1799
J. Phys. Chem. 1995, 99, 1799-1813
Ab Initio Studies of Electronically Excited Carbon Disulfide Qingguo Zhang and Patrick H. Vaccaro* Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 0651 I Received: September I , 1994; In Final Form: November I I , I994@
The excited electronic states of carbon disulfide (CS2) are examined theoretically by exploiting the CIS and CIS-MP2 configuration interaction methods in conjunction with extensive sets of basis functions (e.g., 6-31l+G*). At their respective equilibrium geometries, the lowest-lying states of CS2 are predicted to have a'B2 < b"A2(R) A'A;? B'B2(V) c3B2 symmetry labels and electronic energies given by Xl2; d3A2 C'A2, where the letters in parentheses refer to established spectroscopic designations for the R and V absorption systems. The bent b3A2(R) and C3B2 states are found to correlate with a degenerate level in the linear molecule. Analogous Renner-Teller effects in the 'A,, level give rise to 'A2 and IB2 potential surfaces, the latter of which correlates to the well-studied B1B2(V) state. The presence of an unexpected crossing between the 'Au and 'qcurves of linear CS2 makes definitive assignment for the other member of this Renner-Teller doublet difficult, with an apparent reversal of relative energy ordering encountered as a function of the C-S bond distance. The implications of this effect, as well as the influence exerted by neighboring electronic manifolds (e.g., the hitherto unobserved d3A2surface which supports spin-orbit allowed electric dipole transitions from the X'Z; ground state), are discussed in terms of recent studies performed on the near-ultraviolet photochemistry and photophysics of CS2. While ab initio properties predicted for the b"A2(R) state are in good accord with previous spectroscopic measurements, the calculated equilibrium geometry, barrier to linearity, and vibrational frequencies for the B'B2(V) potential surface differ significantly from experimental observations.
I. Introduction Since their first tentative interpretation in the 1929 studies of Wilson,' the near-ultraviolet absorption bands of carbon disulfide (CS2) have been a subject of considerable interest to both the spectroscopy and photophysics communities. Rovibronic features in this spectral region are known to arise from n* x transitions involving a low-lying Jt"x* configuration of the linear molecule. The deceptive simplicity of this zerothorder description conceals the enormous complexity inherent to the behavior of electronically excited CS2. More specifically, the (xgy(x:)' configuration of CS2 results in singlet and triplet levels which, in manifolds of closely spaced &+,A,,, and turn, lead to 8 nonlinear excited states having a total of 16 spinorbit components. Interactions among these states can occur through a variety of mechanisms, giving rise to congested optical spectra that exhibit numerous rotational and vibrational perturbations as well as the unusually strong presence of nominally forbidden electronic transitions. The physical repercussions of these effects are demonstrated most clearly by variations in radiative and nonradiative decay processes, with pioneering work on singlet-triplet couplings and their role in molecular dynamics having been performed on the CS2 system.2 In the near-ultraviolet region, gas-phase samples of CS2 exhibit a richly structured absorption spectrum extending from roughly 3800 to 2900 A. The first methodical attempt to assign these features was that of Kleman,3 who grouped various sets of transitions into bands or systems designated as R, S, U, and V with the so-called V bands being considerably stronger than all of the others. Figure 1 illustrates the spectral regions spanned by the rovibronic structure comprising each of these bands. Also shown is the more recently identified T system which Jungen et a1.4 have attributed to transitions originating from vibrationally excited levels of the ground electronic state.
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Abstract published in Advance ACS Abstracts. January 15, 1995.
61
0022-3654/95/2099-I 799$09.00/0
I 4300
A
I 3600 A
I 2900 A
Figure 1. Synopsis of near-ultraviolet bands in the CS2 spectrum. Approximate spectral regions spanned by the so-called R, S, T, U, and V absorption systems of CS2 are illustrated. The designations for these bands derive from the 1963 work of Kleman3 and do not follow the usual spectroscopic nomenclature for excited electronic states.
Owing to the deceptive simplicity of its rovibrational features and the complete absence of any observable triplet splittings, the R system initially was misassigned as a singlet-singlet electronic transition from the linear X'Z; ground state to a l i n e d or bent? excited state of 'Z: or 'B2 symmetry. Magnetic rotation experiments reported by Kusch and Loomis,6 as well as Zeeman studies by D o ~ g l a s , ~ Milton,* .~ and Hougen? have demonstrated conclusively that the R system involves the B2 spin-orbit component of a nonlinear excited surface having 3A2 character. Similar measurements performed on cryogenic CS2 samples by Hochstrasser and Wiersma'O showed that this triplet state correlates with the 3Aulevel of the linear molecule. Detailed analysis of K-rotational structure in the ultraviolet spectra of Kleman3 led Jungen et al.4 to conclude that the surface is the lower-lying member of the Renner-Teller doublet arising from the degenerate 'A,, state. The S and U systems, located to the blue of the R absorption bands, were assigned to 0 1995 American Chemical Society
1800 J. Phys. Chem., Vol. 99, No. 6, 1995
I I
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Zhang and Vaccaro
b
140"
S - C S Bending Angle Figure 2. Electronic origins for the CS2 absorption spectrum. Electronic assignments for the R, S, T, U, and V absorption systems
of CS2, as derived from experimental studies, are shown along with the structural parameters ascribed to the equilibrium geometries for each potential surface. Distortion of the molecular framework from linearity lifts the double degeneracy associated with the 'Au and 3Au levels of the linear configuration, thereby giving rise to two pairs of Renner-Teller states. The oscillator strength for each absorption band scales in proportion to the thickness of the transition arrow with the V X system being the most intense feature in the near-ultraviolet spectrum of CS2.
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singlet- triplet transitions that terminate on excited vibrational levels within the same 3A2state."-13 At the shorter wavelengths corresponding to the so-called V bands (uiz., 3300-2900 A), the absorption spectrum of CS2 gradually loses its simplicity and becomes difficult, or even impossible, to analyze through the use of conventional spectroscopic techniques.13 Building upon the earlier work of Kusch and loo mi^,^ Douglas and Milton8 showed that features in this spectral region exhibit much less pronounced magnetic effects than those found in the case of the R system. By combining this information with their own experimental findings regarding the parallel nature of rovibronic structure within the V bands, Jungen et aL4 concluded that most of the V system stems from transitions between the linear X'C; ground state and an excited singlet surface of IB2 symmetry. In the 2300-1500 region, CS:! is known to exhibit an exceptionally strong absorption owing to the presence of a bent-from-linear IB2 XlCl transition14 where the upper state correlates to a '&+ level in the linear configuration of the n~c1ei.I~ Excluding this higher-lying state from participating in the formation of nearultraviolet spectral features, Jungen et al? argued quite convincingly that the IB2 surface involved in the relatively weak V bands must correlate with the 'Au level of the linear molecule. The vastly different intensities observed for these two IB2 X'c,' systems follows from the electric dipole-allowed and -forbidden character ascribed to I&+ 'Cp' and IAU IC: transitions, respectively. As the molecular framework distorts from linearity, the doubly-degenerate lAu state of linear CS;! can be resolved into two distinct surfaces, one having IB2 symmetry while the other has IA2 symmetry.I6 Based on their systematic analyses of K-rotational structure, Jungen and co-workers4 suggested that the IB2(V) component lies higher in energy than the corresponding 'A*(T) state, where the letters in parentheses refer to established spectroscopic designations for the V X and T X absorption systems. A mechanism based upon Coriolisinduced vibronic interactions between the two Renner-Teller surfaces was invoked to explain the finite oscillator strength ascribed to the nominally forbidden 'A2(T) XlCl transition.
A
-
-
-
-
-
-
-
Figure 2 summarizes our present understanding of electronically excited CS;! as derived from experimental measurements. In contrast to the vast number of experimental studies performed on CS;! and its excited electronic states, very few theoretical investigations have been attempted. For diatomic species, the pattern of energy levels resulting from an isolated n3n*configuration of electrons was predicted by Recknagel in 1934.17 As part of a review on semiempirical calculations for simple molecules containing excited n3n*configurations, Mulliken18 discussed the ultraviolet spectrum of CS2 in connection with the analogous C02 system. Rablais et al.15 applied the semiempirical Mulliken-Wolfsberg-Helmholtz (MWH) and Pariser-Parr-Pople (PPP) methods to a variety of molecules and molecular ions having 16 valence electrons (e.g.,CS2). Only the singlet manifold was treated explicitly in this work with somewhat limited information reported for the excited potential surfaces of CS2. A more recent ab initio investigation of electronically excited CS2 was reported by Kasahara et a1.I9 in conjunction with their experimental measurements of spectrally-dispersed laser-induced fluorescence in the V X system. This analysis was concerned primarily with structural parameters for the V state and their relationship to intensity patterns for observed vibronic features. While various aspects of their spectroscopic assignments were contested by Ochi et aL20in a subsequent study, the computational results of Kasahara and co-workers have not been reexamined in their entirety prior to our work. Following completion of a preliminary version of this paper, Tseng and Poshusta2' published an ab initio treatment of CS2 within its ground and lowest-lying B2 [uiz., B1B2(V) and a3B2] states. Aside from providing optimized structural parameters and vibrational frequencies, these authors uncovered the existence of a symmetrically-bentgeometrical conformation lying -26 OOO cm-' above the global (i.e., linear) minimum of the X'C: surface. Although this highly excited ground state conformer could be implicated in the numerous spectroscopic perturbations that characterize the near-ultraviolet absorption bands of CS2, the investigation of such effects is beyond the scope of the present electronic structure calculations. Measurements performed in our laboratory through the use of both laser-induced fluorescence22and degenerate four-wave mixing23*24 spectroscopies have revealed significant complications in the near-ultraviolet bands of CS2, with several overlapping vibronic transitions identified in regions previously thought to contain individual features. Similar observations have been reported in two recent experimental studies conducted with subDoppler spectral resolution under supersonic molecular beam condition^.^^.^^ In order to interpret these findings and further elucidate the nature of low-lying electronic states in the CS2 system, a series of ab initio calculations have been performed on both the singlet and the triplet manifolds. Aside from providing a relative energy ordering for the excited states, this work has enabled structural parameters and vibrational frequencies to be predicted for the equilibrium geometry of each potential surface. After a brief discussion of the methods employed for our analysis, the computational results will be presented and compared with data derived from previous experimental and theoretical studies. While good agreement is found in most cases, certain discrepancies point to a need for further research efforts. Our calculations also yield information regarding the "optically dark" states of CS;! that are not directly accessible by conventional one-photon techniques but, nevertheless, often make their presence known in the guise of spectroscopic perturbation^.^^ + +
J. Phys. Chem., Vol. 99, No. 6, 1995 1801
Electronically Excited Carbon Disulfide
11. Methodology The GAUSSIAN 92 ab initio program,28 with its recent implementation of the configuration interaction method involving all single excitations (Le., CIS) and corresponding secondorder perturbative corrections (Le., CIS-MP2),29was employed for most of the calculations performed upon electronically excited states of CSZ. The CIS level of theory uses as a reference the single-determinant, Hartree-Fock wave function, YHF,derived from the ground state configuration of the system under investigation:
1
YHF = -IX~
... Xj-1 Xj Xj+l ..*Xn-1 XnI
XZ
fi
(1)
xi,
where n denotes the number of electrons and with i = 1, 2, ...,n, represents a spin orbital expressed in terms of a convenient set of N atomic basis functions, 45: N
The electronic portion of the molecular Schrodinger equation, as defined under the Bom-Oppenheimer a p p r o ~ i m a t i o nis ,~~ solved variationally so as to generate a set of N spin orbitals {XI,
22,
* * a ?
