Hydrogen -a tom Photo fragment Spectroscopy to the ground-state products H + OH(X) 1s t,he dominant result following H20 photoab- sorption in the wavelength range of the B-X absorption band, despite the facts that (i) symmetry constraints dictate that-this asymptote may_ be Leached only as a result of non-adiabatic coupling from the B state to either the A or X state surface^^^-^' and (ii) there have been no reports of the successful observation of nascent OH(X) fragments following H20 photolysis at these wavelengths. In the present work we employ a new version of the technique of photofragment recoil spectros~opy,~~ originally pioneered by Wilson and coworkers,"2 to a study of H20 photodissGciat_ion at photon energies around 10 eV (to the high-frequency side of the peak of its B - X absorption).As with most other versions of the method, photofrag- ment time-of-flight (TOF) spectra are recorded and transformed to yield a spectrum of the photofragment translational energies from which, by energy conservation, the internal energy disposal may be deduced. The novel feature introduced in this work is the method of detecting the nascent photofragment. It (in this case the H atom) is selectively ionised by laser-induced excitation and its dynamics monitored via the ion. The general technique is blessed with a wide range of applicability and high sensitivity.A detailed description of its application to the detection of H atom photofragments appears e l ~ e w h e r e . ~ ~ The H atom TOF spectra so obtained show clearly resolved structure which, upon analysis, is found to be associated with the various different rotational states in which the OH(X) product is produced. This product is formed with a highly excited, inverted rotational state population distribution, thus accounting for the failure of all previous attempts to observe nascect QH( X ) fragments by LIF following photoexcitation of H,O within the region of its B-X transition. Previous studies of H20 photolysis at these excitation energies have revealed the nascent electronically excited OH( A) photofrag- ments to possess highly excited inverted rotational state population distributions also.17-23 In both cases a qualitative explanation for the high levels of product rotational excitation may be found by considering the topology of the one, or more, potential-energy surface( s) sampled as the molecule proceeds along the HO- H dissociation coordinate: a more quantitative rationale must await a more complete knowledge of the relevant potential-energy surfaces35'43-45 and of the possible non-adiabatic couplings between them. 26-30 Experimental Here we provide only a brief description of the experimental design and procedure. The experimental set-up, shown schematically in fig. 1, consists of a crossed molecular beam-laser beam arrangement with a time-of-flight spectrometer for analysis of H+ ions produced in the beam intersection region as described below.The parent molecule gas of interest, entrained in an inert carrier gas (usually a 1 : 2 mixture of H20 at 40 "C and Ar; stagnation pressure ca. 150 Torr) is expanded through a pulsed nozzle and then constrained to flow through a capillary of length 15 mm, inner diameter 2.5 mm before emerging into the interaction region within the reaction chamber. The gas beam is crossed at right angles to its axis by the dissociation (L,) and the H-atom detection (L,) laser beams, which counterpropagate through the chamber with a crossing angle of ca. 3". The ionisation laser pulse (pulse duration ca. 15 ns) is delayed 6 10 ns with respect to the photolysing laser pulse (duration ca. 10 ns). Hydrogen atoms produced uia dissociation channels ( l ) , (3) and (4) during the photolysis laser pulse are ionised selectively in the beam intersection region by resonant two-photon excitation: H(n=l)+vacuum ultraviolet (121.6nm) - H(n=2) with the first step at the Lyman-a line.46 The 121.6nm radiation is produced by ( 5 ) H( n = 2) + ultraviolet (364.8 nm) + H+ + eH.J. Krautwald, L. Schnieder, K . H. Welge and M. N. R. Ashfold 101 Fig. 1. Schematic diagram of the experimental arrangement for photoatom spectoscopy (PAS). frequency-tripling 364.8 nm laser light (pulse duration ca. 15 ns) in a cell containing krypton gas47-53 and focused into the reaction chamber (beam diameter ca. 0.2mm, photon flux ca. lo9 per pulse) so as to overlap spatially with the centre of the dissociating laser beam axis.The 364.8 nm radiation, traversing the reaction chamber as a slightly divergent beam, is back-reflected by a spherical mirror and has converged to a diameter of ca. 3 mm at the beam intersection region. The sum energy of a 121.6 and a 364.8 nm photon coincides very closely with the H-atom ionisation limit, resulting in practically zero recoil energy in the ionisation process. This is an essential requirement for this technique of photoatom spectroscopy (PAS), the utility of which depends on the validity of the assumption that the measured ion time-of-flight spectrum is an accurate monitor of the dynamics of the photolysis event by which the H atoms were formed. Experiments were conducted at three photolysis wavelengths A D = 122.0, 125.1 and 126.2 nm (10.16,9.91 and 9.82 eV, respectively), chosen because they could be generated with relatively high intensity (ca.10l2, 1013 and 10l2 photons per pulse, respectively) by four-wave mixing in mercury ~ a p o u r . ~ ~ Radiation emerging from the Hg mixing cell was focused into the interaction region within the reaction chamber, where it had a beam diameter of ca. 0.9 mm. The TOF spectrometer consists of two field-free sections (see fig. 1). The first comprises two parallel flat metal grids placed symmetrically about the plane containing the intersecting molecular and laser beams; this point of intersection defines the spec- trometer axis. The first part of the total flight path from the intersection is defined in length (do = 30 mm) and solid angle (0.52 Sr) by an aperture of 8 mm diameter in one plate, covered by a fine-mesh copper grid, Go.The second flight section is guided by a cylindrical tube and defined in length by grids GI and G, 401 mm apart. Go and G, are separated by a distance of 1.5 mm. This design allows for the possibility of manipulat- ing the drift velocity of the ions by applying a small potential to the second section. Ions passing through G2 are accelerated first by the grid electrode G3 to ca. 50V and then further to ca. 4 kV onto the cathode of the SEM detector (Johnston, type MM1-SG). Signals from the detector are recorded time-resolved by a transient digitiser (Biomation 6500,1024 channel capacity, 500 MHz maximum speed) are accumulated for a preselec- ted number of laser shots and transferred to a microprocessor for subsequent data102 Hydrogen-atom Photofragment Spectroscopy 10 20 flight time/ps 30 ps Fig.2. H+-ion TOF spectrum resulting from H20 photolysis at 125.1 nm. [ E ( R v ) = 9.9 eV.] handling. The maximum resolution obtained with this spectrometer is 15 meV (at a kinetic energy of 1.6eV), although in the present experiments resolution has been sacrificed (A& = 0.08 eV) in order to improve the signal strength. The measured TOF signal distribution S ( t) is converted into a translational energy distribution S( Etr) in the laboratory frame by the transformation S( t) d t = S( Etr) dE,, (6) where dEtr/dt = mZ2t-3, with time increments equal to the transient digitiser step size used. In the transformation from measured flight time to energy the electric potential distribution applied to the spectrometer sections was, of course, taken into account.The observed H atom TOF distribution is affected by the transmission of the spectrometer and the overall resolution in a complex fashion. Because these experiments are still in a preliminary state we refrain from detailed discussion of these effects, but some aspects of the problem are addressed in the following section of this paper. Results Only one dye laser is required to generate the necessary frequencies for the four-wave mixing process in Hg that gives rise to the 125.1 nm photolysis wavelength. Production of the other two photolysis wavelengths necessitated use of two dye lasers, the outputs of which were synchronised and spatially overlapped in the mixing cell.The resulting vacuum ultraviolet output intensities were an order of magnitude lower, and the photo- fragment translational energy spectra obtained at these wavelengths were of correspond- ingly poorer