An ab initio study of some noble gas monohalides

Transcription

1 JOURNAL OF CHEMICAL PHYSICS VOLUME 114, NUMBER 5 1 FEBRUARY 2001 An ab initio study of some noble gas monohalides Gerald J. Hoffman a) and Mitchell Colletto Department of Chemistry, The College of New Jersey, P. O. Box 7718, Ewing, New Jersey Received 15 September 2000; accepted 10 November 2000 Results from high-level ab initio calculations on NeF, ArF, KrF, XeF, and XeCl are reported and compared to experiment and to previous calculations. CCSD T results for NeF and ArF ground state potentials show agreement with experimental potentials to within the probable uncertainty of the measurement. In addition to CCSD T, multireference averaged coupled-pair functional calculations are performed on KrF, XeF, and XeCl as well as calculation of spin orbit coupling of the noble gas atom. Very good agreement with experiment is observed for XeF using this technique, while poor agreement is observed for KrF; this casts some doubt on the experimental potential for KrF. Results for XeCl show semiquantitative agreement with experiment. Finally, the potentials for the charge-transfer states of XeF, XeCl, and KrF and their spectroscopic constants are presented. Improved agreement over previous calculations is observed with some experimental measurements of these constants, for XeCl in particular American Institute of Physics. DOI: / I. INTRODUCTION The noble gas monohalides, as a class of molecules, share some unusual and interesting properties. Their most important property, from a practical point of view, is the use of many of these molecules as the lasing medium in highpowered excimer lasers. The ground states of all of these molecules are weakly bound compared to typical covalently bound molecules; however, because excitation involves a net transfer of an electron from the noble gas atom to the halogen atom, the excited states are very strongly bound, held together by electrostatic attraction between the noble gas cation and the halide anion. These ground and excited state properties are what make the noble gas halides good laser media, as there is a large transition moment between the ground state and two of the charge-transfer states, and the respective bonding properties of the upper and lower states guarantee a population inversion. The importance of these molecules as laser media, as well as their unusual behavior, provides motivation for trying to understand them better. Many experimental studies have been performed on the noble gas monohalides in order to characterize their molecular potentials. Gas-phase fluorescence and photoassociation studies 1 11 and matrix isolation studies have provided much information about both the excited and ground states of some of these molecules. Atomic scattering studies have given detailed information about the ground state potentials, as well as the two other low-lying neutral states However, there have only been a limited number of computational studies on these molecules The most significant early calculations 20,21 provided a vivid picture of the chargetransfer states of the noble gas monofluorides and the xenon monohalides at a time when little was known about them; yet despite the useful information these papers still contain, the authors computational technique gave repulsive ground a Author to whom correspondence should be addressed. states, in contradiction to the experimental result. More recently, two ab initio studies have been published that succeed in showing minima in the ground state potentials for some of these molecules. 23,24 It is necessary to implement a computational technique that includes a high degree of electron correlation in order to obtain such minima. In the present study, we show the results of ab initio calculations on NeF, ArF, KrF, XeF, and XeCl using a variety of techniques and basis sets; the resulting potentials for each molecule are then compared to the corresponding experimental potential. Coupled-cluster theory calculations including singles, doubles, and noniterative triples CCSD T were applied to all of these molecules to determine their ground state potentials. The CCSD T potentials for NeF and ArF agree quite well with experiment, but significant deviation between calculation and experiment is observed for KrF, XeF, and XeCl. For these three molecules, multireference averaged coupled-pair functional MR-ACPF calculations were performed in order to take into account some of the mixing of neutral and charge-transfer states that is known to occur. 20,21 In general, agreement between the MR-ACPF potentials and experiment is significantly better. Finally, the effect of the spin orbit SO coupling of the noble gas atom is calculated from the MR-ACPF results, and its influence on the potential is assessed in each case. Also, in performing MR-ACPF-SO calculations, potentials for the lowest six states of each molecule were obtained, that is, the three neutral or covalent states, and the three charge-transfer or ionic states. The ionic potentials are also compared with experimental results, as well as previous calculations. II. COMPUTATIONAL DETAILS All calculations were performed on the Cray T90 at the San Diego Supercomputer Center SDSC using either GAUSSIAN or MOLPRO The following basis sets were used for the noble gases: /2001/114(5)/2219/9/$ American Institute of Physics

