Vibronic effects in magnetic vibrational circular dichroism of the triply degeneratevibration. Theoretical analysis for the ν6 vibration of tungsten hexacarbonylM. Pawlikowski and T. R. Devine Citation: The Journal of Chemical Physics 83, 950 (1985); doi: 10.1063/1.449422 View online: http://dx.doi.org/10.1063/1.449422 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/83/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Vibronic theory of magnetic vibrational circular dichroism in systems with fourfold symmetry: Theoreticalanalysis for copper tetraphenylporphyrin J. Chem. Phys. 96, 4982 (1992); 10.1063/1.462741 Erratum: Magnetic vibrational circular dichroism of transition metal hexacarbonyls [J. Chem. Phys. 8 3, 3749(1985)] J. Chem. Phys. 87, 5051 (1987); 10.1063/1.453751 A theoretical analysis of the main effects in magnetic vibrational circular dichroism J. Chem. Phys. 85, 5405 (1986); 10.1063/1.451605 Magnetic vibrational circular dichroism of transition metal hexacarbonyls J. Chem. Phys. 83, 3749 (1985); 10.1063/1.449137 Vibronic coupling effects in magnetic vibrational circular dichroism. A model formalism for doubly degeneratestates J. Chem. Phys. 81, 4765 (1984); 10.1063/1.447526

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Vibronic effects in magnetic vibrational circular dichroism of the triply degenerate vibration. Theoretical analysis for the Va vibration of tungsten hexacarbonyla)

M. Pawlikowskib)

Division o/Chemistry, National Research Councilo/Canada, Ottawa, Canada KIA OR6

T. R. Devine Department 0/ Chemistry, University 0/ Illinois at Chicago, Chicago, Illinois 60680

(Received 13 July 1984; accepted 12 March 1985)

The MVCD and infrared absorption spectra of a triply degenerate vibration are discussed in the frame of a simple molecular model applicable for molecules of cubic symmetry. The presented results show that vibronic contribution to infrared intensity can dominate or compete with ground state contribution and the vibronic effects cannot be neglected in the MVCD analysis. The model is successfully applied to the MVCD spectrum of v 6 vibration in the W(CO)6 molecule. The estimation of the excited d 1 T/u state magnetic moment is made on the basis of this analysis.

I. INTRODUCTION

An external magnetic field applied to molecules makes left- and right-handed circularly polarized photons interact nonequivalently with a molecule. Consequently, the mole­cule becomes optically active and magnetic circular dich­roism (MCD) can be observed.

The theory of this phenomenon has been extensively developed and modified during the past years. 1 At the same time, a significant effort has been made to detect MCD effect for the infrared excitations in a molecule. As a result, mag­netic vibrational circular dichroism (MVCD), much weaker than its electronic counterpart, has been detected2 and MVCD spectra were reported for a variety of small, highly symmetric molecules.2--4 The first attempt to calculate the MVCD spectra has been also made5 with the use of the fixed partial change model (FPC) employed previously in the stud­ies addressed to "natural" vibrational circular dichroism.6

The results of this model, however, were found to be unsup­ported by the experimental data. 3

,4 Particularly, the magni­tudes of A 1 and Bo terms were found to be much greater than those predicted by the FPC calculations. Moreover, the MVCD analysis of benzene and its 1,3, 5-substituted deriva­tives4 shows that this discrepancy is not accidental and the inclusion of vibronic effect was suggested to improve the agreement with the experiment. The comparison between experimental data and predictions for other currently used models 7,8 leads to a similar conclusion. These models differ in details from the FPC model but their common feature is that MVCD effect is described without explicit reference to the dynamical interaction between electrons and nuclei. It was suggested however, before, that the inclusion of such interaction can lead to a better description of natural circular dichroism spectra,9-11

In a recent studyl2 we have discussed the simple molec-

:1 Issued as NRC No. 23764 Visiting Scientist, Summer 1984. Ipermanent address: Department of Chemistry, Jagiellonian University, Krakow, Karasia 3, Poland.

