J. Phys. Chem. 1983, 87,718-719
718
Theoretical Calculatlon of the Lowest Electronic Excited States of BO2 VlJaya Saraswathy, James J. Dlamond, and Gerald A. Segal" Department of Chemisty, Universiv of Southern California, Los Angeles, California 90089-0482 (Received: November 22, 1982)
Extensive configuration interaction calculations are reported for the first three doublet states of BOz. Agreement with available experimental data is excellent and the position of the C2Z,+state is predicted.
The electronic excited states of BO2,a linear molecule which presents a classic example of the Renner-Teller effect, have been the subject of a number of experimental studies. Johns' has reported a detailed analysis of absorption from X2 ground state to states identified by him as the A211u and 22u+ excited electronic states. Renner-Teller molecules are of fundamental interest and there have been a number of recent reports of data on these excited states of BO2 obtained by a variety of technique^.^-^ According to Johns, Tofor the ?-nu and ?-ZU+ excited states is 18291.6 and 24597.9 cm-l, respectively. BO2, however, should possess a third low-lying electronic excited state, a state of Qg+ symmetry. In the Dmhpoint group of the molecule, optical transitions to this state are electric dipole forbidden although it should be accessible via two-photon absorption. Such an experiment is difficult to carry out in the absence of any knowledge of the energy a t which the state might be found and it is the purpose of this Letter to report theoretical calculations directed toward determining its location. To the best of our knowledge, no previous theoretical study of the excited electronic states of BO2has been reported. As a calibration on the accuracy to be expected from our calculation, we report companion results on the A211, and B2ZU+excited states as well.
%
Computational Details Extensive configuration interaction calculations were carried out on these states by using perturbational CI techniques which we have described elsewhere5 and the program PEPCI (program of efficient perturbational CIh6 The geometry of the X211, ground state was assumed to be that reported by Johns, rBo = 1.265 A. The Gaussian orbital basis sets chosen were the (9s, 5p/4s, 2p) contractions of the Huzinaga' atomic bases reported by Dunning for boron and oxygen.8 This was augmented by a single set of Gaussian s and p Rydberg functions of exponent 0.015 centered at boron and additional (sp) Rydberg sets of exponent 0.03 centered a t the oxygens. With this basis set, an SCF calculation was carried out on the X211gground state in the Nesbet approximationg with symmetrized (1)J. W. C. Johns, Can. J . Phys., 39, 1738 (1961). (2)S.McIntosh, R.A. Beaudet, and D. A. Dows, Chem. Phys. Lett., 78,270(1981);R.A.Beaudet, K. G. Weyer, and H. Walter, ibid.,60,486 (1979);K.G.Weyer, R. A. Beaudet, R. Straubinger, and H. Walter, Chem. Phys., 47, 171-8 (1980);K. G.Weyer, W. Schultz, R. A. Beaudet, and H. Walter, J. Chem. Phys., 72, 589 (1980). (3)K. Kawaguchi, E. Hirota, and C. Yamada, Mol. Phys., 44, 509 (1981). (4) D. R. Coulter, C. Y. R. Wu, and D. A. Dows, Chem. Phys. Lett., 60,51 (1978). (5)G.A. Segal, R. W. Wetmore, and K. Wolf, Chem. Phys., 30, 269 (1977). (6)J. J. Diamond, G . A. Segal, and R. W. Wetmore, to be published. (7)S. Huzinaga, J . Chem. Phys., 42, 1293 (1965). (8)T.H.Dunning and P. J. Hay, 'Modern Theoretical Chemistry", Vol. 3,H. F.Schaefer, Ed., Plenum Press, New York, 1977.
