Metastable States in Some Transient Molecules by High-resolution Laser Spectroscopy BY EIZI HIROTA Institute for Molecular Science, Okazaki 444, Japan Received 26th November, 1980 The A”’A” (050) t %’A’ (000) band of the chlorocarbene molecule was observed by laser excitation spectroscopy. For the upper (050) state only one series Jo,J of rotational levels ( J = 0-25) was identified. The series was found to be heavily perturbed at J = 8-10; two lines were observed for each of these three J values. The perturbed spectral lines were very susceptible to an external mag- netic field; the observed Zeeman coefficients were as large as 1.0 GHz T-’ for the J‘ = 9 lines. The origin of the perturbation is discussed, based upon the observed term values and Zeeman effects. Two models, i.e.electronic Coriolis interaction and singlet-triplet mixing, were examined in detail ; the spectra calculated assuming the latter mechanism were found to reproduce qualitatively the observed spectra. It has been realized that metastable electronic states having multiplicities different from that of the ground state often play unique roles in chemical reactions. Triplet states have also attracted much attention in the field of molecular science, because molecules excited to higher electronic states are often transferred to these triplet states by the so-called intersystem crossing. For simple molecules, however, a very limited amount of data has been accumulated on low-lying metastable states, especi- ally on the excitation energies of such states, because spin conservation gives us little chance to observe transitions between two states of different multiplicities.Herzberg and Herzberg’ have established that the ‘Ag state of the oxygen molecule is located at 7918.1 cm-’ above the 3Cg- ground state. However, it is only quite recently that the corresponding states of SO (‘A), and S , (‘Ag)3 were located with respect to the ground states. For another series of molecules NX (X = F, C1 and Br) the location of the ‘A state has been established only for NF.4 The detection of metastable states, particularly in transient molecules, is one of the most challenging problems for high-resolution laser spectroscopy; it obviously requires high sensitivity, and yet high resolution is necessary for an unambiguous identification of the detected state, or even of the molecular species.Although the carbenes play extremely important roles in chemical reactions, spectroscopic data on their metastable states have been very fragmentary. For the parent species, the methy- lene radical CH,, both singlet-singlet and triplet-triplet transitions have been re- ported, but the separation between the singlet and triplet manifolds has long been the subject of controversy; even two recent values for the &‘A, and T3B1 separation (2203 & 280 cm-l and 2833 are still subject to large uncertainties and do not agree well with each other. In contrast to CH2, the two halogenocarbenes, HCF and HCCI, are known to have singlet ground ~ t a t e s , ~ and Merer and Travis have analysed the Z’A” t z l A ’ transitions observed using a 35 ft (10.7 m) grating ~pectrograph.**~ However, nothing has been reported on the lowest triplet states.We have recently repeated the observation of the x+- 3 transitions of both HCF’O and HCC1,l’ by exciting them with a dye laser of high spectral purity. The resolution we achieved, 28088 HCCl LASER SPECTRA although still Doppler limited, is higher than that of Merer and Travis, and may un- ravel the details of perturbations reported in the previous paper^.