2 2220 J. Chem. Phys., Vol. 114, No. 5, 1 February 2001 G. J. Hoffman and M. Colletto TABLE I. Exponents for polarization and diffuse subshells augmenting basis sets used for various atoms. Atom, basis set Polarization subshell exponent Diffuse subshell exponent Ne, SC d s f p Ne, STUT s p Ar, SC d s f 0.90 p Ar, STUT s p Kr, STUT f s 0.07 g 0.55 p 0.04 d 0.06 Xe, SC d a a s f 0.40 b p Xe, STUT c f s 0.03 g 0.55 p 0.02 d 0.05 F, AVQZ c s 0.07 p 0.04 d 0.06 Cl, mavtz s p d a Reference 30. b Reference 31. c Reference 23. AVTZ: The augmented triple-zeta correlation consistent basis sets of Dunning et al. AUG-cc-pVTZ 27,28 used without modification Ne and Ar only. SC: The so-called shape-consistent averaged relativistic effective core potential ECP basis sets of Christiansen et al. 28,29 augmented by s and p diffuse subshells Ne, Ar, and Xe. The XE basis set had in addition two d and one f polarization subshells. 30,31 Exponents for these additional subshells can be found in Table I. 29,30 STUT: The Stuttgart ECP basis sets of Nicklass et al. 28,32 including the polarization subshells provided, and augmented with s and p diffuse subshells. For Kr and Xe, this basis set was further augmented by replacing the single f polarization subshell with three f subshells, and adding a g polarization subshell and a d diffuse subshell also. 23 Exponents for these additional subshells can be found in Table I. Spin orbit ECPs are included for Kr and Xe, in order to allow the calculation of spin-orbit coupling in molecules containing these atoms. The following basis sets were used for the halogens, F and Cl: AVTZ: Same as above. mavtz: Same as AVTZ, except augmented with additional s, p and d diffuse subshells Cl only. Exponents for the diffuse subshells can be found in Table I. AVQZ: The augmented quadruple-zeta correlation consistent basis sets of Dunning et al. AUG-cc-pVQZ, 27,28 augmented with additional s, p, and d diffuse subshells F only. 23 Exponents for the diffuse subshells can be found in Table I. TABLE II. Spin orbit coupling calculations on Kr and Xe compared with experimental values energy in units of ev. Kr Xe MR-ACPF Experiment Coupled-cluster calculations were performed using both GAUSSIAN 94 and MOLPRO 98. CCSD T was the coupledcluster technique of choice because it has been shown previously to result in ground state minima for the xenon monohalides 23 and for KrF. 24 Inclusion of triply excited configurations had a significant influence on the quality of these earlier results. 23,24 For ArF, XeF, and XeCl, GAUSSIAN s CCSD T 33 option was used; results for KrF using this program have been published previously. 24 For NeF, KrF, XeF, and XeCl, the spin-restricted open-shell CCSD T option RCCSD T 34 of MOLPRO was used also. Earlier calculations have shown that there is a significant amount of multiconfigurational character to the ground state of the monohalides of the heavier noble gases Kr and Xe ; 20,21 this suggests the choice of a multireference technique might yield better results for these particular molecules. The multireference averaged coupled-pair functional option MR-ACPF, 35 one of the multireference configuration interaction MRCI techniques in MOLPRO, was chosen as a technique to study KrF, XeF, and XeCl as it has been used previously on XeF with good results. 23 However, as ACPF is only approximately size consistent, a calculation on each molecule is performed at large internuclear separation 50 Å in order to provide a reference energy for the separated atoms. The basis sets used were STUT including the SO ECP for the noble gas, and AVQZ for fluorine, or mavtz for chlorine. The wave functions resulting from a simultaneous multiconfigurational self-consistent field MCSCF calculation on the six lowest states three neutral and three charge-transfer were used as input for the MR- ACPF step. MR-ACPF calculations were performed for each symmetry of the MCSCF wave function 2 and the two Cartesian components of 2, and in each, two reference states were included neutral and charge-transfer. Note that these 6 states correspond to the six possible arrangements of 11 electrons in the 6 molecular orbitals