Ab initio study of the BiSe and BiTe electronic spectra: What happens with X 2 X 1 emission in the heavier Bi chalcogenides?

Transcription

1 JOURNAL OF CHEMICAL PHYSICS VOLUME 120, NUMBER APRIL 2004 Ab initio study of the BiSe and BiTe electronic spectra: What happens with X 2 X 1 emission in the heavier Bi chalcogenides? Rainer M. Lingott, Heinz-Peter Liebermann, Aleksey B. Alekseyev, and Robert J. Buenker Bergische Universität Wuppertal, Fachbereich C, Theoretische Chemie, Gaußstr. 20, D Wuppertal, Germany Received 31 December 2003; accepted 26 January 2004 A series of spin orbit configuration interaction calculations has been carried out for the BiSe and BiTe molecules and analyzed in comparison with data obtained earlier for the isovalent BiO and BiS systems. An avoided crossing caused by the spin orbit interaction between the X 2 and A 4 electronic states is shown to have a decisive effect on the lower-energy spectrum in each case. Irregularities in the X 2 3/2 state vibrational manifold occur as a consequence of this nonadiabatic interaction, and the v vibrational number for the onset of these perturbations is found to gradually decrease in going from BiO to BiSe, in agreement with experiment. In BiTe the shape of the X 2 potential curve is so altered by the avoided crossing that its minimum becomes shifted to a significantly larger distance than for the X 1 state, unlike the case for BiSe or the lighter Bi chalcogenides. This characteristic appears to be the root cause for the fact that the X 2 state has not yet been found experimentally in the BiTe spectrum, despite careful searches in the expected energy range. Radiative lifetimes have also been calculated for the low-lying states of both the BiSe and BiTe molecules, and these results are found to be consistent with experimental observations American Institute of Physics. DOI: / I. INTRODUCTION One of the most interesting aspects of relativistic interactions for molecular systems is their capacity for producing avoided crossings in the potential energy surfaces of electronic states of different spin multiplicity. Such effects clearly become more pronounced as the atomic number of the constituent nucleus increases. A prominent example of this type which has been the subject of a detailed experimental study 1 is the BiO molecule. It has an X 2 ground state similar to that of its isovalent counterpart NO, and the first excited state is 4 in both cases. For the lighter NO system transitions between these two S states are quite weak, however, and thus the first strong band system occurs for spin-allowed transitions from X 2 to the A 2 state. It is probably for this reason that the first experimental assignments for the low-energy transitions of BiO, summarized in Ref. 2, assumed that the A 2 was also the lowest upper state actually observed in this spectrum. Ab initio configuration interaction CI calculations subsequently found 3 that the transition energy to the first 2 excited state was much too high to justify such an assignment, however. Instead, it was found that the spin orbit interaction was sufficiently strong to lead to heavy mixing between the X 2 and 4 states, and that this effect caused transitions between their various multiplets to be unexpectedly strong. The calculations also showed that a strongly avoided crossing occurs for the 3/2 components of these two states, which fits in well with the experimental observation 1 that there were strong perturbations in the energy level structure of the X 2 3/2 state for v 6. The latter result is very sensitive to the relative position of the X 2 and 4 potential energy curves. Experimental data obtained by Meinecke 4 indicate that the value of v for which analogous perturbations occur in the spectra of isovalent systems gradually decreases from BiO to BiTe. Spin orbit CI calculations for the BiS molecule 5 were consistent with these observations, with the onset of perturbations in the X 2 state occurring one quantum lower than in the BiO spectrum. A general tendency was noted in the calculations to underestimate the 4 excitation energy, and this caused a discrepancy of one quantum number in each case. A number of higher-lying excited states, including the 2 and 4 multiplets, could also be unambiguously assigned on this basis. In addition, transition moments were computed for each pair of electronic states and partial radiative lifetimes for the associated vibrational states were obtained using these data. In the present study ab initio spin orbit CI calculations are reported for the two heavier members in this series, BiSe and BiTe. In the latter case the degree of perturbation of the X 2 levels appears to be so great that it has not been possible to find any X 2 X 1 emission experimentally. 