^^^ Because low- lying triplet states may cause such perturbations, analyses of perturbed spectra may give us a clue to the nature and position of the unknown triplet states. In the present work we concentrated mainly on the HCCl A’A” (050) +- X’A’ (000) band, because this band showed one of the most conspicuous perturbations.EXPERIMENTAL The experimental set-up we used in observing laser excitation spectra was described in detail in a previous paper.12 A Varian 15 in. (0.38 m) magnet, which delivers a magnetic field up to 2.3 T, was employed in measuring Zeeman effects of the observed spectra. Optics of telescopic configuration focused the fluorescence light onto a photomultiplier placed out- side the electromagnet, Polarization of the laser light was chosen such that the AM = 0 and AM = f l selection rules were satisfied, respectively, for Q and P branch transitions. This choice is most convenient, because larger JMJJ components showing larger Zeeman effects appear most strongly. RESULTS Just as Merer and Travis found,g we also could identify only transitions that ter- In addition to the pP1, PQ1, and By using minated in one of the Jo,J levels in the 3 (050) state.PR1 branches, two axis-switching branches “Qo and O R 2 were observed. TABLE TE TERM VALUES AND MOLECULAR CONSTANTS OF THE J I A ” (050) Jo,J LEVELS OF HCCl (IN cm-’) J obs.” obs. -calc. J obs.’ obs. - calc. 1L 2L 3L 4L 5L 6L 7L 8L 8U 1.210 3.628 7.255 12.086 18.130 25.377 33.817 43.425 43.954 0.000 - 0.001 -0.002 - 0.006 - 0.004 -0.001 -0.000 - 0.004 - 0.01 5 9L 9u 10L 1ou 11u 12u 13U 14U 15U 54.188 54.706 65.980 66.681 79.928 94.41 3 110.1 13 127.023 145.130 0.022 0.025 -0.013 - 0,000 - 0.009 - 0.005 0.000 0.005 - 0.002 parameters in eqn (16)b parameters in eqn (6)b B 0.596 52 (53) B 0.596 52 (53) R 0.000 000 006 (11) IT 0.000 000 006 (11) SE 1.464 (68) SE 1.549 (63) E‘ 0.250 9 (59) U 0.027 12 (62) b -0.000 005 2 (35) D -0.000 005 2 (36) 6 8 -0.017 60 (69) SB -0.017 61 (70) a Uncertainties are 0.005 cm-’ or less.Values in parentheses denote standard errors and apply to the last digits of the constants. ground-state parameters determined from ground-state combination differences, the upper-state term values1’ reproduced in table I were calculated. As shown there we observed two J’ = 9 lines of nearly equal intensities, and also one satellite each for J’ = 8 and 10. These observations clearly indicate that, with increasing J , a series of per-E . HIROTA 89 turbing levels approaches the Jo,s series from the high-frequency side, crosses the latter near J = 9, and goes to lower frequencies.Then we examined the effects of the magnetic field on the observed spectra; we inspected only the pP, and "Q1 branches carefully, because they are the strongest among the observed branches and free from overlapping. The two J' = 9 lines were found to be split into two groups of unresolved Zeeman components for magnetic fields higher than 0.8 T, and we could follow the peaks of the two groups up to ca. 2 T. Fig. 1 illustrates the Zeeman patterns observed for the two J' = 9 Q and P lines. The T 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . o 1 . 2 1 . 4 1 . 6 1 . 8 Q P L T 0.0 0.2 0 . 4 0 . 6 0 . 8 1.0 1 . 2 1 . 4 Q P U FIG. I .-Observed Zeeman patterns for the "Ql(9) and pPI(lO) transitions of the HCC1A""A" (050)t Z'A' (000) band. The magnetic field is varied from 0 (top) to 1.8 or 2.0 T (bottom).The abscissa scale is 0.049 983 cm-'/division. The higher- and lower-frequency lines are designated as U and L. higher-frequency lines showed a marked asymmetry in the Zeeman pattern; the lower Zeeman components move to lower frequencies much faster than the upper Zeeman components move to higher frequencies. The asymmetry is much smaller for the lower-frequency J ' = 9 lines. The Zeeman splitting between the two groups of components is ca. 1.5 GHz at 1 T. For J ' = 8 and 10 the Zeeman effects could be examined only for the main lines; the satellites were too weak to record their Zeeman " broadened '' spectral patterns. The J ' = 8 lines showed some peculiar Zecman shifts at ca. 0.8 T ; the Zeeman components jumped to higher frequency by ca.0.02 cm-'. After 1 T they stayed at nearly the same frequency without showing any appreciable further broadening. The Zeeman effects of the J' = 10 lines were found to be even smaller; the Zeeman components moved to lower frequencies as the mag- netic field was increased. The Zeeman coefficients were ca. -0.2 GHz T-', an order of magnitude smaller than those of the J' = 9 lines.90 HCCl LASER SPECTRA The analysis was started by fitting the observed term values to the followingex- pression : F(J) = FJ(J + 1) + F2J2 ( J + 1)2 + F3J3(J + 1)3 +h* I!