Xji
..., Xn, Xn+l, .'.( 20,
*e*,
XN}
(3)
having optimized expansion coefficients, c5,. For the reference ground configuration, the first n of these spin orbitals are occupied while the remaining N - n functions constitute unoccupied or virtual orbitals. Promotion of electrons from each occupied orbital, i = 1, 2, ..., n } , to every virtual orbital, i = n 1, n 2, ..., N), produces n(N - n) singly excited configurations of the form
{xi;
+
{xi;
+
where an electron has been "excited" from orbital xj to orbital A linear combination of the Yvla) configurations provides a good first-order representation for states that contain substantial single-excitation character:
xa (cf.expressions 1 and 4).
n
N
j=1 a=n+l
Solution of the corresponding secular equation for the molecular Hamiltonian, with variational adjustment of expansion coefficients embodied in the definition of YCIS,generates eigenvalues and eigenvectors which closely approximate the exact energies and wave functions for the excited electronic states of interest. While the CIS method provides a reasonably good approximation for excited states that posses mostly singleexcitation character, quantitative treatment of the dynamical correlations that exist between electrons often demands the inclusion of higher-order excitation processes. In analogy with the Meller-Plesset perturbation theory used to correct HartreeFock energies, a second-order scheme (viz., MP2) has been devised and implemented for the incorporation of correlation effects into CIS calculation^.^^ Despite its lack of a rigorous theoretical foundation, the CIS-MP2 method is expected to include the additional double and triple promotion channels required to properly account for the influence of electron correlation. As such, excited potential surfaces calculated via the CIS-MP2 procedure should prove to be more reliable than those obtained without recourse to the MP2 correction. However, the apparent similarities between the CIS-MP2 and
standard second-order MZller-Plesset formulas do not imply that excited and ground electronic states are treated at the same level of approximation. Consequently, a transition energy evaluated as the difference between the CIS-MP2 energy of an excited state and the MP2 energy of the ground state may be less accurate than that determined through use of the computationally-comparable CIS and restricted Hartree-Fock (RHF) methods. On the other hand, the overall shape and relative ordering of electronically-excited potential energy surfaces should be more adequately represented by the CIS-MP2 technique rather than by the CIS scheme alone. The reliability of the CIS and CIS-MP2 methods has been tested on a variety of molecular species, including formaldehyde,29q31pyridine,29porphine,29e t h ~ l e n e ,bicy~lobutane,~~ ~~,~~ and a~etaldehyde,~' with analyses reported for both valence and Rydberg electronic states. In all cases, computed structural parameters, transition energies, and vibrational frequencies have been found to be in good agreement with available experimental data. Bolstered by previous success of the CIS and CIS-MP;! techniques, the present work has exploited this level of theory, in conjunction with relatively large sets of basis functions, to examine the first four excited triplet and first three excited singlet potential energy surfaces of the CS2 system. All excited state calculations were restricted to valence shell electrons with polarization and diffuse functions incorporated until reasonable convergence of numerical results was achieved. In spite of its size consistency, CIS-MP2 is not considered to be a variational technique. Consequently, the examination of basis set quality for subsequent ab initio calculations was based on the CIS level of theory. Table 1 presents a compilation of absolute and transition energies obtained by using various basis sets to describe two representative geometries of electronically-excited CS2, one linear and the other bent with an S-c-S bond angle of 140'. In both cases, the two C-S bond distances were fixed at the common value of 1.6 A. Our goal in constructing this table was to identify the optimal choice, in terms of maximum accuracy and minimum computational time, of a triple-l; quality 6-3 11G basis. Results are compiled in order of decreasing absolute energy for the first excited singlet states of the linear and bent CS2 structures. Also included in this analysis are two triple-l; correlation-consistent basis sets (viz., CC-PVTZ and AUG-CC-PVTZ), as recently given by Dunning and c o - ~ o r k e r s ,which ~ ~ , ~ serve ~ as a reference standard for critical evaluation of the 6-31 1G basis and its various expansions. Careful inspection of Table 1 shows the 6-31 1+G* basis to provide a good compromise between accuracy and computational effort. While not substantially larger than the parent 6-31 1G basis, incorporation of polarization and diffuse functions, as required for proper treatment of correlation effects in excited states, results in roughly a 0.1 hartree reduction of absolute energy. The AUG-CC-PVTZ basis, which is nearly double the size of 6-311+G*, produces only an additional -0.03 hartree decrease in ab initio energies, with roughly a 50 times increase in relative expenditure of central processor time. Consequently, unless otherwise stated, the 6-31 1+G* basis set was employed for all calculations performed on the CS2 system.
III. Results and Discussion A. Ordering of Excited Electronic States. Figure 3 shows potential energy curves derived for the lowest-lying electronic states of CS2 through use of the CIS-MP2/6-311+G* level of theory. In order to obtain these results, the two C-S bond distances were held fixed at the common value of 1.6 8, while the S-C-S bending angle was varied over a range of 4~60"
Zhang and Vaccaro
1802 J. Phys. Chem., Vol. 99, No. 6, 1995
TABLE 1: Critical Evaluation of Basis Set QualiW ab initio basis set STO-3G 3-31G 4-31G 6-31G 6-311G 6-311'G 6-311G* 6-31lfG* 6-311(2+)G* 6-311(3+)G* 6-31lG(2d) 6-31lG(3d) 6-31lG(3df) CC-PVTZ AUG-CC-PVTZ
basis set ref 56,57 58-60 61 61-63 64,65 64-66 64,65,67 64-67 64-68 64-68 64-67 64-67 64-67 34 35
cpu time 0.03 0.05 0.06 0.07 0.40 0.47 0.62 1.00 1.66 5.52 1.25 2.31 6.36 20.15 49.88
8.445 07 3.394 03 0.239 49 -0.638 55 -0.692 58 -0.696 98 -0.780 82 -0.785 66 -0.786 77 -0.787 12 -0.789 97 -0.797 16 -0.805 65 -0.814 28 -0.815 75
linear geometry AE('%) 4.306 4.086 4.127 4.099 4.122 4.082 4.052 3.998 3.993 3.992 4.018 3.981 3.959 3.975 3.956
E(A'A2) 8.430 83 3.388 49 0.235 44 -0.647 15 -0.701 51 -0.706 17 -0.789 72 -0.794 48 -0.795 15 -0.795 45 -0.797 48 -0.804 01 -0.81 1 06 -0.820 48 -0.822 39
AE('A,)
4.629 4.316 4.362 4.326 4.343 4.303 4.240 4.187 4.181 4.180 4.186 4.143 4.120 4.142 4.114
bent geometry AE(A) AE(B) 3.541 2.983 2.856 3.257 2.918 3.309 3.241 2.844 3.278 2.896 3.210 2.839 2.809 3.167 3.099 2.751 3.094 2.749 3.094 2.749 3.128 2.784 3.086 2.747 3.083 2.748 3.096 2.753 3.058 2.727
AE(C) 4.221 3.869 3.902 3.885 3.920 3.878 3.743 3.691 3.685 3.684 3.676 3.630 3.613 3.636 3.612
a The CIS level of theory was used to examine various sets of basis functions for two representative geometries of CS2, one linear and the other bent with an S-C-S bond angle of 140'. In both cases, the two C-S bond distances were fixed at 1.6 A. Tabulated quantities include the name and primary reference for each basis, as well as the relative computational effort (Le., cpu time relative to that for 6-311+G*)required for a single point electronic structure calculation. The absolute ab inito energy for the first excited singlet state [i.e.,E('2;) or E(A'A2)], referenced to a value of -832 hartrees, provides a good indication for the quality of each basis set. Transition energies (in eV) between the X'2: ground state and the three lowest-lying excited singlet surfaces (viz., '$; X and doubly-degenerate 'Au X for the linear configuration or A1A2 X, BIB? X, and CIA2 X for the bent configuration) are also presented.