ular model applicable to the analysis of the MVCD spectra of doubly degenerate vibrations, It has been shown, in the lowest order of perturbational approach, that the degenerate vibrational levels of the ground state manifold can, in gen­eral, borrow magnetic moment from doubly degenerate elec­tronic states. This borrowing mechanism is dynamical in character, i.e" it occurs through the momentum operators rather than vibrational coordinates as the intensity borrow­ing mechanism does. As a result, the MVCDA 1 andBo terms were obtained and shown to account correctly for the ob­served experimental data. The same mechanism operates for a triply degenerate vibration. 17

In the present paper we will study the influence of vi­bronic coupling effects on the MVCD spectrum of triply degenerate vibrations, The molecules studied belong to te­trahedral (T, Th, Td ) or octahedral (O,Oh) symmetry point groups. For these molecules, the triply degenerate infrared active vibration can, in general, couple the totally symmetric ground state to a large number of triply degenerate, optically allowed excited electronic states. Moreover, the excited states themselves can be involved in many kinds of vibronic effects. 13 These, if included at the same time, can create diffi­cult practical problems, To make the problem easily tracta­ble, we restrict, for the sake of model presentation, the num­ber of vibrational modes to one. It is also assumed that only one excited electronic state is coupled to the ground state via vibration of interest. At this level of simplification, we will deal with the Herzberg-Teller and Jahn-Teller vibronic coupling mechanism, Both of them give rise to MVCD for the fundamental line and overtones. Due to the apparent absence of the published experimental data, we give here the numerical estimation of the orders of magnitUdes expected to be observed for the MVCD spectrum of a triply degener­ate vibration. To this end we performed numerical calcula­tions to avoid a cumbersome and somewhat inaccurate per­turbational treatment used previously. 12 As an example, we also present the analysis of the experimental MVCD spec­trum for the V6 vibration of the W(CO)6 molecule. These

950 J. Chem. Phys. 83 (3).1 August 1985 0021-9606/85/150950-06$02.10 @ 1985 American Institute of Physics

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M. Pawlikowski and T. R. Devine: Magnetic vibrational circular dichroism 951

experimental data became available due to the recent stud­ies20 performed by one of us (T.R.D.).

II. MODEL FORMULATION

To discuss the influence of vibronic effects on the MVCD spectrum of a triply degenerate vibration it is con­venient to begin with the simplest model considering one vibrational mode in a four-state molecular system of cubic symmetry. Let Qx' Qy, and Qz denote the mass-weighted normal coordinates of an infrared active vibration. Let us also assume that this vibration couples selectively the totally symmetric ground state to a given triply degenerate elec­tronic state (Ifo~, Ifo~, Ifo~). Therefore, we will ignore the

(,_E," Hox Hoy

Hox ho + ..10 - Ep.u Hxy

Hoy Hxy ho + ..10 - Ep.u

Hoz Hxz Hyz

where Ep.u is the vibronic energy associated with the wave function (1),..10 is the energy gap between ground and excited state potential and ho has the form

(2a) j= x,y,z

We will assume that the adiabatic coupling matrix elements HaP depend linearly on the vibrational coordinates and that quadratic and higher order terms13

•14 in Q can be ignored.

The symmetry arguments applied for the molecules of T symmetry lead us to the following parametrized form of the adiabatic coupling matrix elements:

(3)

where A and K are the Herzberg-Teller (HT) and the Jahn­Teller (JT) coupling constants, respectively. Notice that, for molecules of T symmetry, JT and HT mechanisms will, in general, operate at the same time since only one symmetry species is available for the triply degenerate modes. In the group 0 (Td ), however, there are two species of triply degen­erate vibrations tl and t2• Only the infrared active tl (or t2 in Td ) vibration can couple the totally symmetric ground state to the optically allowed T 1(T2) electronic excited state. This vibration cannot be JT active and thus A :;60, K = O. The sim­ilar conclusion applies for molecules of Th and Oh symmetry where the inversion center does not allow the u-type vibra­tion to be JT active. With these restrictions, all molecules with cubic symmetry can be discussed in the same calcula­tional scheme.