quality. Fig. 2 shows a complete H' ion TOF spectrum resulting from H20 photolysis at 125.1 nm. Signal was accumulated from 5000 laser shots at a 10 Hz repetition rate. To cover this time region with 20ns digitiser channel width the drift velocity of the H' ions in the second flight section of the TOF spectrometer was shifted by applying a 5 V potential between grids G, and G2. No signal was detectable at times d 11 ps, and by ca. 30ps the ion signal has fallen to a negligible level. Tests were made to ensure that no significant ( < 0.1 % ) ion signal derived from use of the vacuum ultraviolet probe or the vacuum ultraviolet photodissociation laser alone.Fig. 3 shows this TOF spectrum transformed into a spectrum of the total kinetic-energy release. The energy resolution is ca. 0.08 eV and, to a first approximation for the spectrometer set-up used, independent of the magnitude of the translational energy. Higher resolution (ca. 0.05 eV)H. J. Krautwald, L. Schnieder, K. H. Welge and M. N. R. Ashfold 103 N = kinetic energy/eV Fig. 3. Transformation of the TOF spectrum, shown in fig. 2, into a spectrum of total kinetic energy. Above the spectrum are the energies corresponding to different rotational levels, N, of the OH radical in the u”= 0 vibrational level of the ground (X) and the first excited ( A ) electronic states. 0 1 2 3 4 5 kinetic energy/eV Fig.4. Spectrum of total kinetic energy for H+ ions produced via H 2 0 photolysis at 122.0nm. [ E (hv) = 10.2 eV.] could be achieved (at the expense of signal-to-noise ratio) using lower laser powers. Fig. 4 and 5 display the corresponding translational energy release spectra for H atoms produced via H 2 0 photolysis at 122.0 and 126.2 nm, respectively. Although of poorer quality these spectra show a similar overall appearance to that obtained at the 125.1 nm photolysis wavelength. Energy conservation dictates that E ( hvD) + Ei,t( H20) - Do( HO - H) = E,, where104 Hydrogen-atom Photofragment Spectroscopy 0 1 2 3 4 5 kinetic energy/eV Fig. 5. Spectrum of total kinetic energy for H+ ions produced via H20 photolysis at 126.2nm.[ E ( h v ) =9.8 eV.] Thus, given Do( HO-H) = 5.1 l8 f 0.05 eV,55 it should, in principle, be possible to derive the population of OH radicals in a specific internal quantum state k by monitoring the number of H atoms ( Hk) in the corresponding translational-energy group. In practice we find that the position of the peaks in the translational-energy release spectrum allows unambiguous identification of the v and N quantum numbers of the OH states populated in the dissociation, but we recognise that interpretation of the individual peak heights requires caution because of possible experimental effects as indicated below. Shown above each translational-energy spectrum are the energies corresponding to the different rotational levels, N, of the OH radical in the u” = 0 vibrational levels of the ground ( X ) and first excited ( A ) electronic states.Energies for the ground-state levels were obtained by fitting the term values (averaged over the spin-orbit- and A-splittings) given by Dieke and C r o ~ s w h i t e ~ ~ to a third-order polynomial in N ( N + 1) and extrapolating to higher N. Term values for the A-state levels were taken directly from the 1iteratu1-e.~~ For best agreement between the observed and ‘calculated’ energy scales it was necessary to set the effective HO-H bond dissociation energy to 5.05 eV. About half of the offset (ca. 0.07 eV) from the literature Do value may be attributed to the contribution from E,,,(H,O) under the gas inlet conditions used in these studies. The rest may be due to experimental uncertainty.The three translational-energy spectra clearly demonstrate that the bulk of the detected H atoms are formed in association with rotationally excited but vibrationally cold OH(X) radicals. It is impossible to account for the structure resolved in these spectra in terms of vibrational excitation of the nascent OH fragments. However, we are not able to exclude the possibility that a small fraction of the OH(X) photoproducts are formed in vibrationally excited levels. For example, spectral simulations that assume the same overall rotational-state intensity distribution as that observed and attributed to formation of OH(X, u = 0) suggest that a contribution of s 20% from the dissociation channel leading to H + OH(X, v = 1 ) would be hard to discern with the present spectral resolution. We now turn to a consideration of the information that may be derived from the heights of the individual peaks resolved in the translational energy spectra. Necessarily this requires some (brief) discussion of factors that will cause differences from the idealised 1 : 1 correlation between the population of OH radicals formed in a specific quantum state and the number of H atoms detected with the appropriate correspondingH.J. Krautwald, L. Schnieder, K. H. Welge and M. N. R. Ashfold 105 I I I I I I I I I I I 1 - + c .- +-I + 3 ++ d P - a - m - + + 0 - .- 4 + + - * u - + + 2 - ++ ++ + - +++ 0 - . . . . . . . . . . . . . . . . . . . . . . . . I l l 1 I I I I L I I kinetic energy. Further experiments using this PAS technique will be necessary before it is possible to give a full appreciation of the various factors that might cause a translational-energy-dependent H-atom detection efficiency.Here we simply list some of the more obvious and comment on their likely effect on any observed TOF distribution. As in all TOF experiments there will be a tendency to miss the slowest particles; with the present set up this may come about as a result of the following factors. (i) The initial parent molecular velocity. The parent beam is perpendicular to the TOF axis; thus for the slowest particles the resultant H-atom velocity vector in the laboratory frame will fall outside the detection solid angle. Obviously the contribution from this loss mechanism increases with decreasing recoil energy; with the present experimental geometry we expect major loss of H+ ions with recoil energy < 0.3 eV.(ii) Collisional deflection, the probability of which will scale with the flight time. (iii) Space charge effects, the consequences of which are hard to assess quantitatively but, qualitatively, can be expected to lead to a reduction in the overall resolution and to have the greatest relative impact on slow particles. Proving experiments involving the much-studied 266 nm photodissociation of HI39 suggest that none of these effects are significant for 'slow' H+ ions with recoil energy 30.3 eV. Because of the relative sizes of the vacuum ultraviolet dissociation (L,) and probing (L,) beams the present experiment also discriminates against the fastest H atoms.Model calculations with the appropriate beam diameters and overlap conditions indicate that free flight out of the excitation-ionisation region will cause a 20% reduction in the detection efficiency for H atoms with 2 eV recoil energy (rising to 50% for 4 eV recoil energy) relative to that for H atoms with a translational energy of 1 eV. Finally, we recognise that the 121.6 nm bandwidth (Av == 50 GHz) used will introduce some degree of Doppler selection which could lead to a discrimination in favour of particular H-atom velocity groups. Further work is required before it will be possible to comment on this effect in detail. Most of the H atoms resulting from H20 photodissociation at 125.1 nm are associated with total translational energies < 3.5 eV.In view of the foregoing discussion we consider the overall shape of that part of the observed distribution assigned to the H + OH(X) dissociation channel to be genuine, including the maximum ( N " = 44) and the decline in population to higher N". Spectra obtained at the other excitation wavelengths peak and decline at very similar recoil energies. Fig. 6 shows a plot of the OH(X, = 0)106 Hydrogen-atom Photofragment Spectroscopy rotational-state population distribution resulting from photolysis at 125.1 nm. Popula- tions are derived by best-fit simulation of the experimental spectrum, assuming each H + OH( X ) , u = 0, N" product channel to have an associated energy peak of Gaussian lineshape (0.08 eV f.w.h.m.), and then correcting for the calculated effects of H-atom flight out of the detection region.The crucial observation that the OH( X, ZI = 0) fragments are formed with a highly excited, inverted rotational-state population distribution which, nevertheless, cuts off before the energetically allowed maximum is considered further in the next section. From this distribution it is possible to estimate a value of 0.68 for ( fR), the fraction of the total energy available to the H + OH(X) dissociation channel that is partitioned into product rotation. This, together with our estimate that vibrational excitation (fv) cannot exceed 0.02 leads to the conclusion that the fractior. appearing as translational energy ( fT) =: 0.3. Fig. 3-5 provide a base for quantitative estimation of the problems associated with the transmission loss of the slowest H atoms.Previous photofragment emission studies of the H+OH(A) product channel resulting from photolysis in this wavelength region have identified a very high level of rotational excitation in the OH(A) fragment, with a rotational state population distribution that peaks near the highest N' level permitted by energy c~nservation.