of a diatomic molecule resulting from interaction of the outer p subshells of each. The energy of the lowest 2 state is taken to be the ground state energy. The MR-ACPF results for all six states, described above, were used to perform spin orbit calculations on KrF, XeF, and XeCl using MOLPRO with the STUT noble gas ECP basis sets, including the spin orbit ECPs. Again, this follows the lead of the previous study on XeF, 23 although we have chosen a different method by which to perform this calculation. Because all states are calculated simultaneously, they all have the same reference energy. Spin orbit couplings of the J 1/2 and J 3/2 states for Kr and Xe calculated using this technique compared with experimental values are shown in Table II. The calculated values are about 10% smaller than the experimentally measured values; as SO coupling is a

3 J. Chem. Phys., Vol. 114, No. 5, 1 February 2001 Noble gas halides 2221 relatively small component of the overall calculation, this level of agreement is judged to be sufficient for the purposes of this study. MOLPRO is capable of calculating spin orbit coupling either with all-electron basis sets, or with ECP basis sets, but not both in the same calculation. Hence, the spin orbit effects of the halogens are neglected by the chosen technique, as only all-electron basis sets were used for these atoms in our calculations. Calculations on XeCl were attempted using the STUT ECP basis sets for both Xe and Cl, including both spin orbit ECPs, but the resulting covalent potentials bore no resemblance to the experimental potentials, so this strategy was abandoned. Since the spin orbit couplings of the noble gas ions in the case of each molecule are more than ten times greater than those of the corresponding halogen atoms Xe ev and Kr ev vs F ev and Cl ev, one may assume that the couplings of the noble gases have the greatest influence, in effect justifying the approximation made in these calculations. However, at the outset, it is not clear how great an effect this approximation will have on the calculated potentials. Assuming the errors due to all of the other approximations implicit in these calculations do not dwarf the neglect of halogen spin orbit coupling, it is possible to judge the effect of this neglect after the fact, on comparison of the calculated potentials with the experimental ones. All calculated potentials were corrected for basis set superposition error BSSE point-by-point using the counterpoise technique. 36 While this technique does no better than estimate the BSSE, such a correction reduces an artificial bias toward dissociation energies that are too large, and bond lengths that are too small, 24 particularly for weakly bound species, such as those investigated in this work. In the specific case of the molecules reported on here, the differences between corrected and uncorrected bond lengths are quite small for the monofluorides 0.01 Å 0.08 Å, while that for XeCl is much more substantial 0.44 Å. FIG. 1. NeF potentials, computed using CCSD T and a variety of Ne basis sets, and corrected for BSSE, compared with experiment. III. RESULTS AND DISCUSSION A. Ground state potentials Calculated ground state potentials as compared with experimental potentials for NeF, ArF, KrF, XeF, and XeCl are shown in Figs. 1 5, respectively. The experimental curve shown in each plot is either the most recently published one, or the best accepted one from atomic scattering experiments ,37 1. NeF and ArF Of the molecules studied here, NeF and ArF are the most weakly bound, with dissociation energies less than 0.01 ev. Thus it is somewhat surprising that the calculated results agree with the experimental potentials for these two molecules as well as they do. Tables III and IV summarize the bond length and dissociation energy comparisons for NeF and ArF, respectively. All calculated bond lengths for NeF lie within 0.06 Å of its experimental value, while those for ArF lie within 0.12 Å of its experimental value. All calculated dissociation energies for both molecules lie within ev of their respective experimental values. These differences may well lie within uncertainties of the experimental potentials. Furthermore, the calculated and experimental potentials agree very well on the attractive portion, at separations greater than the minimum, proceeding toward separated atoms. This is significant because the scattering experiments from which these potentials originate 17,18 measure the attractive wall of the potential most accurately. 11 The forces that hold these two molecular species together are clearly van der Waals in nature. Hence, one gen- FIG. 2. ArF potentials, computed using CCSD T and a variety of Ar basis sets, and corrected for BSSE, compared with experiment.