Let us consider the vibronic transition tPp (O')-tPp' (0"). The transition matrix elements of the electric and magnetic dipole operators can be expressed as

I

presence of other electronic states. To take an advantage of symmetry arguments, the electronic states are represented in the "crude" Born-Oppenheimer (CBO) approximation. In this representation, the electronic states are adiabatically coupled through the electronic potential operator. 14 Taking this coupling into account we can express the total (vibronic) wave function in the terms of the crude BO states as follows:

tPp(O') = Ifo gA ~.u + Ifo ~A ;.u + Ifo ~A ~.u + Ifo ~A ~.u' (1)

where p numbers the levels of the vibronic manifold and the index 0' = A,€, 8,x,y,z, xy, xz,yzrefers to its symmetry. The vibrational components A;'u (a = 0, x, y, z) are now ob­tained with the equation that results from the variational principle (see Ref. 15). It reads

H~ )C") Hxz A ;.u = 0 (2) Hyz A~.u'

ho + ..10 - Ep.u A ~.u

[(tPp(O')IMltPp'(O")] = L (A ~.ulmnc5ij ij

+ (Ifo ?IMe lifo J) IA ~'.u')' (4)

[(tPp(O')IDltPp'(O")] = L (A ~.uldnc5ij ij

+ (Ifo ?IDe lifo J) IA ~'.u')' where i,j = 0, x, y, z and ( ... ), ( ... ) denote integration over electronic and nuclear coordinates, respectively. Me and mn are the electronic and nuclear components of the total mag­netic dipole operator M. Similar notation for the total elec­tric dipole operator D is used. The matrix elements (Ifo ?IMe lifo J) and (Ifo ?IDe lifo J) can be determined by the well­known selection rules for the operators discussed here. The simple group-theoretical analysis performed for the mole­cule of T symmetry yields the fo\lowing result:

(Ifo g IMe lifo J) = - (Ifo JIMe lifo g) = iMoej ,

(5)

(1fo?IMeIIfoJ) = -iM1€ijkek,

where ej forj = x,y, z are the Cartesia!1 unit ve~tors and €ijk is the totally antisymmetric tensor. Mo and MI represent, respectively, the magnetic transition moment and intrinsic magnetic moment of the excited electronic state.

Using the same symmetry arguments for the electronic dipole operator we get

(Ifo g IDe lifo J) = (Ifo JIDe lifo g) = Doep (6)

(Ifo ?IDe lifo J) = DII€ijk lek,

where Do is the electric transition moment and DI results from intrastate mixing via the electronic dipole operator. For the molecules with an inversion center (Oh ,Th), we must put Mo = 0 and DI = 0 since the magnetic and electric di-

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952 M. Pawlikowski and T. R. Devine: Magnetic vibrational circular dichroism

pole operators have mutually exclusive selection rules. The same restriction applies to the molecules of 0 and Td sym­metry.

Now, let us address the problem of the operators dn and mn • These can be expressed in the Cartesian displacement coordinates as

(7a) a

(7b)

where Pa' P a' and R~ denote, respectively, Cartesian dis­placement, momentum operator, and equilibrium position vector of ath nucleus with mass Ma and charges Za' Alter­natively, the operators (7a) and (7b) can be expressed in the terms of normal coordinates. However, the determination of the force field sufficiently accurate to reflect subtle distor­tions arising from nuclear motions is one of the most difficult aspect of normal modes calculations. To this end, we restrict the discussion to molecules for which the nuclear charge-to­mass ratio is approximately the same for all nuclei. In that case, the second term in Eq. (7a), considered as the classical quantity vanishes as a result of the conservation of the mass center during nuclear motions. 16 Similarly, the first term in Eq. (7b) can be neglected due to the separability of the vibra­tional and rotational degrees offreedom. 16 The second term in Eq. (7b) however, is, in principle always different from zero. To keep the model presentation independent on the particular force field we will neglect this term as hopefully small. In fact, as it was shown elsewhere, 12 the second term in Eq. (7b) can play sometimes an important role in the inter­pretation of MVCD experimental data for benzene and its derivatives. Due to the apparent absence of MVCD experi­mental data little is known about this matter for molecules of cubic symmetry. For this reason, we will put dn ~O and mn

~O. In this case, the MVCD and intensity of the infrared absorption spectrum will be entirely of vibronic origin.