~'~' Necessarily these OH( A) fragments are formed in conjunc- tion with near-zero kinetic-energy H atoms; these are not detected in the present experiment. Nevertheless it is possible for us to support previous of the branching between product channels ( 1 ) and (3) at these photolysis wavelengths. Knowing the form of the OH(A) rotational-state population distribution to be expected at this photolysis wavelength2' it is possible to get a reasonable match with the experi- mental spectrum shown in fig. 3 at energies down to ca.0.3 eV if we assume a branching ratio OH(A) : OH(X) = 0.10. Discussion A quantitative interpretation of the H atom time-of-flight distributions reported in this work is precluded by (i) uncertainties in the kinetic-energy dependence of the experi- mental H-atom detection efficiency (see previous seciion) and (ii) our incomplete knowledge of the full potential-energy surface for the B ' A , state of water, and of the various non-adiabatic couplings involving this state. Nevertheless, the MRD-CI calcula- tions of Theodorakopoulos et aL,35943,44 and especially those for the asymmetric stretching potentials of several of the singlet states of H20,35 are of sufficient quality that we can provide a qualitative rationale for tbe observed distributions. Results of these a6 initio calculations relating to the A and B states of water are shown in fig.7, which displays three-dimensional representations of the relevant potential-energy surfaces as a function of R(H0-H) and the angle LHOH. The topologies of these surfaces have been discussed previously25-30~35743-4s and will only be summarised here. For linear configurations there is a conical intersection between the 'II and E surfaces, the lower component of whigh gives the ground state in bent H20. Because of this conical intersection the upper ( B ) surface has a deep well in the asymmetric dissociation coordinate, with a minimum at R = 0.16 nm (see fig.7); its shape at shorter R (HO - H) distances is complicated ky Rydkerg-valence interaction^.^^ Further compli- cations arise from the fact that the A and B states both derive from an electronically degenerate 'I3 state in f,he linear configuration. As a result there is a 'seam of intersection' between the A and B surfaces at the linear geometry for all asymmetric stretching distances R < 0.16 nm (the geometry associated with the conical intersection). Bending, and the accGmpanying Renner-Teller effect;' lifts this degeneracy, with the result that, whilst the B state potectial-energy surface shows a minimum at linear configurations, the minimum in the A state surface at short R(H0-H) lies at a bent geometry comparable to that of the electronic ground state.1 +H. J. Krautwald, L. Schnieder, K . H. Welge and M. N. R. Ashfold 107 .OH(X) LHOHI" LHOH/" Fig. 1. Three-dimensional representations of parts of the potential-energy surfaces for the 2 'B1 and B ' A , states of H20 plotted as a function of LHOH bendisg angle and the HO-H dissociation coordinate [after ref. (33)]. A, small part of the ground ( X ) state surface, in ths region-of its conical intersection with the B-state surface, is included in the latter plot. The A- and B-state surfaces are degenerate for linear geometries, and are separated (horizontally) only for clarity of presentation. Shown also are three representative classical-trajectories for a configuration point moving away from the Franck-Condon region (F.C.) of the B-state surface, as discussed in the text.The present work lends strong support t,o previous suggestions 12,40 that the photofrag- mentation of H 2 0 molecules from the B electronic state occurs predominantly via dissociation channel (l), despite the fact that the adiabatic correlation for this state upon asymmetric distortion is with the products of channel (3). It also reveals the nascent OH(X) fragments to be formed with little vibrational excitation but with a highly inverted rotational-state population distribution. Such energy disposal is strik- ingly reminiscent of that o b ~ e r v e d ~ ~ " - ~ ~ for the dissociation pathway (3), leading to formgticn of electronically excited OH( A) fragments following excitation of H 2 0 within the B-X continuum. As in the latter, more widely s t ~ d i e d , ~ * ' ~ - ~ ~ case it is possible to interpret the observed product quantum-state distributions bx considering the more likely classical trajectories for dissociation originating on the B state surface. W,e identify three classes of trajectory starting from the Franck-Condon region of the B state surface, as displayed in fig.7, and consider the eventual fragmentation pattern associated with each. Necessarily therefore this discussion recognises no contri- bution from channel (4), to which our experiment is in any case insensitive. For each case the initial motion for which the potential has the steepest gradient is bending towards linearity. However, as the LHOH angle opens, the detailed trajectory of the configuration point will be sensitively dependent upon the balance between the asym- metric stretching (radial) and bending (angular) motions possessed by the molecule108 Hydrogen -a tom Photofragmen t Spectroscopy when prepared on the state surface.Those trajectories (type I) which experience the greatest radial acceleration may pass _directly outside [ i.e. large R( HO- H)] the conical intersection and thus remain on the B state surface where the curvature of the potential ensures strong rotational excitation of the OH(A) photoproduct as first suggested by F l o u q ~ e t ~ ~ and frequently demonstrated e~perimentally.~”~-*~ Mechanisms can be envisaged whereby all trajectories for which the radial acceler- ation is insufficient to carry the configuration point outside the conical intersection end up at the H + OH(X) dissociation limit.Those with sufficient associated stretching motion to be drawn into the deep w ~ l l arising as a result of the conical intersection (type 11) will emerge on the ground (X) state potential-energy surface in a region where it is ~ a l c u l a t e d ~ ~ to be gently repulsive along the dissociation coordinate but still to retain significant angular anisotropy, with a minimum at bent geometries. Indeed, for type -11 trajEctories passing through the conical intersection the angular properties of the B and X state potential are such that it is quite conceivable that all of the available energy could be partitioned into rotational excitation of the OH(X) fragment. On the other hand, trajectories which start out from the Franck-Condon region with little radial accelzrationitype 111) pass through linearity at least once at relatively short R ( HO-H).The B and A states are degenerate in this linear configuration, and Dixon3’ has shown how vibronic- inteEaction (the Renner-Teller effect) can provide a mechanism for the irreversible B - A radiationless transition. At short R(H0-H) the A state surface shows a marked angular anisotropy, with a_mini_mum near LHOH= 105” (see fig. 7). Thus type I11 trajectories which undergo B-A transfer at these shqrt R(H0-H) separations will experience an angular acceleration on both the B- and A-state surfaces before reaching the_ gently repulsive, isotropic longer range region of the dissociation coordinate of the A-state surface leading, again, to Ha+ OH(X).Here a significant difference beiween the A- and X-state surfaces becomes evident. The a6 initio calculations show the A-state surface to have lost all of its angular anisotropy by R b 0.16 nm, at which point its potential energy is still ca. 0.8 eV above the asymptotic limit for H+OH(X). Thus for trajectories that lead to eventual dissociation on the A-state surface this part of the total available energy cannot be available for product rotational excitation. Whilst recognising the inherent difficulties associated with detec- tion of the slowest fragments in any time-of-flight experiment, it is relevant to note that we observe no structure that is obviously attributable to rotationally excited OH(X) fragments within 0.8eV of the origin of the kinetic-energy spectra obtained at any of the three excitation wavelengths siudie_d.Such a result provides support for previous discussion^^^ of the importance of B - A radiationless transfer in promoting dissociation channel (1). Finally, we must consider the vibrational energy disposal in this fragmentation process. The measured kinetic-energy release spectra may be interpreted without assum- ing formation of any OH(X) fragments with 0”) 0, but this conclusion may require some revision if and when higher resolution TOF data becomes available. Such a low level of product_vibrational excitation is consistent with the very similar 0-H bond lengths in H20( X) and OH( X), and mirrors that reported previously for the correspond- ing dissociation channel leading to OH( A) fragrnent~.’