= [fo +flJ(J + 1) + f 2 J 2 ( J + 1>”13, (1) where the + and - signs apply, respectively, to the higher- and lower-frequency levels with the same J value (referred to as J U and JL). The energy origin was taken to be at the J = OL level, because the observed term values were given relative to this level.The observed term values of J up to 15 were thus analysed by a least-squares method, and were well-reproduced by eqn (1) except for J = 8U, 9L, 9U and lOL, as listed in table 1. A pair-wise energy-level interaction model, as exemplified by eqn (l), is obviously insufficient to account for the observed Zeeman effects, because both of the J’ = 9 levels showed Zeeman patterns that moved more to lower frequency than to higher frequency with increasing magnetic field. Eqn (1) comprises two models to be discussed later. DISCUSSION Perturbations in the A’A’’ excited electronic state can be ascribed to one or more of the following three mechanisms: (i) interactions with other vibrational states with- in the manifold of the same electronic state, the $A” state in the present case (here the interaction is of either Coriolis or Fermi type), (ii) interactions with highly excited vibrational states associated with the ground electronic state, ZlA’, and (iii) inter- actions with higher vibrational states of the lowest triplet state, G3A”.We may easily eliminate the first mechanism, because it cannot explain the observed Zeeman effects. As discussed by Merer and T r a v i ~ , ~ the HCCl molecule is isoelectronic with HNO, and thus we expect one lA’ and one ’A” as the low-lying singlet states which are derived from a ‘A state in the limit of a linear configuration. Therefore, when the two states come close, we might have a large magnetic moment due to the orbital motion of the electron.This is the mechanism (ii) mentioned above, which is also referred to as an electronic Coriolis interaction. The two states interact with each other by the per- turbing Hamiltonian : H’ = -2CR,J,L,, 9 which is derived by expanding the rotational Hamiltonian HR = zRg(Jg - L,)2. In eqn (2) R, denotes a rotational constant, Jg and L, the total and orbital angular mo- menta, respectively, and g the gth principal axis. The Zeeman Hamiltonian takes the form 9 where 2 denotes a space-fixed axis taken parallel to the applied external magnetic field H, g , the g factor for a magnetic moment associated with the orbital motion, .B, the Bohr magneton, and mZg a direction cosine. Because all vibronic states in the A manifold belong to A” symmetry and those in 8 to A‘, only L, and Lb have non-zero matrix elements between 2 and 8.Since the interaction takes place even for zero magnetic field, we need to retain only AJ = 0 matrix elements of QZg, in so far as weE. HIROTA 91 consider only one perturbing level for each perturbed level. proximation the interaction matrix element is given by In a symmetric-top ap- + (g,P/2)(~IL,lJ)[J(J + 1) - K(K ic l)l+M/H/[J(J + 1)1 ( 5 ) for AK = A l , where A, B and C are the rotational constants and (f( . . . 12) denotes a vibronic matrix element. Rotational functions with K, = even are A' and those with K, = odd are A". Therefore, we may list candidates for the perturbing levels as follows: perturbed level in 2 80,s 90,9 100,lO Comparison of these combinations with eqn (4) and (5) indicates that the most prob- able candidate for the perturbing level is J1,J-l.Again using a symmetric-top approxi- mation the term values including Zeeman energies are given by the following matrix form: F(J) = BJ(J + 1 ) + DJ2(J + 1)2 + HJ3(J + + 6E/2 I? (6) SE/2 + SBJ(J + 1)/2, U[J(J + l)]" + U,M,H/[J(J + 1)]* +[ symmetric, - 6E/2 - SBJ(J + 1)/2 where B denotes the average of the effective rotational constants of the two interacting states, i.e. B = (Bx + B A ) / 2 , SB = B, - BA, 6E = Exo - Eao, where Exo and EAo are energies of the two unperturbed series, f J1,j-1 and 2 Jo,j, in the limit of J = 0 and b and are higher-order terms representing contributions from molecular asymmetry and centrifugal distortion effects. The two constants in the off-diagonal position are given by and The term values in the limit of weak field thus become F(J) = BJ(J + 1) + DJ2(J + 1)2 + HJ3(J + 1)3 + 6E/2 j-{[SE + SBJ(J + 1)]'/4 + U2J(J + 1) + 2UU,M,H])*, (9) where the + and - signs