4 A number of other electronic states have been observed for both molecules, 4,6,7 however, and so it is possible to make numerous comparisons between experiment and theory for all four of the BiX systems mentioned. II. DETAILS OF THE SPIN ORBIT CI TREATMENT The ab initio calculations are based on relativistic effective core potentials RECPs. The core electrons of the bismuth atom are described by the RECP of Wildman et al., 8 so that only the 5d, 6s, and 6p shells need to be treated explicitly in the self-consistent-field SCF and CI treatments, /2004/120(16)/7476/7/$ American Institute of Physics

2 J. Chem. Phys., Vol. 120, No. 16, 22 April 2004 BiSe and BiTe electronic spectra 7477 TABLE I. Technical details of the MRD-CI calculations of BiSe. a C 2v symm. N ref /N root SAFTOT/SAFSEL C v notation c p 2 2 B 1,2 126/ / A 1 140/ / A 2 116/ / B 1,2 142/ / A 1 135/ / A 2 161/ / A 1 23/ / B 1,2 14/ / a The number of selected SAFs and the c p 2 values over reference configurations for the lowest roots of each symmetry are given for r 4.70a 0. SAFTOT designates the total number of generated, SAFSEL the number of selected SAFs, and N ref and N root refer to the number of reference configurations and roots treated, respectively. just as in the analogous calculations for BiS. 5 Shapeconsistent RECPs of the same type are employed for the selenium and tellurium atoms, 9,10 in which case only six outer s and p electrons are described by basis functions. The valence basis set for the Bi atom consists of the (6s6p5d)/ 4s4p4d contracted Gaussians optimized by Wildman et al. 8 for use with the corresponding RECP augmented with a single f function with an exponent of The Se and Te valence basis sets are constructed from the primitive Gaussian sets taken from the database at with additional d and f functions optimized at the CI level for the present study. The resulting basis sets are (4s4p5d1 f )/ 4s4p2d1f for Se and (4s4p5d1 f )/ 4s4p2d1f for Te. The computational procedure employed in the present study is basically the same as for BiS. 5 The first step is to carry out an SCF calculation for the 2 4 * 2 ground state. At this stage, as well as in the subsequent CI step, the calculations are carried out with the spin-independent part of the RECP AREP and include all relativistic effects other than spin orbit coupling. The standard multireference single- and double-excitation MRD CI approach is then employed to obtain the S electronic energies, wave functions, and properties. This MRD-CI method makes use of configuration selection and perturbative energy extrapolation techniques 11 and employs the TABLE-CI algorithm for efficient handling of the various open-shell cases which occur. Five outer electrons of the Bi atom and six each from Se and Te are included in the CI active space 11-electron CI. A selection threshhold of T ( )E h has been used for the calculations of both BiX (X Se,Te) systems, which are carried out in formal C 2v symmetry. Technical details regarding the numbers of reference configurations and roots treated, as well as the sizes of the generated and selected CI spaces, are given in Table I for the BiSe molecule. The BiTe calculations are of similar quality. Finally, the importance of higher-than-double excitations in the overall CI treatment has been assessed by applying the generalized multireference FIG. 1. Computed potential energy curves for the low-lying states of BiSe. analog of the Davidson correction 15,16 to the extrapolated T 0 eigenvalues for each root. The next step in the theoretical treatment is to employ the S eigenfunctions as a contracted basis for an additional CI in which the spin orbit SO interaction is included in the Hamiltonian LSC-SO-CI. 17 The estimated full-ci energies described above are placed on the diagonal of the corresponding Hamiltonian matrices. The off-diagonal spin orbit matrix elements are obtained by employing pairs of selected CI wave functions with M S S and applying spinprojection techniques and the Wigner-Eckart theorem. 