.’~-~~ However, a6 initio MRD-CI c$culations for the symmetric stretching potentials of H2044 show the minimum in the B-state surface to lie at larger 0-H bond lengths.Franck-Condon considerations might thus suggest that dissociation proceeding via this surface would give rise to some product vibrational excitation. That such appears not to be the case for either H + OH dissociation channel is presumed to be because the slope of the potential for this symmetric motion is too shallow to compete with the combined bending/asymmetric dissociative motion. Further djscussion of this point must await the availability of a more complete picture of the B-state potential surface.H. J. Krautwald, L. Schnieder, K . H. Welge and M. N. R. Ashfold 109 Conclusion In this study we have demonstrated the utility and sensitivity of a new form of photofrag- ment translational spectroscopy by applying the technique to an investigation of the photodissociation dynaFic5 of the water molecule following excitation at various wavelengths within its 23-X absorption band.Measurements of the nascent H atom TOF spectra reveal a dominant role for the dissociative channel leading to ground-state H + OH products, but the OH(X) fragments are observed to carry very high levels of rotational excitation. Such energy disposal may be understood by considering the form of the various potential-energy surfaces sampled by the molecules as they evolve along this dissociation coordinate. The observed high level of fragment rotation explains the failure of previous attempts to monitor these OH(X) photoproducts by LIF (the corresponding levels in the first ekcited state of OH are heavily predissociated), and highlights one of the potential advantages of the new technique: its universality.Possible limitations, particularly the difficulties associated with efficient detection of those species that recoil with the fastest and the slowest velocities, are also considered. We are grateful to NATO for the award of a travel grant. M.N.R.A. thanks Prof. R. N. Dixon for numerous helpful discussions. References 1 M. Shapiro and R. Bersohn, Annu. Rev. Phys. Chem., 1982, 33, 409. 2 J. P. Simons, J. Phys. Chem., 1984, 88, 1287. 3 T. Carrington, J. Chem. Phys., 1964, 41, 2012. 4 K. H. Welge and F. Stuhl, J. Chem. Phys., 1967,46, 2432.5 F. Stuhl and K. H. Welge, J. Chem. Phys., 1967, 47, 332. 6 L. J. Stief, W. A. Payne and R. B. Klemm, J. Chem. Phys., 1975, 62, 4000. 7 T. G. Slanger and G. Black, J. Chem. Phys., 1982, 77, 2432. 8 M. T. Macpherson and J. P. Simons, Chem. Phys. Lett., 1977, 51, 261. 9 I. P. Vinogradov and F. I. Vilesov, Opt. Spectrosc., 1976, 40, 32; 1978, 44, 653. 10 L. C. Lee, L. Oren, E. Phillips and D. L. Judge, J. Phys. B, 1978, 11, 47. 11 L. C. Lee, J. Chem. Phys., 1980, 72, 4334. 12 0. Dutuit, A. Tabche-Fouhaile, I. Nenner, H. Frohlich and P. M. Guyon, J. Chem. Phys., 1985,83, 584. 13 P. Andresen and E. W. Rothe, Chem. Phys. Lett., 1982, 86, 270; J. Chem. Phys., 1983, 78, 989. 14 P. Andresen, G. S. Ondrey and B. Titze, Phys. Rev. Lett., 1983, 50, 486. 15 P. Andresen, G.S. Ondrey, B. Titze and E. W. Rothe, J. Chem. Phys., 1984, 80, 2548. 16 P. Andresen, V. Beushausen, D. Hausler, H. W. Lulf and E. W. Rothe, J. Chem. Phys., 1985,83, 1429. 17 H. Okabe, J. Chem. Phys., 1980, 72, 6642. 18 A. Gedanken, J. Mol. Spectrosc., 1980, 82, 246. 19 J. P. Simons and A. J. Smith, Chem. Phvs. Lett., 1983, 97, 1. 20 J. P. Simons, A. J. Smith and R. N. Dixon, J. Chem. SOC., Faraday Trans. 2, 1984, 80, 1489. 21 C. Fotakis, C. B. McKendrick and R. J. Donovan, Chem. Phys. Lett., 1981, 80, 598. 22 M. N. R. Ashfold, J. M. Bayley and R. N. Dixon, Chem. Phys., 1984,84,35; Can. J. Phys., 1984,62,1806. 23 A. Hodgson, J. P. Simons, M. N. R. Ashfold, J. M. Bayley and R. N. Dixon, Chem. Phys. Lett., 1984, 24 M. P. Docker, A. Hodgson and J. P. Simons, Mol.Phys., 1986, 57, 129. 25 S. Tsurubuchi, Chem. Phys., 1975, 10, 335. 26 F. Flouquet and J. A. Horsley, J. Chem. Phys., 1974, 60, 3767. 27 F. Flouquet, Faraday Discuss. Chem. SOC., 1977, 62, 143. 28 J. N. Murrell, S. Carter, I. M. Mills and M. F. Guest, Mol. Phys., 1981, 42, 605. 29 E. Segev and M. Shapiro, J. Chem. Phys., 1982, 77, 5604. 30 R. N. Dixon, Mol. Phys., 1985, 54, 333. 31 R. Schinke, V. Engel and V. Staemmler, Chem. Phys. Lett., 1985,116,165; J. Chem. Phys., 1985,83,4522. 32 R. Schinke, V. Engel, P. Andresen, D. Hausler and G. G. Baht-Kurti, Phys. Rev. Lett., 1985,85, 1180. 33 V. Engel, R. Schinke and V. Staemmler, J. Chem. Phys., 1986, in press. 34 K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure, IV. Constants of Diatomic 107, 1; Mol. Phys., 1985, 54, 351. Molecules (van Nostrand Reinhold, New York, 1979).110 Hydrogen-atom Photofragment Spectroscopy 35 G. Theodorakopoulis, I. D. Petsalakis and R. J. Buenker, Chem. Phys., 1985,96, 217. 36 J. W. C. Johns, Can. J. Phys., 1963,41, 209. 37 H. T. Wang, W. S. Felps and S. P. McGlynn, J. Chem. Phys., 1977, 67, 2614. 38 E. Ishiguro, M. Sasanuma, H. Masuko, Y. Morioka and M. Nakamura, J. Phys. B, 1978, 11, 993. 39 P. Gurtler, V. Saile and E. E. Koch, Chem. Phys. Lett., 1977, 51, 386. 40 M. N. R. Ashfold, M. T. Macpherson and J. P. Simons, Top. Curr. Chem., 1979, 86, 1. 41 L. Schnieder, H. J. Krautwald, M. N. R. Ashfold and K. H. Welge, to be published. 42 K. R. Wilson, in Symposium on Excited State Chemistry, ed. J. N. Pitts Jr (Gordon and Breach, New 43 G. Theodorakopoulos, C. A. Nicolaides, R. J. Buenker and S. D. Peyerimhoff, Chem. Phys. Lett., 1986, 44 G. Theodorakopoulos, I. D. Petsalakis, R. J. Buenker and S. D. Peyerimhoff, Chem. Phys. Lerr., 1984, 45 V. Staemmler and A. Palma, Chem. Phys., 1985,93, 63. 46 H. Zacharias, H. Rottke, J. Danon and K. H. Welge, Opt. Commun., 1981, 37, 15. 47 D. C . Hanna, M. A. Yuratich and D. Cotter, Nonlinear Optics of Free Atoms and Molecules, Springer 48 R. Mahon, T. J. McIlrath, V. P. Myerscough and D. W. Koopman, IEEE J. Quantum Electron., 1979, 49 G. C. Bjorklund, IEEE J. Quantum Electron., 1975, 11, 287. 50 Y. M. Yiu, T. J. McIlrath and R. Mahon, Phys. Rev. A, 1984, 20, 2480. 51 D. Cotter, Opt. Commun., 1979, 31, 397. 52 R. Wallenstein, Opt. Commun., 1980, 33, 119. 53 H. Langer, H. h e l l and H. Rohr, Opt. Commun., 1980, 34, 137. 54 R. Hilbig and R. Wallenstein, IEEE J. Quantum Electron., 1983, 19, 1759. 55 D. R. Stull and H. Prophet, JANAF Thermochemical Tables (Natl Stand. Ref. Data Ser., US Natl Bur. 56 G. H. Dieke and H. M. Crosswhite, J. Quantum Spectrosc. Radiat. Transfer, 1962, 2, 97. York, 1970). 84, 164. 105, 253. Series in Optical Science, Vol. 17 (Springer, Berlin, 1979). 15, 444. Stand., Washington, D.C., 1979), vol. 9. Received 9th June, 1986

ISSN:0301-7249    

DOI:10.1039/DC9868200099