4 2222 J. Chem. Phys., Vol. 114, No. 5, 1 February 2001 G. J. Hoffman and M. Colletto TABLE III. BSSE corrected CCSD T bond lengths and dissociation energies for NeF compared with experimental values. a Reference 18. Basis set R (Å) D e (ev) AVTZ/AVTZ SC/AVTZ STUT/AVTZ Experiment a FIG. 3. KrF potentials, computed using a variety of techniques and the STUT/AVQZ basis sets, and corrected for BSSE, compared with experiment. eral conclusion that can be drawn from these results is that CCSD T performs very well in describing van der Waals bound species. This should not be surprising, as other coupled-cluster studies have accurately determined the structures of van der Waals complexes, such as the triatomic noble gas Cl 2 complexes KrF and XeF Comparing the CCSD T results for KrF and XeF with experiment in Figs. 3 and 4, it is apparent that even with the inclusion of triply excited configurations, coupled-clusters is not giving a realistic picture of the bonding. While agreement on the attractive wall of the potential is reasonably good, the dissociation energy calculated using either CCSD T or RCCSD T falls far short of experiment. As has been stated previously, this can be ascribed to the shortcomings of single-reference coupled-cluster theory in properly accounting for the mixing of the covalent ground state with the ionic excited state of the same symmetry ( 2 ). Thus one expects that MR-ACPF will give a ground state potential closer to experiment. Furthermore, possible influence of SO coupling from the noble gas atom on the potential may be significant. Potentials for MR-ACPF and MR-ACPF-SO calculations are displayed in Figs. 3 and 4 also; bond length and dissociation energy data are summarized in Tables V and VI for KrF and XeF, respectively. For XeF, MR-ACPF shows a clear improvement in bond length and dissociation energy over the CCSD T results, and the MR-ACPF-SO result R e 2.34 Å, D e ev is very nearly in quantitative agreement with the experimental values R e 2.31 Å, D e ev, 17 and at least as good as the result of the most recent calculation R e 2.31 Å, D e 0.13 ev, but not BSSE corrected. 23 On the other hand, agreement between calculation and experiment on the attractive portion of the potential is not of the highest quality. This lack of agreement may be due to neglect of relativistic effects not taken into account by either the relativistic ECP for Xe or the technique of calculation. Correlated all-electron Dirac Fock calculations on XeF 2 and XeF 4 have resulted in quantitative agreement with experiment in bond length and dissociation energy, 39 and it is possible a similar treatment for XeF would show a higher level of quality than the results presented here. For KrF, the MR-ACPF potential lies just slightly below the one for RCCSD T, and including SO coupling has just a very small effect on this result. Despite good agreement between experiment and calculation on the attractive wall, none of the calculated bond lengths and dissociation energies are TABLE IV. BSSE corrected CCSD T bond lengths and dissociation energies for ArF compared with experimental values. Basis set R (Å) D e (ev) FIG. 4. XeF potentials, computed using a variety of techniques and basis sets, and corrected for BSSE, compared with experiment. a Reference 17. AVTZ/AVTZ SC/AVTZ STUT/AVTZ Experiment a

5 J. Chem. Phys., Vol. 114, No. 5, 1 February 2001 Noble gas halides 2223 TABLE VI. BSSE corrected computed bond lengths and dissociation energies for XeF compared with experimental values. Technique Basis set R (Å) D e (ev) CCSD T SC/AVTZ RCCSD T STUT/AVQZ MR-ACPF STUT/AVQZ MR-ACPF-SO STUT/AVQZ Previous calculation a Experiment b a Reference 23; this calculation used the same basis sets and a computational technique similar to MR-ACPF-SO here. The minimum was determined without correcting for BSSE; correcting for BSSE at the uncorrected minimum yields the energy in parentheses. b Reference 17. gas monofluorides, KrF shows the largest discrepancy between our best calculation and the accepted experimental potential. It is possible that the KrF ground state potential has not yet been characterized accurately by experiment. FIG. 5. XeCl potentials, computed using a variety of techniques and basis sets, and corrected for BSSE, compared with experiment. at all close to those from the experimental potential depicted in Fig. 3. In the case of XeF, we saw that MR-ACPF-SO gave nearly quantitative agreement with experiment; for KrF, however, this level of theory gives a bond length more than 0.2 Å longer, and a dissociation energy that is slightly more than half of the experimental value. This particular experimental potential is the most recent and is based on data from all previous scattering experiments, which sample the attractive portion of the potential, as well as fluorescence experiments, which sample the repulsive wall at separations shorter than the minimum. 