The solutions ofEq. (2) were found by numerical proce­dure in which A ~.u were expanded in the basis set of eigen­functions of Hamiltonian (2a). The number of basic func­tions was large enough to eliminate the truncation effect. For the convenience, the following dimensionless quantities were introduced:

J o = .Jo(1/fl )-1, .x = A (I/fl )-I(Ii/il )1/2,

K = K(I/fl )-I(Ii/il )112.

III. RESULTS AND DISCUSSION

Customarily, the magnetic circular dichroism spectra are analyzed in the term of three components commonly called A, B, and c. 1 A and C terms result from the magnetic properties of the final (A term) and initial (C term) states involved in a transition. The presence of B term is universal and originates from the mixing ofvibronic states through the external magnetic field.

The MVCD and absorption spectrum can be calculated from I

(8)

dv= yDrf,

where v is the energy of the absorbed light (cm- I), y( = 3.26 X 1038 mol g-I cm -3 S2) is the constant used to convert dipole matrix element units to extinction unit l and H is the magnetic field strength./(v) is normalized to unity intensity distribution of the individual absorption line as­sumed here to be a Gaussian:

I [(V - E )2] I(v) = rfii exp - T ' (8a)

where r is the width of the band at 1/ e of its maximum. Since the initial (ground) state is nondegenerate, Co is

equal to zero. Thus the MVCD spectrum is temperature in­dependent and the MVCD line shape is entirely determined by the relative magnitudes and signs of A I and Bo terms, which, for randomly oriented molecule, are given byl

The infrared absorption is proportional to

Do =..!.. I [(t,bo(A )IDIt,bp(u)], [(t,bp(u)IDIt,bo(A)]. 3 u

(9a)

In Eqs. (9) and (9a) we put u, u' = x, y, z and Gpu is given by

G = I [(t,bp(u)IDIt,bdu")] X [(t,bdu")IMIt,bo(A)] pu ku" E ku" - EOA

_ I [(t,bp(u)IMIt,bdu")] X [(t,bdu")IDIt,bo(A )] ,

ku" E ku" - Epu

(9b)

where transition matrix elements are defined by relation (4). Figure 1 presents the typical MVCD spectra of the fun­

damental line for different values of HT coupling param­eters. Mo, DI , and K are equated to zero, thus the first over­tone will be inactive as it can happen for molecules of Th(d)

and Oh symmetry. Figure 1 shows that for not very small.x the A I term

dominates the MVCD spectrum leading to bisignate line shape with a (small) asymmetry resulting from theBo contri­bution. Such MVCD structure is expected if the degenerate vibrational levels have a significant vibrational magnetic moment which, in the present case, is ofvibronic origin. The decrease of HT coupling parameter leads to MVCD spec­trum governed predominantly by the Bo term. This behavior can be demonstrated in terms of AI/Do and Bo/Do ratios which are directly accessible from the analysis of MVCD spectral moments. For the weak coupling case when X.c::Jo, the analytical expressions for AI/Do and Bo/Do can be de­rived in the same way as for doubly degenerate vibrations. 12

The results obtained for theiundamentalline are l7

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M. Pawlikowski and T. R. Devine: Magnetic vibrational circular dichroism 953

o o )(

\1.1 <l

4.0

3.0

2.0

1.0

900

\1.1 600

300

,"\ I \ x3 / \ .~·Y x20

I 1.1 \ , ........ j ./ , .. ,.\ .......... .