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1986, 82, 111-124 The Rotational Reflection Principle in Photodissociation Dynamics Reinhard Schinke* and Volker Engel Max-Planck-Institut f u r Stromungsforschung, 0-3400 Gottingen, Federal Republic of Germany Rotationally inelastic effects in the direct dissociation of a triatomic molecule are investigated. The calculations are performed on three levels of accuracy: the exact close-coupling method, the energy sudden approximation and very simple classical trajectory calculations. Rotational state distributions are usually smooth and highly inverted. They are explained as a one-to-one mapping of the ground-state wavefunction onto the quantum-number axis mediated by the so-called classical excitation function obtained by exact trajectory calculations on the excited-state potential-energy surface.We call this effect the rotational reflection principle. It should be applicable whenever many states are accessible provided that the rotational-transla- tional coupling is strong enough to excite them. Under certain circumstances rotational rainbows due to the maximum of the excitation function become prominent. The rotational reflection principle establishes a unique relation between the angular part of the ground-state wavefunction, the anisotropy of the excited-state potential and the final rotational distribution. Many recent experimental distributions are qualitatively similar to those predicted by the rotational reflection principle. In two cases, ClCN and H,CO, quantitative calculations on ab initio potentials are performed, and good agreement with experiment is found.The dissociation of a molecule following the absorption of a photon is an old but still interesting field of photo~hemistry.'-~ With the availability of modern detection methods complete specification of the fragment states is possible and receives most attention in recent year^.^-^ Unlike the case of normal scattering, the distribution of initial coordinates and momenta is specified because the parent molecule is prepared in a particular vibrational-rotational state within the electronic ground-state manifold. An interesting question is therefore to what extent the distribution of final momenta, i.e. the quantum states of the fragments, 'reflect' the initial preparation of the parent molecule.If the so-called final-state interaction due to the potential-energy surface (PES) within the excited electronic state is negligibly weak, the initially prepared polyatomic wavefunction is not distorted (except for the dissociation coordinate) while the fragments separate. In such cases the final distribution of internal quantum states is primarily determined through the resolution of the parent wavefunction in terms of the asymptotic fragment wavefunctions.6 An excellent example for a pure Franck-Condon (FC) distribution is the dissociation of water in the first absorption band.7 Since the corresponding excited- state PES has roughly the same bending angle as the ground state, rotationally inelastic effects are extremely unimportant.8 The final-state interaction is the coupling between the translational motion and the internal degrees of freedom of the fragments induced by the dissociative PES, Vex.In this study we will analyse rotational state distributions following the dissociation of a triatomic molecule, and the final-state interaction is simply the anisotropy of Vex, i.e. the torque a Vex/ay. It is usually strong (compared to vibrational coupling, for example) and can produce high rotational excitation in ordinary atom-molecule collisions?,1o 111112 Rotational Rejection Principle Therefore it is most plausible to expect that the potential anisotropy is also the determin- ing factor in the ‘half collision process immediately following the excitation through the photon absorption. If the final state distributions ‘reflect’ the potential anisotropy it should be possible to extract valuable information from the measurements which would be difficult to obtain otherwise.An ‘inversion’ is obviously facilitated if the distributions exhibit distinct structures which are directly related to the parameters of the system, e.g. the excited-state PES. Such structures are known in normal atom-molecule scattering and are called ‘rotational rainbows’? Their analysis and resolution for many scattering systems has tremendously advanced our understanding of rotational energy transfer in molecular collisions.9-’ Closely related structures exist in the direct photodissociation of triatomic molecules. 12-14 They reflect the angular dependence of the parent wavefunction and, more importantly, the anisotropy of the dissociative PES.We call this effect the rotational reflection principle. The corresponding distributions are usually smooth and highly inverted functions of the rotational quantum number. They are either symmetric around the maximum or asymmetric with a fast decay at the high-energy side. Many measured distributions show the same qualitative beha~iour,’~-~l and therefore we believe that the rotational reflection principle is widely applicable to the interpretation of dissociation processes. In this contribution we will elucidate the rotational reflection principle by calculations on three levels of sophistication: the exact quantal close-coupling method, the energy sudden approximation and ultra-simple classical trajectory calculations.Most of the calculations are performed for a model system which, however, is typical for a linear-to- bent transition. In two cases, H2C0 and ClCN, the corresponding dissociative PES are known, at least to some extent, and the new effect will be manifested by direct comparison of the calculated and the measured distributions. Theory In this article we discuss the rotational distribution of the diatomic fragment following the direct photodissociation of a triatomic molecule: ABC+ho + A+BC(j). (1) All vibrational degrees of freedom are omitted, and the parent molecule is assumed to be in the rotational ground state, J = O . As usual, the quantal photodissociation cross- section is calculated from the Golden Rule expression 4 j , 0) = 4(+gr(R, ~)lPI+:;w, .>)I2 (2) where +gr and represent the nuclear wavefunctions in the electronic ground and excited states, respectively.The superscript ( - j ) indicates an outgoing boundary condi- tion in state j.” In eqn (2) R and r are the usual Jacobi coordinates appropriate to describe the A+BC dissociation channel. In the present work we follow very closely the detailed formulation of Balint-Kurti and Shapir~,’~ who give explicit expressions for the various cross-sections. In order to facilitate the calculations and to make the discussion more transparent we introduce the following assumptions. The total angular momentum within the excited electronic state is zero, and the coordinate dependence of the transition moment p is ignored. The ground-state wavefunction is parametrized as + g r ( R Y ) = R-’+gr,R(R)+gr,y(y) (3) + g r , R ( R ) = ~ X P [-a,(~ - +gr.y(r)=%ex~ [ - Q ~ ( Y - Y ~ ) ~ I + ~ x P [ - Q ~ ( Y + Y ~ ) ~ I I ( 5 ) (4)R.Schinke and K Engel 113 where R is the distance between A and the centre-of-mass of BC and cos y = r / Rr. Eqn (4) and ( 5 ) are appropriate for the vibrational ground states of the stretching and bending modes, respectively. Close-coupling Within the exact close-coupling (CC) formulation the dissociative wavefunction is expanded as f&"( R, y ) = R-' c x;?(-j)( R) q0( y, 0) ( 6 ) j ' and the radial functions are solutions of the coupled equations23 with the boundary conditions x;:'-"(R) - 0 R-0 x;?'-J)( R) - ki;''2[exp (i kj.R) Sjjr + Sjj. exp (-i kjtR)] R-ffi for open states (k,?. > 0) x;:(-j)(R) - 0 R - + a for closed states (kj'.< 0). In eqn (7) p is the A-BC reduced mass and the wavenumbers are defined by k,?=2p[E - - B j ( j + l ) ] (9) where B is the rotational constant of BC and E is the total available energy to be partitioned into translation and rotation. The potential matrix elements in eqn (7) are A (: : id)' V?