apply, respectively, to 2 Jl,J-l and 2 J0.j.An analysis using eqn (1) mentioned earlier gave the parameters in eqn (9), which are listed in table 1 . The Zeeman coefficient in the weak-field limit, i.e., -J(UU,/A)M,H, is obtained by expanding the square root in eqn (9), where A2 = [SE + SBJ(J + 1)12/4 + UzJ(J + 1). (10)92 HCCl LASER SPECTRA The Zeeman effect observed for J' = 9, ca. 1.0 GHz T-I, thus requires that I(R(L,IZ)l - 0.10. On the other hand, from the observed U value, 0.027 12 (62) cm-', we obtain I(fIBL,JZ)I = 0.019 18 (43) cm-'.If we may take the B constant of about 0.6 cm-I out of the integral which seems rea- sonable for a strong (vertical) vibrational transition, the vibronic integral of L, be- comes I (f ILb IX) I - 0.032, (12) which is smaller than that [eqn (Il)] obtained from the Zeeman effect by a factor of three. Furthermore, eqn (6) requires that the Zeeman effects of the higher- and lower-frequency lines be of the same magnitude, but opposite in sign. This predic- tion does not agree with the observation that negative Zceman effects predominate for both J' = 9 lines. Eqn (6) also fails in reproducing the Zeeman effects observed for the J' = 8 and 10. It is obvious that a pair-level interaction model such as mechanism (ii) cannot ex- plain the observed Zeeman effects of the J' = 9 levels. Mechanism (iii), singlet- triplet mixing, does better.In this scheme the Zeeman effect mainly arises from the magnetic moment associated with the electron spin S = 1 in the triplet state. The Zeeman Hamiltonian is thus given by Hz = -gsPSzH = -gsPMsK (1 3) whereg, isclose to the free-electron g factor, 2.0023, and Sz and Ms denote, respectively, the 2 component of the spin angular momentum operator and its eigenvalue. The Zeeman energy in the limit of weak magnetic field is given by Ez = -gsP(Ms)H, (14) where ( M s ) = ([J(J + 1) - S(S + 1) - N(N + 1)1,"2J(J + 1)]>MJ- (15) A coupling scheme J = N + S is used, where N denotes the angular momentum of the molecular rotation. The average value of M, is thus equal to M,/Jfor N = J - 1, M,/[J(J + l)] for N = J , and -MJ/(J + 1) for N = J 4- 1, in the case of S = 1.For a near-degenerate case such as the J' = 9 levels, the Zeeman energy is divided equally between the two levels. Therefore, the Zeeman coefficient is 13-14 GHz T-l for N = J & 1 and 1.4 GHz T-l for N = J . The last case reproduces well the ob- served Zeeman coefficient of J ' = 9. In the following we will thus assume N = J for the perturbing triplet levels. Following Hougen's discussion'3 of the symmetry of the spin functions, we may choose candidates for the perturbing levels among rotational levels in the ii3A" state as follows: perturbed level in 2 8 0 . 8 90.9 ~ 0 0 , I O According to Stevens and Brand,14 first-order or direct spin-orbit interaction is allowed for HCCl, because of its low symmetry.We will refer to this interaction as (11. AsE . HIROTA 93 second-order interactions they have discussed the spin-orbit and orbital-rotation coupling [referred to as (2.1)] and spin-orbit and vibronic coupling [referred to as (2.2)]. The selection rules for (1) and (2.2) are AN = 0, & 1, AK = 0, & 1 , and those for (2.1) are AN = 0, & l , AK = 0, &2. An exact selection rule for the singlet- triplet interaction is AJ = 0 and, as the observed Zeeman effects indicate, N is equal to J for the perturbing triplet levels. Therefore, we arrive at a selection rule AN = 0. Because the perturbed levels in 2, have K (i.e. K,) nearly equal to zero, AK = 0 matrix elements, which are proportional to K, will be small. The AN = 0 and AK = & I interaction, which primarily couples 2 Jo,J with a" Jl,J, gives a matrix element that is nearly independent ofJ. The term values are then expressed in the following matrix form: We will designate it as €'.F ( J ) = BJ(J + 1) i- D J ~ J t i y + R J ~ ( J + 113 + [ ( m / 4 ) + EQI+ I, +[""2 + S m J + 1)/2, E' C.C., - 6€/2 - GBJ(J + 1)/2 where the constants are defined in a way similar to the case of eqn (6), except that the ground-state x is replaced by a". The parameters obtained by the least-squares analysis are included in table 1. Finally the AN = 0 and AK = A2 interaction will mainly