摘要:

Zeeman Effect of Oriented Molecules in Solids at Low Temperatures* BY ROBIN M. HOCHSTRASSER AND TIEN-SUNG LIN Laboratory for Research on the Structure of Matter and Dept. of Chemistry The University of Pennsylvania Philadelphia, Pennsylvania 19 104 Received 29th September 1969 An account is given of the use of the optical Zeeman effect in determining the zero-field splitting parameters and the signs of spin-orbit interaction matrix elements for triplet states of organic mole-cules. The results for pyrazine pyrimidine and s-triazine are used to exemplify the effects. These experiments involve high resolution studies of the spectra of single crystals at 4.2 K in polarized light and in magnetic fields ranging from 6 to 50 kG. The detailed study of the electronic spectra of farily large organic molecules in magnetic fields is dependent upon the availability of magnetic fields that are high enough to cause spectral effects that are larger than the linewidths in absorption and emission transitions.The linewidths in very low-temperature condensed-phase spectra are frequently as sharp as 0.5 cm-l and seldom as broad as 5 cm-'. For g = 2 the Zeeman energy is about 0.2 cm-l/kG so in order to obtain well resolved spectra one requires fields in the range 20-100 kG. The interpretation of Zeeman effects of oriented molecules is straightforward for very high fields. At lower fields the zero-field magnetic anisotropy of the state under study will perturb the conventional high-field Zeeman patterns. Although the zero-field splittings (ZFS) for organic molecules are normally smaller than the line-widths in the optical spectra it is possible to observe perturbations on the Zeeman levels when gPH is as large as approximately 10 x ZFS.Under these circumstances the ZFS can be determined even although the splittings cannot be directly observed. This means that we are able to measure the ZFS for any excited state that displays absorption lines that can be split in fields of less than ca. 20 kG. The information obtained from the high field Zeeman studies of singlet-triplet transitions is focused upon the spin symmetry of the substates responsible for the electric dipole transitions. In complex molecules we find that mainly one of the zero-field substates is involved in the electronic transition but in certain cases two of the substates are active.When this is the case it becomes possible to determine experimentally the relative signs of the two spin-orbit coupling matrix elements. The purpose of this paper is to present a summary of experimental results aimed at the two molecular structural features mentioned above. In particular the paper will refer to results for the triplet nn* states of the diazines-pyrazine (I) and pyrimidine (11) and for s-triazine (111). * This research is supported in part by the Advanced Research Projects Agency Contract SD-69, and in part by a U.S. Department of Health Grant G.M.-12592-05. 10 ROBIN M . HOCHSTRASSER AND TIEN-SUNG LIN 101 ZERO-FIELD SPLITTINGS The lowest triplet state of (I) and (11) are nn* states in which a non-bonding electron has been promoted into the n* system.The electronic distribution in the excited state is not known although it was suggested that considerable reorganization of charge occurs on excitation. We confirmed this for pyrimidine by showing that the electric dipole moment in the 3nn* state is only 0.88 D less than in the ground state (po = 2.2 D) whereas a localized orbital description predicts that the dipole moment should actually reverse direction in the excited state. Contrary to earlier assump-tions 6-8 the lowest triplet state of (111) is 3A; nn* type.5 So these three molecules represent interesting nn* prototypes. With pyrazine a phosphorescence modulation e.p.r. experiment has provided values of the ZFS parameters and we therefore have a check on the optical method... .. .. rx Y FIG. l.-Axis designations and polar vector labels for pyrazine (I) pyrimidine (II) and s-triazine 0. The method used lo depends on the fact that at low applied magnetic fields H,, the magnetic substates are not exact eigenstates of S,. Instead the three substates are each different superpositions of the zero-field spin states crx,~,.,~ referred to the principal axes of the magnetic anisotropy. In an ideal experiment the direction y is chosen to be perpendicular to the direction of one of the axial vectors R,,R,,R,. The one chosen is that which has the same transformation properties as the spin-state that carries the electric dipole strength of the transition. For the purpose of discussion we assume this to be the y direction (as it is in fact for (I).With this arrange-ment the field can be anywhere in the plane H 9 = 0. The high field H Zeeman pattern consists of two lines of equal strength corresponding to transitions to spin states 2-*(a,,+io,) and 2-*(aY-iaz). At lower fields the Zeeman pattern still consists of two lines but the spin functions associated with each upper state are not the same. The actual spin functions give a diagonal representation of the Hamil-tonian : The matrix (a I Z I aj) is easily found and for the ideal experiment SYax = 0 so only the a, and o, states are mixed. Since only o, carries the property that enables effective spin-orbit interaction to occur the ratio of the intensity of transitions into the upper to those into lower spin substate is of the form : -+ 2 = g ~ H S - X S ~ - Y S ~ - Z S ~ .(1) r+/r- = [(I +a)/(i -412. (2 102 ZEEMAN EFFECT OF ORIENTED MOLECULES At fields for which gPH2 10 D the coefficient is given by perturbation theory as a = (2gPH)-'(Y-Z). (3) The ratio in eqn. (2) is greater or less than unity depending upon the sign of a. There-fore the ordering of the zero-field substates is readily determined by this method. In eqn (1) and (3) X Y and 2 are the principal values of the S D S tensor where D includes spin-spin dipolar coupling and spin-orbi t interaction. EXCITON EFFECTS The Zeeman experiments are most readily done with pure crystals since in that way the orientations are known and the very weak singlet-triplet transitions cf = lo-' -lo-") can be easily seen in single crystals having a length of ca.0.1-1 cm. However, the intermolecular interactions (exciton effects) may be larger than the ZFS and often as much as 1-20 ~ r n - ' . l ~ - ' ~ Under these circumstances only the triplet exciton states can be observed optically and the associated spin is quantized in the crystal symmetry directions i.e. only the average molecular anisotropies are observable. In this case the appropriate Hamiltonian is where A B and C are the principal magnetic directions in the crystal. The conversion between A B and C and X Y and 2 is just a geometric averaging that is dependent upon the principal values. Since the location of the principal axes of a crystal having reasonably high symmetry presents no experimental problem it turns out to be advantageous if the transition of interest shows an exciton splitting.Hexciton = gpHySy- AS - BS," - CS,? (4) LOW-FIELD RESULTS FOR THE AZINES The results are summarized in table 1. The assignments are from high-field Zeeman-effect studies and those for pyrazine and pyrimidine are in agreement with previous work.2*1s Pyrazine crystals show an exciton splitting of 6.4 cm-l and the results refer to the low energy component. All the electric dipole activity of the lower exciton component is in the cr spin state while the transition is polarized along the a-axis which is parallel to the N-N axis of pyrazine.16 Fig la shows a weak field spectrum of the lowest exciton component of a pyrazine crystal. TABLE 1 0,O energy state (cm-1) assignment f (a) DeXpt (cm-1) D(b) 5s (calc.) pyrazine 26 247.6 3B3u(n71*) 8 x lo-' +0.3 +0.31 pyrimidine 28 907.6 3BI ( l t ~ *) 4 x lo-' +0.045 +0.16 +0.14 s-triazine 28 935.0 3Al;(n7c*) 1 x 10-9 - 0.05 - 0.08 Thef-number is an estimate based on relative crystal thicknesses required for the same absorption as observed in pyrazine for which an f-number as quoted has been measured from solution spectra.l The numbers in the table are probably upper limits.b We are indebted to 0. Zamami-Khamiri and H. F. Hameka for providing us with numerical solutions via the Fourier convolution method for some integrals. Pyrimidine crystals show no factor group splitting of the singlet triplet transition and a weak field spectrum is shown in fig. 16. The high field spectra of pyrimidine are of special interest and are discussed below.The experimental ZFS result is subject to an uncertainty due to our lack of knowledge of the precise spin couplin ROBIN M . HOCHSTRASSER AND TIEN-SUNG LIN 103 scheme. One result as given presumes that the intermolecular interaction is vanishingly small. The other extreme which would have the exciton interaction much larger than the ZFS would lead to Dexpt = 0.16 cm-l. The triazine crystal is nearly uniaxial 17*18 and has particularly simple spectra; no exciton splitting is observed but the magnetic axes of the crystal nearly coincide with those of the molecule. The energy separation between the pair a, a, and a (the active I I 26245'0 2 6 2 50.0 I . I 2 8 905.0 289 10.0 8KG ,J' , 289300 28935'0 28940'0 wavenumber (an- I) FIG. 2 . L o w field Zeeman spectra of pyrazine (upper) pyrimidine (middle) and s-triazine (lower).These spectra refer to single crystals at 4.2 K with the magnetic field directed along the following crystallographic axes. For pyrazine the b-axis; for pyrimidine the b-axis; and for s-triazine, perpendicular to c. state) is very small as evidenced by the very slight asymmetry in the spectra even at very low fields (fig. lc). However the spectra clearly show that oz is the highest energy spin component illustrating how easy it is to determine the sign of D by optical methods. COMPARISON OF THEORY AND EXPERIMENT The experimental values in table 1 have an uncertainty of about 15 % and the number for triazine could be less than that quoted by as much as 20 %. These uncertainties are based on a 5 % uncertainty in the intensity.However there is no question that for pyrimidine and triazine the calculated and experimental results are more at variance than suggested by comparisons in table 1. D, is the spin-spin interaction computed at the nitrogen atoms assuming that the lone pairs are in sp2 hybrid orbitals in the ground and excited states. These calculations give the correct ordering of the The fault lies with the method of calculation 104 ZEEMAN EFFECT OF ORIENTED MOLECULES spin states in every case. However rough estimates of the second order spin-orbit interaction energy based on calculations on observed transition probabilities and on our knowledge of the symmetry of nearby states suggests that the spin-orbit energy contributions to the zero-field splitting are significant in all three cases.Perhaps for pyrazine the spin-orbit energy and the two-centre spin-spin interaction almost cancel, thus accounting for the fortuitous agreement between Dabs and Dss. A further possibility is that the sp2 model for N-lone pairs is not correct for excited nn* states. A knowledge of gxx gyy and gzz would greatly assist in answering these questions. SIGNS OF SPIN-ORBIT INTERACTION MATRIX ELEMENTS Anticipating the high magnetic field experiments eqn (5) gives the form of the transition moment amplitude for a singlet-triplet transition for the rth (r = 0 f 1) magnetic substate of the excited level i : -+ mor = ax$ + ayr9 + azt-2 ( 5 ) where ax a and a are the magnitudes of the moments along x y and z induced by spin-orbit interaction.The intensity for absorption of light polarized in a space fixed direction; is of the form, For a wide range of organic molecular types one of the coefficients in (9 say y is much larger than the other two in which case Ibr = I ayr I cos2 8,. However if one of the other coefficients say z is also non-zero the intensity becomes The intensity is therefore determined by constructive or destructive interference of the transition moment amplitudes. The effect of this interference is strongly to modify the dependence of the Zeeman pattern (i.e. Ibo Ibl) on the direction 6 even when I a, I is much smaller than I ay I '. The measurement of for different directions b then leads to the relative signs of the complex numbers ayz and azy-the corresponding matrix elements for the field free spin states a and ay.The geometric forms of azr etc. have been tabulated l9 previously, An interesting aspect of this effect concerns the interaction of the system with circularly polarized light. For the case axrXaz,wO for all r the triplet state always interacts identically with right and left circularly polarized light. However in the case described by eqn. (7) for light propagating along the x-axis and with a magnetic field along the x-axis the moments for transitions to m = f 1 states becomes Ibr = I a y r cos &,y+ cos ebz I 'a (7) 4 m f 1 = [(p k v)(2 + i9) + (p J v)(2 - i9)I. (8) It follows that transitions to m = 1 states at high field will involve different cross-sections for the absorption of left and right circularly polarized light.If p = v the system behaves like an L = 1 state the m = +1 state now interacting with only one type of circular polarization. p and v are the spin-orbit expansion coefflcients exclusive of spin quantities but including the magnitude of the transition moment to the mixing singlet state; i.e., + P = CAE&!<To I Hs0 I ST> I mzi I (9) i The sum is over all singlet states Sf having 2 polarization with transition moment &, separated from the triplet state T~J! by AES1. These results imply that even in systems where all the angular momentum is effectively quenched there exists the possibility o ROBIN M . HOCHSTRASSER AND TIEN-SUNG L I N 105 observing strong (pseudo-A-type) magnetic circular dichroism. In addition they imply that magnetic optical rotation should be observed to a certain degree in all singlet triplet transitions even in molecules having low symmetry.The interference between transition moment amplitudes is displayed in the high-field Zeeman spectra of pyrimidine l6 shown in fig. 3. The large effect caused by FIG. 3.-Schematic summary of the high field Zeeman spectra of the pyrimidine crystal at 4.2K. The subscripts refer to the orthorhombic a b and c axes of the pyrimidine crystal. E and H refer to the directions of the electric vector of the absorbed light and of the external magnetic field. changing the direction of the electric vector is accounted for by a very small amount of activity in the a state. In fact 93 % of the total intensity corresponds to the Ta,+So transition and only 7 % to Ta,-+So.The experiments show that the matrix elements of the orbital angular momentum coupling T(aJ to y-polarized singlets has opposite sign to those coupling T(a,) to z-polarized singlets. The result agrees with a theoretical analysis that utilizes nitrogen one-centre terms of the form <P,(n) I L I px(n)> and (pz(n) I L 1 px(n)) for the y and z polarized intensity respectively The unshared pairs n are presumed to be in hybrid sp2 0 z ) orbitals. L. Goodman and M. Kasha J. Mol. Spectr. 1958 2 58. J. E. Parkin and K. K. Innes J. Mol. Spectr. 1965 15,407. V. G. Krishna and L. Goodman J. Chem. Phys. 1962,36,2217. H. Baba L. Goodman and P. C. Valenti J. Amer. Chem. SOC. 1966,88,5410. Robin M. Hochstrasser and T. S. Lin in course of publication. J. P. Paris R. C. Hirt and R. G. Schmitt J. Chem. Phys. 1961,34,1851. J. S. Brinen and L. Goodman J . Chem. Phys. 1961 35 1219. M. Sharnoff Chem. Phys. Letters 1968 2,498. * K. K. Innes J. P. Byrne and I. G. Ross J. Mol. Spectr. 1967 22 125. lo Robin M. Hochstrasser and T. S. Lin J. Chem. Phys. 1968 49,4929. l1 Robin M. Hochstrasser J . Chem. Phys. 1967 47 1015. l2 R. H. Clarke and Robin M. Hochstrasser J. Chem. Phys. 1967,47 1915. l3 R. H. Clarke and Robin M. Hochstrasser J . Chem. Phys. 1968,49 3313. l4 H. Sternlicht and H. M. McConnell J. Chem. Phys. 1961 35 1793. l5 E. F. Zalewski Ph.D. Diss. (University of Chicago Chicago Ill. 1967). l6 Tien-Sung Lin Ph.D. Diss. (The University of Pennsylvania Philadelphia Pa. 1969). l7 P. J. Wheatley Acta Cryst. 1955 8 224. l9 Robin M. Hochstrasser and G. Castro J. Chern. Phys. 1968,48,637. P. Coppens and T. M. Sabbine Mol. Cryst. 1968 3 507

ISSN:0430-0696    

DOI:10.1039/SF9690300100

出版商:RSC    

年代:1969

数据来源: RSC

摘要:

Exchange Effects on the Electronic Spectra of Antiferromagnetic Salts of Mn2+ BY C. J. MARZZACCO AND D. S. MCCLURE Frick Chemical Laboratories Princeton University Princeton New Jersey Received 21st Nouember 1969 The electronic absorption spectra of several antiferromagnetic Mn2+ salts are compared. The strongly interacting bridged compounds such as CsMnCl3*2H20 and MnClz.2Hz0 absorb about an order of magnitude more strongly than the isolated systems such as CszMnC14-2Hz0 and MnS04-4Hz0. The intensity of the bridged compounds is less temperature dependent than that of the isolated systems whose intensities show the dependence expected of a vibronic coupling mechanism. External magnetic field effects on the spectra of CsMnClz*2H20 MnClz.2Hz0 and MnS044Hz0 are compared.MnSO4.4Hz0 shows a normal Zeeman splitting of its absorption bands. The lack of such splitting in the bridged compounds both below and above their ordering temperatures is interpreted as resulting from a cooperative intensity mechanism in these crystals. The effects of magnetic symmetry on the spectrum of CsMnC1,-2HZO below TN are discussed. Polarizations found in this spectrum are shown to be anomalous. We have been investigating the electronic spectra of a variety of Mn2+ salts whose Nbel temperatures vary from less than 1 to about 100 K. The crystal structures of these salts range from isolated octahedrally coordinated manganese units to one ; two- or three-dimensional structures formed with F Cl or Br bridging units. In all of the compounds we discuss the ground state of Mn2+ is 6A there being an electron in each of the five d orbitals.This is the state of maximum spin multi-plicity ; therefore all electronic transitions are spin forbidden. If the ion is at a site of inversion symmetry the transitions will also be parity forbidden. In such cases we expect the zero phonon lines to be magnetic dipole and to have low intensities, f = ca. - 10-l1. It is likely that vibronic mechanisms would induce electric dipole absorptions with intensities about an order of magnitude greater than this. In antiferromagnic salts such as MnF another intensity mechanism has been f0und.l In such systems with strong exchange interactions the appearance of spin-wave sidebands to the electronic transitions often results. This phenomenon is general and leads to enhanced intensity in strongly coupled antiferromagnets.In this paper we discuss some of the effects strong exchange interactions have on the spectra of antiferromagnetic salts. Manganese is ideal for such a study since it exists in a large number of salts with a variety of exchange interactions. EXPERIMENTAL Crystals of CsMnC13*2H20 were grown from a room-temperature aqueous solution containing a 1 1 molar ratio of CsCl and MnC12*4H20. The MnC12-2H20 crystals were obtained by evaporation of MnC12-4H20 aqueous solutions at 70°C. The MnS044H20 crystals were obtained from freshly prepared solutions of commercial hf.nSO4*4H20 powder. Other crystals were prepared as described elsewhere.2 The intensity comparisons and temperature dependence of absorption experiments were performed by Lohr2 using a Cary 14 spectrophotometer.The higher resolution experi-10 C. J . MARZZACCO AND D . S . MCCLURE 107 ments were done with a Jarrell-Ash 3.4m spectrograph having a 30000 line/in. grating. Magnetic field experiments were performed with the pulse magnet described el~ewhere.~ RESULTS A N D DISCUSSION SPECTRAL COMPARISONS OF WEAKLY AND STRONGLY INTERACTING SYSTEMS The room temperature spectrum of MnF is shown in fig. 1 and is typical as far as band positions are concerned of all manganese salts. These absorption bands result from transitions within the d shell and are spin forbidden. The intensities of these transitions in the compounds vary over several orders of magnitude and are compared in table 1. The bridged compounds have nearest neighbour exchange interactions which are ca.1-2 cm-1 and the transitions are about an order of magnitude stronger than those of the non-bridged compounds. It is interesting in particular to compare Cs,MnC14*2H,0 and MnC12*2H20. Both crystals contain trans-MnC14.2H20 units (site symmetry C2J but in MnCl,~2H20 the manganese ions are linked to each other by sharing Cl-Cl octahedron edges to form a linear chain while in Cs2MnCl4.2H20 the MnCl,*2H20 units exist as monomers. The visible and near u.-v. bands of the bridged compounds are on the average an order of magnitude stronger than those of the non-bridged structures. wave length A FIG. 1 .-Room temperature absorption spectrum of MISZ viewed with unpolarized light propogating along the c-axis.The temperature dependence of absorption intensity also varies with the exchange interaction as can be seen in table 2. Crystals having isolated groups such as MnSO,. 4H20 and MnCl*4H20 show increased intensity with temperature and are typical of hydrates of other divalent transition metal ions.4 This is the behaviour expected of a vibronic intensity mechanism. The intensities of bridged compounds on the other hand are decreased with temperature and by 8 % at most. These results suggest that the vibronic mechanism is not the dominant mechanism in the bridge compounds. THE CsMnCl,-2H20 SPECTRUM By examining the optical spectra of these compounds in some detail above and below their ordering temperatures in and out of magnetic fields we can get more information about the nature of the electronic transitions occurring.CsMnCl3.2H20 is one of the crystals we have been investigating. It is composed of cis-MnC1,*2H2 108 ELECTRONIC SPECTRA OF SALTS OF Mn2+ TABLE 1 .-ABSORPTION STRENGTHS OF BANDS IN VARIOUS Mn2+ SALTS ~b 1 2 3 4 5 6 7 8 Cs2MnCl4.2H20 light L t o needle axis ; 77 K tran~-Mn(OH~)~Cl~ unbridged 24 000 27 600 29 000 36 360 43 000 0.41 0.34 0.21 76 100 MnSO4.4H2O light 11 c Mn(H20)4(0S03)2 unbridged 18 500 22 830 24880 27 860 29 580 32 260 40320 1.18 0.58 0.60 1.06 0.33 0.31 0.89 MnC12-4H20 light 11 a ci~-MnC1~(0H~)~ unbridged 18870 22730 24600 27470 29070 31 750 39680 1.89 0.55 0.62 2.34 1.12 1.07 5.36 CsMnC13-2H,0 light 11 a 77 K ci~-Mn(oH~)~Cl~ share one C1 18 520 22220 24090 27030 28 820 31 200 37 740 42370 3.6 6.9 4.4 5.5 0.80 4.1 13.7 64.5 MnCl,*2H20 light 11 b tran~-Mn(OH~)~C1~ share two C1 18 980 21 050 24 130 26 800 28 650 30770 39220 3.48 1.35 2.65 4.21 4.80 ~ 0 .7 3 -12.2 TABLE 2.-TEMPERATURE DEPENDENCE OF ABSORPTION STRENGTHS.Qlb band 1 2 3 2 % increase MnSO*4H20 unpol. light [I a axis 300 K 1.27 0.78 0.49 2.52 23 77 K 0.96 0.71 0.38 2.05 MnC12*4H20 300K 1.89 0.55 0.62 3.06 52 77 K 1.26 0.39 0.36 2.01 MnC12-2H20 unpol. light to (010) face 300 K 3.48 1.35 2.65 7.48 -8 77 K 4.01 2.59 1.56 8.16 CsMnC13*2Hp0 light 11 a 300K 3.4 6.6 4.6 14.6 -2 77K 3.6 6.9 4.4 14.9 a The numbered column headings refer to the upper state of the transition corresponding to each absorption band 1 (4T1) 2 (4T2) 3 (4A1?E) 4 (4T2) 5 (4E) 6 (4T1) 7 (4A2) 8 (4T1).The first row of numbers under each compound is the band maximum in cm-l. The second row isfx 10". The temperature is about 300 K unless otherwise noted. The composition of the coordination sphere, and the nature of the bridge between nearest neighbours are given. b these data are taken from ref. (2). units linked together in linear chains by sharing one of their Cl- ions through a bridge.5 Adjacent chains are held together by hydrogen bonds between H20 and C1. The crystal is orthorhombic with the chains parallel to the a axis. The space group is P,, and there are 4 Mn2+ ions per chemical unit cell. Each Mn ion is at C. J . MARZZACCO AND D. S . MCCLURE 109 site of C2 symmetry the C2 axis being parallel to the b crystallographic axis. The electric dipole moments at adjacent Mn2+ sites along the chain are in opposite directions.The three-dimensional magnetic-structure of CsMnCl,.2H20 has been determined by Spence et aL6 using nuclear magnetic resonance techniques. Long-range spin-ordering occurs in this crystal below 4.8 K. Below this temperature the spins become directed along the b-axis with nearest neighbours along the chain having opposite spin orientations. The magnetic space group is PZb c'ca' and there are eight sublattices per magnetic cell. The magnetic cell is therefore twice the chemical cell with the doubling along b. 2.0 0.5 /J NQ POLARIZER 00 15,000 25,000 35,000 45,000 energy (cm-l) FIG. 2.-Absorption spectrum of CsMnCl3.2H20; see note p. 118. The complete spectrum of CsMnC1,=2H2O at 77 K is shown in fig.2 and is similar to that of other Mn compounds. We have studied the 27,000 cm-l absorption region of this crystal in most detail because it is rich in structure. This is the 4T2(D)+-6A transition region and is highly structured in all the compounds we have observed. Fig. 3 shows the low energy portion of this transition at 2.0 K. This strongly polarized spectrum has a weak sharp absorption line at 26,737 cm-1 followed by an asymmetric band with its sharp edge 20 cm-l above the origin. The c-polarized spectrum shows no sideband intensity; however the origin appears about as strong as it does in the b-polarized spectrum. Polarization studies on all three faces of the crystal indicate that the sideband is electric dipole and that the origin is largely electric dipole in nature.The same spectrum at 4.2 K is shown in fig.4. Here we see a severe broadening of both the sideband and the origin. The sideband has lost most of its asymmetric shape and its maximum has shifted to the red by 6 cm-l. The origin shows a one wavenumber red shift and a shoulder appears on its low-energy side. We believe that the sharp origin at 2.0 K is a pure exciton band and that the side-band is due to the simultaneous excitation of excitons and magnons of opposit 110 ELECTRONIC SPECTRA OF SALTS OF Mn2+ I . .,-37 25 3740 wavelength 8, FIG. 3.-Portion of the “T,(D)+ 6A transition of CsMnC13-2H,0 at 2.0 K; see note p. 118. wavelength 8, FIG. 4.-Portion of the 4T2(D)+- 6A transition of CsMnCl3-2H2O at 4.2 K; see note p. 118.wavevectors.* Spinwave sidebands of such shape have been reported in the spectra a several antiferromagnetic salts especially MnF,.l The asymmetric shape can be accounted for by considering the dispersion and density of states of the exciton and m a g n ~ n . ~ A system like CsMnC13-2H20 with no ferromagnetic neighbours is not expected to have a significant exciton disperson and therefore the sideband should represent the magnon dispersion and density of states to a first approximation. The magnetic susceptibility measurements of Smith and Friedberg * indicate a nearest neighbour intrachain exchange interaction of 2 cm-I. Using this exchange inter-action and neglecting the small interchain exchange interactions we can get th C . J . MARZZACCO AND D. S . MCCLURE 111 magnon dispersion by diagonalizing the magnon Hamilt~nian.~ The result for a one-dimensional antiferromagnet is At the zone edge the magnon energy is 20 cm-l.This agrees well with the energy of the sideband maximum. Our analysis of the spectrum is therefore consistent with the susceptibility data. To substantiate further this interpretation we have done high magnetic field studies (30-150 kG) on this state of CsMnCl,-2H20. These fields are above the flop field of 16 kG but smaller than the 200 kG exchange field. At 2.0 K with the field perpendicular to the c-axis we observe the exciton line to split into three lines in a magnetic field. The splitting is not linear with field and there is a shift of the centre of gravity of the lines. In such fields the sideband appears to be unaffected as we would expect for an exciton magnon pair.It is possible that the splitting of the E r g = 4s I J I sin(k,b/2). c POLARIZED SPECTRUM OF CsMnClj2I$o 77 K H = O K G THICKNESS 2.0 rnm H=133KG Ila THICKNESS 3.2mrn + - - - p i 36 50 37 00 3750 wavelength A .I 80 -1 00 FIG. 5.-Effect of magnetic field on the 4T2(D)t 6A Spectrum of CsMnC13-2H20 at 77 K; see note p. 118. exciton line is due to a field-induced-factor group splitting or to the anisotropy being large enough to make the ions energetically inequivalent in these fields. Since we have no information about the magnetic structure of CsMnC13*2H,0 at 2.0 K in such high fields we will not discuss these results further here. We have also taken the spectrum of CsMnC13*2H,0 at 77 K in a field of 133 kG.At this temperature the exciton has disappeared and only the sideband is prominent. Fig. 5 shows the a-polarized spectrum of the 4T2(D) region at 77 K with a magnetic field 133 kG parallel to the b-axis. Again we see no apparent effect on the sideband or on the rest of the spectrum for that matter. Above TN the ground manifold of the antiferromagnetic chain will consist of states with Stotal = 0 1 2 ... . The lac 112 ELECTRONIC SPECTRA OF SALTS OF Mn2+ of a splitting or broadening of the bands indicates that transitions only occur between states of the same total spin. If a single ion mechanism were dominant transitions between states of different spin would be possible and a broadening expected. Spence et al. observe that the transferred hyperfine field at the non-bridging chlorine ions decreases toward zero as the temperature approaches the NCel point from below.6 This does not necessarily indicate that the spins on adjacent ions are not strongly correlated above the NCel temperature.It could mean that the direction of the exchange field is changing so rapidly as to average to zero during the time it takes to undergo a resonance transition. The susceptibility * and specific heat lo studies indicate that considerable ordering exists above TN. The specific heat and susceptibility show rounded maxima at 20 K and these are as expected for an anti-ferromagnetic chain. Since true one-dimensional systems will not show long range ordering until 0 K the NCel point for CsMnCl3-2H20 only occurs because of inter-chain Our results are in agreement with Smith and Friedberg's in indicating considerable order far above the NCel temperature.The effects of symmetry on the spectrum of the CsMnCl3.2H20 crystal are interest-ing. In the paramagnetic region the manganese site symmetry is C2(b) the factor group symmetry is D 2 h and there are four manganese ions per unit cell. The six spin levels of the 6A ground state should be essentially degenerate and each excited level will be a Kramers doublet. Every excited state will transform like r3 or r4. The Ms = $,-$ 3 levels of the ground state will transform as r3 and the Ms = -4 3 -+ levels will transform like r4 in the Cz double group.ll Any excitation from the ground state to a particular excited state will involve r3+r3 r3+r4, r4+r3 and r4+r4 transitions.A r3-)r3 and a r4+r4 transition produces a rl transition moment which will give electric dipole intensity parallel to b. A r3+r4 and r4+r3 transition will yield a r2 transition moment and will be polarized perpen-dicular to b. Since both like (I?,) and unlike (r,) transitions occur in any excitation we would not expect to see strongly polarized spectra in the paramagnetic region. Below TN the manganese site symmetry remains C2(b) and the factor group symmetry remains DZh but there are now eight manganese ions per unit In the exchange field of the neighbouring ions the Kramers degeneracy is removed. At low temperatures each Mn2+ will be in the ground state A( -3) or A(3) depending on the sublattice. An excitation now results from either a like (r,) or an unlike (r,) transition.An exciton will result from a transition between the ground state and one of the low-symmetry crystal-field components of the excited state. A magnon is due to transitions from A( - 3) to A( - 4) on the down sublattices and A(3) to A($) on the up sublattice. Therefore a magnon is an unlike transition and an exciton maybe a like or unlike transition. We can obtain the symmetries of the k = 0 excitons or magnons produced from a particular site transition by using the projection operator technique. l2 The character of the reducible factor group representation ~ X ' - ~ - ( R ) under the symmetry operation of thejth site transition moment vector x,"+ is given by the following expression : 'x'.~.(R) = ~G,(R)x$-g.(R) ; where 6,(R) = 1 if R in site group, where the sum is over all sites.The symmetries of the excitons or magnons is then determined by reducing the reducible factor group representation. The results are shown in table 3. We see that a like (I?,) site transition will give rise to eight excitons only two of which will have electric dipole intensity. Transitions to these excitons are polarized with the electric vector parallel to b. An unlike (r,) site transition a = 0 otherwise C. J. MARZZACCO AND D . S. MCCLURE 113 will give rise to eight excitons (or magnons) two of which will have electric dipole intensity polarized parallel to a and two parallel to c. Physically a 6-polarized site transition produces b-polarized crystal intensity while an ac-polarized site transi-tion produces a- and c-polarized crystal intensity.In the absence of a factor group splitting we expect all electric dipole exciton bands to be either 6-polarized or ac-polarized. The determination of the polarization of a band should be an assignment to the excited state symmetry. TABLE 3.-EXCITON AND MAGNON SYMMETRIES AT k = 0 FOR CsMnC12*2H20 site group factor group type of C2@) D2h polarization excitation rl (like) Mb exciton 2 r; T2 (unlike) ra Ma MC exciton or 2 r; E a magnon 2 r4+ E C TABLE ~.-SYMMETRLES OF EXCITON-MAGNON STATES OF CsMnC13-2H20. The Exciton and Magnon wavevectors are at the centre of the reciprocal lattice faces. exciton magnon exciton-magnon symmetry symmetry symmetry polarization ( L m r,+ J2 r; r,+ r; r: ri r; r; rz r r; rL? r,+ =,.r,+ r,. r; r2 r3 rz rdt r i ri-r; r,- r; r.z r; r; r i r2- rL? r,- r2 r? ri- I-2 r,. r; = Ma I'; = Ea r = iwc r = E~ (UNLIKE) r,+ r; r; ;g r r,+ = forbidden r; = forbidden r; r; =iwb Fi r = E b To find the polarization of the sidebands one first determines the symmetry of the exciton and the magnon at the point in the Brillouin zone of interest. We are most interested in the symmetry points at the zone boundary since these are where the density of states have their maxima. Since we are using u.-v. light the selection rule Ak = 0 applies. Therefore any sideband (i.e. exciton-magnon) state must be composed of an exciton and a magnon of equal and opposite wave vector. The exciton and the magnon of wavevector k will transform as representations of the group of the wavevector.The symmetry of the exciton-magnon state is then found by taking the direct product of the exciton and magnon representations 114 ELECTRONIC SPECTRA OF SALTS OF Mn2+ Since the symmetry of the CsMnC1,.2H2O magnetic cell is simple orthorhombic, the reciprocal cell will also be simple orthorhombic. The magnons should have maxima in their density of states at the centre of the faces of the reciprocal cell. At these points the group of the wavevector is DZh as it is at k = 0. The symmetry of the exciton magnon states are shown in table 4 ; a like or b electric dipole polarized exciton must give rise to a and c electric dipole sidebands and a and c electric dipole excitons produce b-polarized electric dipole sidebands.* Symmetry indicates that it should not be possible to see electric dipole intensity in an exciton band which is both b- and ac-polarized. Yet we do observe such a mixed polarization for the 26 737 cm-1 band of CsMnC13*2H20. The validity of these selection rules depends on the site symmetry being C2(b) in both the ground and excited states. The symmetry of the ground state depends on the spin orientation which is determined by the anisotropy. The excited-state anisotropy could be different in both magnitude and direction. This would result in the ions near an excited ion having different orientations from those in the ground state. Although such a situation is only conjecture it is the only explanaton we can suggest. The sideband on the other hand has a polarization (ac) which is consistent with the symmetry arguments.In general however most bands in the spectrum are not purely b or purely ac-polarized. THE MnC12.2H20 SPECTRUM Another one-dimensional antiferromagnetic system we have been investigating is MnC12-2H20.13 This system is monoclinic with a chemical space group of C2/m and two molecular units in a cell. The trans-MnCl4.2H,O units are linked together by sharing Cl-Cl edges to form chains along the c-axis. The site symmetry is C, so the parity selection rule applies. This crystal absorbs about an order of magnitude more strongly than Cs2MnCl4-2H2O even though the two salts have identical site symmetries and environments. Calculations by Lohr and Meltzer l4 for the 4T,(D) state of Mn2+ in such an environment predict little magnetic dipole intensity and indeed no sharp absorption is found in MnF which has the same site symmetry although a different crystal field.The NCel temperature of MnCl2.2H20 is 6.8 K and the ions are antiferromagneti-cally coupled along the chain.l The exchange interactions between chains are ferromagnetic for nearest neighbours in the b and a directions. Spence and Rao report that the intrachain and interchain interactions are not much different in this crystal in contrast to CsMnC13-2H20. The spectrum of MnC12-2H20 at 1.8 K in the 4T,(D) region is shown in fig. 6. The spectrum is strongly polarized and there is a doubling of the Elc polarized origin. In fig. 7 the low-energy portion of this spectrum at 1.8 K and 4.2 K is shown. There are rather drastic changes in bandwidth polarization and energy position for a few degrees change in temperature.Although we do not understand the details of these changes they are undoubtedly related to the changes in magnetic structure and order with temperatue. We are most concerned however with the mechanism of absorption. We have looked at the spectrum of MnCl2*2H,O at 4.2 and 77 K in a magnetic field. At 77 K in a 75 kG magnetic field there is only a slight broaden-ing of the spectrum but no shifts. The 4.2 K spectrum is shown in fig. 8. The magnetic field has the effect of collapsing the low energy doublet and has no effect 09 the second band. Although we do not understand the spectrum in detail the collapse of the doublet reminds us of similar phenomena which occur in MnF, and stressed RbMnF,.In these cases a spin flop transition induced by the magneti C. J . MARZZACCO AND D. S . MCCLURE 115 I 37'30 36 ao wavelength 8, FIG. 6.-4T2(D)t 6A spectrum of MnC12*2Hz0 at 1.8 K. FACE q.2 K E IIc 3 .d 1 3 E l c E l c 3 I .-3740 3730 3740 37 30 wavelength FIG. 7.-Low-energy portion of the "T2(D)+ 6A spectrum of MnCI2-2Hz0 at 1.8 and 4.2 K. field causes change in the spin-orbit coupling resulting in appreciable shifts of the substrates of the 4T2 and other degenerate levels. We conclude that the lack of a normal Zeeman effect in this spectrum precludes the possibility of a single-ion intensity mechanism and suggest that cooperative transitions in which total spin remains unchanged are occurring f 16 ELECTRONIC SPECTRA OF SALTS OF Mn2+ MnC1,2H20 ABSORPTION 4.2 K (110) FACE H = 7 5 k G I I c UNPOLARIZED A I I 3740 37 30 wavelength A FIG.8.-Effect of magnetic field on the *T2(D)+ 6A spectrum of McC12*2H20 at 4.2 K. MNSO,*4H 0,77K I I He,= 1672 3 KG He,= 0 24912 m - I U v >-U L1 W z 24844 w 24796 E 11 b HI1 c He 11 b I N - N N” - I I FIG. 9.-Effect of nagmetic field on the 4A,Et. 6A spectrum of MnSO4*4Hz0 at 77 K. THE MnSO4-4H20 SPECTRUM We now contrast the behaviour of the bridged systems with that of several less strongly interacting systems. MnSO,-4H,O is a monoclinic system with a chemical space group P21,n and four molecular groups per unit ce1l.l’ The manganese site symmetry is C1. Although manganese ions are linked together by Mn-O-S-0-Mn bridges the adjacent ions are well-separated.Lohr has investigated the 4A E(G C . J . MARZZACCO AND D . S. MCCLURB I17 transition at 24 000 cm-1 .l* His b-polarized spectrum with the field 11 6 is shown in fig. 9. In zero field the band positions can be accounted for by considering the three bands to be transitions to the three low-symmetry components of A E each orbital state having a quartet spin multiplicity. These three quartet levels are barely split into three pairs of Kramers doublets by the spin orbit coupling which is small for this state. If the g factors of the ground and excited states are both 2. the three line Zeeman spectrum is accounted for. The polarizations observed for this state, however are somewhat anomalous. * The 4T2(D) state of MnS03*4H20 in fig.10 also shows a Zeeman effect. We can ' MnSO 4 H 0 77 K LlGHTIi a Ellb I 4 2 i 1 H.133 kG II c -I-- _____ 36'50 3680 wavelength 8, FIG. 10.-Effect of oagnetic field on the 4T2(D)+ 6A spectrum of MnS044H20 at 77 K. account for the Zeeman pattern of the low energy band in the spectrum by considering the zero field line being due to a transition to a low symmetry orbital component of T2 with a spin of 4. If the g factor with Hex 11 c is taken to be 1.5 for the excited state the experimental pattern is accounted for. The intensity temperature dependence of intensity and normal Zeeman effect observed for MnS0,*4H20 are in sharp contrast to MnC12*2H20 and CsMnC1,-2H20. The single-ion mechanism undoubtedly dominates in MnS0,-4H20 although interion exchange interactions probably have some effect on the spectral polarization.The authors are grateful to Mr. M. Y. Chen for allowing us to use his low-tempera-ture Zeeman studies of CsMnC13=2H,0. Thanks also due to Dr. L. L. Lohr for permitting us to use the 4A,E+-6A Zeeman spectrum of MnS04-4H20. We also thank Dr. R. D. Spence for sending us the unpublished nuclear magnetic resonance results on CsMnC13*2H20 and MnC12-2H,0. This work was supported by the National Science Foundation and the Office of Naval Research. D. D. Sell R. L. Green and R. M. White Phys. Rev. 1967 158,498. P. G. Russell D. S. McClure and J. W. Stout Phys. Rev. Letters 1966 16,176. L. L. Lohr and D. S. McClure J. Chern. Phys. 1968,49,3516. D. S. McClure R. Meltzer S. A. Reed P.Russell and J. W. Stout Optical Properties of Ions in Crystals ed. H. M. Crosswhite and H. W. Mos (Wiley-Interscience Inc. New York 1967), p. 257 118 ELECTRONIC SPECTRA OF SALTS OF Mn2+ 0. G. Holmes and D. S. McClure J. Chem. Phys. 1957,26,1686. S. T. Jensen P. Anderson and S. R. Rasmussen Acta Chem. Scand. 1962,16,1890. R. D. Spence W. J. M. de Jonge and K. V. S. Rama Rao J. Chem. Phys. 1969,51,4694. R. Meltzer M. Lowe and D. S. McClure Phys. Rev. 1969 180,561. T. Smith and S. A. Friedberg Phys. Rev. 1968 176,600. G. J. Butterworth and J. A. Woollam Phys. Letters A 1969 29,259. C. Kittel Quantum Theory of Solids (John Wiley and Sons Inc. New York 1963) p. 58. lo H. Forstat J. N. McElearney and N. D. Love in press. l1 G. F. Koster Space Groups and Their Representations-(Academic Press Inc. New York 1957). l2 D. S. McClure Electronic Specta of Molecules and Ions in Crystals (Academic Press Inc. New l3 B. Morosin and E. J. Graeber J. Chem. Phys. 1965 42 898. l4 R. S. Meltzer and L. L. Lohr J. Chem. Phys. 1968,49,541. l5 R. D. Spence and K. V. Rama Rao J. Chem. Phys. 1970 52 2740. l6 M. Y. Chen and D. S. McClure unpublished results. l7 W. H. Bauer Acta. Cryst. 1962 15,815; 1964 17,863. l8 L. L. Lohr unpublished results. York 1959) p. 9. *Note added in proof The labeled axes of CsMnCI 2H20 are incorrect in the tables and figures. For correction change a to b b to c and c to a. Recent spectral studies of CsMnCI3 2H20 in magnetic fields below its spin flop transition in-dicate that the sharp origin is a zone centre magnon sideband. This analysis is based on a lack of splitting of this band with fields parallel to the b axis of the crystal. No splitting is expected for a magnon sideband transition because such transitions involve spin projection changes on the two sublattices of equal magnitude but opposite sign. The treatment of magnon sideband symmetries and polarizations is not entirely correct. A more complete description will be presented in a future publication