-
'
-
-
-
bent ( i e . ,equal C-S bond lengths) and therefore belong to the Czv point group. However, as discussed in ensuing sections, several of the excited states deviate only slightly from linearity. Symmetry designations for each of the CIS potential curves are shown in Figure 3 with the correlation of labels between linear and bent structures explicitly indicated. At their respective equilibrium geometries, the lowest-lying electronic states of CS2 exhibit a calculated energy ordering of the form
-833.15
h
E
8
P4
W e4
-
-833.16
X'Z: < a3B, < b3A2(R) -= A'A,
-833.17
B*B2(V)< c3B2< d3A2 < C'A, (6)
"'
f 1
120
140
160
180
200
220
240
S-C-S Bending Angle (Degrees) Figure 3. Electronic potential curves for CS2 as a function of the
S-C-S angle. The dependence of CS2 electronic energy upon the S-C-S bending coordinate is calculated at the CIS-MP2/6-311+G* level of theory for a fixed value of the C-S bond distance (viz., 1.6 A). Symmetry labels are affixed to each potential curve with correlations between linear and bent structures indicated explicitly. In contrast to the X'X; ground state, all of the excited singlet and triplet surfaces support nonlinear equilibrium geometries. from linearity. Analogous calculations performed without recourse to the MP2 correction (Le., CIS/6-311+G*) yield essentially the same ordering for electronic states at the linear CS2 configuration, however, significant differences in the separation and topography of excited potential surfaces are discemable. With the exception of the ground state, all of the electronic surfaces considered in this study are found to support a minimum energy configuration of nuclei that is symmetrically
where the letters in parentheses refer to the R and V absorption systems. When standard spectroscopic notation is followed,36 the CIS-MP2 symmetry labels are prefaced by a single letter designation, such as X, A, B, ... or a, b, c, ..., designed to distinguish singlet and triplet manifolds from one another and to specify the relative ordering of electronic states within each manifold. As per convention, capital letter prefixes are reserved for states having the same spin multiplicity as the ground potential surface (viz., X'Z;). The pattern of energy levels resulting from our CIS-MP2 calculations on CS2 is quite analogous to that obtained through application of a variety of theoretical methods to molecules having a n* n electronic transition. This fact stems from the intrinsic properties of a ( ~ ~ ( nsingle-excitation :)' conf i g u r a t i ~ n 'and ~ , ~can ~ be understood readily by reference to the correlation diagram embodied in Figure 3. For the linear geometry of CS2, the electron spin angular momenta couple to yield singlet and triplet manifolds while the electron orbital angular momenta add to generate two Z states (viz., and q-)and one A state (viz., AJ. Consequently, six linear electronic surfaces can be derived from the excited (ng)3(ni)1 configuration: 3Au, 3&-, I&-, 'Au, and In the triatomic CS2 system, the reduction in symmetry from D,h to CzVwhich accompanies distortion of the molecular framework from linearity demands that the doubly-degenerate A, states be resolved into A2 and B, components. As a result of vibronic interactions associated with the Renner-Teller e f f e ~ t , ' ~ , ~ ~ - ~ ~ these components are no longer degenerate and exhibit distinct electronic energies for any value of the bending angle other
-
'c,
J. Phys. Chem., Vol. 99, No. 6,1995 1803
Electronically Excited Carbon Disulfide than 180". Consequently, the 'A, state splits into 'A2 and 'Bz surfaces while the 3A, state separates into 3A2and 3Bzsurfaces. The assignment of the R and V absorption systems to the b3Az and BIB2 states, respectively, follows from consideration of both transition energies and symmetry properties. As depicted in Figure 3, the b3Az(R) and c3BZsurfaces are found to correlate with a degenerate 3A, state in the linear configuration. Previous spectroscopic measurements support designation of the b3Az(R) state as the lower-lying component of this Renner-Teller doublet? While analogous effects in a linear 'A, state give rise to the B1B2(V) and CIA2 surfaces, Figure 3 shows that the BZcomponent is predicted to be of lower energy. This ab initio result contradicts the bent-to-linear correlation of CS2 electronic states established from the interpretation of experimental data.4 Based upon their assignment of the high resolution absorption spectrum for the CSz V X system, Jungen et al? have proposed that the 'Bz(V) component is the upper member of the Renner-Teller doublet arising from the 'A, surface. This conclusion, deduced by correlating the vibronic structure in a linear 'A, state with the K-rotational levels of the corresponding nonlinear (i.e., bent) states, disagrees with predictions of our CIS-MP2 calculations (cf. ensuing discussion). Analogous X system as first reasoning, when applied to the CS2 R analyzed by Klemar~,~ led these same authors to surmise that splitting of the 3A, state results in a pattern of energy levels identical to that depicted in Figure 3 [viz., 3A2(R) lower component and 3Bzupper ~omponent].~ In a series of matrix isolation studies that preceded the experimental findings of Jungen et al., Bajema et al?' uncovered weak bands to the blue of the CSz V X system which they attributed to transitions originating from the ground electronic state and terminating on a low-lying 'A2 surface (viz., C'A2). Their assertion that the bent B'B;?(V) and CIA2 states correlate with the 'A, level of the linear molecule, with the BZcomponent being lower in energy, supports the present theoretical analysis. However, Jungen and co-workers4 have offered an alternative explanation for the matrix isolation results whereby spectral features on the short wavelength side of the V system might correspond to vibronically-induced transitions terminating on the 'qstate. These authors also point to the 1934 work of RodlofP2 where low temperature absorption measurement of solid CSZ samples revealed the presence of weak bands to the red of the V system which could be interpreted as transitions to the lower-lying ('A$ Renner-Teller component. AU of these experimental observations are in accord with the theoretical predictions embodied in Figure 3, where the B'Bz(V) state is interposed between two surfaces of 'A2 symmetry. However, the ab initio correlation between linear and bent excited singlet states of CSZ clearly differs from the conclusions reached by Jungen et al. In particular, our calculations suggest that the global minimum for the bent A'A2 surface, which stems from the linear 'qstate, is lower in energy than the B'Bz(V) equilibrium conformation with the higher-lying CIA2 surface constituting the other member of the 'A, Renner-Teller doublet. Although no rigorous a priori reason exists for the ordering of electronic states to be as indicated in Figure 3, simple physical arguments provide some justification for the predicted pattern of energy levels. To a large extent, the relative energy ordering for the Renner-Teller components of the 'A, and 3Au states can be rationalized in terms of repulsion effects between electronic potential surfaces of the same symmetry.36 In particular, the position of the CIA;?surface as the upper member of the 'A, doublet follows from its repulsive interaction with the lower-lying A'A;! state. At the same time, repulsion of the
A
-
-
-
-833.18
t
1.50
I
1.55
1.60
1.65
1.70
1.75
i
1.80
C-S Bond Length (A) Figure 4. Electronic potential curves for linear CS2 as a function of the C-S distance. The dependence of the CS2 electronic energy upon the C-S stretching coordinate is calculated at the CIS-MP2/6-311+G*
level of theory for a linear configuration of the molecular framework. Solid and dashed curves refer to the singlet and triplet manifolds, respectively, with squares denoting the doubly-degenerate A" states while circles represent the nondegenerate q- levels. A crossing between the 'Au and 'qpotential curves is found to occur at a C-S bond distance of roughly 1.7 A. BIB2 surface by a higher-lying 'Bz state (correlated with tends to push this Renner-Teller component to lower energies. Similar reasoning can be applied to explain the reversed order (viz., b3A2 c3Bz) of splitting calculated for the 3A, state. While physically satisfying, the repulsion arguments used to justify our CIS-MP2 analysis of the A, Renner-Teller splitting depend critically upon the relative position of neighboring electronic states. Indeed, if the 'qsurface is actually higher in energy than the 'A, state then all of the above reasoning can be inverted so as to corroborate the experimental assertion of a 'Bz component as the upper member of the Renner-Teller doublet4 Figure 4 depicts the results of CIS-MP2/6-3 l l + G * electronic energy calculations performed on the 'v3AUand ' s 3 q states of linear C S ~for various values of the common C-S bond distance. While the relative energy ordering of the 3A, and 3qsurfaces remains unchanged as the C-S bond is extended from 1.5 to 1.8 A, the 'A, and 'qpotential curves clearly exhibit a crossing at roughly 1.7 A. Analogous computational studies performed at the CIS/6-3 11+G*level of theory fail to indicate any bond length-dependent changes in the relative energy separation between either the 3Auand 3G or the 'A, and 'qlevels. The curve crossing depicted in Figure 4 gives rise to an unexpected dependence of the 'A, Renner-Teller splitting upon CS2 bond length. For C-S bond distances shorter than -1.7 A, where the 'A, state lies above the 'qlevel, the IB*(V) potential surface can be identified as the lower member of the Renner-Teller doublet. In contrast, elongation of the C-S bond beyond 1.7 8,leads to a reversal of the 'A, - IT- energy ordering with mutual repulsion of the two IA2 states (i.e., one
1804 J. Phys. Chem., Vol. 99, No. 6, 1995
Zhang and Vaccaro
TABLE 2: Structural Parameters for CS2 Electronic State@ C-S bond length (A)
state
label X9; a3Bz b3Az(R) A'A2 BIBz(V)
c'B~ d'A2 CIA2 (I
CIS-MP2 1.56 1.63 1.64 1.64 1.64
MCSCF 1.544 1.618 1.634
MR-CI 1S64
exptl
CIS-MP2 180 125 137 138 127
1.556249
1.644
1.64'
1.645
1.5444 1.57226
1.62 1.62 1.63
S-C-S bond angle (deg) MCSCF MR-CI 180 180 127.6 136 120.6
131
exptl
18049 135.83 1354 1634 160z6
169 167 172
The CIS-MP2/6-311+G*level of theory was used to determine the optimized equilibrium geometry for each electronic potential surface of CS2.