37 The minimum itself must be interpolated between the two data sets, which is a difficult and uncertain process. Comparisons of computed results with the two other potentials from the literature that feature a minimum, given in Table V, show better agreement with respect to bond length, although there is still significant disagreement with dissociation energy. While the calculated results shown here are not free from approximation, and thus not exact, it is nonetheless significant that, of all the noble TABLE V. BSSE corrected computed bond lengths and dissociation energies for KrF compared with experimental values. Technique Basis set R (Å) D e (ev) RCCSD T STUT/AVQZ MR-ACPF STUT/AVQZ MR-ACPF-SO STUT/AVQZ Previous calculation a Experiment b b c c 3.0 d d a Reference 24; this is the BSSE corrected CCSD T result using the SC basis set for Kr and an atomic natural orbital basis set for F. b Reference 37. c Reference 11. d Reference XeCl The comparison between calculated potentials and experiment for XeCl is shown in Fig. 5, and bond length and dissociation energy data are collected in Table VII. Interestingly, while the GAUSSIAN CCSD T calculation falls far short in comparing it to experimental bond length and dissociation energy, the MOLPRO RCCSD T calculation does much better with its dissociation energy. All of the calculated bond lengths are significantly longer than the experimental result, by more than 0.3 Å in all but one case, and the multireference calculations overshoot the dissociation energy, although all are within ev of the experimental value. Note that while the previous calculation has a shorter bond length and larger dissociation energy than any of our results, 23 this difference is because the previous result was not corrected for BSSE. Such correction reduces D e and increases R e. 24 The cause of this discrepancy is not clear, but possible culprits include the neglect of some relativistic effects, as in the XeF calculation, as well as the neglect of the Cl atom in the calculation of the SO coupling. B. Charge-transfer states of XeF, XeCl, and KrF A consequence of performing SO calculations on XeF, XeCl, and KrF is that the energies of the six lowest states are calculated, the lower three covalent and the upper three ionic. Hence, this is an opportunity to update the calcula- TABLE VII. BSSE corrected computed bond lengths and dissociation energies for XeCl compared with experimental values. Technique Basis set R (Å) D e (ev) CCSD T SC/AVTZ RCCSD T STUT/AVQZ MR-ACPF STUT/AVQZ MR-ACPF-SO STUT/AVQZ Previous calculation a Experiment b a Reference 23; this calculation used the same technique and basis sets as RCCSD T here, but was not corrected for BSSE. b Reference 19.

6 2224 J. Chem. Phys., Vol. 114, No. 5, 1 February 2001 G. J. Hoffman and M. Colletto FIG. 6. XeF neutral and charge-transfer state potentials calculated using MR-ACPF-SO and STUT/AVQZ. FIG. 7. XeCl neutral and charge-transfer state potentials calculated using MR-ACPF-SO and STUT/mAVTZ. tions performed on these molecules by Dunning and Hay and published in ,21 The six states can be classified by the quantum number total component of angular momentum along the internuclear axis, either by numbering or by using the spectroscopists letter designation of the state. The latter system will be used here, so the three covalent states are X(1/2) ground state, A(3/2), and A (1/2), while the three ionic states are B(1/2), C(3/2), and D(1/2). In each group covalent or ionic, the two 1/2 states are the split states. In a particular group of states, at infinite atomic separation, the lower 1/2 state will correlate to the same limit as the 3/2 state, which is 1 S 0 2 P 3/2, while the upper 1/2 state correlates to 1 S 0 2 P 1/2. In the calculations presented here, all three covalent states correlate to the same energy at infinite atomic separation because the SO splitting of the neutral halogen has been neglected. However, the depiction of all three ionic states ought to be correct. Figures 6, 7, and 8 show the potential curves for all six states calculated using MR-ACPF-SO for XeF, XeCl, and KrF, respectively. For each of the ionic potentials of each molecule, the harmonic frequency and anharmonicity were determined by numerically integrating the Schrödinger equation using the shooting method to find the first 16 eigenvalues, and then performing a Birge Sponer fit. 40 All of these results are catalogued and compared with experiment and previous calculation in Tables VIII, IX, and X for XeF, XeCl, and KrF, respectively. Among general observations that can be made regarding these results, all of the newly calculated bond lengths are shorter than those previously calculated, and closer to the experimentally measured values, where such measurements are available for comparison. Note, however, that all of the new, shorter calculated bond lengths are still longer than those measured experimentally. Similarly, all of the newly calculated T e s are smaller than previous calculation, and most agree with experiment at least as well as previous calculation. Dipole moments and transition moments as functions of atomic separation were also calculated, but these are not presented here because they are almost quantitatively identical to those published previously. 20,21 For XeF, the newly calculated T e s for each of the ionic states are too small, and except for the C(3/2) state, they do not improve on the results of previous calculation. However, the ordering of the states is correct: the minimum of the C(3/2) state lies below the B(1/2) minimum. Further, the harmonic frequencies of the C(3/2) and the D(1/2) states are closer to the experimental values than previous calculations, while that for the B(1/2) state falls far short. The results for FIG. 8. KrF neutral and charge-transfer state potentials calculated using MR-ACPF-SO and STUT/AVQZ.