18 All electronic states converging to the five lowest S atomic limits have been included in the calculations as well as a number of higher-lying states important in the Franck- Condon region. The resulting CI secular equations are of order 111. Finally, the subsequent computations for transition moments and lifetimes of vibrational levels of the various excited states are carried out using standard methods described elsewhere. 3 III. POTENTIAL ENERGY CURVES The calculated potential energy curves for the BiSe and BiTe molecules are shown in Figs. 1 and 2, and the corresponding spectroscopic constants are compared with experimental values as well as the calculated data for the BiS system 5 in Table II. Nine of the ten states converging to the lowest Bi( 4 S o ) X( 3 P 2 ) dissociation limit are presented in each figure the 7/2 state is omitted, as well as the C 1 1/2 state going to Bi( 4 S o ) Se( 3 P 1 ), Te( 3 P 0 ) in BiSe and BiTe, respectively. We use a capital letter notation for all

3 7478 J. Chem. Phys., Vol. 120, No. 16, 22 April 2004 Lingott et al. FIG. 2. Computed potential energy curves for the low-lying states of BiTe. excited states in this paper, although some of them e.g., A 4, C 4 have different multiplicity than the X 2 ground state. The main reason for this is that the corresponding capital letter notation has been adopted by the spectroscopists who observed these states. We retain their notation, but supply it with indices i 1, 2,... in order of increasing energy to distinguish between various components of multiplets e.g., A 1 4 3/2, A 2 4 1/2, A 3 4 5/2, and A 4 4 1/2. Since the spin orbit coupling is very strong in bismuth chalcogenides, it would be more consistent to characterize each electronic state by the value and its own letter, but we leave this privilege to experimentalists who will be the first to observe these states. It can be seen from the presented data that the A 4 state s excitation energy gradually becomes smaller as the atomic number of the group-via atom increases. The lowest state arising from this multiplet is A 1 4 3/2, and it undergoes a sharply avoided crossing with the X 2 component of the same value in both BiSe and BiTe. The situation is qualitatively similar to that in both BiO Ref. 3 and BiS Ref. 5, as already indicated in the Introduction, but the effect is more significant for the two heavier systems. In BiTe, for example, there is no minimum in the X 2 potential near the ground state s equilibrium bond distance, but rather just a shoulder which gradually goes over into a minimum at notably longer range. No bound vibrational levels have been observed in the BiTe fluorescence spectrum that could be TABLE II. Calculated spectroscopic constants T e in cm 1, r e in Å, and e in cm 1 for the low-lying states of BiX (X S,Se,Te) in comparison with the experimental data Ref. 4. BiS BiSe BiTe State Calc. Expt. Calc. Expt. Calc. Expt. X 2 1 1/2 T e r e a e a b c X 2 2 3/2 T e d r e e d A 4 1 3/2 T e r e e A 4 2 1/2 T e r e a e A 4 4 1/2 T e r e e B 2 1 1/2 T e e e r e e B 2 2 3/2 T e r e e C 1 1/2 T e r e e a Reference 6. b G 1/2 value from Ref. 6. c Reference 19. d Reference 20. e T 0 value obtained from the measurements in an argon matrix Ref. 7.

4 J. Chem. Phys., Vol. 120, No. 16, 22 April 2004 BiSe and BiTe electronic spectra 7479 FIG. 3. Computed potential energy curves for the X 1 1/2 and X 2 3/2 states of BiS, BiSe, and BiTe in comparison. assigned to the X 2 state, which, based on the present calculated data, can be explained by a significant shift of the X 2 minimum to longer distances. The situation for the BiSe system is intermediate between that for BiS and BiTe, as can be judged from Fig. 3. The nonadiabatic effects caused by spin orbit coupling ultimately destroy the basic appearance of the X 2 state except for its inner repulsive limb. The X 1 ground state by contrast is quite regular for each of the BiX systems. Its bond length increases by Å from BiS to BiSe according to the calculations Table II and by nearly 0.2 Å from BiSe to BiTe. As expected, the corresponding vibrational frequencies show a gradual decrease along the same series. In the latter instance comparison with experiment is possible for all three systems, and the calculated results are found to agree within 7 cm 1 in all cases. For BiS and BiSe there is almost no difference in the corresponding results for the X 2 state. The bond length is predicted to be slightly smaller than for X 1 in the case of BiS, but to be slightly larger in BiSe, which can be interpreted as a result of the increasing A 4 influence on the X 2 state in