All excited states are found to support a minimum energy configuration corresponding to a bent (C2J arrangement of the molecular framework in which the two C-S bonds are of equal length. Also tabulated are the structural parameters derived from previous experimental and theoretical (uiz., MR-CI(SD)I9and MCSCFZ1)studies. The experimental S-C-S angle for the A1A2 surface is that assigned by Jungen and co-workers4to the so-called T state.
correlating to 'A,, the other to 'q) making the IB2(V) surface the upper Renner-Teller component. Clearly, the latter situation is more in keeping with previous experimental observat i o n ~ .While ~ a more thorough discussion of this curve crossing will be reserved for a forthcoming it is quite evident that the presence of such an effect can produce additional complications for interpretation of near-ultraviolet features in the CS2 absorption spectrum. More specifically, the extension and contraction of C-S bonds during a vibrational period can result in a temporal modulation of the electronic energy level pattern exhibited by the singlet excited states of CS2. In a previous ab initio study, Kasahara and co-workersi9 examined the electronically excited surfaces of CS;! by employing a multireference configuration interaction level of theory including single and double excitations [MR-CI(SD)]. These calculations utilized a MIDI-4" basis set4 with reference configurations obtained by placing eight electrons into three pairs of valence-type n orbitals. Configurations for subsequent CI analysis were generated by promoting up to two electrons from these preselected reference configurations to each of the virtual (i.e., unoccupied) valence-type orbitals. In contrast to the results derived from our CIS-MP2 treatment, the MR-CI(SD) work, performed with an optimized C-S bond length of roughly 1.65 A, suggests that the IB2(V) excited state becomes degenerate with a lower-lying IA2 surface for linear geometries of the molecular framework. This theoretical prediction that the IB2(V) state is the upper member of the 'A, Renner-Teller doublet appears to be much more in keeping with the experimental findings of Jungen et aL4 However, Kasahara et al. did not investigate the dependence of their reported energy level pattern upon the C-S bond distance. In order to further elucidate the differences that exist between our CIS-MP2 results and the previously reported theoretical work of Kasahara et al.,I9 a limited series of MR-CI(SD) calculations were performed using the COLUMBUS ab initio package45 in conjunction with the 6-311fG* set of basis functions. Guided by the expansion coefficients for CIS wave functions, symmetry adapted reference configurations were selected by distributing four active n electrons among four pairs of n-type orbitals. With the 11 lowest-lying molecular orbitals doubly-occupied (Le., a "frozen core"), configurations for subsequent CI analysis were generated by promotion of either one or two electrons from occupied to virtual orbitals in a manner that retained overall spin and spatial properties. Only the first three excited singlet states, having A2, B2, and A2 representations in a symmetrically bent CS2 geometry, were examined in these preliminary investigations. As in the case of our CIS-MP2 treatment, the MR-CI(SD) calculations revealed a crossing between the 'A, and 'Xi
potential curves of linear CS2 with concomitant reversal of the 'Au Renner-Teller splitting upon elongation of the C-S bond (cf. Figure 4 and accompanying discussion). However, the predicted MR-CI(SD) crossing point is located at a C-S bond distance of 1.55 8, which is substantially shorter than the -1.7 8, value deduced from the CIS-MP2 scheme. Indeed, at the 1.65 A bond length utilized by Kasahara and co-workers for their analysis of CS2 bending potential^,'^ our MR-CI(SD) results show the B1B2(V)and A'A2 states correlating to the 'A, level with the latter surface falling below the former in energy as the molecular framework distorts from linearity. While additional work remains to be done in order to fully reconcile these observations, at this juncture it is apparent that the lowestlying excited singlet states of CS2 [vis., A'A2, B'B2(V), and CIA21 are coupled intimately, with changes in the C-S bond length (e.g., during vibrational motion) serving to modify their relative energy ordering. B. Optimized Nuclear Geometries. Table 2 presents a compilation of structural parameters that have been optimized at the CIS-MP2/6-311+G* level of theory for each of the lowestlying electronic states of CS2. Where possible, findings derived from prior experimental and computational studies are also tabulated. All electronic surfaces are found to support a symmetric equilibrium configuration of nuclei, with the two C-S bond distances being of equal lengths. The stability of predicted structures was assessed by performing a vibrational frequency analysis subsequent to geometry optimization. The absence of imaginary frequencies confirms that the reported structural parameters refer to local minima on the adiabatic potential energy surfaces. As indicated, our CIS-MP2 results compare quite favorably with previous experimental measurements and theoretical calculations. A notable exception can be found in the case of the B1B2(V) state where ab initio predictions of the C-S bond length and S-C-S bond angle are substantially longer and smaller, respectively, than those deduced from spectroscopic studies. The experimental structure obtained for the BiB2(V) state of CS2 follows from a detailed analysis of rovibronic features within the exceptionally congested and extensively perturbed V X absorption system. Based upon averaged spectroscopic constants, Jungen and co-workers4 proposed an equilibrium geometry containing equivalent C-S bond lengths of 1.544 8, with a S-C-S bond angle of 163". This prediction of a relatively small deviation from linearity in the V state is unusual given the bond angles that have been calculated and measured for other electronically excited CS2 potential surfaces. In addition, the reported decrease in C-S bond length following V X excitation (viz., 1.544 1.5562 A) is inconsistent with the weakening of the carbon-sulfur bond that must accompany
-
-
-
J. Phys. Chem., Vol. 99, No. 6, 1995 1805
Electronically Excited Carbon Disulfide a E* + n electronic transition. Indeed, the MR-CI(SD) calculations performed by Kasahara et aZ.,19 as well as recent multiconfiguration self-consistent field (MCSCF) results reported by Tseng and Poshusta,21 suggest an equilibrium geometry that closely resembles our CIS-MP2 prediction. Given the excellent agreement between theoretical and experimental studies on the X'Xgf ground and b3A2(R) excited states, the ab initio equilibrium structure for the V state might be expected to represent a good approximationto physical reality. However, comparison of results obtained at the CIS and CIS-MP2 levels of theory clearly show that subtle differences exist between the B'Bz(V) surface and other low-lying exited states of CS2, with the incorporation of MP2 electron correlation effects into the V state leading to substantial lengthening of the C-S bond distance (viz., from 1.59 to 1.64 A) and reduction of the S-C-S bond angle (viz., from 145" to 127"). Since the pioneering efforts of Jungen et al.," several other spectroscopic investigations of the B'Bz(V) state have been reported. Ochi and co-workers20 performed laser-induced fluorescence studies of the V X system under supersonic free-jet conditions designed to alleviate rovibronic congestion. These authors suggest that a somewhat smaller S-C-S bond angle, on the order of 150°,is more in keeping with the observed pattern of spectral intensities. More recently, Habib et ~ 1 combined a single-mode laser source with a collimated molecular beam of CSz molecules so as to record an extensive series of sub-Doppler fluorescence excitation spectra. Analysis of their data indicates a B'Bz(V) structure quite similar to that originally proposed by Jungen and co-workers, with a slightly larger value for the C-S bond length (viz., 1.572 A) needed to account for measured rotational constants. Given the persistent discrepancies that exist between experimental and theoretical studies of the V state, it is possible that the shallow "doubleminimum" well of this surface (cf.Figure 3), coupled with large amplitude motions of the CS2 nuclear framework, might lead to vibrational averaging effects which, in tum, result in spectroscopically-deduced geometries that deviate significantly from the global minimum energy conformation derived through ab initio calculations. However, the similar topographies of the B'Bz(V) and b3A2(R) potential surfaces (cf. Figure 3), in conjunction with the reasonable quality of computational predictions made for properties of the R state (cf.tables 2, 3, and 7), would seem to refute such arguments. An alternative explanation for differences between the theoretical and experimental equilibrium structures of the BiB2(V) surface follows from consideration of the substantial change in geometry that transpires during the n* n excitation. Simple Franck-Condon arguments imply that the strongest features in a bent-from-linear transition should entail excited state wave functions having significant amplitude at the linear configuration of nuclei. Therefore, the most intense cold bands in the V X system (viz.,the so-called 1OV and 15V bands)4 will involve vibrationally excited levels of the V state which, owing to their proximity to the barrier crest (cf. Figure 3), display vibrationally averaged structures that are closer to linearity than the global minimum of the correspondingpotential energy surface. This mechanism, which relies on a possible, albeit improbable, misassignment of vibronic patterns in the near-ultraviolet CS2 absorption spectrum, can rationalize the large experimental value for the S-C-S bond angle while simultaneously providing justification for the vanishingly weak X transition. Indeed, there intensity of the vibrationless V is precedence in the published literature for this speculation, with Ochi and co-workers20suggesting that the accepted origin of the V system be reassigned to a higher member of the
0.2
b h
-
+
,
,
130
140
I
1
1 ,
I
0.0
0
E
w
-0.2
I
Q
.CI Y
=E -0.4 0
: a
I
8
-0.6
I
il *
0
. I
-0.8
Y
Q I
2
+
+
I
-1.0
-1.2 ~
.
~
~
110
120
150
160
170
180
190
S-C-S Bending Angle (Degrees) Figure 5. Walsh diagram for the valence molecular orbitals of CSz. Molecular orbitals of CSZare calculated by the RHF/6-3 11+G*method with the C-S bond distances fixed at 1.6 A and the S-C-S bond angle varied over the range of 120' to 180". The correlation of orbital
energies and symmetry labels between the linear ( L h ) and bent (C2J structures is shown explicitly. For the ground electronic state configuration, all molecular orbitals up to 7bz are occupied fully. Promotion of an electron into the 3b; and 9a; virtual orbitals accounts for the triplet and singlet manifold of potential surfaces associated with the n* n transition.