(R) = [(2j+ 1)(2j'+ 1 ) y 2 C V","R) and the expansion coefficients are defined by The cross-section for absorbing a photon with energy fto and producing a BC fragment in rotational state j , integrated over the angle of observation and summed over all magnetic quantum numbers, is given by23 aCC(j, 0) - oltCC(j, @)I2 (12) where all constants are omitted which are unimportant for the final state distribution. In order to facilitate the integration over y we expanded the ground-state wavefunction into y, 0) according to114 Rotational Reflection Principle The quantal close-coupling (CC) formulation is essentially exact.However, it has two major drawbacks. First, it becomes impracticable if many states have to be included in the basis expansion (6). Secondly, the interpretation of the CC calculations can be difficult because the quantum state j, appearing on the left-hand side of eqn (13), enters the expression for the amplitude only through the boundary conditions. Therefore, any direct relation between the final state distribution and the potential-energy surface, for example, might be completely obscured. Energy Sudden Approximation If the rotational energy throughout the ‘trajectory’ is small compared to the total energy E, the so-called energy sudden approximation (ESA) 8924-27 can be employed.Under sudden conditions the wavenumbers in eqn (9) are assumed to be independent of j and the coupled equations can be rigorously decoupled.28 Within the ESA the dissociation amplitude is8 tESA(j, 0) - j’: d y sin y q o ( y , O)+,,,(y)~(y) exp M ~ ) I (16) where the one-channel, y-dependent radial wavefunction is a solution of j,, is some effective, but in principle arbitrary, rotational state, which usually is chosen to be the ground state. The main asset of the ESA is its interpretation power, especially within its semi- classical limit as h -+ O.I3 For large rotational states the spherical harmonic in eqn (16) is replaced by its asymptotic limit and the integral over y is evaluated by the stationary phase approximation assuming that the integrand is rapidly oscillating with y.Then the dissociation amplitude can be approximately evaluated from 1/2 +gr,-y(yv)A(yv) exp [G(YA + i ( j +9yvI (19) fESA where the summation runs over all points of stationary phase y v ( j j defined by JESA( y ) 5 dij( y)/dy = * ( j + i ) . (20) JESA( y ) is the so-called classical excitation function. It relates the independent variable y to the final momentumj. The semiclassical sudden approximation has been extremely helpful in the under- standing of rotational rainbows in normal atom-molecule scattering.’ It has been used by us previously to interpret rotational state distributions in direct dissociation proces- ses.’* However, one must be very careful in applying the ESA and if the sudden condition Erot << Etot is not fulfilled throughout the entire collision/dissociation it can give spurious results.Unfortunately, for most of the systems mentioned in the introduction the ESA seems to be not suitable because the final rotational energy is large. We mention the semiclassical ESA in this article because it is a useful link between the quantal CC theory and pure classical calculations which we will outline next.R. Schinke and V. Engel 115 Classical Trajectories The classical Hamilton function for our model system is simply given by29 (21) P2 j' H(R, y, P, j) =-+ Bj2+-+ VeX(R, y ) 2P 2pR2 where P is the radial momentum and j is now the continuous, time-dependent molecular angular momentum. We have explicitly used that for J = 0 the orbital angular momentum 1 is equal to -j.The classical equations of motion are dR P - dt P dy-2j B+- -- dt ( 2iR2) d P dV"" j2 dt aR +* - d j dVex dt dy * -- - (23) Unlike in atom-molecule scattering the initial conditions for a dissociative trajectory are not rigorously defined. Since y ( t ) is the conjugate coordinate to the momentum j ( t ) it is advisable to treat the dependence on the initial rotational angle e~plicitly.'~ Structures within the distribution of final momenta j might be a 'reflection' of the distribution of initial angles. On the other hand, the influence of initial momenta is expected to be weak. Therefore we make the following simple choice of initial conditions: 0 s yo s T, varied systematically jo = 0 Po = 0 Ro( yo) from energy conservation, E = Vex( Ro, yo).Integrating the equations of motion yields the classical excitation function J ~ ~ ( Y ~ ) = A t = 00, yo) (27) which is the analogue of the quantal sudden expression JESA in eqn (20). It depends only on the initial angle yo. The classical cross-section for any final rotational state j ( = 0, 1,2, . . .) is simply given by where the angles yo,y = ~ ~ , ~ ( j ) are defined by J " ~ ( Y O , J = j which is the analogue to eqn (20). The function weights each trajectory according to the quantal distribution function within the elec- tronic ground state. It is absent (except for sin yo) in normal scattering.116 Rotational ReJZection Principle Eqn (29) establishes a direct mapping between the initial independent variable yo and the final rotational angular momentumj.This mapping is unique if only one solution ~ ~ , ~ ( j ) contributes to the cross-section, which is very often the case as we will demonstrate below. The classical and the ESA cross-sections are formally equivalent. In the sudden case the excitation function is derived from a quantum-mechanical phase, and energy conservation is not built in. In the classical case the excitation function is obtained from trajectories which certainly fulfill energy conservation. Quanta1 interference effects due to the sum over several contributions for a givenj are in principle included in the ESA cross-section but not in the classical cross-section. Since J ( y o ) depends only on one independent initial variable very few trajectories (ca.20) must be calculated. A random selection of initial variables and boxing of the final momentum is not ne~essary.~' 332 The Rotational Reflection Principle The classical cross-section depends on two components: the excitation function J ( yo), which is solely determined by the dynamics within the excited state, and the weighting function W ( y o ) , which is primarily determined by the angular part of the bound-state wavefunction. However, owing to the special choice of Ro as the classical turning point " ( y o ) depends also on the radial part of the ground-state wavefunction and therefore on the energy E and the excited state PES. In this section we will discuss classical and exact quanta1 rotational state distributions for a purely model system.The excited state PES is represented by Vex(& y ) = A exp { - a [ R - R + f ( y ) -f( y = O ) ] } f ( y ) = E cos2 y (31) (32) where E controls the strength of the rotational-translational coupling. We show examples for different values of E and different equilibrium ansles ye within the ground state. The other parameters are A = 1.3 eV, a = 2 k' and R = 2 A for the excited state and Re = 2 %i for the ground state. The steepness parameters aR and a? in eqn (4) and ( 5 ) are set such that the f.w.h.m. of the corresponding Gaussians are AR = 0.2 A and Ay = 20°, respectively. The reduced mass is that of OC-S and the rotational constant is that of CO. In the left panel of fig. 1 we show J ( yo) and W ( y o ) for ye = 0 and three values of E < 0 which correspond to linear-to-bend transitions.The excitation function is a smoothly rising function of yo and is zero at yo = 0 and yo= T. It has usually two with two extrema. The particular form of J ( y o ) depends sensitively on details of individual trajectories running on the excited state PES. Under energy sudden conditions it can be shown that the excitation function is well approximated byI2 dRo( Yo) d Yo JESA( yo) = k- = ( ~ P E ) ' ' ~ ~ E cos ( y o ) sin ( y o ) (33) which qualitatively explains the behaviour observed in fig. 1. As the coupling is increased the maximum of J ( y o ) is shifted towards the highest accessible state at the particular energy, j,,,( E ) , and multiple collision effects33 become important: j ( t ) is no longer a monotonically rising function, but shows rather complicated time beha~iour.'