the latter system. The frequencies are lower in the X 2 state of both molecules and the amount of the computed difference is in good agreement with experimental findings. No frequency value is listed in Table II for the X 2 state of BiTe for the reasons already mentioned, but the G 1/2 value is calculated to be 133 cm 1. The X 2 bond length given can be better attributed to the A 4 state, as can be seen from its comparison with the A 2, A 3, and A 4 equilibrium distances. The T e values for the X 2 state have been determined experimentally 4,20 for BiS and BiSe and the calculated values are found to reproduce these data within an accuracy of cm 1. The observed values differ by only 21 cm 1 and indicate that the BiSe value is higher than that of BiS, while in calculations a very small 16 cm 1, but opposite trend is found. There is a fairly sharp drop in the computed T e value for BiTe, however, but the corresponding experimental value to verify this result is not available. The A 1 state in each of the BiX systems has a welldefined minimum Figs. 1 and 2 and Refs. 3 and 5, which position is defined by the avoided crossing with X 2 in each case. The trend toward decreasing excitation energy for the A 4 1 1/2 state in the heavier systems is apparent from Figs. 1 and 2 and Table II. The A 2 and A 4 3 components are considerably less perturbed than their A 1 counterpart. There is a tendency in the present treatment to underestimate the T e value of the A 2 state. The amount of underestimation decreases from 1212 cm 1 in BiS to 686 cm 1 in BiSe. The experimental value for BiTe is not known as accurately as the other two, but the computed result also appears to be too low, in this case by about 1000 cm 1. This general tendency is expected, since the A 4 state should have notably less correlation energy than X 2. One can safely assume that the same trend holds for A 1, and on this basis one is led to conclude that its avoided crossing with X 2 should take place at a slightly larger bond distance than is indicated by the present calculations. The A 3 state has 5/2 symmetry and is therefore even less perturbed by other S states than A 1 and A 2. The binding energy of the A 4 components gradually decreases with excitation energy in each of the BiX systems. This is because they all have the same dissociation limit namely, Bi( 4 S o ) X( 3 P 2 ), the same as for the X 2 components. The amount of ground X 2 1/2 binding energy decreases from BiS to BiTe, with an increase of the chalkogen atom size and decrease of its electronegativity Figs The B 1 and B 2 states come from the first 2 excited state of these systems. The B 2 is dominated by the same 3 * 2 electronic configuration as the A 4 i states and corresponds to the same excited state that is responsible for most of the low-energy NO electronic spectrum. Only the B 2 1 1/2 component has been observed experimentally. 4,7 As expected, the present computed T e values are in better agreement with the experimental data for this doublet state than for the lower-lying 4 Table II. There is again a tendency toward decreasing the B 1 excitation energy from BiS to BiTe. The calculations indicate that the vibrational frequencies of the A 2 and B 1 states are quite similar in each of the BiX systems. The B 2 spin orbit splitting changes rather irregularly from BiS to BiTe, which underlines the fact that it cannot be treated as a first-order perturbation effect. Both B 1 and B 2 are close to the dissociation limit and their potentials reach maxima at intermediate R values Figs. 1 and 2. There is one other electronic state for which experimental T e and e values are available, the C 1 1/2, which derives primarily from the 4 ( *) state. Its dissociation limit is different than for any of the other states discussed above Figs. 1 and 2. The calculated T e values agree with the observed values within 700 cm 1 for BiSe and BiTe. Rea-