7 J. Chem. Phys., Vol. 114, No. 5, 1 February 2001 Noble gas halides 2225 TABLE VIII. Molecular and spectroscopic constants of XeF charge-transfer states from calculations compared with experiment and previous calculation. R e (Å) T e (ev) e (cm 1 ) e x e (cm 1 ) B(1/2) state This work Previous calculation a Experiment b C(3/2) state This work Previous calculation a Experiment c D(1/2) state This work Previous calculation a Experiment b d d b,d a References 20, 21. b Reference 5. c Reference 7. d Reference 10. XeCl were the best of the three molecules. All the newly calculated T e s for XeCl lie within 0.06 ev of the experimental values, and all calculated harmonic frequencies lie within 10 cm 1 of the experimental values. One minor error is that the ordering of the B(1/2) and C(3/2) states is opposite from experimental observation, but then the energetic separation between these two states is very small. For KrF, comparison with experimental data is somewhat difficult because only the B(1/2) state has been characterized to any degree in the gas phase, although some estimates can be found for the D(1/2) state. Such characterization is difficult to perform because the Franck Condon region of the ground state for these transitions lies high on its repulsive wall; spectra must be calculated from assumed potentials and then compared to experiment. Results of three such studies on the B(1/2) state are provided in Table X. The experimental numbers provided in Table X for the D(1/2) state are not as firmly grounded as those for the B(1/2) state; each set has a caveat. The first set of numbers TABLE IX. Molecular and spectroscopic constants of XeCl charge-transfer states from calculations compared with experiment and previous calculation. R e (Å) T e (ev) e (cm 1 ) e x e (cm 1 ) B(1/2) state This work Previous calculation a Experiment b C(3/2) state This work Previous calculation a Experiment c D(1/2) state This work Previous calculation a Experiment b a Reference 21. b Reference 6. c Reference 8. TABLE X. Molecular and spectroscopic constants of KrF charge-transfer states from calculations compared with experiment and previous calculation. R e (Å) T e (ev) e (cm 1 ) e x e (cm 1 ) B(1/2) state This work Previous calculation a Experiment b b 330 b 2.33 c c 336 c 1.4 c 2.27 d d 310 d C(3/2) state This work Previous calculation a D(1/2) state This work Previous calculation a Experiment 2.33 c,e c,e 328 c,e 1.3 c,e f f 1.35 f a Reference 20. b Reference 11. c Reference 9. d Reference 3. e These numbers come from a fit of photoassociative excitation spectra for both B X and D X transitions that the authors found to be unsatisfactory; hence these numbers can t be assumed to be correct. f Reference 15; this is from the analysis of the excitation spectrum of KrF matrix isolated in solid Ne, so these values are expected to be red-shifted from the gas phase values. comes from the attempt of Jones et al. 9 to fit photoassociation excitation spectra, but inclusion of the D X transition produced features in the simulated spectra that did not appear in experiment; hence, the validity of these values is questionable. The second set comes from experimental data for the D(1/2) state from the excitation spectrum of KrF isolated in solid neon; 15 all of the spectroscopic constants from this spectrum are assumed to be red-shifted from their gas phase values. It is interesting to note that, despite the expected red-shift, the e of the D(1/2) state from the Ne matrix is larger than that from the gas phase estimate. No constants from experimental data for the C(3/2) state have ever been published. The newly calculated T e values for the B(1/2) and D(1/2) states fall below the experimental values presented, even the red-shifted T e for the D(1/2) state. This indicates that all of the new T e values are too small. In this light, it is likely that the old and new calculated values for the T e of the C(3/2) state serve as upper and lower bounds, respectively, to the correct value. With regard to vibrational parameters, the new calculated value for the harmonic frequency of the B(1/2) state is slightly larger than either the experimental numbers or the previously calculated e, but agreement is still within 10 cm 1 of most of these values. Interestingly, the newly calculated anharmonicity for this state is quite large. The newly calculated values for the e s of the C(3/2) and D(1/2) states are slightly smaller than the previously calculated ones, but in the case of the D(1/2) state, this smaller value is closer to its experimental estimates.