~ Under such circumstances the ESA breaks down and becomes useless even for a qualitative interpretation.As in atom-molecule scattering9 we distinguish between the classical region if eqn (29) has real solutions, j <jmax, and the non-classical region if eqn (29) has no real solutions, j > j,,,. In the latter case the classical cross-section is identical zero. The boundary between the classical and the non-classical region, j = J,,,, is marked by the classical rainbow singularity.R. Schinke and V. Engel 117 Fig. 1. Left-hand panel: classical excitation function J ( y o ) , eqn (27) ( a ) , and weighting function W( y o ) , eqn (30)( b ) , for ye = 0" and three values of the coupling strength E in eqn (32) [(c) -0.5, ( d ) -1.0 and ( e ) -2.0 A]; the other parameters are given in the text and the energy is E = 1.3 eV.Right-hand panel: Normalized exact quantal (0) and classical (- - -) rotational distributions. In general, eqn (29) has more than one solution. However, owing to the weighting function W( yo), only one orientation angle contributes to the cross-section, i.e. the mapping between yo and j is unique. As a consequence quantal interference structures are expected to be absent. According to eqn (28) and (29) the classical cross-section, shown in the right-hand panel of fig. 1, is a direct reflection of the ground-state wavefunction onto the quantum-number axis mediated by the classical excitation func- tion J ( yo).The maximum of the distribution reflects the maximum of W( yo), as indicated by the arrows. It shifts to higher states as the anisotropy increases. The shape of the distributions depends on W ( y o ) and through eqn (29) also on the curvature of J ( y o ) . We call this mechanism the rotational reflection principle. It is a purely classical effect, although the weighting function is the proper quantum-mechanical distribution function within the electronic ground state. In fig. 2 we show similar results for different ground-state equilibrium angles ye. The anisotropy is the same in each case, i.e. the dynamics on the excited-state PES, and therefore J ( y o ) is not changed. However, the angular region which is projected out is different resulting in different final state distributions.For ye = 20" the maximum region of J ( yo) is probed, leading to a very narrow classical distribution at j , = J,,,, i e . a rotational rainbow. The classical cross-section is identical zero for rotational states beyond j , .118 Rotational Reflection Principle 60 LO 20 h g o C .I c, x LO 2 2 20 C .I c, .I X cd - .; 0 v1 0 I LO 20 n 1 c " 0 10 20 30 LO 0.5 0 Yoyo/ O pci 1 Fig. 2. As in fig. 1 but for E = -1.0 A and three equilibrium angles for the ground state, ye = ( c ) 0, ( d ) 10 and (e) 20". In ref. (14) we present many more calculations changing most of the parameters of the model system. All distributions are qualitatively similar to those in fig. 1 and 2 and can be easily interpreted in terms of the rotational reflection principle. The excitation function, which is the central quantity, can be directly interpreted in terms of individual trajectories.The rotational energy in the examples of fig. 1 and 2 is not negligible compared with the total available energy, and thus the energy-sudden approximation is in general not applicable. An exception is the case of weak coupling, e.g. F = -0.5 A in fig. 1. In order to test the simple classical calculations we compare in fig. 1 and 2 the classical with the corresponding exact close-coupling results. All CC calculations are performed with 40 basic functions, j = 0,2,4, . . . , 7 8 . Since the potential is symmetric about 7r/2 either even or odd states must be included. The agreement between the classical and the exact quantal distributions is astonish- ingly good, both qualitatively and in most cases even quantitatively.Quanta1 effects are most pronounced when the rotational rainbow region, i.e. the maximum of the excitation function is probed. Then the classical distribution becomes singular and the comparison becomes meaningless as far as the shape of the distributions is concerned. However, even in the rainbow case the classical model predicts the maximum at the correct position. The quantal distributions are finite at the rainbow, and tunnel exponentially into the non-classical region. The classical distributions are narrower than the quantal distributions, and this shortcoming is probably due to the over-simplistic choice of initialR. Schinke and V. Engel 119 conditions. Allowing for non-zero initial momenta would certainly broaden the distribu- tions.However, then the simple analytical procedure to calculate the cross-sections would be impracticable, and a Monte Carlo sampling procedure with final boxing would have to be used. At the end of this section we must stress that is is very difficult, if not impossible, to analyse the pure quantal calculations. Only the combination with the classical calculations leads to a detailed understanding of the main mechanism. On the other hand, the CC calculations are necessary in order to test the accuracy of the classical method and to correct for eventual quantal effects. The classical calculations are ca. three orders of magnitude faster than the quantal ones. Examples The main restriction in a quantitative interpretation of photodissociation experiments is the excited-state potential-energy surface (or surfaces), which in most cases is not known.It has been calculated by ab initio methods for the dissociation of water in the first absorption band.34 However, the influence of the final state interaction on the rotational state distribution is extremely weak,8 which makes this system rather 'uninter- esting' in view of the present study. In this section we will briefly discuss two examples which show nicely the rotational reflection principle and for which the corresponding PES is (partly) known. Very recently Waite and D ~ n l a p ~ ~ have calculated an excited-state PES appropriate for the photodissociation ClCN+ A o + Cl+CN( j ) . The final rotational state distribution obtained from classical trajectory calculations using random selection of the initial conditions and boxing of the final momenta agrees very nicely with experiment,*' at least as far as the location of the maximum is concerned.The width of the theoretical distribution is, however, considerably broader than observed experimentally. Since Waite and Dunlap present their results without interpretation we find it interesting to re-examine the dissociation of ClCN in view of the rotational reflection principle using the simple classical method of above and employing their calculated PES. The ground-state wavefunction of ClCN is represented by the form in eqn (3)-(5) with ye = 0" and Re = 2.255 A.35 The exponents aR and ay are adjusted to give f.w.h.m. of 0.131 A and 19", respectively.The excited-state PES is given in eqn (3.1) of ref. (35) and has been used without any changes. The total available energy is 2.083 eV.20 In fig. 3 (left-hand panel) we show the resulting excitation and weighting function. The classical distribution is shown in the right-hand panel (solid line) and clearly manifests the rotational reflection principle. Also shown is the classical distribution of ref. (35). The random 'noise' due to the Monte Carlo procedure has been averaged out. Both distributions are obviously very similar, especially with respect to the maximum. However, they disagree significantly at low rotational states, j d 40, where the prob- abilities of Waite and Dunlap are much larger. We believe that this discrepancy is not caused by our choice for the initial conditions (P,=j,=O) because all exact quantal distributions, in this work and in ref. (14), are also zero near j = 0.However, while we select the initial orientation angle yo from the quantal distribution function within the electronic ground state, Waite and Dunlap seem to select it from the corresponding classical distribution. Different weighting of the trajectories near yo = 0 will certainly lead to different distributions at low rotational states. Exact close-coupling calculations have not been performed yet because of the very high number of rotational states, j 90-100, which must be included to get convergence. However, based on the results in fig. 1 and 2 of this study and the experience made in ref. (14) we are very confident120 80 60 h LO v 4 20 0 Fig.3. Left-hand panel: Classical excitation function J ( y ) ( a ) and weighting function W( yo) ( b ) for the dissociation of ClCN. Right-hand panel: Rotational state distributions as obtained in this work (-), in fig. 5 ( a ) of ref. (35) (---) and from experiment that the simple classical calculations are reasonably accurate. Waite and Dunlap calcu- lated 5000 trajectories3' compared to 20 used in this work. Both classical calculations peak at j = 60, in perfect agreement with experiment, which is also shown in fig. 3. This agreement is remarkable because the calculations do not include a fitting parameter. However, both theoretical distributions are too broad. It would be interesting in future studies to analyse the sensitivity of the distribution with respect to features of the PES and also to calculate the total absorption spectrum, which would provide an additional test for the accuracy of the PES.The photodissociation of formaldehyde has been extensively studied in the past.36 Recently Bamford et al.19 reported CO rotational distributions following the photodis- so ciat i on H2CO+ A o --+ H2+CO(j) and all hydrogen isotope variations, at wavelengths of ca. 29 500 cm-'. The experimental CO distributions for H,CO, HDCO and D2C0 are shown in fig. 4. They are all highly inverted and symmetric about the peak centre. The peak shifts