5 7480 J. Chem. Phys., Vol. 120, No. 16, 22 April 2004 Lingott et al. TABLE III. Calculated radiative lifetimes of excited states of BiSe (v 0): partial lifetimes 1, 2, and 3 for transitions to X 1 2 1/2, X 2 2 3/2, and A 4, respectively, and total lifetime. Values in parentheses are powers of ten. State 1 (s) 2 (s) 3 (s) a s X 2 2 3/ A 4 1 3/ A 4 2 1/ A 4 3 5/ A 4 4 1/ B 2 1 1/ B 2 2 3/ C 4 1 1/ a Partial lifetimes in this column are given for transitions C 1 A 1 and C 1 A 2 the lower line. sonable agreement is also obtained with the vibrational frequencies observed for this state. IV. TRANSITION MOMENTS AND RADIATIVE LIFETIMES The computed potential energy curves discussed have been employed to obtain solutions of the Schrödinger equation for nuclear motion. 21,22 Electronic transition moments have also been calculated for the low-lying dipole-allowed transitions between S states for both the BiSe and BiTe systems, and these results have then been transformed over the -state basis for a large series of internuclear distances. Finally, vibrational transition moments have been computed by integrating the resulting -state electronic transition moments over pairs of vibrational functions. The theoretical treatment is wholly similar to that reported previously for the BiO Ref. 3 and BiS Ref. 5 molecules. Einstein spontaneous emission coefficients have been calculated on this basis and the partial and total radiative lifetimes of a given excited vibrational state by summing over these quantities for all lower-lying levels and taking the reciprocal of this result. The computed v 0 radiative lifetimes are given for a number of the low-lying electronic states of BiSe and BiTe in Tables III and IV. TABLE IV. Calculated radiative lifetimes of excited states of BiTe (v 0): partial lifetimes 1, 2, and 3 for transitions to X 1 2 1/2, X 2 2 3/2, and A 4, respectively, and total lifetime. Values in parentheses are powers of ten. State 1 (s) 2 (s) 3 (s) a s X 2 2 3/ A 4 1 3/ A 4 2 1/ A 4 3 5/ A 2 4 1/ B 4 1 1/ B 2 2 3/ C 4 1 1/ a Partial lifetimes in this column are given for transitions C 1 A 1 and C 1 A 2 the lower line. The partial lifetimes for the X 2 X 1 fine-structure transition are found to be in the 7 14 ms region for both molecules. As already mentioned, no transition involving the X 2 state has ever been found in the BiTe spectrum. We have shown in Sec. III that the X 2 potential minimum has been found in the present calculations at a relatively large bond distance see Fig. 2 of ca Å. The radiative lifetime of the lowest vibrational level of this state is calculated to be 7.6 ms, which is half as long as the computed value for the v 0 level of the BiSe X 2 state, observed experimentally. 4 The corresponding BiS X 2 lifetime has been computed to be 4.1 ms Ref. 5. The A 4 1 3/2 state appears to have a strongly bound potential for both BiSe and BiTe as well as for BiS, 5 which results from the strongly avoided crossing with the X 2 state in each case. It is possible to compute the radiative lifetimes of the A 1 (v 0) states on this basis, but to date experimentalists have not been able to locate either one of them spectroscopically. The A 1 X 1 transition is perpendicular and, as is quite typical for spin-forbidden transitions, the corresponding partial lifetime is found to be in the ms range. The corresponding value for the parallel A 2 X 1 transition is almost three orders of magnitude shorter in the calculations. There is a tendency for this lifetime to increase along the BiS-BiTe series, going from 8.8 s for BiS to 68.6 s for BiTe. The main reason why this transition is relatively strong is because the X 2 and also the 3 2 configurations are mixed rather heavily with A 4 in the Franck Condon region of the X 1 state. Inspection of the coefficients in the SO-CI expansions of the A 2 wave function shows that the level of mixing gradually decreases from BiS to BiTe. Neither the A 3 5/2 nor A 4 1/2 have been observed in the spectra of the BiX systems. The A 3 state has allowed perpendicular transitions to X 2 and A 1, but the computed lifetimes are found to be in excess of 1.0 ms in each case, being shortest for the A 3 X 2 transitions in the lighter systems: 6.2 ms BiO and 11 ms BiS. The A 4 does have parallel transitions to X 1, but the calculations indicate that the corresponding partial lifetimes are also on the order of 1.0 ms for all three BiX systems. It can be noted that there is a strong admixture of B 2 character to the A 4 1/2 state in the BiTe molecule, but this does not lead to significant changes in the characteristic lifetimes of this state. The B 1 X 1 transitions have been found in the emission spectra of both the BiSe and BiTe molecules in an argon matrix, 7 but only relatively crude estimates could be given for the B 1 state T e values on this basis Table II. There is a relatively strong B 1 X 1 transition in BiSe according to the present calculations. The computed partial lifetime is 31.1 s, about 4 times longer than the corresponding value found for BiS. 5 The BiTe value is 3 times longer, 90.1 s. The total radiative lifetime of the B 2 3/2 state is slightly smaller than 1 ms for both systems, approximately an order of magnitude longer than that of the B 1 1/2 state in each case. Finally, the transitions from the higher-lying C 1 1/2( 4 1/2 ) state are found to be notably stronger than for the B 2 states. This finding is qualitatively consistent with the fact that the C 1 1/2 state has been well characterized for both BiSe and BiTe Ref. 4 see Table II. The respective