0022-3654/83/2087-07 18$01.50/0
TABLE I: Generating Spatial Occupations for BO,
state
occupation
weight
X2ng
10,~ l u g 2 2og2 3ug2 2uUz4ug2 3uu2
86.9
ing3 io,' l o g 2 2Ogz 3 O g 2 20,z 4og7 30,2 i n U 3 i n g4nu 3
4.8
inu4
A2n,
1 o U 2 l o g 2 2ug2 3og2 2uU24ug2 30,'
81.6
i n g 4 io,2 i u g 2 2ug* 30g2 20,z 4ogz 3u,2 ln,4 l n g 2 477,
8.4
in,3
B'Zu+
1oU2 l u g 2
2og2 3ag2 20,'
4uEz30,'
85.2
2ug2 3og2 2u,2 4ugl 3u,z i n u 4 i n g 3 4nu
in,4
ing4
io,2
5.4
iog2
C Z c g + 10,' l u g * 2ug2 3 o g 220,' 4og1 30,'
83.0
ing4 io,2 log2 20g2 30gz 20,2 4og2 3ou1 i n , 4 i n g 3 4nu
7.2
in,4
TABLE 11: Electronic Spectrum of BO,
eV
adiabatic' calcd energ$ (TeL eV
2.685 2.998 3.785
2.446 2.998 3.785
verticalu calcd
excitation
X 2 n g-+ A2n, X 2 n g-+ B 2 r U + X2ng + C z r g + a "BO = 1.265 A . eV 'BO = 1.302. state by state basis.
exptl
;ye;g~ eV 2.329 3.039
Relative to E ( X 2 n g )= -4751.053 See text for exact definition o n a
occupation of the partially filled rgshell. Configuration interaction calculations based on these MO's were performed for the ground and first three doublet excited states of BOz. In each case, the three leading configurations of the CI vector were chosen as references and all single and double hole-particle excitations were generated from them. These are, in all cases, a fundamental configuration plus members of the configuration space resulting from a single alternative spatial occupation. The pairs are summarized in Table I as is the weight of each cited spatial occupation in the final state vector. In all cases, the K shell (MO's 1-3) were frozen and the antibonding complement of these MO's, molecular orbitals 40, 41, and 42, were omitted from the CI calculation. This procedure led to CI spaces of the order of 32 000 configuration state functions for each of the four spatial symmetries considered. Results and Discussion Table I1 displays a synopsis of the results of these calculations. The A211u state is fundamentally a ru rg one-electron transition within the occupied manifold. It
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(9) R. K. Nesbet, Reo. Mod. Phys., 35, 552 (1963).
0 1983 American Chemical Society
Letters
is found to have a vertical transition energy of 2.685 eV and oscillator strength f = 0.1. Johns reports the vibrational frequencies for this state and the ground state, so T, for this may be calculated to be 2.329 eV, but his analysis also leads to the conclusion that this state, while essentially linear, has a BO bond length longer than that of the ground state, namely, rBo = 1.302 A. We have carried out a calculation in the A2r, electronic state at this geometry. The energy of A211, state decreases by 0.239 eV leading to a calculated T,of 2.446 eV in the absence of any attempt to locate the theoretical minimum of the potential energy curve. In a similar vein, the energy of the B2Z,+ state, a state which results from excitation of an inner electron from the 4ag MO to fill the l?rg shell, is calculated to be 2.998 eV at the vertical geometry while Johns reports To= 3.039 eV and a BO bond length of 1.273 A as compared to the ground state value of 1.265 A. The available vibrational data on this state indicate frequencies similar to those of the ground state so that our calculated energy is directly comparable to To.It is clear that the order of accuracy of our calculation of this state is similar to that for the 211 state, i.e., accurate to within better than 1000 cm-'. The C2Zg+state is calculated to lie 3.785 eV above the ground state at the vertical geometry. We have carried
The Journal of Physical Chemistry, Vol. 87, No.
5, 1983 719
out a calculation at an OB0 angle of 176' and find the molecule to be linear in this excited state. Additionally we have made a somewhat cursory examination of the state in order to variation of energy with PBO in the obtain an estimate of the magnitude of the Franck-Condon factors for transitions from the ground state. Calculations on the 22g+ state were carried out at rBO= 1.265, 1.284, and 1.302 A. The results were then fitted to a quadratic function whose minimum was found to be at 1.268 A, a value very close to that reported by Johns for the X211, state. While these calculations represent only the roughest of estimates, it is reasonable to conclude that there is little difference between the geometry of BO2 in the 2Zg+state and its geometry in the molecules' ground state and that the Franck-Condon factors should favor observation of this state. Finally, as in all other cases examined to date, the perturbational CI technique which we have employed appears stable and capable of good accuracy. The magnitude of the errors relative to experiment which have been listed above are determined by limitations in the Gaussian basis set, not the CI technqiue employed.
Acknowledgment. This work was supported by NSF Grant CHE 81-06016.