/"\ I \ I \ I II rxI.5

/""'/ \ . \ I l. 6 \! , ..... jX Y "\" i\ .""''''' . \." \'. .I ....... " ...... .

1970 1980 1990 2000 Z/[cm-I]

FIG. 1. The fundamental MVCD and absorption spectra for K = 0 and A = 0.5 (-),A = 0.4(- - -),A = 0.25(-. -. -),A = 0.1 ( ... J. Theotherparam­eters are: ..ao = 20, IiI1 = 2000 cm -I, r = 5 cm -', M, = /3 (Bohr magne­ton),Mo= O,DI =O,Do = 3.16X 10-'8 esucmandH= 4OoooG.

with

41 2i1oM1H (i1~-W'

Bo = ~MIH (1- ~ 2)112 Do ~~~ ~o

(lOa)

(lOb)

D = ~2i1~D~(I_ ~2)-1I2. (lOc) o (~~ _ W ~o

The ratios (lOa) and (lOb) are available from the zeroth and first spectral moments of MVCD spectrum, respectively.

It follows from Eqs. (lOa)-(IOc) that AI and Bo are of opposite signs and their contribution to MVCD spectrum will decrease withA. However, the drop is much stronger for A I than for Bo contribution and Bo will dominate if A is very small. Note that the MVCD spectra with MI and - MI show the mirror-image relationship since A I and Bo contri­bution change signs simultaneously with MI'

Figure 2 presents the sample of MVCD fundamental and first overtones spectra. The parameters are the same as in Fig. 1 but DI = wo, A = 0.5, and Ie is varied. Because MVCD fundamental is little affected by JT coupling effect only the result for Ie = 0 is shown.

As can be seen from Fig. 2 the JT coupling effect modi­fies insignificantly the MVCD overtone shape line but gives rise to the intensity in the absorption and MVCD spectrum. This is due to the relatively large A I contribution that, for A = 0.5, dominates in the MVCD spectrum as for the funda­mental line. However, a small shift between absorption maxima and the nodes of MVCD spectra reveals the increas-

0) b)

40 7.5

3.0 5.0 2.0

0 1.0 Q

2.5 .. 0

>< >< IV <I

-1.0 IV

-2.5 <I

-2.0 -5.0

1000 20 IV IV

500 10

1965 1975 1985 3940 3950 3960 lI[cm-~

FIG. 2. The same plot as Fig. I except now A = 0.5,D, = 2Do' andK = 0(-­-I, K = 0.5 (-), K = I (- . - . -I. (a) Fundamental transition, (b) overtone.

ing presence of the Bo contribution when Ie is varied. To show it, the A liDo and BoiDo as the function of JT coupling pa­rameter are depicted in Fig. 3. The results of MI = - {3 are also given to show the mirror-image relationship between MI and - MI cases.

As can be seen from Fig. 3 (solid lines), A liDo and Bol Do and subsequently A I and Bo contributions are not, in gen­eral, of opposite signs as for MVCD of the fundamental line. Moreover, the Bo can vary within the wide range of magni­tude depending on the JT coupling and intrastate electronic mixing described by parameter D I' In particular, some com­binations of these parameters can cause the disappearance of

100.0

10.0

"0

>< 01 0 III 0

1.0

0.1

-0.1

!

i I i -1.0 -L -----u----- I -

-10.0 :

-100.0

o

......... _ ............... .

0.1

, -0.1 , \ _~ _______ -1.0

.... ---J~)_ (b) -10.0

.. o ><

-I 0 « 0

-100.0

0.5

FIG. 3. Ao/Do (a); Bo/Do (b) as functions of JT coupling parameter K, M, = /3 (-), M, = - /3 (- - -I. The dotted line gives the results obtained from Eq. (lib). The other parameters are the same as in Fig. 2.

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954 M. Pawlikowski and T. R. Devine: Magnetic vibrational circular dichroism

overtone intensity. In this case, the values of AI/Do and Bol Do are not defined as is indicated in Fig. 3.