8 2226 J. Chem. Phys., Vol. 114, No. 5, 1 February 2001 G. J. Hoffman and M. Colletto IV. CONCLUSIONS An ab initio study of the ground state potentials of NeF, ArF, KrF, XeF, and XeCl, and of the charge-transfer state potentials of KrF, XeF, and XeCl, has been presented, and the results compared with experimental results and previous calculations. Of the fluorides, good agreement between calculation and experiment is observed for NeF, ArF, and XeF. For NeF and ArF, theory at the level of CCSD T is sufficient to give quantitative agreement with experiment. For XeF, it is necessary to invoke a multireference technique MR-ACPF and to include SO coupling to achieve quantitative agreement between theory and experiment. This is because of the significant amount of mixing that occurs between covalent and ionic 2 states, and because the SO coupling associated with Xe is large enough to affect the ground state potential. On the other hand, no level of theory attempted here has resulted in quantitative agreement with the best accepted experimental ground state potential for KrF, suggesting possible error in the experimental potential. Application of MR-ACPF to KrF made only a small improvement over CCSD T, and the difference due to SO coupling is almost negligible. Semiquanititative agreement between experimental and calculated potentials is observed for XeCl, suggesting the breakdown of one or more of the approximations made. Overall, the application of high-level ab initio techniques in order to determine accurate results for weakly bound species presents a substantial challenge. The newly calculated charge-transfer state potentials overall show a level of agreement with experiment as good as or better than previous calculation with regard to bond length and, often, with regard to T e and vibrational parameters also. The best agreement is observed for XeCl. While agreement is not as good for XeF and KrF, the correct ordering of the charge-transfer states of XeF is obtained. ACKNOWLEDGMENTS This research was supported by NSF cooperative agreement ACI through a grant of computer time on the Cray T90 at the San Diego Supercomputer Center SDSC, administered by the National Partnership for Advanced Computing Infrastructures NPACI. The College of New Jersey has granted release time from teaching to GJH for the purpose of pursuing research; this grant is gratefully acknowledged. Dr. J. R. Greenberg, Dr. K. Milfield, and especially Dr. J. N. Harvey are thanked for invaluable advice on performing calculations using MOLPRO, and Dr. L. C. Allen for providing library access. Dr. R. J. Cave, Dr. S. K. Knudsen, R. Danell, and A.-M. Chen are thanked for contributions in the early stages of this research. Dr. R. J. Cave is also thanked for his many helpful suggestions during the course of this work, and for his critical review of the manuscript. 1 Excimer Lasers, 2nd ed., edited by Ch. K. Rhodes Springer, Berlin, 1984 provides a broad review of the early work on these molecules. 2 J. Tellinghuisen, J. M. Hoffman, G. C. Tisone, and A. K. Hays, J. Chem. Phys. 64, J. Tellinghuisen, A. K. Hays, J. M. Hoffman, and G. C. Tisone, J. Chem. Phys. 65, J. Tellinghuisen, P. C. Tellinghuisen, G. C. Tisone, J. M. Hoffman, and A. K. Hays, J. Chem. Phys. 68, P. C. Tellinghuisen, J. Tellinghuisen, J. A. Coxon, J. E. Velazco, and D. W. Setser, J. Chem. Phys. 68, A. Sur, A. K. Hui, and J. Tellinghuisen, J. Mol. Spectrosc. 