to higher states with increasing reduced mass. The dissociation of formaldehyde with ultraviolet light on the first sight is very different from direct dissociation.According to Bamford et al.19 formaldehyde is first excited to the S, state, is internally converted back into the So electronic ground state, and finally dissociates on the ground-state PES into H2 and CO. The total energy (at ca. 29 500 cm-') is of the order of the barrier height for molecular dissociation, and it is assumed that the final molecular-state distributions are entirely determined by the dynamics in the repulsive exit valley leading to H2+C0 but not by the highly excited vibrational-rotational motion on the H2C0 side of the barrier. In this sense the dissociation of formaldehyde can be interpreted as direct dissociation starting at the transition state. Since the energy transfer is small (ca. 11 % at the maximum for H2CO) we calculated the CO rotational distribution within the energy sudden limit, i.e. using eqn (16) with the following ingredients: as an angle-dependent initial wavefunction we take the wavefunction at the transition state rather than the true ground-state wavefunction appropriate for a highly excited H2C0 molecule. Since the kinetic energy above theR.Schinke and V. Engel 121 I I 1 1 I 1 0 I 1 20 30 40 50 60 70 CO rotational state Fig. 4. Theoretical (-) and experimental (0) rotational state distributions of CO following the photolysis of (a) H,CO, (b) HDCO and ( c ) D2C0. Adapted from ref. (39). transition state is very small we choose as the initial wavefunction. The y-dependence of A in eqn (16) is assumed to be negligibly weak, and the WKB scattering phase-shift is inserted as the phase +(y).” The transition-state geometry for H2C0 + H2 + CO dissociation is known from ab initio calculation^,^^ giving an angle of yts = 32.6’.The potential-energy surface within the H2 + CO exit channel is also known from ab initio calculation^^^ and has been used without any modification. The only open parameter in the model is the steepness a in eqn (34), which has been chosen to give an f.w.h.m. of 15’, which is certainly not unrealistic. The results of this (almost) parameter-free calculation are compared to experiment in fig. 4.39 The agreement is excellent: both the general shape of the distributions and the peaks are very well reproduced. In fig. 5 we show the excitation function J ( y ) for H2 + CO together with the transition-state wavefunction &,r,y( y ) .The rotational distribu- tion clearly manifests the rotational reflection principle, however, in combination with a rotational rainbow at j , = 43. Purely classical calculations would not be appropriate because the non-classical region, j > j , , is quite extended. In view of fig. 1 and 2 the distribution depends sensitively on the anisotropy of the PES and the transition-state geometry, which was explicitly tested in ref. (39). Therefore the excellent agreement with experiment underlies the accuracy of both ab initio calculations. The shift of the122 Rotational ReJection Principle I I 60 Fig. 5. ( a ) Classical excitation function J ( y) of eqn (20) and the angular part of the wavefunction at the transition state, eqn (34).The horizontal line for j = 30 illustrates the unique mapping beween y and j via eqn (20) or (29). (b) Corresponding rotational state distribution. Adapted from ref. (39). maximum for H,CO, HDCO and D2C0 is simply caused by the p1’2 dependence of J ( y ) , as predicted in eqn (33). Incidentally, we note that the H2 rotational distribution has been calculated within the same model4’ and agrees very well with rnea~urements.~~ However, in this case the anisotropy with respect to the H2 orientation angle is very weak and the pure Franck- Condon distribution dominates. Discussion and Conclusions The rotational reflection principle is a general and simple tool to interpret final rotational state distributions in direct photodissociation processes. The distributions are explained as a unique mapping of the initial bound wavefunction onto the final angular-momentum axis.The mapping is mediated by the classical function, which results from rotationally inelastic scattering on the dissociative PES. Therefore, the final distributions reflect the angular dependence of the initial wavefunction and the anisotropy of the excited state PES above the ground-state equilibrium. Measured rotational state distributions can in principle be ‘inverted’ to determine parts of the dissociative PES. However, the distribu- tions depend sensitively on many parameters, and therefore unique ‘inversion’ is ques- tionable. The rotational reflection principle is a classical effect and can be investigated by simple classical trajectory calculations.Quantal effects are important if the anisotropy is extremely weak, such that the Franck-Condon distribution is dominant ( H 2 0 in the first absorption band), or if rotational rainbows leading to classical singularities are prominent ( H2CO). Quantal interference structures are not important, because usually a single trajectory contributes to a given final rotational state. Rotationally inelastic effects in dissociation and in normal scattering are similar. However, in scattering all initial orientation angles are uniformly sampled, and thus rotational rainbows and eventually interference structures are the dominant structures. Rotational-state distributions are generally smooth and inverted. The shape depends sensitively on the details of the classical trajectories.The degree of inversion is low if the anisotropy of the dissociative PES above the ground-state equilibrium is weak andR. Schinke and K Engel 123 it is high if this anisotropy is strong. Many measured distributions are qualitatively similar to those predicted here and in ref. (14). However, in each case one should first determine the contribution of the pure Franck-Condon distribution before inelastic effects in the dissociation channel are investigated. This is particularly important if the degree of inversion is low and if many initial states are prepared, as in a bulk experiment for example. The rotational reflection principle has definitely been observed in the dissociation of ClCN and H2C0. In both cases the dissociative surface is known to a reasonable extent and the theoretical predictions agree quantitatively very well with the measure- ment.The dissociation of formaldehyde is particularly interesting because it shows the applicability of the reflection principle in unimolecular reactions. In such cases the wavefunction as the transition state is probed rather than the initial wavefunction before the excitation process. If the transition state is well localized, distributions as discussed in this article might be expected. Finally we note that the inelastic reflection principle can also be found in vibrational distributions. The dissociation of CF,I + CF3 + I 42 might eventually be an example for the vibrational reflection principle.43 References 1 M. B. Robin, Higher Excitated States of Polyatomic Molecules (Academic Press, New York, 1978).2 H. 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Golzenleuchter, K-H. Gericke and F. J. Comes, Chem. Phys., 1984, 89, 93. 17 0. Benoist D'Azy, F. Lahmani, C. Lardeux and D. Solgadi, Chem. Phys., 1985,94, 247. 18 N. Sivakumar, I. Burak, W-Y. Cheung, P. L. Houston, and J. W. Hepburn, J. Phys. Chem., 1985,89,3609. 19 D. J. Bamford, S. V. Filseth, M. F. Foltz, J. W. Hepburn and C. B. Moore, J. Chem. Phys., 1985,82,3032. 20 J. B. Halpern and W. H. Jackson, J. Phys. Chem., 1982, 86, 3528. 21 M. Dubs, U. Briihlmann and J. R. Huber, J. Chem. Phys., 1986, 84, 3106. 22 M. Shapiro and R. Bersohn, Annu. Rev. Phys. Chem., 1982, 33, 409. 23 G. G. Baht-Kurti and M. Shapiro, Chem. Phys., 1981, 61, 137; Chem. Phys., 1982, 72, 456. 24 Y. B. Band, K. F. Freed and D. J. Kouri, J. Chem. Phys., 1981, 74, 4380. 25 E. Segev and M. Shapiro, J. Chem. Phys., 1983, 78, 4969. 36 C. B. Moore and J. C. Weishaar, Annu. Rev. Phys. Chem., 1983, 34, 31. 27 0. Atabek, J. A. Beswick and G. Delgado-Barrio, J. Chem. Phys., 1985, 83, 2954. 28 D. Secrest, J. Chem. 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Phys., 42 G. N. A. van Veen, T. Baller, A. E. de Vries and M. Shapiro, J. Chern. Phys., 1985, 93, 277. 43 S. Hennig, V. Engel and R. Schinke, J. Chem. Phys., 1986, 84, 5444. 1985, 83, 4476. Received 30th May, 1986

ISSN:0301-7249    

DOI:10.1039/DC9868200111

出版商:RSC    

年代:1986

数据来源: RSC