To visualize the dependencies depicted in Fig. 3, below we give the analytical expressions for A 1/ Do and Bol Do ob­tained when the condition A. <.a 0 is held. The results arel7

~ 4A. 2.1oMIH Do (.a ~ - W '

(1la)

where

(llc)

As can be seen from Eq. (lla), the AI/Do has the opposite sign than the fundamental line and shows no ie dependence at the level of approximation which guarantees the validity of expressions (lla)-(llc). In contrast, BoiDo can strongly de­pend upon the vibronic A., ie and electronic DI , Do param­eters. In particular, the small changes of JT parameter can produce quite large change of Bol Do ratio. The sensitivity of Bol Do to the values of ie is especially apparent in the region where BoiDo changes the sign. Note that in this region, Eq. (lIb) yields results that closely resemble the exact numerical results. The difference appears as the artifact of the perturba­tion treatment17 which replaces the large number of (small) terms in Eq. (9b) by only one "effective" term when the clo­sure rule is used.

For liel >0.5, the increasing liel causes that BoiDo curve tends to a constant value equal approximately to 12M H (Iifl )-1.1 0- 2. This value does not depend on the electronic transition dipole moment Do.

In conclusion of this section, it should be noted that reasonable values of model parameters yield the MVCD and absorption intensities in the orders of magnitudes of those recently measured by MVCD experiments. Our results have been obtained without ground state contributions that if in­cluded will, in general case, modify the presented results. Such a modification will result from the subtle competition between ground state and vibronic origin contributions that are expected to be of the same order of magnitude especially in the weak HT coupling limit. In such a competition the vibronic effect cannot be explicitly ignored in any order of approximation. In this context, the extension of present treatment by inclusion of multistates, multi vibrational ef­fects is also needed. The simple attempt to extend the present model by inclusion of several vibrational modes of different symmetry will be done in a subsequent paper. 17

IV. APPLICATION

Although the model presented in the last sections is very simple, it is especially interesting to look at the possibil­ity of its application to a realistic molecular system. The hexacarbonyls of Cr, Mo, and W provide a good example for this purpose since the electronic and infrared properties are rather well established for these molecules. 18

•19 Moreover,

the charge-to-mass ratio is roughly the same for all nuclei, so

the arguments used in Sec. II can be applied to simplify the form of operators (7a) and (7b). Due to many similarities in the electronic structures, the MVCD discussion is basically the same for molecules of MO(CO)6' Cr(CO)6' and W(CO)6' We will focus our attention on the last one.

The electronic spectrum of W(CO)6 reveals two low­lying charge transfer transitions 18: IAI ~ ITlu and I I g Alg~ Tlu ' The latter one is much stronger than the for-

mer and is located at Lio = 44 640 cm -I. The transition di­eole moment of IAlg~ ITlu transition can be estimated as Do = 10- 17 cm esu.

The infrared absorption spectrum of W(CO)6 shows a very intense fundamental transition at 1979 cm -I with Emax

= 15000. This transition is associated with C = 0 stretch­ing V6 vibration of flu symmetry. The intensities of other infrared active vibrations are at least one order of magnitude weaker. 19 On the basis of large infrared intensity of the V6

fundamental we assume, in the first approximation, that this vibration couples the ground state (A Ig) predominantly to the d I T lu elec~onic state. With this assumption, HT coupling parameter A and the crude adiabatic quantum energy Iifl can be found with analysis of infrared absorption data. The anal­ysis yields: Iifl = 2053 cm- I

, A. = 0.88. For these param­eters, the absorption and MVCD spectra are shown in Fig. 4. The experimental data (circles) have been obtained by the MVCD technique described elsewhere.20 The theoretical MVCD spectra were calculated with H = 40 000 G and dif­ferent values of the excited state magnetic moment. The ze­roth and first moments of MVCD spectrum are also given

~~ (t3H)-1 = 1.49x10-4 [1.5x 10-4J

~(t3H)-1 =-1.97x 10-6 ~2 .3x 10-6 J

000

1/ \

\ 0

/ <\.0

8

6

4

2

-2

-4

150

100

50

1970 1980 1990 vu:m- I]

Q )(

\U <J

0 0 )(

\jJ

FIG. 4. The comparison between calculations (lines) and the experiment (ci~cles).H = 40 OOOG,r= 8.5cm-',andM, = -{3 (-),M, = O.5{3 (- -­), M, = - O.25{3 (- . - . -I.