-
progression built upon the v2 bending mode of the BiB2(V) state. On the other hand, ab initio calculations, regardless of the particular methodology employed for their execution, are always subject to question owing to the inevitable exclusion of effects that, in hindsight, might significantly influence the description of molecular properties. The structural changes that accompany electronic excitation of the CS2 system can be rationalized through use of the Walsh diagram4 presented in Figure 5. Here molecular orbital energies calculated at the RIP/6-311+G* level of theory are plotted as a function of the S-C-S bending coordinate with the two C-S bond distances held fixed at the common value of 1.6 A. The ensuing discussion will focus on the important frontier orbitals, that is, on the highest-occupied (HOMO) and lowest-unoccupied (LUMO) molecular orbitals which are designated as 2ng and 3n:, respectively, in the linear geometry. Bending of the nuclear framework causes each of these doubly-degenerate orbitals to split, yielding pairs of HOMO and LUMO orbitals labeled as (2a2, 7bz) and (gay, 3b;). Inspection of Figure 5 shows that the 7b2 and 9al orbitals are most affected by bending of the molecular framework, with the latter undergoing a rapid decrease in energy with increasing distortion from linearity. The remaining frontier orbitals, 2az and 3b;, are predicted to undergo only slight changes as a function of the bending coordinate. More specifically, with decreasing S-C-S angle the 9ay and 3b; virtual orbitals drop in energy while the occupied 2az and 7b2 orbitals rise in energy. These trends can be interpreted qualitatively through level repulsion arguments involving neighboring molecular orbitals.
Zhang and Vaccaro
1806 J. Phys. Chem., Vol. 99, No. 6, 1995 The pairs of occupied and virtual frontier orbitals in CS2 will lead to four possible single-excitation configurations each of which generates a triplet and a singlet state of particular symmetry: 9ay 9a; 3b; 3b;
-
2% 7b2 2a2 7b,
1
A, and 3A2
1
B2 and 3B2
'B2 and 3B2 'A, and 3A2
(7)
The Walsh diagram clearly indicates that the ground state (2ad2(7b2)2 configuration attains a minimum energy for the linear C S geometry. ~ Promotion of an electron into the 9a; LUMO will result in equilibrium structures that have exceptionallysmall bond angles, with the overall degree of bending limited by mutual repulsion of the rather bulky sulfur atoms. This bending effect should be most pronounced in the case of 9a; 7b2 excitation channels owing to significant removal of the forces responsible for driving the molecular framework toward linearity (cf. 7b2 orbital in Figure 5). Similar considerations can be applied to configurations involving occupation of the 3b; LUMO, although somewhat larger values for the S-C-S bond angle can be expected. In all cases, electronic excitation should lead to lengthening of the carbon-sulfur bonds as a result of the reduction in C-S bond strength that must accompany a n* n transition. The molecular orbital parentage for each of the excited electronic states of CS2 can be deduced from the corresponding CIS wave functions. At their respective CIS-MP2 equilibrium geometries, the lowest-lying singlet surfaces can be described in terms of the following single-excitation configurations:
-
-
(8) where the symmetry labels of Figure 5 have been used to denote the various molecular orbitals involved in electron promotion processes and only configurations having absolute expansion coefficients in excess of 0.1 are displayed. In a similar manner, the lowest-lying triplet states of CS2 can be characterized by means of the following CIS wave functions:
channel will lead to equilibrium structures that have exceptionally small bond angles, a prediction in keeping with the 125" value derived from our ab initio calculations. %e CIS wave function for the lowest-lying singlet electronic state, A'A2, 2a2 configuration. shows a major contribution from the 9aT Consequently, a somewhat less dramatic distortion from linearity is expected for this electronic potential surface with CIS-MI2 geometry optimization yielding an S-C-S bond angle of 138". Similar considerations can be applied to the B1B2(V)and b3A2(R) states which have character derived from both "bendinhibiting" (Le., 2bT 2a2 or 3b; 7b2) and "bend-inducing" (Le., 9al 7b2 or 9a; 2a2) channels. These competing effects should result in equilibrium structures that display a moderate degree of nonlinearity. The bond angle of 137" predicted for the b3A2(R) surface is quite reasonable given the substantial magnitude of expansion coefficients associated with "bend-inducing" configurations (cf.expression 9). While CIS alone suggests a 140" bond angle for the B'B2(V) equilibrium geometry, the 127" value derived from the CIS-MP2 level of theory points to the involvement of significant electronic correlation effects in this excited electronic state. The CIA2 and c3B2electronic surfaces have major contribu7b2 and 3b; 2a2 singletions arising from the 3b; excitation configurations, respectively. Both of these electron promotion channels will tend to yield equilibrium structures that deviate only slightly from linearity. While this simple interpretation agrees with the S-C-S bond angles of 172" and 169" derived from our CIS-MP2 analysis, the wave function expansions of eqs 8 and 9 indicate that significant character stems from other "bend-inducing" electronic configurations (e.g., 9aT 2a2 in the case of C'A2 and 9a; 7b2 in the case of c3B2). Similar arguments can be used to qualitatively justify the 167" bond angle predicted for the d3A2state. C. Calculated Vibrational Frequencies. Table 3 presents the results of vibrational frequency analyses performed on each CS2 electronic state subsequent to geometry optimization. Where available, frequencies derived from gas-phase spectroscopic measurements also are tabulated. For the ground electronic potential surface, the three normal modes, nominally corresponding to motion along the VI symmetric stretching, v2 degeneratebending, and v3 antisymmetric stretching coordinates, are found to have calculated frequencies that are within 10% of the firmly established experimental values. This type of discrepancy is quite common for ab initio work performed at comparable levels of theory.47 A similar quality of agreement between calculated and measured vibrational frequencies exists for the b3A2(R) potential surface. In the case of the B'B2(V) state, however, the ab initio vibrational analysis clearly is at odds with the single experimentally observed frequency which has been attributed to the bending degree of f r e e d ~ m . ~ . ~ ~ In general, weakening of the C-S bonds subsequent to a n* n transition should manifest itself as a decrease in stretching frequencies between the initial and final electronic surfaces. This breaking of n-bond character, as well as the concomitant transformation from a linear ground state to a bent excited state, will also tend to abate the restoring forces that oppose bending of the molecular framework. Therefore, in addition to a marked lessening of C-S bond strength, the bent-from-linear n* n excitation in CS2 should be accompanied by a reduction in the effective bending frequency. However, the mutual repulsion of sulfur atoms which accompanies extreme distortion from linearity will provide a viable countermechanism for increasing the value of v2 in electronic states that support highly bent equilibrium structures.
-
-
-- -
-
-
-
-
-
-
yV,IS(d3A2) = -0.4Ov(2%1ga;) - o-56y(7b213bi) 0.12y(7b214b;)
-
(9)
As shown in eq 9, the a3B2surface of CS2 stems primarily 7b2 single-excitation configuration. The from the 9ay Walsh diagram of Figure 5 suggests that this electron promotion
J. Phys. Chem., Vol. 99, No. 6,1995 1807
Electronically Excited Carbon Disulfide
TABLE 3: Fundamental Vibrational Frequencies for 12C32S~a symmetric stretch bend state labels CIS-MP2 MCSCF exptl CIS-MP2 MCSCF X'X; 684 727 671.9549 371 429 295 a3B2 861 852 290 b3Az(R) 766 691.53 338 A' A2 760 333 BIBz(V) 817 932 277 317 c3B2 d3A2 CIA2
593 590 560
antisymmetric stretch exptl 398.9649 310.83 2204 5804 44426
CIS-MP2 1637 1140 930 894 840
379 334 338
MCSCF 1572 839
exptl 1558.6949 (940)3
1180 1064 979
For each electronic state, the equilibrium structure deduced from a CIS-MP2/6-311+G*geometry optimization was subjected to a vibrational analysis. The reported frequenciesare in cm-' with V I , v2, and v3 corresponding to motion along the symmetric stretching,bending, and antisymmetric stretching coordinates, respectively. Where possible, values obtained from experimental measurements on the "normal" isotopomer of CS2 (viz., 32S'2C32S) are presented, with parentheses indicating quantities obtained through indirect means. For comparison purposes, the ab initio MCSCF results of Tsene and Poshusta2' are also tabulated. The exDerimenta1vz frequency for the A'A2 surface is that assigned by Jungen and co-workers4 to the bending-vibration of the so-called T system. While ab initio bending and antisymmetric stretching frequencies for all of the electronically excited surfaces are found to be smaller than those for the X'Z: ground state (a minor exception occurs for the c3B2 bending frequency which is predicted to be marginally higher than that of the ground state), the symmetric stretching vibration exhibits a much less systematic and, oftentimes, counterintuitive trend. As shown in Table 3, several excited states display calculated V I frequencies that are substantially larger than the corresponding ground state value. This apparent discrepancy can be explained by realizing that force constants, rather than vibrational frequencies, are more appropriate indicators for the restoring forces that govern a particular vibrational motion. Within the harmonic approximation, the normal vibrational frequency, v, can be recast in terms of the associated force constant, k, and reduced mass, p, by means of the familiar expression:
From this viewpoint, an increase in the CS2 symmetric stretching frequency upon electronic excitation can be attributed not to a counterintuitive enhancement of force constant or bond strength but rather to a substantial change in the corresponding reduced mass. For a symmetric linear triatomic molecule, the central atom remains stationary as the molecular framework executes a normal symmetric stretching motion. Consequently, the effective reduced mass for V I on the linear ground state potential surface of CS2 is equal essentially to that of the terminal sulfur atom. In contrast, distortion of the equilibrium geometry away from linearity demands increasing displacement of the central atom in the symmetric stretching vibration. In the case of CS2, where a relatively light carbon atom occupies the central position, this implies that the bent-from-linearn* n transition will be accompanied by a reduction in the value of p for the V I vibration. Table 4 presents the force constants and reduced masses corresponding to the calculated normal mode vibrations for each of the CS2 electronic states. These results, obtained at the CISMP2/6-311+G* level of theory, display the pattern suggested by the above analysis, with a smaller equilibrium bond angle leading to a larger reduction in the effective value of p for the symmetric stretching motion. On the other hand, the bending and antisymmetric stretching vibrations show a near opposite trend that correlates the smallest reduced mass to near-linear equilibrium geometries. In addition, the variations in p for ~3 are almost negligible, alluding to dominant participation of the central carbon atom in this vibrational mode regardless of changes in equilibrium molecular structure.