6 J. Chem. Phys., Vol. 120, No. 16, 22 April 2004 BiSe and BiTe electronic spectra 7481 partial lifetimes for the parallel C 1 X 1 transitions have been calculated to be 3.4 and 2.5 s, respectively, for these two molecules. The corresponding BiS value is 2.4 s, so there is a high level of consistency in these results. The density of states is relatively high in the energy region in which the C 1 state is found. Although it is predominantly composed of the 4, as much as 50% of the total c 2 sum in its SO-CI wave function comes from other doublet states which have dipoleallowed transitions to the X 1 2 state. V. CONCLUSION The present ab initio spin orbit CI calculations offer a good illustration of how the properties of isovalent molecular systems can be affected by varying the atomic number of one of the constituents along a given column of the periodic table. The most conspicuous feature of the low-energy electronic spectra of the BiX (X O,S,Se,Te) series of molecules is the strongly avoided crossing which takes place between the X 2 2 and A 1 4 states of 3/2 symmetry. In agreement with experiment, the calculations find that the location of this crossing takes place at lower energy relative to the X 1 ground state as the atomic number of the chalcogen atom increases. This happens due to a smaller excitation energy of the A 4 state in the heavier BiX systems. The crossing itself is caused by the spin orbit mixing of the above two S states, but the corresponding matrix element does not differ greatly over the BiX series because of the fact that the key open-shell orbital * is localized mainly on the bismuth atom in all cases. Under these circumstances, it is easy to understand why the vibrational manifold of the lower-energy X 2 state begins to exhibit irregularities at ever smaller v quantum number as one proceeds to the heavier systems. The present work shows that the double-minimum character of the X 2 potential energy curve observed for the lighter systems is no longer present for BiTe Fig. 2. Moreover, the position of the minimum computed for BiTe lies much closer to the corresponding X 1 potential than in any of the other cases. This state of affairs appears to be consistent with the fact that no bound levels of the BiTe X 2 state have ever been observed. In each of the lighter systems the equilibrium bond distances of the X 1 and X 2 state are quite similar, differing by less than Å, but for BiTe the calculations find that the X 2 value is nearly 0.25 Å larger than for X 1. Radiative lifetimes have also been computed for the lowest-lying electronic states of both BiSe and BiTe for comparison with the corresponding values obtained in earlier work for the BiO and BiS systems. Perhaps the most interesting result of this nature is the relatively short lifetime computed for the BiTe X 2 state 7.6 ms. This value is somewhat larger than for BiO 2.7 ms or BiS 4.1 ms, but almost 2 times smaller than the X 2 lifetime for BiSe. So on this basis alone one would find it difficult to explain why X 2 X 1 transitions are observed for BiSe, but not for the heavier system. It appears that the main difficulty hindering the experimental detection of the X 2 X 1 emission for BiTe lies in its strong redshift in comparison with the lighter BiX systems. According to the calculations, the strongest 0 9 band in the v 0 progression lies at 4260 cm 1 in BiTe, while in BiSe the strongest 0 0 band is located at 7060 cm 1. A large difference in the equilibrium distances of the X 2 and X 1 states in BiTe leads to a broad distribution of transition intensities over vibrational levels of the lower state, so that the A(0 9) Einstein coefficient in BiTe is 3.5 times smaller than A(0 0) in BiSe, in spite of the shorter (v 0) value in the former system. Finally, the LIF method applied to observe fluorescence from the X 2 state by exciting it directly or through the A 1 state 4,20 may encounter additional