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M. Pawlikowski and T. R. Devine: Magnetic vibrational circular dichroism 955

for MI = - 0.5p. The corresponding experimental values20

are given in the square brackets. These moments are divided by PH as is usually done.

As can be seen from Fig. 4, the agreement with experi­ment is very good and it was achieved with reasonable values of the relevant parameters. The excited state magnetic mo­ment MI = - 0.5p is reasonable but seems to be too large in view of the recent MCD experimental study of W, Mo, and Cr hexacarbonyls.21 Authors of this study have found very small zeroth and first MCD moments measured for the IA/g-d IT/u electronic transition in the W(CO)6 molecule. On this ground and neglecting the vibronic effects, they con­cluded that the magnetic moment of d I T/u electronic state is small being quenched due to configuration interaction among the orbitals of electronic manifolds.

Leaving aside this possibility, we propose another very efficient mechanism, i.e., nonadiabatic coupling which can be responsible for the quenching of the magnetic moment in d IT/u electronic state. In fact, the presence of strong nona­diabatic effects is supported by the photochemical experi­ments. 22,23 If this is the case, the results obtained solely in the frame of Born-Oppenheimer approximation can be incon­clusive in relation to the excited state magnetic moment. Such a problem still awaits future studies.

To complete the discussion, we have also checked the influence of the second term in Eq. (7b) on the MVCD spec­trum of V6 vibration. Using the force field proposed by Jones etal.24 wefoundm n to be of order 6.7X 10-7 p, This value is too small to given the MVCD spectrum needed and also to compete with the excited state contribution. Thus, we arrive at the conclusion that the vibronic effects playa fundamental role in the determination of the MVCD spectrum of tung­sten hexacarbonyl. We have also demonstrated that the magnetic moment of d I T/u electronic state ofW(CO)6 mole­cule should be larger than it was suggested in order to ex­plain the small MCD A term observed in the region of IA/g-d IT/u electronic transition. This problem remains un­solved until the nonadiabatic effects within excited states

vibronic manifolds are taken into account. We hope to re­turn to this problem in future papers.

ACKNOWLEDGMENTS

This paper was supported in part by National Science Foundation (CRE 81-04997). The critical remarks of Marek Zgierski are appreciated.

Ip. J. Stephens, Adv. Chern. Phys. 35, 197 (1976), and other papers cited therein.

2T. A. Keiderling, J. Chern. Phys. 75, 3639 (1981). ~. R. Devine and T. A. Keiderling, J. Chern. Phys. 79, 5796 (1983). 'T. R. Devine and T. A. Keiderling, J. Phys. Chern. 88, 390 (1984). sL. Laux, V. Pultz, C. Marcott, J. Overend, and A. Moscowitz, J. Chern. Phys. 78,4096 (1983).

6J. A. Schellrnan, J. Chern. Phys. 58, 2882 (1973); 60, 344 (1974). 7S. Datta and F. S. Richardson, Int. J. Quanturn Chern. 9, 525 (1977). 8S. L. Cunningham and J. R. Hardy, Solid State Cornrnun. 6, 769 (1968). 9L. A. Nafie and T. B. Freedman, J. Chern. Phys. 78, 7108 (1983). 10L. A. Nafie, J. Chern. Phys. 79, 4950 (1983). liD. P. Craig and T. Thirunamachandran, Mol. Phys. 35, 825 (1978). 12M. Pawlikowski and T. A. Keiderling, J. Chern. Phys. 81, 4765 (1984). I3R. Englrnan, The Jahn-Teller Effect in Molecules and Crystals (Wiley-

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