-
TABLE 4: Normal Mode Vibrational Parameters for 12C32sZa
state label
xlzi a3B2 b3A2(R) A'A2 B1B2(V) c3B2 d3A2 CIA2 a
force constant ki
8.815 7.205 6.020 5.963 5.350 5.795 5.413 5.373
k2 1.081 1.086 1.375 1.322 0.989 1.200 0.962 0.937
k3 21.028 10.434 6.886 5.354 6.857 10.924 8.889 7.522
reduced mass PI
P2
P3
31.97 16.49 17.42 17.51 13.61 27.92 26.37 29.09
13.31 21.87 20.42 20.30 21.83 14.17 14.61 13.89
13.31 13.64 13.50 13.50 16.51 13.33 13.33 13.32
Effectivereduced masses (u in amu) and force constants (kin mdyd
A) are tabulated for each of the normal mode vibrations in CS2. The subscripts 1, 2, and 3 refer to motion along the symmetric stretching, bending, and antisymmetric stretching coordinates, respectively. Geometry optimizations and vibrational analyses for excited states were performed at the CIS-MP2/6-311+G* level of theory while those for the ground state made use of the computationally-comparableMP2/ 6-31l+G* method.
-
As expected for transitions having mostly n* n character, all of the excited state stretching force constants compiled in Table 4 are found to be significantly smaller than the corresponding ground state values. However, the variations in k ~ , k2, and k3 among the different electronic surfaces do not display a readily discemable pattem. While this is also true for the internal force constants presented in Table 5, the more physical nature of this representation enables the changes in vibrational properties to be correlated with structural parameters (viz.,bond lengths and angles) which, to some extent, serve as indicators for bond strength and bending stiffness. In general, the smallest stretching force constants (viz., k,) are found in excited states that support the largest equilibrium value for the C-S bond lengths. Likewise, the increased repulsion between bulky sulfur atoms in bent equilibrium geometries leads to enhanced bending force constants (viz., ks) for surfaces that display pronounced distortion from linearity. Of course, these assertions must be used with caution since they apply only to states that have essentially identical electronic parentage. Based upon analysis of vibronic progressions in the R X absorption system, Kleman3 has assigned the V I symmetric stretching and v2 bending frequencies of the R state as 691.5 f 1.0 and 310.8 f 0.5 cm-I, respectively. Comparison of spectra derived from various isotopomers of the parent 12C32S2 molecule led to two distinct possibilities for the v3 antisymmetric stretching frequency, with the value of 940 f 50 cm-' selected from extrapolation of observed vibronic structure to the corresponding zero point energy. For the optimized equilibrium
-
1808 J. Phys. Chem., Vol. 99, No. 6, 1995 TABLE 5:
Internal Force Constants for 12C32SP force constant coupling constant ~~
state label
X5; a3B2 b3Az(R) A1A2
B1B2(V) c3B2 d3A2 CIA2
Zhang and Vaccaro
~
~~
ks
kdP
kss
8.397 5.695 4.622 4.466 4.371 5.221 4.686 4.265
0.205 0.284 0.316 0.295 0.244 0.175 0.180 0.174
0.418 0.997 1.697 1.797 1.988 1.048 1.280 1.400
~
ksdl 0.000
0.158 0.196 0.126 0.057 0.030 --0.002 0.006
Internal force constants (in mydn/& are tabulated for the ground and lowest-lying excited states of CSZ. The symbols ks and kd denote the C-S stretching and S-C-S bending force constants, respectively, while k,, and kd represent the stretch-stretch and stretch-bend coupling parameters. The equilibrium C-S bond lengths, 1, used to normalize the bend-related parameters are equal to the CIS-MP2 values presented in Table 2. Calculations for excited states were performed at the CISMP2/6-311fG* level of theory while those for the ground state employed the MP2/6-311+G* method. For precise definition of the GAUSSIAN quadratic force field, see Hehre et uI.~' geometry of the b3A2(R) surface, our ab initio treatment predicts normal mode vibrational frequencies of V I % 766, v2 % 338, and v3 % 930 cm-I. Assignment of the calculated frequencies to the indicated vibrations is definitive, with normal mode displacement coefficients examined so as to confirm the type of nuclear motion executed for each vibrational degree of freedom. Given the inherent limitations of the CIS-MP2 level of theory, the agreement between observed and calculated normal mode frequencies is quite good. Indeed, the alternative choice of v3 obtained from Kleman's isotope studies (viz., 1270 cm-I) is found to be unreasonable in light of the present theoretical results. Further evidence for the quality of excited state vibrational parameters derived from the CIS-MP2 treatment follows from the effects of isotopic substitution. Table 6 presents a compilation of vibrational frequencies and rotational constants obtained for various isotopomers of the parent I2C3?S2molecule. The relatively high natural abundances of the 13C, 33S, and 34S nuclides has enabled spectroscopic measurements to be performed on many of these species. For each electronic potential surface, the tabulated vibrational frequencies are found to obey the Teller-Redlich product rule48 which interrelates among isotopomers the product of vibrational frequencies for modes of the same symmetry. More importantly, the calculated XIZ,f ground state isotope shifts are in excellent agreement with those reported by Smith and O ~ e r e n dand ~ ~by SuzukiSo as part of their systematic analyses of the CS2 vibrational force field. In the harmonic approximation, the ratio of frequencies between various isotopmers will depend only upon the effective reduced mass which, in turn, is a function of the molecular geometry. Consequently,provided that the ab initio equilibrium conformations are good representations of physical reality, the vibrational information contained in Table 6 should assist in the identification of near-ultraviolet spectral features arising from isotopic variants of the parent I2C3*S2species. For this reason, the number of significant digits retained for the calculated spectroscopic parameters is greater than warranted by the absolute accuracy of the CIS-MP2 computational method. The tabulated rotational constants are derived from a mechanically rigid nuclear framework and therefore exhibit none of the inertial defects ascribed to vibrational averaging.48 As part of his pioneering study on the R X system, Kleman3 reported the effects of isotopic substitution on the V I and v2 modes of the R state. More specifically, the 13C32S32S, 12C32S34S, and 13C32S34S isotopomers were found to have the
-
parent v1 = 691.5 cm-I frequency shifted by -10.5, -5.5, and -5.5 cm-l, respectively. halogous measurements on the v2 = 310.8 cm-' fundamental frequency revealed isotope shifts of -5.5, -2.5, and -2.2 cm-I. When described in terms of internal coordinates, the quantitative interpretation of these data required the incorporation of a substantial coupling force constant, ksd, between the stretching and bending degrees of freedom. In particular, this interaction parameter was found to be considerably larger in magnitude than the bending force constant itself. The ab initio results compiled in Table 6 display trends which are in good agreement with the observed changes in vibrational frequency for various CS2 isotopomers. The largest discrepancies occur for the 13C32S34S molecule which, at less than 0.1% natural abundance, presents the greatest challenge for experimental investigation. In addition, the calculated force constants presented in Table 5 corroborate Kleman's assertion of an unusually large value for k,a in the R state. This condition, which also is predicted to exist in both the a3Bz and A'A2 potential surfaces, stems primarily from the unique combination of masses (viz., light central atom and massive terminal atoms) encountered in the CS2 system. Although our calculated vibrational frequencies for the XlZ; ground state and b3A2(R) excited state are in keeping with established laboratory values, they disagree substantially with previous experimental findings for the B1B2(V) surface. Owing to the rovibronic congestion and spectral complexity that characterize the V bands, definitive analysis of the pertinent excited state has presented a quite formidable challenge, with several research groups reporting conflicting results. Early gasphase absorption measurements by Ramasa~try,~' as well as subsequent matrix isolation work by Bajema et ~1.:' identified a vibrational progression of -580 cm-' which was assigned, through comparison with known X'Z,f vibrational constants, to the symmetric stretching frequency of the electronically excited surface. Based upon the insignificant change in C-S bond lengths revealed by their high resolution studies on the V system, Jungen et aL4 concluded that symmetric stretching X