74, H. Helm, D. L. Huestis, M. J. Dyer, and D. C. Lorents, J. Chem. Phys. 79, C. Jouvet, C. Lardeux-Dedonder, and D. Solgadi, Chem. Phys. Lett. 156, R. B. Jones, J. H. Schloss, and J. G. Eden, J. Chem. Phys. 98, K. Johnson and J. Tellinghuisen, Chem. Phys. Lett. 228, G. Lo and D. W. Setser, J. Chem. Phys. 100, J. Goodman and L. E. Brus, J. Chem. Phys. 65, B. S. Ault and L. Andrews, J. Chem. Phys. 65, G. Zerza, G. Sliwinski, N. Schwentner, G. J. Hoffman, D. G. Imre, and V. A. Apkarian, J. Chem. Phys. 99, C. Bressler, W. G. Lawrence, and N. Schwentner, J. Chem. Phys. 105, C. H. Becker, P. Casavecchia, and Y. T. Lee, J. Chem. Phys. 69, ; 70, V. Aquilanti, E. Luzzatti, F. Pirani, and G. G. Volpi, J. Chem. Phys. 89, V. Aquilanti, R. Candori, D. Cappelletti, E. Luzzatti, and F. Pirani, Chem. Phys. 145, V. Aquilanti, D. Cappelletti, V. Lorent, E. Luzzatti, and F. Pirani, Chem. Phys. Lett. 192, T. H. Dunning, Jr. and P. J. Hay, J. Chem. Phys. 69, P. J. Hay and T. H. Dunning, Jr., J. Chem. Phys. 69, G. F. Adams and C. F. Chubalowski, J. Phys. Chem. 98, D. Schröder, J. N. Harvey, M. Aschi, and H. Schwarz, J. Chem. Phys. 108, G. J. Hoffman, L. A. Swafford, and R. J. Cave, J. Chem. Phys. 109, GAUSSIAN 94 Revision E.1 M. J. Frisch, G. W. Tracks, H. B. Schlegel et al. Gaussian, Inc., Pittsburgh, PA, MOLPRO is a package of ab initio programs written by H.-J. Werner and P. J. Knowles, with contributions from J. Almlöf, R. D. Amos, A. Berning et al. 27 T. H. Dunning, Jr., J. Chem. Phys. 90, ; R. A. Kendall, T. H. Dunning, Jr., and R. J. Harrison, ibid. 96, Basis sets were obtained from the Extensible Computational Chemistry Environment Basis Set Database, Version 1.0, as developed and distributed by the Molecular Science Computing Facility, Environmental and Molecular Sciences Laboratory which is part of the Pacific Northwest Laboratory, P.O. Box 999, Richland, Washington 99352, and funded by the U.S. Department of Energy. The Pacific Northwest Laboratory is a multi-program laboratory operated by Battelle Memorial Institute for the U.S. Department of Energy under Contract No. DE-AC06-76RLO Contact David Feller, Karen Schuchardt, or Don Jones for further information. 29 L. F. Pacios and P. A. Christiansen, J. Chem. Phys. 82, ; M. M. Hurley, L. F. Pacios, P. A. Christiansen, R. B. Ross, and W. C. Ermler, ibid. 84, ; L. A. LaJohn, P. A. Christiansen, R. B. Ross, T. Atashroo, and W. C. Ermler, ibid. 87, Gaussian Basis Sets for Molecular Calculations, edited by S. Huzinaga Elsevier, Amsterdam, H. Bürger, R. Kuna, S. Ma, J. Breidung, and W. Thiel, J. Chem. Phys. 101, A. Nicklass, M. Dolg, H. Stoll, and H. Preuss, J. Chem. Phys. 102, J. A. Pople, R. Krishnan, H. B. Schlegel, and J. S. Binkley, Int. J. Quantum Chem. 14, ; J. Cizek, Adv. Chem. Phys. 14, ; G. D. Purvis and R. J. Bartlett, J. Chem. Phys. 76, ; G.E.Scuseria, C. L. Janssen, and H. F. Schaefer III, ibid. 89, ; G.E. Scuseria and H. F. Schaefer III, ibid. 90, ; R. J. Bartlett and G. D. Purvis, Int. J. Quantum Chem. 14, ; J. A. Pople, M. Head- Gordon, and K. Raghavachari, J. Chem. Phys. 87, P. J. Knowles, C. Hampel, and H.-J. Werner, J. Chem. Phys. 99, ; J. D. Watts, J. Gauss, and R. J. Bartlett, ibid. 98, H.-J. Werner and P. J. Knowles, J. Chem. Phys. 89, ; P.J. Knowles and H.-J. Werner, Chem. Phys. Lett. 145, S. F. Boys and F. Bernardi, Mol. Phys. 19, D. Cappelletti, F. Pirani, and V. Aquilanti, private communication June 2, This potential was first published in Ref F. Y. Naumkin and F. R. W. McCourt, J. Chem. Phys. 107, ;

9 J. Chem. Phys., Vol. 114, No. 5, 1 February 2001 Noble gas halides 2227 ibid. 109, ; S. M. Cybulski and J. S. Holt, ibid. 110, G. L. Malli, J. Styszynski, and A. B. F. Da Silva, Int. J. Quantum Chem. 55, ; J. Styszynski and G. L. Malli, ibid. 55, For each set of points, a nonlinear least-squares fit to the functional form of a Rittner potential was performed. The difference between the best-fit Rittner function and the calculated points was obtained, and if any of these residuals exceeded 0.01 ev, a second nonlinear least-squares fit was performed using a function with properties that mimicked the variation observed in the residuals. The potential function used in the numerical integration of the Schrödinger equation was then the sum of the Rittner function and the residuals function.