ISSN:0430-0696    

DOI:10.1039/SF9690300106

出版商:RSC    

年代:1969

数据来源: RSC

摘要:

Measurement of Molecular Magnetic Susceptibility Anisotropies BY W. H. FLYGARE AND R. L. SHOEMAKER * Noyes Chemical Laboratory University of Illinois Urbana Illinois Received 6th October 1969 The rotational energy levels of a rigid spin-free molecule in the presence of a high magnetic field are determined. Terms up to H4 dependence are included and all rotational-electronic corrections are included through second order in the electronic states. The results show that in the absence of near rotational degeneracies the field-dependent perturbation is well described by the three diagonal g-values (guu gbb and gcc) and two independent magnetic susceptibility anisotropy components ((2xua -xbb -xcc) and ( 2 u b -~uu-xcc)). These five molecular %man parameters can be extracted from the analysis of pure rotational spectra in high magnetic fields.The magnetic susceptibility anisotropies for about 40 molecules have been determined recently by these techniques and the results are listed here. Ring currents and group anisotropies are also discussed. Magneto-optic and electro-optic phenomena are manifestations of a response of matter to an impressed electric or magnetic field. The magnetic susceptibility tensor describes the non-linear response of a molecule to an external magnetic field. This paper reviews the equations and experimental methods used recently to measure the magnetic susceptibility anisotropies in a number of molecules. Until the recent work described here most measurements of magnetic susceptibility anisotropies on diamagnetic molecules have been bulk measurements on molecular crystals with lower than cubic symmetry.l This method is limited to relatively large molecules which form well-known crystal structures.The major limitation with the bulk method is that the effects on the anisotropies due to intermolecular interactions in the solid state are unknown. The magnetic susceptibility anisotropy in the hydro-gen molecule has been determined by molecular-beam-magnetic resonance methods.2 The anisotropies in the diatomic NaF KF RbF and CsF molecules have been given to an accuracy of about 50 % by molecular-beam-electric-resonance methods. It is difficult to use the molecular beam techniques to extend the measurements to polyatomic molecules. Also approximate anisotropies have been given for N2 , C02 CO NO CH3-CH3 CH2=CH2 and cyclopropane by a measurement of the Cotton-Mouton effect in compressed gases.4 In this paper we show that by combining high resolution microwave spectroscopy with high magnetic fields the magnetic susceptibility anisotropies can be measured on any molecule which has an assignable microwave spectrum.These measurements are at low pressures and provide values of the susceptibility anisotropies for single unperturbed molecules. Measurements on a large number of molecules have been completed and the results are discussed here. THEORY The rotational energy of a molecule in a magnetic field can be expressed by a Taylor series expansion about the zero field. Excluding the effects of nuclear spin, * National Science Foundation Predoctoral Fellow.11 120 MEASUREMENT OF MAGNETIC SUSCEPTIBILITY ANISOTROPIES Wo is the zero-field or rigid-rotor energy. Hi Hj Hk and Hl are the Cartesian com-ponents of the magnetic field along the i j k I = x y and z laboratory-based co-ordinate system. The derivatives are all evaluated at zero field. We now define the derivatives of W. The components of the magnetic dipole moment are defined by The components of the quadratic magnetic susceptibility are defined by The components of the cubic magnetic susceptibility are defined by The components of the quartic magnetic susceptibizity are defined by Substitution into eqn (1) gives 1-11 = -(awlam,. (2) x i j = - (a2 w/amHj)Oo* (3) Y i j k = -(a3 w/aHiaHjaHk)OOO* (4) q i j k l = - (a4w/aHlaHjaHkaH~)OOo0.( 5 ) All vector and tensor components in eqn (6) are described in the laboratory-based framework. In order to obtain the rotational dependence we must relate the molecu-lar fixed pa xag yasy and qagya components to the laboratory-based coordinates by the direction cosine transformation 1 1 W = W o - x b 4 0 i H i - C H i 4 i a x a p 4 g j H j -i a 2i,j asp - H i 4 i a y a ~ y ~ B j ~ y k H j H k + * . o -6 i j k a,B,y where the sums over a b y and S are over the molecular fixed axes. We choose the molecular fixed axes as the centre-of-mass principal inertial axes a b and c. We now simplify eqn (7) by specifying a single non-zero laboratory plane polarized magnetic field Hz which give W. H . FLYGARE AND R . L. SHOEMAKER 121 The magnetic dipole moment pa is the rotational moment and is proportional to the rotational angular momentum.The proportionality constant is the molecular g-value. The appropriate expression is where po is the nuclear magneton JB is the projection of the rotational angular momentum on the fi = a b or c principal inertial axes and gsa is one of the elements of the g-value tensor. Substitution of eqn (9) and the rigid rotor (in the principal inertial axis system) energy expression for Wo gives (10) H,4 - C +za+zBqaB y c d y z 4 6 z + * 24 a ~ Y ~ We now anticipate the results of a first-order (in J) energy calculation by noting that the symmetry of the direction cosines causes many of the terms in eqn (10) to give a zero first-order correction in J. The non-zero first-order corrections from the g-value term are derived in ref.5. Thus we can write the Hamiltonian components from eqn (10) which contribute only to the first-order energy in J in the rigid rotor basis. The result is J," H,3 H A = C- -HzpoCJ.saa4a=-'~4:- c #3cryaBy+pz#yz-a 2 I a a 2 a 6 a,b,y The symmetric components in the last term are combined according to qaabb = Ybbaa = rabab = rabba = qbaab = Ybaba and the remaining two cyclic alternates with a c and 6 c. Before deriving the matrix elements for the energy in eqn (1 1) it is convenient to rewrite the equation in terms of the elements of the corresponding 2nd 3rd and 4th rank irreducible spherical tensors. This change gives wher 122 MEASUREMENT OF MAGNETIC SUSCEPTIBILITY ANISOTROPIES x = &(xaa + Xbb + xcc), v = s[raaaa + r b b b b + ??ccccl.(13) The transformation properties of the direction cosine combinations in eqn (12) are related to the corresponding spherical harmonics (or spherical irreducible tensor elements) by The Y i and Y; will couple off-diagonal elements in M. Thus if we consider only the first order energy in J z and M the Y& Y! and Yg terms vanish giving 6-8 3H4 H4[ 1 I[ M’-J(J+t)] C(gaaaa - v)( Jg”) - -24 J(J+l) (2J-1)(2J+3) a The reduced matrix element denoted by (Jzll [I Jz) is best evaluated by computer technique^.^ The ( -M ’) is a 3-j coefficient.1° In addition to the strictly first-order terms in eqn (15) terms of higher order will appear as follows : ~ N D ORDER IN M.-Terms second order in M will lead to the yaaps terms as mentioned above.~ N D ORDER IN J AND z.-Terms second order in J and z will lead to H2 terms involving elements in the g tensor,11 H4 terms involving elements in the x tensor, H6 terms involving elements in the y tensor and also H6 terms involving the y tensor and products of the g and x tensors. In general the 2nd-order terms in the rotational states will be unimportant l1 and we can return to eqn (15). Eqn (15) shows that the ya-aa-q and xaa-x anisotropies both have the same rotational dependence. Thus it is important to show that the values for the q anisotropy terms are actually smaller than the x anisotropy terms in eqn. (15). To obtain explicit functions for the g x y and y tensor elements we write the exact zero nuclear spin Hamiltonian describing a molecule in a magnetic field.We then use standard perturbation theory to obtain the desired quantities as defined in eqn (2)-(5). The appropriate Hamiltonian i W. H . FLYGARE AND R . L . SHOEMAKER 123 Pk is the linear momentum which is replaced by -ihVk in quantum mechanics qk is the charge (including sign) of the kth particle A(rk) is the vector potential at the kth particle &k) is the scalar potential and V is the potential energy. For an external magnetic field along the space fixed z direction we can choose : 4 = 0 ; V-A=O. Using the c.m. as origin and remembering that we are considering a single plane-polarized magnetic field component H = H we can write the vector potential as where i and j are unit vectors. Substituting into eqn (16) expanding separating the nuclear and electronic components introducing the electronic and nuclear angular momenta and using p = eA/2rnc gives Lz,+-(X,2+y:) h2Vi eH Z, e2H2 2," ;{-q-%E 8c2 M , p is the Bohr magneton e is the electronic charge L, and L, are the electronic and nuclear angular momenta respectively c is the speed of light xf and x, are the electronic and nuclear coordinates M is the mass of the nth nucleus m is the electron mass.2 is the atomic number of the nth nucleus and the sums over i and n are over electrons and nuclei respectively. We now proceed to compute the energy by perturbation theory using the Hamil-tonian in eqn (19). The energy is given by E = E'o'+E(1'+E'2'+ . . . (20) Assuming a rigid molecule and the validity of the Born-Oppenheimer approxi-mation allows the standard separation of variables in eqn (19) and the normal zero-order solutions for the electronic and rotational motion.Thus initially we will ignore vibration giving R 0 TAT1 0 N A L ZERO - ORDER YROt(hM) J z and M are the standard asymmetric top rigid-rotor quantum numbers. ELECTRONIC ZERO-ORDER Y!ii E," is the rigid rotor or zero-order rotational energy and E,"1 is the zero-order electronic energy. The sum of these two terms give E(O) in eqn (20). The remaining terms in eqn (19) will act as perturbations and give the higher-order corrections 124 ME AS U R E M E N T 0 F MAGNETIC S U S C E P TI B I L IT Y A N I S OTR 0 PIES First we make the first and higher-order corrections to the electronic energy and then consider the rotational effects to first order as in our previous discussion starting with eqn (1).We consider two stages of development concerning the electronic contributions to eqn (20). First we discuss the contributions through second order in electronic correction using the zero-order electronic function and then we acknowledge the electronic-rotational coupling and compute the effects on E‘l’ and higher order terms for a rotationally perturbed electronic function. In the second case we again include corrections only through second order in the electronic states. A. ZERO-ORDER ELECTRONIC FUNCTION From eqn (22) the zero-order electronic function is given as Yi1. Using this function and the perturbation in eqn (24) allows the contributions to eqn (20) to be computed. 1ST ORDER; E61,‘ 2ND ORDER; E62,’ C.C.in the last term indicates the complex conjugate. The primes indicate that the terms in the summations are excluded where the associated indices are equal. We now consider the additional contribution to the values in eqn (25) and (26) with an electronic wavefunction which has been corrected for the rotational-electronic coupling. B. ROTATIONALLY CORRECTED ELECTRONIC FUNCTION The electronic wave function in the presence of rotation is given by 5 9 7 This additional effect adds the following contributions to the energy in addition to the results listed in eqn (25) and (26). The sum over a in eqn (27) is over the principal inertial axes a b and c W. H . FLYGARE A N D R . L . SHOEMAKER 125 (0 I La I m>(m I C(X?+Y?) I k ) ( k I L a I 0) ( E O - - Ek) e2H2 i The last two terms in eqn (28) are corrected to third-order in electronic states and will be dropped.There are no additional terms in eqn (26) involving second-order corrections in electronic states by the use of the expression in eqn (27). Adding the zero-order energies in eqn (21) and (22) the rotational energy in eqn (23) the electronic contributions in eqn (25) (26) and the first two terms of eqn (28) gives the energy of a non-vibrating molecule to second-order in the electronic states. The energy contains terms up to the fourth power of the field :8 W = E,+E,+H{ -z-Lzn-z-z'( e z n P J a (OILaIk)(kILzIO)+c.c. 2c n Mn a Iaak> 0 ( 0 - Ek) We now return to eqn (1) and the definitions in eqn (2)-(5) to identify the most important terms in the p vector and the x y and y tensors.Using eqn (6) and remem-bering that H = H gives (all quantities are still defined in the space-fixed axis system) A direct comparison of eqn (29) and (30) allows expressions to be written defining each of the elements in the p vector and x y and y tensors. These definitions only include corrections from the electronic-rotational coupling to second order in electronic states. We now return to the development following eqn (6) which relates the space-fixed x y and z axes to the molecule-fixed principal inertial a b and c axes. The connection is through the direction cosines which leads to the rotational dependence. Following the introduction of the direction cosines in eqn (29) we now consider which terms appear in the rotational energy to first-order in J.The last term in the H2 bracket of eqn (29) fails to enter first order in J because of the symmetry of the direction cosines and will not survive the development to the expression in eqn (12). We can now define the quantities in eqn (12) which survive to second-order in electronic correction and also which survive to first order in J. These results are obtained according to the above discussion and by direct comparison with eqn (12) and (29) 126 MEASUREMENT OF MAGNETIC SUSCEPTIBILITY ANISOTROPIES M, is the proton mass. Eqn (31) gives the well-known expression for the rotational g-val~e.