difficulties due to nonradiative depopulation of X 2, since the experimental excitation energies are comparable with the X 2 X 1 crossing point energy see Fig. 2. Altogether, it means that in order to find the X 2 X 1 emission in BiTe, one should search for very weak bands in the low-energy cm 1 spectral range, being aware of the possibility of X 2 nonradiative deactivation. The A 1 3/2 state also has a radiative lifetime in the 5-ms range for both BiSe and BiTe according to the calculations, but it has never been observed in any BiX spectrum. The A 2 1/2 state has relatively strong parallel transitions to X 1 with partial lifetimes in the s range. This state has been observed experimentally for both BiSe and BiTe, consistent with the computed strength of this transition. The B 2 1/2 (B 1 ) state has also been observed for both of these systems, but not the corresponding 3/2 state. In the former case one can argue about the notation employed for this state since there is heavy mixing with the A 4 4 1/2 over a large range of internuclear distance. The calculations indicate that the transitions of the B 2 state are notably weaker than for B 1 in both molecules, which is probably the main reason why they have not yet been observed. Finally, the C 1 state, which has a dominant contribution from the 4 S state, is found to have a much shorter lifetime than any of the lower electronic states. This result is thus consistent with the fact that the C 1 state has been relatively well characterized experimentally for both BiSe and BiTe as well as for the lighter chalcogenides of bismuth. In summary, it may be concluded that on the basis of the present spin orbit CI calculations it is possible to give a consistent explanation of the whole scope of experimental data available for the Bi chalcogenides to date as well as to make a number of predictions about positions and radiative properties of electronic states to be observed. ACKNOWLEDGMENTS The authors are very grateful for numerous discussions with Professor E. H. Fink, Dr. K. D. Setzer, and Dr. O. Shestakov during the course of the present study. This work was supported in part by the Deutsche Forschungsgemeinschaft within the Schwerpunktprogramm Theorie relativistischer Effekte in der Chemie und Physik schwerer Elemente. The financial support of the Fonds der Chemischen Industrie is also hereby gratefully acknowledged. 1 O. Shestakov, R. Breidohr, H. Demes, K. D. Setzer, and E. H. Fink, J. Mol. Spectrosc. 190, K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure, Vol. 4, Constants of Diatomic Molecules Van Nostrand Reinhold, Princeton, A. B. Alekseyev, H.-P. Liebermann, R. J. Buenker, G. Hirsch, and Y. Li, J. Chem. Phys. 100,

7 7482 J. Chem. Phys., Vol. 120, No. 16, 22 April 2004 Lingott et al. 4 F. Meinecke, M. Sc. thesis, University of Wuppertal, R. M. Lingott, H.-P. Liebermann, A. B. Alekseyev, and R. J. Buenker, J. Chem. Phys. 110, R. F. Barrow, O. V. Stobart, and H. Vaughan, Proc. Phys. Soc. 90, F. Ahmed, J. Chem. Phys. 82, S. A. Wildman, G. A. DiLabio, and P. A. Christiansen, J. Chem. Phys. 107, M. M. Hurley, L. F. Pacios, P. A. Christiansen, R. B. Ross, and W. C. Ermler, J. Chem. Phys. 84, L. A. LaJohn, P. A. Christiansen, R. B. Ross, T. Atashroo, and W. C. Ermler, J. Chem. Phys. 87, R. J. Buenker and S. D. Peyerimhoff, Theor. Chim. Acta 35, ; 39, ; R. J. Buenker, S. D. Peyerimhoff, and W. Butscher, Mol. Phys. 35, R. J. Buenker and R. A. Philips, J. Mol. Struct.: THEOCHEM 123, S. Krebs and R. J. Buenker, J. Chem. Phys. 103, S. Krebs and R. J. Buenker, in Recent Advances in Multireference Methods, edited by K. Hirao World Scientific, Singapore, 1999, pp E. R. Davidson, in The World of Quantum Chemistry, edited by R. Daudel and B. Pullman Reidel, Dordrecht, 1974, p G. Hirsch, P. J. Bruna, S. D. Peyerimhoff, and R. J. Buenker, Chem. Phys. Lett. 52, ; D. B. Knowles, J. R. Alvarez-Collado, G. Hirsch, and R. J. Buenker, J. Chem. Phys. 92, R. J. Buenker, A. B. Alekseyev, H.-P. Liebermann, R. Lingott, and G. Hirsch, J. Chem. Phys. 108, A. B. Alekseyev, H.-P. Liebermann, and R. J. Buenker, in Recent Advances in Relativistic Effects in Chemistry, edited by K. Hirao World Scientific, Singapore, in press. 19 P. Patino, J. H. D. Eland, and R. F. Barrow, J. Phys. B 17, R. Breidohr, K. D. Setzer, O. Shestakov, and E. H. Fink private communication. 21 J. W. Cooley, Math. Comput. 15, M. Perić, R. Runau, J. Römelt, S. D. Peyerimhoff, and R. J. Buenker, J. Mol. Spectrosc. 78,