transition. Consequently, motion is not active in the V these authors reassigned the 580 cm-' progression to one built upon bending vibrations of the V state. Kasahara and cow o r k e r ~have ~ ~ employed both experimental and theoretical means to unravel the equilibrium geometry and vibrational structure of the V state. Using an "unconventional" vibrational assignment that was later refuted by Ochi et u ~ . , ~ Oin conjunction with numerical solution of a one-dimensional Schrodinger equation for semiempirical bending potentials, these authors have proposed a bending frequency of -370 cm-' for the V X spectrum, Habib state. In a more recent study of the V and co-workers26utilized similar model potentials in order to describe the bending motion of electronically excited CS2 molecules. Interpretation of their high resolution data led to an optimized one-dimensional potential well with the four lowest-lying bending vibrations (Le., nominally corresponding to u2 = 0, 1, 2, and 3 of the V state) separated by energy gaps of 444, 435, and 446 cm-I. While a definitive explanation demands additional studies, the discrepancy between experimental and theoretical vibrational analyses for the B1B*(V) potential surface suggests several interesting possibilities. Assuming, for the moment, that the CIS-MP2 calculations are good approximations to physical reality, the computational results in Table 3 show that a systematic reduction in bending frequency occurs upon electronic excitation of CS2. This prediction is in keeping with previously mentioned arguments regarding a bend-from-linear x* n transition. Obviously, the 580 cm-I value ascribed to +
+
-
J. Phys. Chem., Vol. 99, No. 6, 1995 1809
Electronically Excited Carbon Disulfide
TABLE 6: Spectroscopic Constants for CS2 Isotopomers" CS;! isotopomer vibrational frequency rotational constant state S S vl (cm-I) v2 (cm-') v3 (cm-I) A (cm-') B (cm-I) C (cm-') label C 12 32 32 684.06 371.17 1637.26 0.1088 X'g 12 32 34 673.88 370.3 1 1633.48 0.1056 12 32 33 678.84 370.73 1635.30 0.1071 358.91 13 32 32 684.06 0.1088 1583.18 13 32 34 673.87 0.1056 358.02 1579.27 12 32 A' A2 332.51 32 760.36 0.1134 4.7841 0.1 108 893.91 12 32 34 754.63 0.1101 4.7619 0.1076 329.25 891.67 12 330.85 892.73 32 33 757.43 0.1117 4.7726 0.1092 13 32 32 745.75 0.1134 4.4733 327.84 865.08 0.1106 13 32 34 739.81 4.45 11 324.70 862.78 0.1101 0.1074 BIB;! 12 32 277.31 816.73 839.68 32 0.1226 3.1329 0.1179 274.32 813.82 12 32 34 0.1189 3.1184 0.1146 834.86 815.39 12 32 33 3.1254 275.78 837.04 0.1207 0.1 162 32 790.83 13 32 274.16 821.33 0.1226 2.9294 0.1176 787.98 13 34 32 2.9149 271.26 816.23 0.1189 0.1143 12 CIA2 32 559.94 32 338.47 128.1304 978.99 0.1005 0.1004 552.10 34 12 32 0.0975 0.0974 337.36 127.5357 976.73 555.92 33 12 32 0.0989 337.90 127.8236 977.82 0.0989 13 32 558.69 32 328.06 119.8059 946.68 0.1005 0.1004 550.80 34 13 326.97 119.2112 32 0.0975 0.0974 944.35 a3B2 12 32 32 861.23 290.34 1139.55 2.9860 0.1264 0.1212 32 34 855.63 287.19 12 1136.38 2.9722 0.1226 0.1178 12 1137.90 0.1245 32 33 858.36 288.73 2.9789 0.1195 13 32 32 842.32 1103.47 2.7920 0.1209 287.11 0.1264 13 32 34 1100.20 2.7782 836.55 284.04 0.1226 0.1175 12 32 b3A2 32 765.89 338.06 0.1143 930.37 4.6510 0.1115 34 12 32 760.21 928.00 4.6294 334.71 0.1109 0.1083 12 32 33 929.13 762.99 336.35 0.1125 4.6399 0.1099 32 13 32 750.95 0.1143 900.41 4.3488 0.1113 333.39 34 13 32 745.07 897.97 4.3272 330.17 0.1109 0.1081 12 32 c3B2 32 593.48 379.20 0.1023 72.1136 1179.60 0.1021 34 12 32 585.43 0.0993 71.7788 1176.86 317.82 0.0991 12 32 33 7 1.9409 1178.18 589.35 378.50 0.1007 0.1006 32 1140.70 13 32 591.57 367.84 0.1023 67.4284 0.1021 32 0.0993 34 13 1137.87 583.42 366.51 67.0937 0.0991 32 12 d3Az 32 590.24 334.34 0.1018 50.8537 1063.88 0.1016 34 12 32 582.59 332.90 50.6176 1061.42 0.0988 0.0986 33 586.31 333.60 12 32 0.1002 50.7319 1062.60 0.1001 587.39 13 32 32 324.90 0.1018 47.5498 1028.81 0.1016 34 323.52 579.64 13 1026.26 32 0.0988 47.3137 0.0986 Vibrational and rotational parameters are presented for the most prevalent isotopomers of CS2: 32S'2C32S (89.3%), 32S12C34S (7.9%), 32S'2C33S (1.4%), 32S'3C32S(0.99%), and 32S'3C34S(0.08%) where the numbers in parentheses refer to natural abundances. The equilibrium structure for each electronic surface, as derived from a CIS-MP2/6-31 liG* geometry optimization, was used to determine the symmetric stretching (Y'),bending (vz),and antisymmetric stretching (vg) vibrational frequencies as well as the A, B, and C rotational constants. the v2 mode of the V state by Jungen et aL4 departs from this trend. More recent work,19.26performed under supersonic molecular beam conditions, indicates a somewhat lower bending frequency on the order of 400 cm-'. A plausible, albeit improbable, rationalization for these laboratory findings would be a misassignment of rovibronic features in the near-ultraviolet absorption spectrum. There has been speculation that the established origin of the V X system actually corresponds to transitions between the vibrationless ground state and an excited vibrational level of the V state.20 The "doubleminimum" topography of the BIB~(V)surface, with its unusual pattern of energy level spacings obscured by the conspiring effects of spectral congestion and rovibronic perturbations, might therefore lead to an erroneous identification of the v2 bending frequency. However, before any serious reinterpretation of experimental facts can be undertaken, it is quite evident that further theoretical analyses of the B1B2(V)state are required in order to access the reliability of detailed ab initio predictions. As indicated in Table 3, the experimentally-determined bending frequency of the so-called T state has been assigned tentatively to the v2 mode of the A'A2 surface. The original work of Jungen et aL4 suggested that the pertinent excited state, which gives rise to weak absorption features located to the red
-
-
of the V X system (cf.Figure l), is of ]A2 symmetry with transition intensity obtained by means of a Coriolis-induced vibronic interaction. Since detailed analysis of rotational structure within the V bands implied that the 'B2(V) state was the higher-lying member of the Renner-Teller doublet arising from the 'Au level of linear CS2, these authors proposed that the T state represents the corresponding lower-lying component (cf. Figure 2). In contrast, for C-S bond distances near the optimized value of -1.6 A, CIS-MP2 calculations predict the B'B2(V) surface to be the lower member of the IAu doublet with a subjacent state of IA2 symmetry (viz., A'A2) correlating to the '% level of the linear molecule (cf. Figure 3). The predicted bending frequency of 333 cm-' for this A1A2potential surface is in reasonable agreement with the 220 cm-' value deduced by Jungen and co-workers for the excited electronic state of the T system. D. Calculated Transition Energies and Oscillator Strengths. Table 7 presents a compilation of electronic transition energies calculated as the difference in absolute energy between the ground and excited potential surfaces at their respective equilibrium geometries. These ab initio values were derived from analyses based upon comparable levels of theory, with results obtained through use of the CIS and RHF methods,
1810 J. Phys. Chem., Vol. 99, No. 6, 1995
Zhang and Vaccaro
TABLE 7: Calculated Transition Energies and Barrier Height@ transition energy (eV) state CIS CIS-MP2 MR-CI MCSCF exptl label a3B2 2.78 3.65 3.08 b3Az(R) 3.46 4.16 3.253 A'A2 3.94 4.3 1 (3.64)4 B'B*(V) 4.29 4.40 4.29 3.834 4.62 3.8326 c3B2 3.62 4.59 d'A-2 4.14 4.15 CIA2 4.34 4.80
CIS 3116 1212 1716
447
barrier to linearity (cm-I) CIS-MP2 MR-CI MCSCF 5274 3544 4800 3847 3331 2060 3300
exptl (330013 (280014 130O4
1o o o 2 6 16 113 13
123 195 68
a Transition energies, defined as the energy separation between the distinct equilibrium geometries of the linear ground and bent excited states, and barriers to linearity are presented for each of the low-lying potential surfaces of CS2. Both the CIS/6-31liG* and CIS-MP2/6-311+G*levels of theory were employed for the excited state calculations while the ground state was treated by the computationally-comparableRHF/6-311+G* and MP2/6-31l+G* methods, respectively. Vibrational zero point effects are not taken into account. Previous ab initio results, obtained from the MR-CI(SD) studies of Kasahara et a1.I9 and the MCSCF work of Tseng and Poshusta,2'are shown. Where available, laboratory findings are also tabulated with parentheses serving to designate quantities especially prone to experimental uncertainties. The experimental values for the A'A2 state are those deduced by Jungen and co-workers4for the so-called T system.