~-* Eqn (32) shows that the rotational measurement of xaa gives three terms two of which are the traditional molecular magnetic susceptibility l2 composed of the diamagnetic xL and paramagnetic x:~ components.However an additional term involving a sum over nuclear coordinates also appears in xaa. This additional term is the effective nuclear diamagnetic susceptibility and will be at least MP/m smaller than the corresponding electronic diamagnetic susceptibility term x&. Our present methods of measuring the values of xaa in eqn (32) from an analysis of the rotational perturbations described in eqn (12) are not accurate enough to justify consideration of the above nuclear contribution to the diamagnetic susceptibility. Thus in most cases, d ~ a a xaa+~:a* Returning to eqn (12) we wish to assess the importance of the q tensor terms on the first order (in J ) rotational energy. It is evident from eqn (12) and (15) that the x0la-x term and a qaaaa-q term have the same dependence on a J,z,M rotational state.Thus our measurements (from eqn (15)) can only yield the value of (Xaa-X)+ ( H 2 / 2 4 ) ( y a a c a - y ) from an analysis of the rotational spectra. We now attempt to estimate the importance of the (qaaaa-q) term. The ratio [ ( H 2 / 2 4 ) y a a a a / ~ a J will give an estimate of the relative magnitude of this term. Consider yaaaa from eqn. (34) : the value of (0 I C(b:+c) [ k f ) is the electronic second moment average value between the ground and the excited kth electronic state. We use the average energy closure approximation to evaluate the summation i.e., i where AE is an average excitation energy which is usually estimated as the ionization potential.In any event assuming AE r 3 eV and (0 I z(c:+b:) I 0) r 10-14 cm2 W. H . FLYGARE AND R . L . SHOEMAKER 127 erg/G2 and substituting qaaaa and Xaa into Assuming a typical value of Xaa 21 the above ratio gives Laa Thus even at fields up to lo6 G the effects of the y tensor are negligible. Simple estimates also show that the y tensor elements would not appreciably affect the rotational energy levels. As a result of these considerations it is evident that the first order expression through H2 terms in eqn (15) will give a more than adequate description of the energy of a rotating molecule in a high magnetic field. Care must be exercised however if near-rotational degeneracies are present as pointed out in the discussion following eqn (15). The remaining difficulties in the extraction of the g-values and Xaa-X values of magnetic susceptibility anisotropy arise from vibration-rotation interactions.An approach that will correct for vibration-rotation interactions is to use perturbation theory to correct the rotational state and then use the corrected rotational function to compute the values of (J,") in eqn (15). This approach has been used to evaluate the g-values and xaa-x values in trimethylene sulphide in the presence of large rotational coupling with the low-energy ring-buckling vibration. The above equations and considerations can also be worked out in the presence of nuclear spin in the absence or presence of zero-field nuclear-molecule coupling. * 14-1 The Zeeman effect in the presence of the nuclear spin is considerably more complex but the determination of g-values and X0la-x values is still possible.In addition, anisotropies in the nuclear magnetic shielding can also be obtained.8* l7 TABLE THE MAGNETIC SUSCEPTIBILITY ANISOTROPIES (IN UNITS OF erg/G2 mOI) FOR THE SIGNS OF THE ELECTRIC DIPOLE MOMENTS HAVE ALSO BEEN MEASURED IN SOME OF A NUMBER OF LINEAR AND SYMMETRIC TOP MOLECULES. THE PARALLEL AXIS IS THE SYMMETRY AXIS. THE MOLECULES AND ARE LISTED. molecule X I - x I] ref. -ocs+ NNO HC f CF 9.27 50.10 19 10.1 f0.15 21 5.19 50.12 20 -HCr CCH3 + 7.70 rt0.14 22 HC C-C E CCH3 13.08 f0.16 23 FCH3 -CICHs + BrCH3 ICH3 -NCCHS + CNCH3 0 50.9 24 - 3.0 f 1.5 25 + 1.32 &0.20 25 +8.2f0.80 16 + 7.95 f0.40 26 3- 8.50 30.40 26 + 10.98 410.45 26 10.6 +0.6 27 13.5 f0.7 2 128 MEASUREMENT OF MAGNETIC SUSCEPTIBILITY ANISOTROPIES NUMBER OF ASYMMETRIC TOPS.THE RESULTS ARE GROUPED INTO TWO CATEGORIES; RINGS TABLE 2.-MAGNETIC SUSCEPTIBILITY ANISOTROPIES (IN UNITS OF erg/G2 mOl) FOR A AND OTHERS. THE FOLLOWING CONVENTION IS USED TO GIVE THE RESULTS 2 IS THE AXIS PERPENDICULAR TO THE HEAVY ATOM PLANE AND THE X AXIS IS IN THE HEAVY ATOM PLANE ALONG THE AXIS WITH THE LARGEST ELECTRIC DIPOLE COMPONENT. molecule RINGS benzene pyridine fluorobenzene thiophene pyrrole furan cyclopr opene ethylene sulphide ethylenimine ethylene oxide 1,3 -c yclohexadiene trimethylene sulphide trimethylene oxide formaldehyde ketene formic acid acetaldehyde carbonyl fluoride vinylidene fluoride cis- 1 ,2-difluoroethylene methylene fluoride OF2 0 3 so2 water propynal propene dimethyl ether dimethyl sulphide OTHERS x*X--XYY 0 -2.1 f2.5 - 3.6 f0.6 -0.3 f0.6 + 5.2 f0.5 + 2.8 f0.4 - 6.6 f0.5 - 2.2 f0.4 -4.0 f0.5 - 5.8 f0.4 - 1.1 f1.8 + 1.2 f0.7 - 2.5 fO.5 + 9.6 f1.4 - 1.6 f0.6 - 2.0 f0.5 -0.5f1.5 - 1.2 f0.7 - 3.3 f0.5 - 2.4 50.6 + 1.6 f0.4 +1.5f1.0 - 38.4 h4.0 - 1.1 f0.5 - 1.1 f0.6 - 1.5 f0.8 -4.7 f0.3 3.9 f0.4 0.5 f0.5 x z s - + h X + XYY) - 59.7 -57.4 k2.0 - 58.3 f0.8 -50.1 fl.1 -42.4 f0.5 - 38.7 f0.5 - 17.0 f0.5 - 15.4 f0.4 - 10.6 f0.7 - 9.4 f0.4 - 7.4 f2.2 +22.8fl.O + 16.8 50.7 - 12.0 f0.9 - 6.4 f0.3 - 8.9 f 1.8 - 3.5 zk0.8 - 2.7 f0.7 - 2.0 f0.4 + 2.6 h0.6 + 1.6 f0.5 + 6.6 f l .O - 40.3 f5.0 - 4.7 f0.4 - 0.6 f0.6 - 6.3 f0.4 6.7 f 1.2 4.6 f0.5 3.5 f0.7 ref. a 28 29 30 31 30 32 33 31 34 35 13 13 11 36 37 38 39 39 39 39 40 40 40 24,41 42 43 44 44 J. Hoaran N. Lumbroso and A. Pacault Compt. rend. 1956,242 1702. RESULTS In the absence of near rotational degeneracies and nuclear spin the three diagonal elements in the g-value tensor (gas g b b and gcc) and the two independent magnetic susceptibility anisotropies ((2xaa - Xbb - xCc) and (2xbb - xaa - xcc)) can be obtained by the use of eqn (1 5 ) and the experimental results. The experimental method is to combine high-resolution microwave spectroscopy (on gases at low pressures) with a high-field electromagnet.In 1967 we reported the first measurement of a molecular magnetic susceptibility anisotropy by microwave spectroscopy ; these results on formaldehyde were accomplished with a standard 12 in. circular magnet with fields up to 11 000 G.'* We have subsequently acquired a better magnet facility which provides fields up to 30 000 G over a full 72 in. length.19 The first work on the new magnet facility was the work on HC=CF reported in 1968.20 Since then we have reported the measurement of the magnetic susceptibility anisotropies in a large number of r n o l e ~ u l e s . ~ ~ - ~ ~ We list the results here on a number of typical systems. Linear and symmetric to W . H . FLYGARE A N D R . L . SHOEMAKER 129 molecules are listed in table 1. Asymmetric tops are listed in table 2.The result on benzene from the crystalline data is also included for comparison. All other molecules were done in our laboratory. It is interesting to note the surprisingly small value for the anisotropies in the acetylenic molecules as shown in table I. The results on methyl acetylene and methyl diacetylene indicate that the value of xl -xII in acetylene should be less than 7.0 x erg/G2 mol. This magnitude is considerably smaller than the estimates based on the interpretation of proton chemical ~ h i f t s ~ ~ ~ ~ or the interpretation of ' 3C-H nuclear spin-spin The anisotropy in methyl isocyanide is quite large however. It is also interesting that the anisotropies in the ClCH3 BrCH and ICH3 series differ only by 2 x The first part shows the anisotropies for a number of ring compounds.The in-plane anisotropies are relatively small throughout the series of six- five- four- and three-membered rings. The unsaturated six- and five-membered rings show large values for xzz-$(xxx+xyy) which indicates the presence of a ring current. Indeed the small value for xzz - +(xxx + xyy) observed in 1,3-~yclohexadiene indicates that previous estimates of the ring current contribution to the value of xzz-+(xxx+xyy) may be too small. The existence of ring currents can also be inferred from the comparison of xzz-j(xxx + xYy) values for cyclopropene ethylene oxide and ethylene sulphide with the corresponding ring-opened forms propene dimethyl ether and dimethyl sulphide. The ring-opened forms all give substantially smaller values of [ xzz-+(xxx+~yy) I.It is also surprising to note the positive values of 1 x z z - + ( x x x + ~ y y ) I in the saturated four-membered rings. The results on formaldehyde indicate a large anisotropy for the C=O bond in that molecule. In addition the molecular g-values molecular quadrupole moments,' and aniso-tropies in the second moment of the electronic charge distributions are available from the experimental data for all of the molecules listed in tables 1 and 2 ; and the individual elements in the magnetic susceptibility tensors can be determined if the bulk magnetic susceptibility is known. Additivity rules for the values of the out-of-plane second moment of the electron densities have also been developed which enable the bulk susceptibilities to be estimated from the known anisotropies.The support of the National Science Foundation is gratefully acknowledged. erg/G2. Table 2 lists the anisotropies for a number of asymmetric tops. A review of the available data up to 1965 is in A. A. Bothner-By and J. A. Pople Ann. Reu. Phys. Chem. 1965 16,43. N. J. Harrick R. G. Barnes P. J. Bray and N. F. Ramsey Phys. Rev. 1953 90 260; N. F. Ramsey and H. R. Lewis ibid. 1957 108 1246; W. E. Quinn J. M. Baker J. T. La Tourrette and N. F. Ramsey ibid. 1958 112 1929. W. Drechsler and G. Graff 2. Phys. 1961,163,165 ; G. Graff and 0. Runo'lfsson ibid. 1965, 187 140 ; and G. Graff R. Schonwasser and M. Tonutti ibid. 1967 199 157. A. D. Buckingham W. H. Prichard and D. H. Whitten Trans. Faraday SOC. 1967,63,1057. J. R. Eshbach and M.W. P. Strandberg Phys. Rev. 1952 85 24. The rotational dependence of gaa is given in ref. (7). The gaa rotational dependence is also dis-cussed in detail in ref. (8). The general rotational dependence of the Xaa tensor elements is given in ref. (8). The rotational dependence of the y and -4 tensors is given here for the first time. B. F. Burke and M. W. P. Strandberg Phys. Reu. 1953 90 303. W. Hiittner and W. H. Flygare J. Chern. Phys. 1967 47 4137. Terms up through H 2 are given in this reference. A more complete Hamiltonian is obtained by D. Sutter A. Guarnieri and H. Dreizler 2. Naturforsch. 25a 222 (1970) by starting with the Lagrangian function of a free molecule in an external magnetic field. An additional term was found which can be described by an effective Stark effect due to the translation of the molecular charges in a magnetic field.The resultant effect will be negligible for molecules with second-order Stark effect but the effect will lead to broadening of K # 0 symmetric top transitions. The present work extends the original work by Huttner and Flygare up through H4 terms in the magnetic field. s.1-130 MEASUREMENT 0 F MAG N ETI C S U SCEP TJB I LIT Y A N I SOTRO P I ES For instance the value of the (Jd I &E 1 Jd) can be obtained analytically by expansion accord-ing to methods outlined in the appendix of ref. (4). l o M. Rotenberg R. Bivins N. Metropolis J. K. Wooten Jr. Tize 3-j arid 6-j Symbols (The Tech-nology Press Cambridge Mass. 1959). l W. Huttner M. K. Lo and W. H. Flygare J . Chem. Phys. 1968,48 1206.l 2 J. H. Van Vleck The Theory of Electric and Magnetic Susceptibilities (Oxford University Press, Oxford England 1932). l3 R. C. Benson H. Tigelaar S. Rock and W. H. Flygare J . Chem Phys 52 in press. l4 C. K. Jen Phys. Rev. 1949 76 1494. l5 W. Hiittner and W. H. Flygare J . Chem. Phys. 1968 49 1912. l6 R. L. Shoemaker S. G. Kukolich and W. H. Flygare unpublished results. l7 D. Vander Hart and W. H. Flygare Mu/. Phys. 1970,18 77. l 8 See ref. (8) and W. H. Flygare Amer. Chem. Soc. Meeting (Miami Beach April 10 1967). l9 W. H. Flygare W. Huttner R. L. Shoemaker and P. D. Foster J . Chem. Phys. 1969,50 1714. 2o R. L. Shoemaker and W. H. Flygare Chem. Phys. Letters 1968 2 610. 21 W. H. Flygare R. L. Shoemaker and W. Hiittner J . Chem. Phys. 1969 50 2414.22 R. L. Shoemaker and W. H. Flygare J . Amer. Chem. Soc. 1969 91,5417. 23 R. L. shoemaker and W. H. Flygare unpublished results. 24 S. G. Kukolich and W. H. Flygare Mol. Phys. 1969 17 173. 2 5 R. G. Stone J. M. Pochan and W. H. Flygare hiorg. Chem. 1969 8 2647. 26 D. VanderHart and W. H. Flygare Mul. Phys. 1970 18,77. 27 J. M. Pochan R. L. Shoemaker R. G. Stone and W. H. Flygare J . Chem. Phys. 1970 52, 28 J. H. S. Wang and W. H. Flygare J . Chem Phys 1970 52 in press. 29 W. Huttner and W. H. Flygare J. Chem. Phys. 1969 50,2863. 30 D. H. Sutter and W. H. Flygare J. Amer. Chem. SOC. 1969 91,4063. 31 D. H. Sutter and W. H. Flygare ibid. 1969 92 6895. 32 R. C. Benson and W. H. Flygare J. Chem. Phys. 1969 51 3087. 33 D. H. Sutter and W. H. Flygare Mol. Phys. 1969 16 153. 34 D. H. Sutter W. Hiittner and W. H. Flygare J. Chem. Phys. 1969 50 2869. 35 J. M. Pochan and W. H. Flygare J. Amer. Chem. SOC. 1969,92 5928. 36 W. Huttner P. D. Foster and W. H. Flygare J. Chem. Phys. 1969 50 1710. 37 S. G. Kukolich and W. H. Flygare J. Amer. Chem. Soc. 1969 91 2433. 38 W. Hiittner and W. H. Flygare Truns. Faraday SOC. 1969 65 1953. 39 R. Blickensderfer J. H. S. Wang and W. H. Flygare J . Cheni. Phys. 1969 51 3196. 40 J. M. Pochan R. G. Stone and W. H. Flygare ibid. 1969 51,4278. 41 S. G. Kukolich J. Chem. Phys. 1969,50 3751. 42 R. C. Benson R. S. Scott and W. H. Flygare J . Phys. Chem. 1969 73 4359. 43 R. C. Benson and W. H. Flygare Chem. Phys. Letters 1969 4 141. 44 R. C. Benson and W. H. Flygare J . Chem. Phys. 1970 52 5291. 45 J. A. Pople J . Chem. Phys. 1962 37 60. 46 J. A. Pople Proc. Roy. SOC. A 1957 239 541 and 550. 47 H. Heel and W. Zeil 2. Elektrochem. 1960 64 962 and W. Zeil and H. Buchert 2. phys. 48 G. S. Reddy and J. H. Goldstein J. Chem. Phys. 1962 36 2644 ; ibid. 1963 39 3509. 49 See appropriate references and discussion of the ring-current and local contributions to This work on formaldehyde was published in ref. (1 1). 2478. Chem. (Frankfurt) 1963 38 147. Xzr-41(Xxxi-Y,yy) in ref. (35)

ISSN:0430-0696    

DOI:10.1039/SF9690300119

出版商:RSC    

年代:1969

数据来源: RSC

摘要:

Light Scattering from Magnetic Systems* BY P. S . PERSHAN Division of Engineering and Applied Physics Harvard University, Cambridge Massachusetts 021 38 Received 7th October 1969 The development of laser light sources and the accompanying technological developments in optical signal processing techniques has facilitated light scattering experiments that were beyond previously existing practice. In this paper we discuss experiments in which light is inelastically scattered from various magnetic systems. The relation between the microscopic mechanisms responsible for these scattering and the microscopic mechanisms responsible for the conventional magneto-optical effects (i.e. Faraday and Kerr effects) is similar to the relationship between the microscopic mechanisms responsible for electron spin resonance phenomena and static electron paramagnetic susceptibilities.Allowing for the possibilities of occasional exceptions almost all magneto-optical effects can be explained in terms of some magnetically induced perturbation of the optical frequency dielectric constant. 1-3 This perturbation is usually slowly varying when compared with the optical frequency for which the dielectric constant is specified. At optical frequencies the dielectric constant or more fundamentally the complex conductivity a(w) = jw(4n)-l[&(w)- 11 of any material is dominated by the orbital motions of the electrons in the material. Thus a discussion of the micro-scopic origins of magneto-optical effects must centre around the manner in which magnetic forces influence those orbital motions.Making use of the observed fact that magneto-optical phenomena can often be classified as either paramagnetic or diamagnetic the relevant magnetic force for this discussion can be taken as either a macroscopic magnetic field in diamagnetic systems in which case the dielectric constant is taken to be a function of this field &(If) or else as in para- ferro- anti-ferromagnetic systems the dielectric constant is usually assumed to depend on the expectation value of the various unpaired electron spins in the material. Material systems for which the magnetic and magneto-optical properties are ascribed to itinerant or Bloch electrons can be more complex since spin and magnetic field effects are not clearly separable.' In this article we discuss various inelastic light scattering (i.e.Raman scattering) phenomnae that relates to the above-mentioned spin-dependent magneto-optical effects. We consider first the general theoretical ideas relating the two phenomena and then describe some experiments that have been performed and discuss the results of these. THEORETICAL DISCUSSION The earliest treatments of spin-dependent magneto-optical effects related the contribution of a given ion to the dielectric constant to the mean or expectation value, * Work supported in part by the Advanced Research Projects Agency SD-88 by the Joint Services Electronics Program (U.S. Army U.S. Navy and U.S. Air Force) under Contract N00014-67-A-0298-0006 and by the Division of Engineering and Applied Physics Harvard University Cambridge, Massachusetts.5* 13 132 LIGHT SCATTERING FROM MAGNETIC SYSTEMS of the spin of that ion. Since the characteristic frequencies that describe the pre-cession of spins are always much smaller than typical optical frequencies one can develop an adiabatic approximation for spin motion that is analogous to the Born-Oppenheimer approximation for nuclear motions. In Placzek's basic treatment of Raman scattering from phonons he assumes the optical dielectric constant can be expanded as a power series in the various nuclear displacements. Thus the optical frequency dielectric constant is taken to be instantaneously dependent on the nuclear configuration. The approximation is useful only because the characteristic nuclear frequencies are small when compared with the optical frequencies.Similarly the spin-dependent dielectric constants can be expanded as a power series in the various spin operators of a given system. For simplicity we consider an isotropic non-magnetic solid that contains a dilute concentration of paramagnetic impurities. If an external magnetic field were applied in the z-direction in order to align these spins one obtains parametric magnetic magneto-optical effects that can be related to the off-diagonal elements in the dielectric tensor,6 where for simplicity we may take A to be a real phenomenological constant. N is the number of ions per cm3. This is a good approximation if one can neglect optical absorption at the frequency o. For a paramagnetic N(S,) = -xparaHD.C. where, except for a multiplicative factor xpara is the paramagnetic susceptibility and E ~ ~ ( C ~ ) ) = ~ ? T ~ A x ~ ~ ~ ~ H ~ .~ from which one obtains an expression for the Verdet constant V, ~~,~(u)) = - 4niNA(S,) (1) V = +47~~A~~,,,n-li-~[rad G-l cm-l] (2) where n is the field free index of refraction at u) = 2nd-l. A more general discussion than presented here relates the average dielectric energy per unit volume to the free energy of this spin From this one obtains an effective Hamiltonian that will describe the interaction between the optical fields, at frequency o and the spins. The dielectric energy is where E is the complex vector amplitude of the optical frequency electric field. For linearly polarized light E can be taken as real. The spin-dependent part of U is SU, and from eqn (1), U = -(87~)-l[E E(w)* E" +E* E(O) El (3) 6U = + iNA(S,)[E,E%-E,E:].(4) Equating SU = N(X',ff) where ( ) implies a thermal average and Xeff is the " effective Hamiltonian " per ion (X'eff) = A(S,)[E,E,*-E,,E,*]. In fact a more general description of the interaction between the spin variable and the optical fields is in which E(t) is intended to indicate that the complex vector describing the optical field at frequency o = 2d-1 can also be a function of time providing it varies slowly compared to o. For example from (Xeff) = iA[E(t) x E*(t)] (S) one obtains the static Faraday effect. However in addition to this static effect eqn (5) has a term of the type Zeff = iA[E,,(t)E,*(t) - E,(t)E,*(t)]S,. In the presence of the external d.c. magnetic field the spin S can exist in any one of 2S+ 1 states of energy W = gpHm = ho,m and this term in Xeff connects states of different m.That is if the field E, were at frequency u) while E was at frequency u))+o, this effective Hamil-tonian would induce transitions. A more practical experiment is simply to have one incident field say E at frequency o and let E, be simply the vacuum fluctuations of Zeff = iA(E(t) x E*(t)] S (3 P. S . PERSHAN 133 the field at cu a,. From this term one predicts the cross-section for a spontaneous Raman scattering event in which one flips one individual spin. From knowledge of the Verdet coefficient this cross-section can be unambiguously obtained. Under favourable circumstances the cross-section for this type of event per ion is of the order (da/dCl)- For a concentrated system of ions N - loz1 ~ m - ~ one obtains an experimental cross-section of N lo-" cm2.This appears to be about the order of magnitude for the one magnon cross-section observed in light scattering from anti-ferromagnetic FeF .9 Actually the most significant experimental results on light scattering from magnetic systems has been on antiferromagnetic samples. The one relevant experiment on dilute paramagnetic systems done by J. P. van der Ziel in collaboration with the was not a light scattering experiment. Rather, circularly polarized light was incident on various systems with large Verdet constants in the absence of any externally applied magnetic field. From eqn (9 this has the effect of lifting the 2S+ 1 degeneracy of the various spin levels.If thermal equilibrium is established in the presence of circularly polarized light a magnetization results. The effect termed the inverse Faraday effect (IFE) was experimentally confirmed. This experiment thus established Xeff as a true effective Hamiltonian. There have been a number of theoretical papers in which the phenomena of light scattering from magnetic systems has been treated in much more detail than any of the present author's own contributions. Thorough understanding of these pheno-mena requires a more complete review of these contributions than we shall attempt here. Loudon lo and Moriya l1 have prepared such detailed reviews. Here we emphasize only the most important physical results. cm2. I FeF2 T- IS 'K R -4 P-v I I 1 First one observes that eqn 5 was written down for an ion in either a cubic or isotropic environment.In general for an isolated ion Zeff = i[E(t) x E*(t) A S ] where A is a second rank tensor that reflects the symmetry of the site. Secondly, since most of the relevant experiments are not done on dilute paramagnetic systems, it is not possible to treat the scattering events from different spins as independent. The consequence is that one must take where C specifies the sum over all ions in the system. Considering the fact that the optical wavelength is much larger than the interatomic dimensions the dependence of A on Rl can be neglected and since A@,) reflects the periodicity of the crystal one 134 LIGHT SCATTERING FROM MAGNETIC SYSTEMS obtains a wave vector selection rule.In single magnon Raman scattering from a pure antiferromagnet one observes the same frequencies that are observed in microwave, or infra-red antiferromagnetic resonance studies i.e. the Brillouin zone centre magnons. For FeF the energy of this magnon is at approximately 50 cm-l. The magnetic Raman spectrum for FeF at 15 K is shown in fig. 1. The one magnon line at 50 cm-I is clear. We note the polarization of this spectrum. Incident light polarized along the z axis of the crystal (spins are aligned along this axis) and scattered light perpendicular to this axis (x or y axis) is as predicted by eqn (6). The spectrum at 157 cm-1 is a two magnon scattering event that we discuss below. The simple relation between the one magnon Raman cross-section and the Faraday effect referred to above is not obtained in systems with more than one magnetic ion per magnetic unit cell.From the expectation value of eqn (6) one may obtain an expression for the magnetic contribution to the dielectric tensor. The expression for this contribution will contain some linear combination of the A(R,) (S,). In general this linear combination will not be the same as appears in the expressions for Raman cross-section. Knowledge of the various (S,) will however enable one to express the { A(R,)} in terms of the magneto-optical coefficients and from this express the Raman cross-sections in terms of these magneto-optical coefficients. The present magneto-optical effects required some mechanism for the spin forces to influence the orbital motion of the electrons.For an isolated ion or in some cases, even for the one magnon effects in the concentrated magnetic systems this mechanism turns out to be the one ion spin-orbit coupling effects.7v10911*16 The discussion of this follows the same line as Van Vleck's earlier treatment of the Verdet constant.6 A much stronger effect than spin-orbit coupling and which will also couple orbital motions to spins is exchange coupling. The effective Hamiltonian arising from exchange couplings is quadratic in the spin operators not linear as in the previous discussion. The effective Hamiltonian due to exchange effects is l2 (7) where repeated indices imply summation. All terms are symmetric with respect to indices p and v Q, and R, are symmetric and antisymmetric with respect to the interchange of two ionic spins or the indices p and z respectively and XQYL,, = 0.If a centre of inversion is located half way between the two ions Rj = 0. In the analysis of experiments to date the first term has been dominant. The expectation value of eqn (7) will yield certain magneto-optical coefficients. For example consideration of only the leading term in eqn (7) for a tetragonal ferro-magnetic crystal with only one magnetic ion per unit cell, z e f f = EE(t)Ev(t)(PTSj S + Q![p'prSjpSlz + R?{pzSjpSl'pr) where the prime on the summation is meant to restrict the sum to one cm3 of sample. From this it follows that Eqn (9) is derived on the assumption that the spin ordering has not induced any magneto-elastic distortion that would also contribute a similar term.In principle, strain measurements can separate the contribution of eqn (9) from such an effect. Verdet coefficients can readily be obtained from eqn (9). For a completely aligned ferromagnet at 0 K the leading term in eqn (7) does not predict any allowed spin transitions. The only spin operators are S,,S, or Sj*Sl*. The first are diagonal and the second are zero for the ground state. Antiferro-magnets like FeF, for example have adjacent spins oppositely aligned even at 0 K P. S. PERSHAN 135 and in these Sj+Sl- can induce a two-spin excitation. A transformation to spin wave operators converts the implied summation over j and I into a summation over wave vectors in such a way that the excitation corresponds to simultaneous creation of one spin wave with wave vector k and a second with wave vector -k.Considering the fact that spin wave energy versus k surfaces are particularly flat near the zone boundaries the density of magnon states per unit of energy shows a sharp peak near these zone boundaries. The effect is that the two magnon energies also show a peak near twice these values. Experimentally however the observed peak is about 4-5 cm-l lower than the one predicted by these simple considerations. Elliott et aLf4 have explained this as being due to the fact that the Pj,l are vanishingly small unless j and I are near each other. The effect of this is that in order properly to estimate the excitation energy one must include magnon-magnon interactions. This can be done in terms of an Ising-like approximation.14 The energy to flip one spin is just 2rSJ, where J is the exchange integral r is the number of neighbours and S is the spin per ion.To a good approximation this corresponds to the energy of a zone boundary magnon. The energy to flip two spins not near each other is just twice this. If, however the two spins are adjacent the excitation energy is 4rSJ-2J. This energy is reduced by a fraction (2rS)-l of the simple two magnon energy. For r = 8 and S = 2 (as in FeF,) this corresponds to about 3 %. Taking 4rSJ = 154 cm-l in FeF,, this shift is about 5 cm-l as observed. Recently light scattering has also been observed from magnetic impurities in these antiferrornagnets. For example from Fe l7 and Ni 1 7 s i 8 in MnF, and Ni in RbMnF3 and KMnF3.19 Thorpe has interpreted the two magnon spectral line shapes for these last two by means of Green’s function calculations.In view of the considerable theoretical interest 20*21 in magnetic impurity problems these experiments have been of considerable interest. Finally we draw attention to the fact that these light scattering experiments can obtain very precise measurements of magnon frequencies as a function of temperature or other external variab1es.l 8* The following relationship between the temperature shifts of zone boundary magnon energies and the magnetic heat capacity has been shown 23 to satisfy available heat capacity data to the accuracy with which the magnon energies are known. The relationship which has been empirically satisfied for all cases in which T50.7 TN is Ao(T) = h-l[S(S+ 1)]-* CM(T’) dT’ (10) s where C,(T’) is the magnetic contribution to the heat capacity at temperature T ’ ; S is the spin of the ions.The significance of this is that experimentally it is often impossible to separate the magnetic and lattice contributions to the heat capacity of a given The application of eqn (10) to light scattering data may well provide the most accurate measure of magnetic contributions to measured heat capacities. P. S. Pershan J. Appl. Phys. 1967 38 1482. Y. R. Shen Phys. Rev. A 1964,133,511. L. D. Landau and E. M. Lifshitz Electrodynamics of Continuous Media (Pergamon Press Inc., New York 1960) p. 251. See for example M. Born and K. Huang Dynamical Theory of Crystal Lattices (Oxford University Press Oxford 1962) chap.4 p. 166. G. Placzek Marx’s Handbuch der Radiologie IV 1934,2,209. See for example J. H. Van Vleck and M. H. Hebb Phys. Rev. 1934 46 17. ’ P. S. Pershan J. P. van der Ziel and L. D. Malmstrom Phys. Rev. 1966 143,574. * P. A. Fleury S. P. S. Porto L. E. Cheesman and H. J. Guggenheim Phys. Rev. Letters 1966, 17 84 136 LIGHT SCATTERING FROM MAGNETIC SYSTEMS J. P. van der Ziel P. S. Pershan and L. D. Malmstrom Phys. Rev. Letters 1965 15 180. lo R. Loudon Ada Phys. 1968 17 243. l1 T. Moriya J . Appl. Phys. 1968 39 1042. l2 T. Moriya J . Phys. SOC. Japan 1967 23,490. l 3 P. A. Fleury and R. Loudon Phys. Rev. 1968 166 514. l4 R. J. Elliott M. F. Thorpe G. F. Imbusch R. Loudon and J. B. Parkinson Phys. Rev. Letters, l5 M. F. Thorpe Phys. Rev. Letters 1969 23,472. l6 Y. R. Shen and N. Bloembergen Phys. Rev. 1966 143,372. l7 A. Oseroff and P. S . Pershan Phys. Rev. Letters 1968,21 1593. l8 P. Moch G. Parisot R. E. Dietz and H. J. Guggenheim Phys. Rev. Letters 1968,21 1596. l9 see ref. (15) and also A. Oseroff P. S. Pershan and M. Kestigian Phys. Rev. to be published. 2o S. W. Lovesey J . Phys. C. Proc. Phys. SOC. 1968 1 102. 21 T. Tonegawa and J. Kanamori Phys. Letters 1966 21 130. 22P. A. Fleury Phys. Rev. 1969,180 591. 23 P. S. Pershan and A. Oseroff Phys. Rev. B 1970 1 2359. 24D. T. Teaney Specijic Heats of Ferro- and Antiferrornagnets in the Critical Region Critical Phenomena (Proc. Conf. Washington D.C. 1965) ed. M. S. Green and J. V. Sensers (N.B.S. Misc. Publication 1966 273). 1968 21 147

ISSN:0430-0696    

DOI:10.1039/SF9690300131

出版商:RSC    

年代:1969

数据来源: RSC

摘要:

Microwave-Optical Double Quantum Studies of Short-Lived Triplet Systems BY MARK SHARNOFF Dept. of Physics University of Delaware Newark Delaware 1971 1 USA. Received 16th September 1969 An optical method for the detection of the e.p.r. of phosphorescent systems is described and applied to the study of triplet excitations in crystalline benzophenone at 4.2 K. The signals observed can be grouped into two categories which are very different in structure saturation behaviour and relaxa-tion time. The signals in one of these categories are shown to arise from triplet excitons. It requires more than one characteristic time to describe the propagation of these excitons ; the characteristic times are in the neighbourhood of 1.5 x 10-l1 s and 2 x 10-lo s. Magneto-optical activity charac-teristics and magnetic fine structure principal values of the excitons are presented.The radiofrequency or microwave fields employed in magnetic resonance studies conventionally serve not only to excite the resonances in question but also to convey to the experimenter the information that resonance has taken place. Only the first of these functions is essential. While the detection of resonance through its reaction on the radiofrequency or microwave field is both convenient and practical the first detection method to be attempted was apparently calorimetric. Other methods of detection more sensitive in many cases than the direct radiofrequency or microwave methods include in addition to the optical pumping technique,2 the utilization of the effects of saturation of resonance upon the electrical conductivity or upon the optical emission intensities 4 * 5 of conducting or optically emitting samples.Our concern in this paper will be with the interrelation of the latter method of resonance detection with some magnetic and magneto-optical properties of short-lived molecular and crystalline systems having a spin degeneracy of three. By the term " short-lived " we mean systems whose lifetimes are sufficiently short as to make it difficult or impossible to investigate their paramagnetism by conventional radiofrequency or microwave spectroscopy. The limitation of the conventional methods arises because the signals which they produce are proportional to the number of paramagnetic systems in the sample under study. The shorter the lifetime of a transient triplet state the smaller the obtainable concentration of systems in this state in a given sample.From a practical standpoint a triplet system will be con-sidered short-lived if its lifetime is smaller than 10 ms. Consider now a transient state which emits a quantum of visible light as it dis-appears and suppose an ensemble of these states to be created with the help of an ultra-violet lamp. If each ultra-violet photon absorbed in the sample produces one of these transient states then the rate at which visible quanta are emitted by the sample is equal to the rate at which ultra-violet quanta are absorbed independently of the lifetime of the transient state or the concentration in which it is produced. Any method of extracting magnetic resonance signals from the sample luminescence would be inherently free of the concentration-imposed limitations of conventional e.p.r.or n.m.r. spectroscopy. A basis for an optical method of detection of the e.p.r. of phosphorescent triplet 13 138 MICROWAVE-OPTICAL DOUBLE QUANTUM STUDIES states is shown in fig. 1. The method relies on the fact that while the orbital charac-teristics of the three triplet sublevels are nearly identical their radiative properties are vastly different. It not infrequently happens that only one of the three triplet levels is radiative. It is supposed that this is the case in fig. 1. The populations of the three levels will then be determined by the rapidity of spin-lattice relaxation pro-cesses which act to bring the populations into thermal equilibrium with the thermal reservoir of phonons in the sample.At temperatures in the liquid helium range these spin-lattice relaxation processes are usually inhibited and the population of the radiative level may become considerably smaller than those of the two non-radiative levels because the latter have no means of becoming de-excited except by relaxation transitions to the radiative state. Under steady-state ultra-violet excitation the phosphorescence intensity will be nr/zr where z is the lifetime of the radiative level. FIG. 1.-Level populations n and phosphorescence intensities for a triplet system having energies Ea, Er and Eb. Left portion microwaves off; right portion when one of the microwave transitions is saturated. If the transition between levels Y and a is now saturated by means of an intense microwave field the phosphorescence intensity will become 3(n + n,J/zr which is much larger than before.If the microwave field is removed the phosphorescence will return to its former intensity with a characteristic time z,. If the microwaves are pulsed on and off with a period z comparable to or longer than z the phos-phorescence will modulate with the same period as the microwaves. A similar result obtains when the transition between levels r and b is periodically saturated. Again, the phosphorescence is stronger with the microwaves on than with the microwaves off. If a magnetic field H is applied to the sample the triplet levels will mix with one another in a way which depends upon the orientation and strength of the magnetic field and the analysis of the behaviour of the populations becomes complicated because each level acquires in general some radiative character.Other complica-tions arise when the characteristic spin lattice relaxation times are short compared to 7,. These complications have been treated in detail and we shall not pursue their numerical ramifications. Two qualitative points remain clear. First, by varying the repetition rate of the microwave pulses it is readily determined whether or not the spin-lattice relaxation times are short or long compared to z or to z (we assume the latter to be known through other measurements). Secondly so long as z is either very short or very long compared to the spin lattice relaxation times th MARK SHARNOFF 139 radiative matrix elements of the three triplet sublevels can be inferred from a know-ledge of the way in which microwave saturation of the three e.p.r.transitions in turn increases or decreases the phosphorescence intensity. When an external magnetic field is present such measurements must be repeated three times once for each principal axis of the triplet system. The microwave-optical double quantum method also reveals all the information normally forthcoming from conventional e.p.r. techniques the principal values and orientations of the corresponding principal axes of the g-tensor and of the tensor of magnetic dipolar coupling between the two unpaired electrons,lO the hyperfine coupling constants spin-lattice and spin-spin relaxation times and saturation be-haviour of the resonance lines.In order to delineate the scope and power of the optical method we shall describe some results recently obtained in our studies of triplet excitations produced by ultra-violet irradiation of pure orthorhombic single crystals of benzophenone. Because no conventional e.p.r. spectrum of these excitations has been reported in spite of their widely noted ability to transport and transfer energy,l they are properly considered to be shortlived. Their radiative lifetimes 7r are approximately 6 ms.12 f v) 9680 9700 9720 9740 .-magnetic field in gauss FIG. 2.-One of the two sharp resonance observed with H parallel to the c-axis. Microwave carrier frequency 24.61 GHz ; modulation frequency 4 kHz. T = 4.2 K. About 300 mW of microwave power were incident upon the microwave cavity.The K-band e.p.r. of these excitations detected optically at 4.2 K with microwaves modulated at 200 Hz consisted of broad continua which were more or less finely structured depending upon crystalline orientation. Sometimes at very high micro-wave power levels a single sharp line 1.5-20 g in half width,14 would be superposed upon each of the structured continua. In some cases the integrated intensity of the sharp lines was as much as 30 % of the total. While the structured continua were present at all orientations of the crystal the sharp lines were clearly apparent only when the magnetic field lay nearly parallel to the a-axis or nearly parallel to the bc-plane of the crystal. Saturation of the continua produced only increases in the phos-phorescence intensity.Saturation of the sharp lines produced increases for the low field Am = f l transitions but only diminutions for the high field Am = +1 transitions in the phosphorescence intensity. The significance of these results is clear the spin lattice relaxation times of the continua are long and those of the sharp lines short in comparison to 7,. When the microwave modulation frequency was increased to 4 kHz the sharp lines suffered no observable diminution in ampli-tude while because of the slow spin-lattice relaxation the continua disappeare 140 MICROWAVE-OPTICAL DOUBLE QUANTUM STUDIES completely in some cases and were at worst never prominent. In this way it was possible to make detailed studies of the sharp lines (fig.2 and 3) without interference from the complicated structure of the continua. We shall here be concerned mainly with the sharp lines and shall refer to an earlier publication l5 for an analysis of the structured continua. m Y ..-5 x r! Y .- s c .I I I I I I I I 9705 9715 9725 ’ magnetic field in gauss FIG. 3.-The same resonance as in fig. 2 but observed with only 15 mW of incident microwave power and with somewhat higher amplification. To one familiar with the characteristics of e.p.r. lines in proton-rich solids a structureless line of width approaching 1.5 g indicates a spin system which has been exposed to local magnetic fields which fluctuate severely. Since a migratory electronic excitation-such as a triplet exciton-should experience local fields whose fluctuations are certainly larger and perhaps more rapid than those which could be produced by molecular vibration or hindered rotation at 4.2 K it is evident that the sharp lines should be associated with those excitons which the experimenter was attempting to study.The short spin-lattice relaxation times observed for these lines spurred the experimenter to perform the most critical test of his working hypothesis which he could devise examination of the degree of saturation l6 of the signals as a function of microwave power. At issue is the question of whether the e.p.r. lines are inhomogeneously broadened,16 the linewidth arising because different triplets in different parts of the sample are exposed to different nearly static local fields or whether the lines are homogeneously broadened.In the latter case the observed linebreadths form a record of the Fourier transform of the correlation function of the local field which a triplet system experiences during its lifetime and which if the systems are mobile, must be the same for every triplet. should be homogeneously broadened. Clearly the e.p.r. lines of a triplet exciton The saturation behaviour of optically detected e.p.r. signals is different from that of signals detected conventionally via the reaction of the spin system upon the micro-wave field.16 For optically detected signals it is the dzflerence between the saturated and unsaturated values of the longitudinal component of the magnetization which is detected. Thus if g(o) represents the e.p.r.absorption profile for a homogeneously broadened line subjected to very weak microwave fields the longitudinal component of the magnetization will have the form r 1 MARK SHARNOFF 141 Here Mo is the unsaturated value of the longitudinal magnetization HI the amplitude and o the angular frequency of the co-rotating component of the microwave field y the gyromagnetic ratio and Tl the spin-lattice relaxation time. The shape and half-width of the signal will vary with the microwave power level. If we define a spin-spin value of the dimensionless quantity x 007 0.7 70 I I I I I I l l ) I I I 0 1 1 1 1 1 I & 1 1 1 1 1 v1 c., .A c 100: b E Y .d s F .-Y a 3 I I I I I ' I I I I I I t I I I I I I I l l 1 1 1 0.3 3 30 300 microwave power in milliwatt FIG.4.-Peak signal amplitudes as a function of microwave power for the resonance whose profile appears in fig. 2 and 3. Microwave modulation frequency 4 kHz. The solid curve indicates the behaviour of a homogeneously broadened resonance. relaxation time T2 by the relation T2 = ng(omax) (a definition rigorously correct for Lorentzian lines) and set x = 2y2H:TlT2 the peak signal amplitude as a function of the microwave power level incident upon the cavity (to which x is proportional) will be A logarithmic plot of this function appears in fig. 4. The logarithmic plot of the saturation behaviour of the peak amplitude of an optically detected inhomogeneously broadened resonance would by contrast give a straight line of slope 4. The shape and half-width of the inhomogeneously broadened signal would be independent of the degree of saturation.In fig. 2 and 3 are shown recorder tracings of the sharp high field Am = 5 1 line observed with H parallel to the c-axis. The shape of the signal is accurately Lorentzian at highest power levels and approximately Lorentzian at substantially lower power levels where the half-width becomes a constant 1.5 G. Saturation studies of this line were carried out with the help of a calibrated attenuator and the peak signal amplitudes observed at various power levels plotted with typical errors indicated, in fig. 4. These three figures clearly show that the line is homogeneously broadened. Similar results were obtained for other directions of H. At lower microwave power, the high-field lines observed with H parallel to the b- or to the a-axis had half widths of 8-1 1 G.They were observed to saturate to a degree characterized respectively by x = 1.7 and x = 1.0 at full microwave power. From these values of x and from the amplitude H1 = 1.2 G calculated at full microwave power from the cavity Q and geometry we obtain values of the spin lattice relaxation time TI = 1.1 x s, (H 11 c); Tl = 1 . 5 ~ s (H 11 a). About 70 % of the linewidth observed with H 11 c arises from the spin-lattice relaxation. Mpeak(x) = Max/( 1 + x) (homogeneously broadened lines). (2) s (H 11 b ) ; and Tl = 0 9 m U .-d 5 I I & I 7100 7400 magnetic field in gauss FIG. 5.-Sharp line and part of one continuum observed with H parallel to the 6-axis. Microwave carrier frequency 24.51 GHz ; modulation frequency 200 Hz.Microwave power incident upon cavity 300 mW. e' u 2 value of the dimensionless quantity x 0.3 3 30 300 microwave power in milliwatt FIG. 6.-Saturation behaviour of the signals depicted in fig. 5 . Solid circles sharp line ; open circles shoulder (continuum). Solid curve homogeneously broadened resonance dashed line : inhomogeneously broadened resonance MARK SHARNOFF 143 continua thus come from excitations which are localized on individual molecules. The existence of continua rather than discrete inhomogeneously broadened lines, suggests that the localized excitations do not reside on chemical impurities but on benzophenone molecules near physical defects or dislocations of the lattice. Some of these molecules should act as traps of excitation.The breadth and shape of the continua suggest that while some of these molecules may be significantly mis-oriented with respect to crystal axes the principal types of mis-orientations are few in number and slight in nature. The angular variations in the breadths of the continua indicate that the most common mis-orientation involves a rotation of several degrees about the c-axis from the " normal " orientation. What then do our signals have to say about the " Wanderlust " of the exciton? We recall first that the exciton signals consisted of one high field and one low field line; and secondly that if all excitations were localized on " properly " oriented individual molecules four pairs of signals would have been ob~erved.'~ The lack of any indication in our exciton signals of the four magnetically distinct molecular orientations of the benzophenone lattice is cogent proof that the excitons are not confined to individual molecules or even to chains of magnetically equivalent molecules.The exciton conveys excitation to all molecules in the crystal and the transport is so rapid that most of the fine structure that would be present in a static system is motionally smoothed out. The theory of motional narrowing provides a way of calculating the transport rate in question. Let AH be the interval between, say the two high field transitions that would be observed in the static case with H parallel to the bc plane and let 6H be the half-width of the exciton signal. If it be assumed that the transport arises from a random hopping of excitation from one molecule to another the characteristic time of the process would be z = 46H/(yAH2).Taking typical values AH = 250 G and 6H = 4 G from our bc-plane data we find z = 1.5 x s. A similarly short characteristic time is required of a hopping process that would produce spin-lattice relaxation as rapid as indicated by our saturation data. We do not believe however that the motion of the exciton is as " simple " as a random hopping process. Such a process would produce for H parallel to the ab or ac plane a motional collapse of fine structure similar to that observed for H parallel to the bc plane. No such complete collapse is observed here however. Instead the narrow exciton signals acquire sidebands which are located near the positions expected for signals from localized excitations.The patterns give the impression that the characteristic time of random hopping were suddenly lengthened by a factor of ten! It seems likely that this paradox could be resolved by an analysis which assumes that the propagation of the exciton is basically coherent rather than random. In coherent propagation the several exchange coupling constants would preserve their identity as characteristic frequencies of a multiply periodic motion. The motional narrowing would accordingly require several characteristic times for its description.lg While our proposal is tentative it is interesting that the short and long characteristic times of our data can be translated into exchange integrals (J = (4nch~,)-~) of 0.19 and 0.02 cm-' which are close in value to those required by the Tlc.So Davydov splittings.20 Our remaining magneto-optical data appear in table 1.Since only part of the total phosphorescence emanates from excitons rather than traps the individual numbers in parentheses are not so significant as their ratios to one another. These data when analysed along the lines of a previous investigation show that the exciton spin sublevel which is quantized along the b-axis 2o is optically dominant furnishing about 75 % of the exciton phosphorescence. The spin sublevel quantized along th 144 MICROWAVE-OPTICAL DOUBLE QUANTUM STUDIES a-axis furnishes about 25 %. These values in conjunction with the TI c So polariza-tion ratios 21 Ib I I = 2.5 1 0 indicate that the spatial factors in the exciton wavefunctions responsible for most of the radiative intensity of Tl-S0 transitions must transform 2o like the A and B3 representations of the point group D2.This deduction is in good agreement with those which might be drawn from the Zeeman spectroscopic r e s u h 2 TABLE ~.-EXTREMAL VALUES IN GAUSS OF THE MAGNETIC FIELDS CORRESPONDING TO THE Am = &l e.p.r. TRANSITIONS OF TRIPLET EXCITONS IN BENZOPHENONE. THE NUMBERS IN PARENTHESES INDICATE THE CHANGES IN PHOSPHORESCENCE INTENSITY WHICH ACCOMPANIED SATURATION OF THE TRANSITIONS. direction of H II a I! b II c low field resonance 8 289rt2 7 332f1.5 7 773 f l (+0.15 %) (f1.6 %) (+0.9 %) high field resonance 9 168f2 10 134fl 9 720 f0.5 (-0.15 %) (-1.2 %) (-1.1 %) microwave frequency GHz 24.60 f0.02 24.64 f0.02 24.64 f0.2 The magnitudes of the principal values of the magnetic dipolar coupling tensor can be extracted from the magnetic extrema by well-known formulae 22; their signs are given by analysis of the signs of the microwave-optical double quantum signals, which indicate that the energies of the spin sublevels occur in the order E < B < Eb.We thus obtain 23 A/hc = -0.0273 cm-'; B/hc = t-0.0873 crn-'; in fair agreement with the values which would be predicted from our earlier fine structure analysis. C/hc = -0.0605 cm-I, This work was generously supported by the National Science Foundation. C. J. Gorter Physics Today 1967 20 76. A. Kastler J. Phys. Radium 1950 11 255. M. Gukron and I. Solomon Phys.Rev. Letters 1965 16 667. J. Brossel and A. Kastler Compt. rend. 1949 229 1213. S. Geschwind G. E. Devlin R. L. Cohen and S. Chinn Phys. Reu. A 1965 139 314. M. Sharnoff J. Chem. Phys. 1967,46 3263. M. Sharnoff MoZ. Cryst. 1969 9,265. M. Sharnoff Chem. Phys. Letters 1968,2,498. Because of an algebraic error in this work the signs of both D and E were incorrectly reported. R. M. Hochstrasser J. Chem. Phys. 1964 40 1038. ' A. L. Kwiram Chem. Phys. Letters 1967,1 272. lo C. A. Hutchison and B. W. Mangum J. Chem. Phys. 1961,34,908. l2 R. A. Keller J. Chem. Phys. 1965 42,4050. l 3 A. S. Gaevskii V. G. Roskolod'ko and A. N. Faidysh In?. Con$ Luminescence (Budapest), l4 Half-width is defined as the full width between points at which intensity is 50 % of the maxi-l5 M.Sharnoff J. Chem. Phys. 1969,51,451. l6 A. M. Portis Phys. Rev. 1953 91 1071. l7 A. Abragam Principles of Nuclear Magnetism (Oxford University Press London 1961), l 8 The multiplicity of exchange constants arises because there are four molecules per unit cell in preprints part B.3 p. 51. mum. chap. X p. 450. the orthorhombic phase of benzophenone MARK SHARNOFF 145 In the random walk model of exchange narrowing the several exchange constants add together to produce a lumped hopping probability whose reciprocal is the only observable characteristic time of the narrowing process. 2o R. M. Hochstrasser and T.-S. Lin J. Chem. Phys. 1968,49,4929. 21 S . Dym R. M. Hochstrasser and M. Schafer J. Chem. Phys. 1968 48 646. 22 J. H. van der Waals and M. S . de Groot Mol. Phys. 1959,2 333. 23 These values are very different from those derived from Zeeman intensity patterns in ref. (20). We believe that the values obtained therein are questionable since they were calculated from an expression [eqn (1 1) of that article] in which the coupling of an electron spin with an electric field properly represented (ref. (24)) by the operator [(efi/4m2c2)E x p - a,] was incorrectly replaced by an operator containing the orbital angular momentum of the electron. Such a re-placement is not warranted when the electric field to which the electron is exposed is not spher-ically symmetric. 24 W. Pauli Die Allgemeinen Prinzipien der Quantenmechanik in Handbuch der Physik ed. S. Flugge (Springer-Verlag Berlin 1958) vol. V part 1 p. 161

ISSN:0430-0696    

DOI:10.1039/SF9690300137

出版商:RSC    

年代:1969

数据来源: RSC

摘要:

Magnetic Circular Dichroism of Charge-Transfer and Coupled-Chromophore Systems BY B. R. HOLLEBONE S. F. MASON AND A. J. THOMSON School of Chemical Sciences University of East Anglia Norwich Received 27th August 1969 The magnetic circular dichroism (MCD) of 1 ,lo-phenanthroline and of its chelate complexes, [Cu(phen),]+ and [M(phen)J2+ where M is an iron-group or group 2B metal ion have been recorded over the frequency range 16000-50000 cm-'. The results show that the strongp- and P-band of phenanthroline at 37 000 and 44 O00 cm-' respectively are mutually perpendicularly polarized and that the weaker a-band at 30 OOO cm-' has vibronic components of mixed polarization. There is no inter-ligand exciton contribution to the Faraday terms governing the MCD in the ligand absorption region of the spectra of the complex ions the MCD of the complex resembling that of the free ligand in this region.The charge-transfer band of the copper@) and iron-group metal complexes is associ-ated with an A-term in the MCD spectrum indicating that the hole generated in the d ' O or strong-field d6 ground electron configuration by the charge-transfer excitation lies partly or largely respec-tively in an orbital doublet in the excited state. The magnetic circular dichroism of a variety of transition-metal and lanthanide complexes in the frequency region of the d-+d or f4f and the charge-transfer transi-tions have been recorded and analyzed but few studies have been reported of the corresponding spectra in the frequency region of the ligand transiti0ns.l.The ligand MCD of a number of metal porphyrins with approximate square-planar co-ordination has been investigated,l* but the principal interest in tetrahedral and octahedral chelated complexes which form the subject of the present study has been the metal-ion and charge-transfer transitions hitherto. In contrast the ligand transi-tions of chelated metal complexes have attracted particular attention in the field of natural optical activity in connection with the determination of absolute stereo-chemical configuration and of the symmetries of the excited ligand ~ t a t e s . ~ The application of exciton theory to tris-chelated hexacoordinated metal complexes with D3 symmetry indicates that the ligand excitations which are long-axis polarized in the free ligand e.g.(I) are strongly optically-active giving rise to two major circular dichroism (CD) bands with opposed signs and equal areas. For complexes with a quasi-closed-shell electronic ground state such as the tris-1 10-phenanthroline complexes of metal ions with a strong-field d6 electronic configuration these two major CD bands are due to transitions from the lA ground state to the lA2 and lE exciton states and for the purpose of determining absolute configuration it is of crucial importance to distinguish the CD bands arising from the non-degenerate and from the doubly-degenerate exciton transition respectively. In principle the Faraday effect provides a straight forward method for distinguish-ing between the non-degenerate lAl -+ A2 and the doubly-degenerate 'A -+ lE, ligand exciton transitions.The former is expected to give rise only to a B-term, whereas the latter should be associated with an A-term.lg In addition the MCD spectra of strong-field d6 and d10 metal phenanthroline complexes are expected to clarify problems relating to the metal-to-ligand charge-transfer transitions. In the upper states resulting from these transitions the hole in the (tzJj sub-shell of the D3 14 B . R . HOLLEBONE S . F . MASON AND A . J . THOMSON I TI 2 m I 14 148 MCD OF CHARGE-TRANSFER SYSTEMS tris-chelated complexes may be either an orbital singlet a, or an orbital doublet e, and similarly the hole in the (d)lo shell of the DZd complex [Cu(phen),]+ may be either an orbital singlet bZ or an orbital doublet e. In the present work the MCD spectra of 1 ,lo-phenanthroline(I) [Cu(phen),]+(II) and [M(phen),12+(III) where the metal ions M are cadmium(II) mercury(II) iron(I1) and ruthenium(II) have been measured in order to investigate these expectations.EXPERIMENTAL The MCD spectra were measured with solutions of the ligand or complex ion in a cylindrical cell located at the centre of the room-temperature bore of a liquid-helium super-conducting magnet (Oxford Instruments Ltd.) with an optimum field strength of 48 000 gauss, using the Jouan Dichrograph CD185 or a CD spectrophotometer designed in these labora-tories. In the latter instrument covering the wavelength range 185-1 200 nm light from a Uvispek monochromator fitted with either a silica or a glass prism passes through a quartz Rochon prism and a rotating achromatic combination of quartz retardation plates to give left- and right-circularly polarized light at 4 Hz.After traversing the sample the modulated radiation is detected by a photomultiplier either a cooled RCA 7102 for the 1 200-600 m range or an EM1 6256B for the 600-185 nm region. The ratio of the a.c. to the d.c. signal which are separately amplified is displayed on a chart recorder giving the differential optical density for left- and right-circularly polarized light. The compounds were prepared by standard methods. The sample concentrations for the MCD spectra were the same as for the absorption spectra. The sign convention chosen is that used by Stephens,l the Verdet constant of water being taken as negative. The Faraday rotations are expressed as molar ellipticities per unit gauss [el,.RESULTS The absorption and MCD spectra of the strong-field d6 iron(I1) and ruthenium(I1) tris-phenanthroline complexes in the region of the ligand absorption above 30 000 cm-l do not differ significantly from the corresponding spectra of 1 lo-phenanthro-line when appropriately weighted to allow for the three ligand molecules in each complex ion (fig. 1 and 2). Less remarkably the MCD of the dl0 cadmium(I1) and mercury(I1) tris-phenanthroline complexes do not differ appreciably from that of the free ligand. There are no indications from the MCD spectra of the exciton states resulting from the instantaneous Coulombic interaction between the transitional charge distributions c\f the three ligands in these tris-chelated complexes either for the long-axis or the short-axis polarized excitations near 37 000 and 44 000 crn-l, respectively (fig.1 and 2). These exciton states are evident from the natural CD spectra of the optical isomers of the tris-phenanthroline metal complexes notably, for the long-axis polarized ligand excitations and it is concluded that purely Coulombic interactions between chromophores give vanishing matrix elements for the Faraday effect. Electron exchange between the chromophores of a composite molecule appears to be essential for non-zero A- B- or C-terms connected with the electronic transitions involving two or more chromophores. The strong charge-transfer band in the visible region of the tris-phenanthroline complexes of the iron-group metal ions suggests that charge-transfer configurations contribute to the various electronic states of these complexes so that n-electron delocalization between the ligands through the metal ion is non-vanishing.From the dipole strength of the visible charge-transfer absorp-tion given by [Fe(phen),12+ a value of 11 000 cm-1 has been estimated for the n-electron resonance integral between the metal ion and the ligand a value of about one-half of the normal carbon-carbon n-electron resonance integral for aromatic systems. Direct bonding between the n-systems of the ligands also obtains in th B . R . HOLLEBONE S . F . MASON AND A . J . THOMSON 149 5 4 3 w - 2 2 , 2 1 (nm) 500 400 300 3 4 < (lo4 cm-’) 0 + 6 +4 5: c 2 5 0 -2 - 4 - 6 FIG.1.-Upper curves the absorption spectra of [Fe(phen)J’+ (-) and of 1,lO-phenanthroline (- . -). Lower curves the MCD of [Fe(phen)3]’+ (- -) and of 1,lO-phenanthroline (. . .); solvent, water. A (nm) 5 0 0 400 3 0 0 200 - + I 0 - +5 E El -0 -5 -I 0 v (lo3 cm-l) FIG. 2.-The absorption spectrum (upper curve) and MCD (lower curve) of [R~(phen)~]’f; solvent, water 150 MCD OF CHARGE-TRANSFER SYSTEMS tris-phenanthroline metal complexes on account of the close proximity (2.79 A) of the nearest-neighbour nitrogen atoms of different ligands. A resonance integral of some 800 cm-l has been estimated for the consequent interaction. These interactions affording a degree of n-electron delocalization throughout the d6 complex ions(III) do not appear to be appreciable enough (fig.1 and 2) to give rise to observable inter-ligand Faraday matrix elements. Inspection of the wave-functions for the ligand exciton states in a tris-chelated complex indicates that the matrix element of the magnetic moment operator between the components of a doubly-degenerate state vanishes whether the state arises from long-axis or short-axis polarized ligand excitations (I) when elements between orbitals on different ligands are ignored. Similarly the magnetic moment operator does not connect the non-degenerate excitations of different ligands in a complex amongst themselves nor with the degenerate excitations and there are no non-vanishing inter-ligand Faraday terms in the point-dipole exciton approximation. The MCD of the free phenanthroline ligand shows vibronic structure in the region of the a-band originating at 30 000 cm-I and B-terms with opposed signs and com-parable magnitudes associated with the p- and P-bands at 37 000 and 44 000 cm-l, respectively (fig.1). The latter observation indicates that the transitions responsible for the p - and P-band are mutually perpendicularly polarized supporting the natural CD evidence that the p-band is long-axis and the P-band short-axis polarized (I). The polarized excitation and fluorescence spectra of 1,lO-phenanthroline give a uniform degree of polarization ( p = +0.23) over the frequency range investigated,6 25 000-39 000 crn-' showing less resolution than the MCD spectrum. The degree of polarization found ti is intermediate between that expected for emission polarized parallel (+ 0.50) and perpendicular (- 0.33) to the absorption polarization suggesting a degree of mixed long- and short-axis polarization over the region of the a- and the p-band.The perpendicularly-polarized components are defined by the MCD bands of opposite sign in this region (fig. 1). The MCD spectrum of the bis-complex [Cu(phen),]+ (fig. 3) exhibits a distinct A-term in the visible region. The ratio (A/D) is estimated to be -0.54pM from the peak-to-trough separation and from a gaussian fitting procedure to be - 0.6pM. (B+C/kT)/D is obtained from the gaussian fitting procedure and has a value of - 5 x 10-5pM cm which is reassuringly small in comparison with AID value. In contrast the analysis of the visible region of the MCD spectra of the tris-chelated complexes [Fe(phen),12+ (fig.l) and [Ru(phen),]'+ (fig. 2) yields results that suggest B terms of opposite sign are dominating the spectrum. A peak-to-trough analysis yields (AID) ratios for the charge-transfer region of 1.7PM and l.8pM for [Fe(phen),12+ and [R~(phen)~],+ respectively. However although satisfactory fitting of both spectra may be obtained using a progression of gaussian components on both a wavelength and wavenumber plot the sum of the A-term parameters thus obtained varies widely depending upon the plotting bases chosen and on the number of gaussian components. On the other hand the B-term parameters obtained are stable to the fitting procedure chosen suggesting that indeed B terms are dominating the spectra of the tris-chelated complexes in the charge-transfer region.The ratio (B/ D) is about + 0.004 and - 0.004 for the low and high energy regions respectively, of the charge-transfer bands of both [Fe(phen),12+ and [Ru(phen),12+. Charge-transfer transitions occur for the bis-chelated complex [Cu(phen),]+ of symmetry DZd from the filled d-shell with orbital symmetry either b or e into empty ligand orbitals of symmetry e(t+h) a2(x) or b,(x). The ligand n-orbitals are either symmetric ($) or anti-symmetric (x) with respect to a two-fold rotation about the short axis of the free ligand (I) of symmetry C2"' which becomes a C axis in th B . R . HOLLEBONE S. F. MASON A N D A. J . THOMSON 151 bis-chelated complex The ratio (AID) can be estimated for the three one-electron transitions that on symmetry grounds alone are expected to generate non-zero A-terms.The expression for A for a molecule with a unique axis is given by Stephens et a l l o The results obtained are as follows. ground excited one-electron AID state state configuration ( 8 ) l A l -+ 1E [ m e 3 ( 4 1 + 0.5 l E [b me3 (41 -0.5 lE [el(ll/)bt(d)l O* These values have been obtained assuming that each E excited state consists only of the configuration given in parenthesis beside it and that the d-orbitals are pure octahedral orbitals. The former condition will only be true in the limit of a large distortion from tetrahedral geometry. In the present case the distortion is undoubtedly very small so that configuration interaction will ensure that the two E states (arising from occupation of the X-type ligand orbitals) will consist of about 50% of the two configurations.Since AID is equal and opposite in each case the observed A / D should be close to zero. 1 (m) 5 0 0 40 0 1 1 I I I I I 5 2 0 2 5 3 0 V ( lo4 cm-') FIG. 3.-The absorption spectrum (upper curve) and MCD (lower curve) of [Cu(phen),]+" solvent, iso-amyl alcohol. Comparison with the observed value of AID shows that the charge-transfer transition is predominantly e4(d)+b:k) and that the transition e4(d)+a:k) has a very low intensity. This assignment is in disagreement with that suggested by Day and sander^.^ They concluded from an examination of the effect of substituents in * The value of zero is obtained if matrix elements of Lz between orbitals on different ligands are ignored 152 MCD OF CHARGE-TRANSFER SYSTEMS the 1,lO-phenanthroline ligand upon the energy of the visible absorption band that the transition involved transfer of an electron into the $ ligand orbital.The charge-transfer transitions of the tris-chelated complexes are from the t,d sub-shell into ligand orbitals of type x with symmetries a and e or ligand orbitals of type $ with symmetries a and e. Again the ratio AID can be estimated for the six possible transitions to excited E states. They are given below. ground excited state state 'Al -+ 'E, lEb lEC l E d lEk? lEf AID ( B ) +0.5 - 0.5 O* + 0.5 - 0.5 O* These values were obtained assuming that the d-orbitals are pure octahedral d-orbitals and that the various Estates consist only of the configurations in parentheses beside them.Since the trigonal splitting is small the states E, Eb and E will consist of almost equal mixtures of the three configurations given beside them and the approximation that the d-orbitals are pure octahedral should be appropriate. Thus a vanishingly small ratio (AID) is predicted if the one electron transitions e4(d)+a:(~) and e4(d)+e1k) have equal intensity and similarly for transitions into ligand orbitals of type $. Thus the observed MCD spectra of both [Fe(~hen)~]~+ and [Ru(phen),12+ suggest that these transitions have similar probabilities leading to the absence of observable A terms. Clearly the MCD spectra give no help in deciding whether the charge-transfer is into ligand orbitals of type x or $. Day and Sanders have suggested that ligand orbitals $ are involved on the basis of the effect of ligand sub-stituents upon the energy of the charge-transfer band of [Fe(phen)J2+.The polarized crystal spectra of the tris-bipyridyl complexes of Fe(I1) and Ru(I1) ' show that the excited state involved has E symmetry. We are currently examining the MCD spectra of d5 tris-chelated 1,lO-phenanthroline complexes to see whether the expected C terms resolve the difficulties. We thank the S.R.C. for a Research Fellowship (B. R. H.) and for the circular dichroism spectrophotometer. We are grateful to Mr. R. E. Waddell and Dr. R. G. Grinter for supplying computer programmes and to Mr. D. J. Robbins for assisting in the calculations. A. D. Buckingham and P. J. Stephens Ann. Rev. Plzys. Chem. 1966 17 399. P. N. Schatz and A. J. McCaf€ery Quart. Rev. 1969 23 522. S. F. Mason Inorg. Chim. Acta Rev. 1968 2 89. 4P. Day and N. Sanders J. Chem. SOC. A 1967 1530 and 1536. D. H. Templeton A. Zalkin and T. Ueki Acta Cryst. 1966 21 A154 (supplement). H. Gropper and F. Dorr Ber. Bunsenges. physik. Chem. 1963 67 46. ' R. A. Palmer and T. S . Piper Inorg. Chem. 1966,5 864. * C. J. Ballhausen Introduction to Ligand FieZd Theory (McGraw-Hill New York 1962). lo P. J. Stephens W. Suetaka and P. N. Schatz J. Chem. Phys. 1966,42,4592. L. E. Orgel J . Chem. SOC. 1961 3683. * The value of zero is obtained if matrix elements of Lz between orbitals on different ligands are ignored