couple A J0,j with a" J2,J-2 and gives a matrix element nearly proportional to [(J - I)(J -f 2)]+. Therefore, the term values will take a form that is very similar to the case of the electronic Coriolis interaction, eqn (6).To calculate the Zeeman effects we have to enlarge the 2 x 2 matrix of eqn (16) so as to take into account the Zeeman interactions between the J = N and J = N 1 levels of the triplet state. (ln the following we fix the N value at No.) The J = No 1, N = No levels (called F, and F3) are mixed by the spin-spin interaction with J = No &- I , N == No $r 2, so that the Zeeman effects must be modified as follows: ( J = No f l(H,(J = No t 1) = g,p[cos20,+,/(N + 1) - sin20,+,/(N + 2)]M,H, ( J = No - lIH,IJ = No - 1) = - g,P[cos20,_,/N - sin20,-,/(N - l)]MJH, ( J = No + 1 IHZ/J = No) = - g,/J[N/(N -1 I)] { [ ( N + 1)' - MJ2I/"(2N + 1)]>".os 0 N + 1 , {(N' - MJ2)/[(N + 1)(2N + I)]>+:cos ON-1, ( J = No/Hz/J = No - 1) = - gSP[(N + 1)/N] where No has been replaced by N in the right-hand sides for simplicity, and 0, is given by 0, = (1/2)tan-'( Y / X ) , (17) with X = B(2N + 1) - (3/2)~[1/(2N + l)], Y = 3a[N(N + 1)]*/(2N + l), and o! denoting the spin--spin interaction constant.more familiar notation, corresponds to ( 3 / 2 ) ~ . ] Fl - F2 separations were estimated from [Note that A, which may be a For simplicity, the F3 - Fz and and F3 - F2 = - [ N / ( 2 N - I)]. Fl - F2 = - [ ( N + 1)/(2N + 3 ) ] ~94 HCCl LASER SPECTRA [see eqn (23) of Raynes]15. Other spin-spin and spin-rotation interaction terms have been neglected. It was also assumed that fluorescence intensities are proportional to the amount of singlet character in the resulting levels. Because the MJ components were not resolved, each component was Doppler-broadened using a calculated f.w.h.m. of 0.029 cm'l and intensities of neighbouring lines were summed to give the cal- culated patterns in fig. 2. 1 0.0 0-2 0.4 0.6 Q P L Q P U F-G. 2.-Calculated Zeeman patterns for the "Q1 (9) and pP1 (10) transitions of the HCCl xlA" (050)t 2"A' (000) band, which are to be compared with the observed patterns of fig. 1. The observed Zeeman effects of J' = 9 require the I;; and F3 levels to be placed above the F2 level interacting with the singlet level. This means that the spin-spin coupling constant a must be negative, although the 2 constant of NCl, an isoelectronic molecule, is + 1 .776 cm-1.16 The molecular constants listed in table 1 lead us to expect that theX9,,, level is higher than the a" 91,9 or 92,7 level when the perturbation is absent ; the unperturbed separation between a" 91.9 or 92,7 and 29,,, is calculated to be -0.120 or -0.036 cm-l, although the standard errors, 0.130 or 0.126 crn-l, are larger than their respective calculated values.On the other hand, the observed fluorescence in- tensity is obviously stronger for J' = 9L than for J' = 9U, and the observed Zeeman patterns shown in fig. 1 are better reproduced with a positive unperturbed separation than with a negative separation. The spectra shown in fig. 2, which are to be com- pared with the observed spectra of fig. 1, were obtained using an a of -7 cm-I and an unperturbed separation of +0.165 cm-l. The Zeeman effect of the J' = 9L level is fairly well-reproduced, but the agreement is less satisfactory for the J' = 9U level.The remaining discrepancies, including those in the least-squares fitting for the J = 8U, 9L, 9U and 1OL levels mentioned earlier, may indicate the presence of otherE . HIROTA 95 perturbing levels. The present model also fails to explain the Zeeman effects observed for J' = 8 and 10, which thus still remain to be explained. The author thanks Dr. M. Kakimoto and Mr. Y. Endo for taking laser excitation He is also grateful to Jon T. Hougen for critical reading of the Calculations in the present work were carried out at the Computer spectra of HCCl. manuscript. Center of the Institute for Molecular Science. L. Herzberg and G. Herzberg, Astrophys. J., 1947, 105, 353. ' I. Barnes, K. H. Becker and E. H. Fink, Chem. Phys. Lett., 1979,67, 310. I. Barnes, K. H. Becker and E. H. Fink, Chem. Phys. Lett., 1979, 67, 314. K. P. Huber and G. 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