as well as the CIS-MP2 and MP2 methods, tabulated for comparison. Barriers to linearity, defined as the separation in energy between linear (with optimized bond distances) and equilibrium configurations of the molecular framework, are also presented for each of the CS2 excited states. Where available, predictions reported by previous computational studies and experimental findings deduced through interpretation of spectroscopic measurements are included for reference purposes. While not considered explicitly in the ensuing discussion, vibrational zero-point effects are expected to shift calculated transition energies downward by amounts correspondingto 10.1 eV. Similar reasoning suggests that effective barriers to linearity might be lowered by as much as 500 cm-' depending upon the detailed topography of a particular CS2 potential surface. Given the inherent discrepancies that are expected to accompany application of the CIS29and RHF47methods, the ab initio transition energies are found to be in reasonable agreement with experimental findings. The greater stability imparted to the ground state by the MP2 level of theory, as opposed to that obtained for excited states via the CIS-MP2 scheme, results in MP2-based estimates of electronic transition energies which are substantially higher than those calculated through the use of the more comparable CIS and RHF treatments. The transition energies predicted for excited states that are not optically accessible from the ground potential surface should assist in unraveling the nature of spectroscopic perturbations which are found to permeate the near-ultraviolet absorption bands of CS2. As shown in Table 7, significant differences exist between theoretically predicted and experimentally measured barriers to linearity, with the few available laboratory findings being 2-3 times smaller than values obtained from a variety of computational studies. One notable exception occurs in the case of the b3A2(R) potential surface, where the barrier height suggested by our CIS-MP2 treatment (3544 cm-I) is in good accord with that deduced from the interpretation of spectroscopic data (3300 cm-l). Even when the effects of vibrational zero point energy are taken into account, the quality of this agreement seems to be quite extraordinary. In contrast to predictions made for the b3A2(R) state, ab initio barrier heights for the AIA2 and B1B2(V) surfaces are found to be significantly larger than those obtained through spectroscopic X measurements. From their detailed analyses of the V absorption system, Jungen et a1.4 suggested that the V electronic state supports a barrier to linearity of roughly 1300 cm-I. This assertion has been corroborated by the more recent studies of Ochi et ~ 2 . and 2 ~ Habib et ~ 1 Analogous . ~ ~ experiments on the red-shifted T bands by Jungen and co-workers4 provide a tentative barrier height of -2800 cm-' for the pertinent excited
-
state. These laboratory findings must be compared with the 3331 and 3847 cm-' values predicted for the V (viz., BIB4 and T (viz., AIA2) states, respectively, by our CIS-MP2 treatment. Since the CIS-MP2 barrier height for the B'B?(V) surface is in reasonable accord with ab initio values obtained in previous MCSCP' and MR-CI(SD)19 calculations, the disagreementwith experimental observations transcends the computational methodology exploited for a particular study. Similar differences between theoretical predictions and laboratory findings also exist for the equilibrium geometry (cf. section IIIB) and vibrational frequencies (cf. section IIIC) of this excited electronic state. While a definitive explanation for these discrepancies awaits future experimental and theoretical studies, it is possible, although unlikely, that a misassignment of rovibronic features in the near-ultraviolet CS2 spectrum could partially be responsible. On the other hand, more sophisticatedelectronic structure analyses are required before attempting any credible reinterpretation of the vast body of spectroscopic information that exists for the V state. In the absence of nonadiabatic and spin-orbit effects, onephoton electric dipole selection rules allow only excited electronic states of IB2 symmetry to be accessed from the X'Zi (i.e., 'AI) ground potential surface. The resulting transition will be parallel in nature, with the corresponding dipole moment oriented along the CS2 figure axis (viz., along an axis parallel to that interconnecting the two sulfur atoms). These predictions have been corroborated experimentall? in the case of the B1B2(V)state which forms the upper level of the optically active V X absorption system. The presence of significant spin-orbit interactions will relax electric dipole symmetry restrictions so as to include all electronically excited states having a B2 spin-orbit c o m p ~ n e n t . ~A~ magnetic ,~~ dipole mechanism, giving rise to Perpendicular transitions, can also optically couple the ground electronic state to higher-lying surfaces of A2 symmetry (e.g., A'A2 or C'Az). However, our experimental studies of the CS2 spectrum in a supersonic freejet environment (Le., Trot-= 2 K) have failed to uncover any evidence of rovibronic features having perpendicular character:2 a fact that can be attributed to the considerable reduction in oscillator strength which accompanies magnetic dipole transitions. Within the calculated manifold of triplet states, only the b3A2(R) and d3A2 surfaces have a spin-orbit component of B2 symmetry. Consequently, dipole-allowedrovibronic transitions should exist from the ground electronic state to each of these electronically excited levels. While the b3A2(R) state gives rise
-
J. Phys. Chem., Vol. 99, No. 6, 1995 1811
Electronically Excited Carbon Disulfide
-
to the well-known R X absorption system at -3800 A, there have been no definitive reports of spectral features attributed to a higher-lying 3A2potential surface.25 Instead, the S and U systems, which appear in the vicinity of 3500 A, are believed to involve transitions that terminate on excited vibronic levels within the R Jungen and co-workers4 have ascribed the neighboring T bands to the lower-lying (Le.,'A2 in their scheme) component of the 'A,, Renner-Teller doublet, with a Coriolis-induced vibronic coupling mechanism invoked to explain appearance of the electric dipole-forbidden X'Z; transition. Given the present ab initio results, the electronic parentage of near-ultraviolet absorption features in CS2 would seem to be in need of further clarification. In particular, the d3A2potential surface, with its spin-orbit allowed transitions predicted to occur in the region spanned by the socalled T and V systems, must be taken into account. Likewise, the numerous perturbations found in the optical spectrum of CS2 can be interpreted in terms of interactions among the various electronic potential surfaces that coexist within a small range of excitation energies. Since the d3A2 state is predicted to have a near-linear equilibrium geometry (cf.Tables 2 and 7), the C2, symmetry restrictions utilized in the above analysis of transition moments should be reconsidered under a Dh. point group. As shown in Figure 3, the d3A2 surface correlates with a 'q- state in the linear configuration. This level gives rise to two spin-orbit components which have symmetry labels of and While both of these spin-orbit states support one-photon, electric dipole-allowed transitions from the XIZi ground potential surface, only the latter (viz., results in parallel spectral features comparable to those observed throughout the R, S, T, U, and V absorption systems of CS2. Consequently, as long as spin-orbit interactions are reasonably large in X transition should manifest a nonzero magnitude, the d oscillator strength irrespective of distortions from linearity in the electronically excited d3A2 state. Indeed, recent high resolution Zeeman studies performed on jet-cooled samples of CS2 by Nishizawa et aLZ5have alluded to participation of the d3A2 or '&- potential surface in near-ultraviolet bands formerly assigned to the V system. Figure 3 demonstrates that the B1B2(V) state correlates to a 'A, level in the linear configuration. The nominally forbidden 'Zl transition accounts for the relatively nature of a 'A,, small oscillator strength of 2.7 x loT4attributed to the V X absorption system.I5 Nevertheless, the B1B2(V) XIZi transition is by far the strongest of the near-ultraviolet features in the CS2 spectrum, a fact that stems from the absence of other fully allowed singlet-singlet transitions and the substantial spin-orbit interactions required for the appearance of singlettriplet transitions. Intensity borrowing via a second-order vibronic coupling mechanism predicts a V X transition moment that scales as e2 where e denotes the degree of distortion of the S-C-S bond angle from l i ~ ~ e a r i t y . ~ ~ . ~ ~ Figure 6 presents calculated oscillator strengths for the B'B2X'Z; transition as a function of the S-C-S bending (V) angle. These computational results were obtained at the CIS/ 6-311+G* level of theory with the two C-S bond distances fmed at the common value of 1.6 A. While essentially forbidden X system rapidly gains at a linear configuration, the B(V) oscillator strength with increasing distortion of the molecular framework away from linearity. This vibronically-induced dipole moment attains a maximum value for a bond angle of roughly 130°, a value quite comparable to that predicted for the equilibrium structure of the electronically excited B1B2(V) surface. The dotted curve in Figure 6 represents a fit of the ab
0.040
c c)
2
0.035
x
0.030
f
+
n,,
c.
c)
-
--
+
-
+
+
120
140
160
200
180
220
S - C S Bending Angle (Degrees)
-
240
-
Figure 6. Coordinate dependence of transition moments for the V X system of CS1. The interconnected symbols denote V X oscillator strengths calculated at the CIS/6-311+G* level of theory for ground
state geometries of CS2 having fixed C-S bond distances (viz, 1.6 A) and a varying S-C-S bond angle. Nominally forbidden in the linear configuration, the transition moment rises rapidly with increasing distortion of the molecular framework away from linearity. The dotted curve depicts the quadratic angular dependence of oscillator strength as deduced from second-order vibronic coupling models.
initio oscillator strengths to the quadratic form (Le., e*) suggested by intensity borrowing arguments. As expected, this description proves to be valid only for small displacements from the linear geometry. The rapid increase in V X oscillator strength predicted to accompany distortion of the CS2 nuclear framework from linearity has important ramifications for interpretation of the ultraviolet spectrum in this triatomic molecule. On the one hand, this absorption system should exhibit intense hot band transitions originating from vibrationally excited ground state levels that have significant amplitude along the S -C-S bending coordinate. Such features have been observed in experimental studies performed under both bulk-gas4 and free-jet19%20,22 conditions. In particular, the latter work has revealed strong hot band structure in spite of the substantial cooling of vibrational degrees of freedom which occurs during the supersonic expansion process. The vibrational dependence of the V X oscillator strength has even greater significance for the interpretation of emission processes originating from the electronically-excitedB(V) state. In accord with expectations derived from the Franck-Condon principle, rovibrational levels of the B'B2(V) potential surface should exhibit intense "downward" transitions to ground state levels that involve considerable displacement along the bending coordinate. The large amplitude nuclear motion of such X'Z; levels necessitates a high degree of vibrational excitation, thereby producing a large red shift between the maxima of absorption and emission spectra. These predictionshave been corroboratedby recent dispersed f l u o r e ~ c e n c e 'and ~ , ~stimulated ~ emission pumping23~24~5s experiments, with the later readily accessing rovibrational eigenstates located more than 2.5 eV above the vibrationless zero point energy of the ground electronic potential surface.
-
+
IV. Summary and Conclusions The CIS-MP2 method, in conjunction with extensive sets of basis functions, has been used to examine the nature of n* n transitions in the near-ultraviolet spectrum of CS2. At their respective equilibrium geometries, the lowest-lying electronic states are predicted to have an energy ordering given by:
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Zhang and Vaccaro
1812 J. Phys. Chem., Vol. 99, No. 6, 1995
X'X:
< a3B, < b3A2(R) < A'A, < B'B2(V) < c3B,