ISSN:0430-0696    

DOI:10.1039/SF9690300146

出版商:RSC    

年代:1969

数据来源: RSC

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DlSCUSSIO N REMARKS Prof. J. H. van der Waals (Leiden) said I have two questions concerning the interesting results on zero-field splittings presented by Hochstrasser. (i) Pyrazine : the transition studied is into the triplet exciton band for which the zero-field splitting is expected to be less than for the free molecule. It would seem however that the data of table 1 are roughly equal to those observed for the isolated molecule in phosphorescence modulation experiments of the type described by Sharnoff. (ii) Pyrimidine From the phosphorescence polarization studies of Krishna and Goodman and their analysis of spin-orbit coupling in this molecule one would expect radiative decay to be predominantly y-polarized from the a spin component. Hochstrasser’s results seem to indicate that decay is mainly via a,.Could you explain the situation a little more fully? y-Polarized decay from a would confirm a B orbital symmetry of the phos-phorescent state ; it would then further indicate that for pyrimidine in MO terminology the anti-symmetric linear combination (n-) of the nitrogen lone-pair orbitals is of higher energy than the symmetric one. This result would be interesting since it is opposite to the situation encountered in pyrazine where n- is of much lower energy than n+.2 Prof. R. M. Hochstrasser (University of Pennsylvania Penrt.) said In reply to van der Waals the D values quoted in the table in our paper are referred to the anisotropy in the free molecules. With reference to the axis designations the D values in table 2 are as follows : pyrimidine and s-triazine D = -92.pyrazine D = - 3 Y ; For pyrazine we observe an exciton splitting and so the exciton zero-field splitting is first measured and subsequently transformed to the assumed axes of the molecular anisotropy. For s-triazine the crystal and molecular axes nearly coincide-to the extent that the crystal is nearly uniaxial. For pyrimidine there are two possible values of D. The first (given in the table) assumes that the intermolecular exchange interaction is negligible compared with the Z.F.S. energy spread. The second (mentioned in the text) assumes the opposite and leads to a larger and intuitively more reasonable value of D that is in fair agreement with spin-spin calculations. However our experiments above cannot be used to decide which value of D for pyrimidine is the proper one and both values are subject to an error of +20 %.In response to his second question perhaps eqn (9) has caused confusion; as inferred in the next paragraph ,u is much less than v. Actually 93 % of the electric dipole activity resides in the transition involving az just as he expected. The transi-tion is mainly y-polarized (via a,) and about 7 % is z-polarized (via a,,). According to the low field measurements (adopting an exciton coupling scheme) the active a, spin state is lowest (at - 0.1 cm-l) and the inactive a spin state is highest (at + 0.08 cm-l). In reply to vander Waals’ second question just what type of non-bonding molecular orbitals are best used for the excited states of pyrimidine and pyrazine is not clear.Experimentally we find that in both cases the excited state wave-function is free from Krishna and Goodman J. Chem. Phys. 1962,36,2217. Clementi J. Chem. Phys. 1967 46 4737. 15 154 GENERAL DISCUSSION nodes through the nitrogen. In addition pyrimidine has a large dipole moment change on excitation. Dr. P. Day (Oxford University) said We have also been looking at the polarized spectrum of CsMnCl3*2H,O down to liquid helium temperatures.l We have deter-mined the intensity variation of the 4A 4E band not simply at 300 and 77 K as McClure has done but at a large number of temperatures from 4 to 300 K. The form of the variation is shown in fig. 1. The band area was estimated as the product of the maximum optical density and the half-width to lower frequency from a Cary 14 trace the temperature being measured by a gold/iron against chrome1 thermo-couple.The figure shows that although McClure's general conclusion about the I 1 I I 1 0 00 2 0 0 300 K FIG. 1. lack of temperature variation between room temperature and 77 K in this salt is confirmed the detailed variation is complicated. In particular the band area reaches a shallow maximum at about 60-70 K dropping rather more sharply towards lower temperatures. It seems likely that the intensity variation below 30 K is a result of inter-chain ordering and indeed the entire curves bear some superficial resemblance to that of the bulk susceptibility against temperature.2 Dr. D. W. Davies (University of Birmingham) said The values for diamagnetic anisotropies obtained by Flygare and his coworkers for cyclic systems by microwave spectroscopy throw light on a question probably first treated by Ehrenfest in 1925, viz.the contribution of delocalized n-electrons or ring currents. I shall concentrate on benzene a molecule that has interested theoreticians and experimentalists for more than a century. The diamagnetic anisotropy of benzene was measured experimentally in 1956 by Hoarau et aZ.,5* who obtained the value -59.7 x c.g.s. units. This value, L. Dubicki and P. Day unpublished observations. T. Smith and S. A. Friedberg Phys. Reu. 1968 176,600. W. H. Flygare and R. L. Shoemaker this Symposium. P. E. Ehrenfest Physica 1925 5 388. J. Hoarau N. Lumbroso and A. Pacault Compt. rend. 1956,242 1702. J . Hoarau Contribution exptrimentale et thkorique 2 I 'ktude magnktique des mol&des (Thesis, Paris 1956) GENERAL DISCUSSION 155 obtained from crystal measurements is consistent with the microwave value for fluorobenzene obtained by Hiittner and Flygare.' Pochan and Flygare have reported the value for the diamagnetic anisotropy of 1,3-~yclohexadiene as - (7.4+ 2.2) x If this is interpreted as meaning that the diamagnetic anisotropy of a C-C double bond is - (3.7 & 1.1) x the delocalization or ring current contribu-tion to the anisotropy of benzene is - (48.6+ 3.3) x with an optimistic assessment of the error.that the whole of the diamagnetic anisotropy of benzene was due to this delocalization contribution which may be called AxL. The assumption was questioned by Berthier et al.,4 and a detailed discussion was given by H ~ a r a u ~ who pointed out that the anisotropy of an isolated pn-electron Axp and the anisotropy of the a-bonds Ax" might also be important a view that was supported by other worker^.^-^ Davies summarized the arguments and suggested that AxL has the value -41 x There has however been much controversy about the anisotropy of C-C and C-H a-bonds and workers in nuclear magnetic resonance spectroscopy have suggested values based on experimental chemical shift measurements that would require the whole of the anisotropy of benzene to be attributed to the a-electrons.The anisotropies given by Davies lo in 1963 for sp bonds would lead to an upper limit of about 20x for the magnitude of this contribution. The corrected value for the diamagnetic anisotropy of ethane obtained by measurements of the Cotton-Mouton effect is consistent with these 1963 bond anisotropies.As Axp has a different sign from AxL and Axu there is good reason why I AxL+Af I should be greater than 5 9 . 7 ~ is a lower limit. The experimental evidence provided by Flygare and Shoemaker l2 seems to agree well with these other arguments. It was suggested by London and it may be that the value I AxL I = 41 x Dr. M. G. Corfield (University of Manchester) said It is relevant to elaborate upon Davies's discussion of the magnetic susceptibility anisotropy of benzene. In the absence of any reliable data from the gaseous state the proposed theories have relied upon the estimate given by Hoarau et al. for the crystalline state of benzene.I now present the results of recent measurements of the magnetic birefringence of benzene in the vapour state. These give directly the molecular magnetic suscep-tibility anisotropy. The total magnetic birefringence can be expressed in terms of the molar Cotton-Mouton constant as given by Buckingham et aL2 : where qap:76 is a coefficient representing the modification of the electric polarizability by the magnetic field and a = +aaa x = +xaa are the mean electric and magnetic W. Huttner and W. H. Flygare J. Chem. Phys. 1969 50,2863. J. M. Pochan and W. H. Flygare J. Amer. Chem. SOC. 1969 91 5928. F. London J. Phys. Rud. 1937 8 397. G. Berthier M. Mayot A. Pullman and B. Pullman J. Phys. Rad. 1952 13 15. T. Itoh K. Ohno and H. Yoshizumi J.Phys. SOC. Jupun 1955 10 103. D. P. Craig M. L. Heffernan R. Mason and N. L. Paddock J. Chem. SOC. 1961 1376. ' D. W. Davies Nature 1961 190 1102. * D. W. Davies Trans. Furaday SOC. 1961 57 2081. D. W. Davies The Theory of the Electric and Magnetic Properties of Molecules (Wiley 1967), p. 122. A. D. Buckingham W. H. Prichard and D. H. Whiffen Trans. Furuduy Soc. 1967 63 1057. l o D. W. Davies Mol. Phys. 1963 6,489. l 2 L. Dubicki and P. Day unpublished observatrons. l 3 J. Hoarau N. Lumbroso A. Pacault Compt. rend. 1956 242 1702. l4 A. D. Buckingham W. H. Prichard and D. H. Whiffen Truns. Furuday SOC. 1967 63 1057 156 GENERAL DISCUSSION susceptibilities. For benzene temperature studies of the vapour have shown that the direct polarization term (qaa:as - +qaa:BB) makes a negative contribution of approxi-mately 10 % to the total birefringence.From our results the anisotropy of the magnetic susceptibility (xzz - +(x, + x,,)) is - (6 1 2) x erg/G2 in agreement with the crystal value quoted by Professor Flygare. Measurements have also been carried out on hexafluorobenzene and the total birefringence found to be 40 % lower than that of benzene. Unfortunately the optical polarizability data for C6F6 are not available and it is not possible to calculate the anisotropy in the magnetic susceptibility. Dr. Chan Iu Yam and Dr. J. Schmidt (Leiden) (communicated) We present results of two kinds of experiments on pure zone-refined single crystals of benzophenone, where a method similar to that of Sharnoff is used to detect transitions between the spin levels of the lowest phosphorescent triplet state in zero magnetic field.lines at 5.3782 4.1 127 and 1.2666 GHz in good agreement with the values [ D I = 0.152 cm-I and I E I =0.021 cm-l reported by SharnofX2 The 1.3 GHz line is very weak but it can be greatly enhanced by " pumping " of the 5.4 or 4.1 GHz transition. The (1) STEADY STATE RESONANCE EXPERIMENTS AT 4.2 K.l We have observed three The linewidth is seriously affected by the " pumping " see fig. 1. U I MHz dL t ___) V 1:2667 G H z FIG. 1 .-The optically detected zero-field transition of phosphorescent benzophenone at 1.2666 GHz. The lower signal is the normal line ; the upper one is obtained with " pumping " of the 5.3782 GHz transition. Amplitude modulation of the microwave power at 160 Hz together with phase sensitive detection at the output of the photomultiplier.T = 1.3 K. original linewidth of 0.6 MHz increases to -4 MHz in the electron double resonance signal which is about equal to the linewidth observed for the other two transitions. All lines become weaker on increasing the temperature and are not observable at 14 K. The lines appear to be inhomogeneously broadened the line-widths remain constant upon variation of microwave power over a wide range. Moreover in the electron double resonance experiment the shape of the 1.3 GHz line is strongly J. Schmidt and J. H. van der Waals Chem. Phys. Letters 1968,2,640. M. Sharnoff J Chem. Phys. 1969 51,451 GENERAL DISCUSSION 157 dependent upon the precise " pumping " frequency.Based on these considerations we believe that the observed signals must be attributed to localized excitations. (2) We have obtained the kinetic data of population and depopulation of the individual spin-components of the localized triplet excitations. By lowering the temperature from 4.2 to about 1.3 K the relaxation rates between the spin-levels can be made much lower than their individual decay rates of these levels. In this situation the molecules in the different levels decay independently. With the method of microwave-induced delayed phosphorescence it is then possible to measure directly the individual decay rates k(p) (p = x y z) of the spin levels the relative radiative decay rates kJfl) the relative steady state populations N(fl) and the relative populating rates P ( p ) .The results are summarized in fig. 2. They show that T, decays much faster than Ty and T and moreover is by far the most radiative level. The three populating rates however are roughly equal which is in contrast to measure ments of Dym of Hochstrasser,2 who for benzophenone molecules " isolated " in pyridine found populating via T to be dominant. As an explanation we suggest that the " trapped " benzophenone excitations are populated via triplet excitons. From the experiments of Sharnoff we know that the spin-lattice relaxation times of k 5 - ' 6 3 2 . 1 6i-5 39'4 k O/c 90.3 5 - 3 4.7 FIG. 2.-The kinetic data of the individual spin levels of the phosphorescent triplet state of benzo-phenone. for the order of the energies of the levels.For k(4 k(y) and k ( 4 the accuracies are 12 3 and 5 % (standard deviations). For ks") kp) and k:") the (estimated) errors are 2 20 and 20 %. The results for N([i and P(p) are less reliable ; we We follow the conclusions of Sharnoff 33 estimate their errors to be about 30 %. excitons are very short s). If the lifetime of the excitons is longer than s, thermal equilibrium will be established between their spin levels before they are trapped As a result one finds about equal populating rates of the three spin levels of the localized triplet excitations. An account of this work will be presented in Chem. Phys. Letters. Dr. J . Schmidt (Leiden) said I have a question to Sharnoff concerning the optical Do you detection of the e.s.r. transitions of the triplet excitons in benzophenone.J. Schmidt W. S . Veeman and J. H. van der Waals Chem. Phys. Letters 1969 4 341. S. Dym and R. Hochstrasser J. Chem. Phys. 1969,51,2548. M. Sharnoff J. Chern. Phys. 1969,34,451. ' see the previous contribution of M. Sharnoff 158 GENERAL DISCUSSION think that you really observe the signals in the phosphorescence of the excitons or via the phosphorescence of the “ trapped ” triplet excitations? Prof. M. Sharnoff (University of Delaware) said In reply to Schmidt the double quantum signals which we attribute to excitons arise directly from the phosphorescence of the excitons. These signals can be readily observed at microwave modulation frequencies in the kHz range and above. Signals from the trapped excitations are, however best observed at microwave modulation frequencies in the neighbourhood of 200 Hz and diminish rapidly in amplitude as the modulation frequency is increased above 200Hz.The disappearance of the trap signals with increasing frequency shows that the characteristic times for spin-lattice relaxation or de-excitation of the traps cannot be much shorter than -2 111s. This means in turn that the spin-sublevel populations of the traps and hence the phosphorescence which emanates from traps cannot follow changes in the exciton spin populations which occur at kHz rates and faster. Our observation of exciton double quantum signals under microwave modulation at 4 kHz thus clearly rules out the possibility that their detection occurs via the phosphorescence of the trapped excitations.Analysis of the amplitudes of the exciton signals indicates that between 30 and 95 % of the phos-phorescence we observed during our experiments originated from the excitons. Prof. M. Sharnoff (University of Delaware) said I would ask Hochstrasser whether Schmidt et aZ.’s measurements of the radiative decay rates of the trapped excitations in nominally pure benzophenone crystals agree with those which his group has measured for benzophenone in pyridine and/or other hosts ? Regarding the question of linewidths of absorption spectra in real chemically pure crystals at low temperatures has he a quantitative explanation why the linewidths of the resolved 0 - 0 band magnetic components in the TcS absorption spectrum of benzophenone are as large as 0.2 cm-l at 4.2 K? This value is several orders of magnitude larger than the residual linewidths of ca.0.0001-0.001 cm-l which we observed in our e.s.r. study of excitoiis in benzophenone. Prof. R. M. Hochstrasser (University of Pennsylvania) said As I understand it Schmidt has observed apparent relative radiative decay rates for benzophenone in a benzophenone crystal. Direct absorption from the ground state into each of the three triplet substatesl shows that the electric dipole activity is 75 % T and about 25 % Ty. It is not clear what happens subsequent to light absorption. In the pure crystal if T were the only spin state involved in intersystem crossing the T’ and T, states would still obtain some direct population to the extent that JAB (T,(A)/T,(B)> is non-zero for two differently oriented molecules A and B between which there is an exchange interaction JAB.Actually our benzophenone decay results give a lifetime of 5.2 x s at 4.2 K in pyridine and only a very slight and inconclusive change is observed on lowering the temperature to 2 K. Regarding Sharnoff’s question about the linewidth of the electronic transitions, I assume that the exciton-phonon scattering (orbit-lattice interaction) width is much larger than the width due to spin-lattice relaxation. The exciton-phonon interaction is only one of the factors involved in the spin-lattice relaxation which also requires coupling with higher states having different spin quantization. Thus the magnetic resonance lines should be much narrower and should sharpen between 4.2K and 0 K.The crystal is not perfect so it is possible that some additional line broadening Dym Hochstrasser and Schafer J. Chern. Phys. 1968,48 646. Dym and Hochstrasser J. Chem. Phys. 1969 51,2458 GENERAL DISCUSSION 159 of the electronic spectrum occurs because of strain but this is related to the electric dipole strength of the transition and to the change in dipole moment following electronic excitation. Dr. W. A. Runciman (A.E.R.E. Harwell) said Judging from experience with inorganic crystals I suspect that some inhomogeneous line broadening will occur due to lack of crystal perfection in organic crystals. Even in imperfect crystals the line shape is not always Gaussian and Gordon Davies of King's College London (private communication) has shown that some lines in diamonds which are far from perfect crystals are best described as bi-Lorentzian a line shape which can be regarded as intermediate between Lorentzian and Gaussian.The formula for the bi-Lorentzian is obtained by squaring the expression in the denominator of the Lorentzian formula. Dr. P. Day (Oxford University) said The reason that the lowest charge transfer band of Fe(phen)g+ appears to result from the transition d+r9 and not d-+n8 as expected need not be that 718 and n9 have crossed over in going from the free to the complexed ligand. An SCF calculation on the hypothetical monophenanthroline complex carried out within the ZDO approximation and including configuration interaction among fourteen charge transfer and fifteen n-~* configurations ' has shown that the first four charge transfer states which include transitions both to Z 8 and ng lie between 21 600 and 23 000 crn-l.However three quarters of the total dipole-strength of the four bands is concentrated in the one at highest energy which is in fact d+n9. Thus the variation in energy of the absorption band envelope with ligand substituent can be explained although it may still be that the other transi-tions which do not contribute much to the dipole-strength could have a substantial influence on the MCD. Dr. A. J. Thomson (University of East Anglia) said In reply to Day we have measured the room temperature MCD spectrum of R~(bi-pyridyl)~+ which has the low spin d5 ground state configuration. From the magnitude of the ellipticities, the expected C terms are being observed in the region of the ligand +d transitions at 15 OOO cm-' (C/O = - 1.96) at 26 300 cm-l (C/D = +0.06) and at 30 000 cm-l (C/D = +3.50).In contrast to the d6 tris-chelated complexes the MCD spectra now allow an unambiguous assignment of the charge-transfer transitions. The C/O ratios are predicted to have the following signs and magnitudes (in Bohr magnetons) n6[e($)i+ d+$ ; n6[a,($)]+d +* ; ?[e(X)I+ d+ 4 ; ndai(X)l+d -3. Thus the lowest energy C.T. band contains the transition r7[al(x)]+d the bands at higher energy containing all or some of the other three transitions (see fig. 1). Now the effect of lowering the oxidation state of the central metal ion from 3 + to 2+ will be to bring the levels x and + of the ligand closer in energy. Thus the charge-transfer transitions observed in Fe(phen)g+ now metal to ligand in nature, should be closer in energy compared with those of the Fe3+ and Ru3f complexes.Thus our interpretation of the spectra of the d5 complexes leads us to expect that the transitions of both types d-+X and d++ will lie under the visible charge transfer band of the d6 complexes. This is borne out by the calculations of Sanders and Day. N. Sanders and P. Day J. Chem. SOC. A in press. XS and xg of 1,lO-phenanthroline (x and X s of bi-pyridyl) have 'A and $ symmetry respectively 160 GENERAL DISCUSSION w bD 0 .-( Ru(1II) (bi-pyridyl)s-absorption MCD and CD spectra 3 ! Two further pieces of evidence support this conclusion. First the breadth of the visible charge-transfer band of Ru(phen):+ which is 6000 cm-l at half-height com-pared with the breadth of 3000 cm-1 at half-height of the lowest energy charge-transfer band of the Rubhen):+ suggests the presence of a number of underlying electronic transitions in the former case. Secondly the natural circular dichroism of the d5 and d6 tris-chelated complexes is in good agreement with the assignment proposed, the complexity of the C.D. in the visible charge-transfer band of the d6 complex now being assigned as suggested by the MCD spectra. S . F. Mason Inorg. Chim. Actu. Rev. 1968 2 89

ISSN:0430-0696    

DOI:10.1039/SF9690300153

出版商:RSC    

年代:1969

数据来源: RSC

摘要:

AUTHOR INDEX* Badoz J. 27. Barth G. 49. Billardon M. 27. Bird B. D. 70. Boccara A. C. 27. Bowen E. J. 94. Briat B. 27 70 95. Buckingham A. D. 7. Bunnenberg E. 49. Corfield M. G. 155. Cox P. A. 92. Davies D. W. 154. Day P. 70 94 95 154 159. Denning R. G. 84. Dickinson J. R. 14. Djerassi C. 49. Elder D. 49. Flygare W. H. 119. Hochstrasser R. M. 100 153 158. Hollebone B. R. 146. Lester T. E. 14. Lin T-S. 100. McCaffery A. H. 14 96. McClure D. A. 106. Marzzacco C. J. 106. Mason S. F. 146. Pershan P. S. 131. Piegho S. B. 14. Records R. 49. Rivoal J. C. 70. Runciman W. A. 94,95 159. Schatz P. N. 14,92. Schmidt J. 156 157. Sharnoff M. 95 137 158. Shashoua V. E. 61. Shiflett R. B. 14. Shoemaker R. J. 119. Spencer J. A. 14 84. Stephens P. J. 40,94. Thomson A. J. 146 159. Waals J. H. van der 153. Yam C. I. 156. * The references in heavy type indicate papers submitted for discussion

ISSN:0430-0696    

DOI:10.1039/SF9690300161

出版商:RSC    

年代:1969

数据来源: RSC