Ab initio study of spectroscopic and radiative characteristics of ion-pair states of the Cl 2 molecule

Transcription

1 JOURNAL OF CHEMICAL PHYSICS VOLUME 115, NUMBER NOVEMBER 2001 Ab initio study of spectroscopic and radiative characteristics of ion-pair states of the Cl 2 molecule D. B. Kokh, a) A. B. Alekseyev, b) and R. J. Buenker Theoretische Chemie, Fachbereich 9, Bergische Universität-Gesamthochschule Wuppertal, Gaußstrasse 20, D Wuppertal, Germany Received 19 June 2001; accepted 29 August 2001 Electronic structure and radiative characteristics of low-lying ion-pair states of Cl 2 converging to the Cl ( 3 P, 1 D) Cl ( 1 S) limits are studied. Ab initio calculations of potential energy curves for the valence and ion-pair states and dipole moments for transitions between them are carried out employing the multireference single- and double-excitation configuration interaction MRD-CI method, including spin orbit coupling. It is shown that the lowest two pairs of the 0 u,1 u ion-pair states arise from an avoided crossing between the 3 u and 3 u parent S states, which leads to notably anharmonic shapes of the corresponding potential curves and their mixed S nature. This causes significant radial coupling, resulting in the strongly perturbed character of the 0 u and 1 u states observed experimentally. In contrast, their gerade counterparts run parallel to one another and exhibit much less perturbation. Spectroscopic properties of the computed adiabatic curves are in very good agreement with the available experimental data. Dipole moments have been calculated for parallel ion-pair valence state transitions and radiative lifetimes have been obtained for the adiabatic ion-pair states. A reanalysis of the experimental bound free emission spectra from the D0 u ( 3 P 2 ) state N. K. Bibinov et al., Chem. Phys. 254, is given American Institute of Physics. DOI: / I. INTRODUCTION The chlorine molecule has received much attention over the years as a benchmark system for the study of the electronic structure and spectroscopy of diatomic molecules. Investigations of the ion-pair states of Cl 2 were initiated with the first observation of laser emission at 258 nm. 1 The upper state of the laser transition has been assigned to the 3 g state correlating with the Cl ( 3 P) Cl ( 1 S) ions at its dissociation limit, which is a common situation among halogen species. As a result, the spectroscopic and radiative characteristics of the low-lying ion-pair states are of special interest. The first experimental examination of the spectroscopy of the low-lying ion-pair states in Cl 2 was carried out in 1982 by Ishiwata, Fujiwara, and Tanaka. 2 They employed a multiphoton excitation technique, which ensured selective population of rovibrational levels of ion-pair states through an intermediate valence B0 u state and locally perturbed A1 u and B 0 u states. In a series of subsequent studies, Ishiwata et al and Al-Kahali et al. 17,18 obtained detailed information concerning gerade states converging to the lowest ionic dissociation limit, as well as some data for several states of u symmetry. The latter have proven to be more difficult to investigate because of strong homogeneous and heterogeneous perturbations. Most of the experimental studies have made use of the theoretical investigation of the Cl 2 electronic structure reported by Peyerimhoff and Buenker 20 years ago. 19 This a Author to whom correspondence should be addressed: Electronic mail: kokh@uni-wuppertal.de b Present address: Institut für Physikalische und Theoretische Chemie, Universität GH Essen, Universitätstr. 5, D Essen, Germany. study gave a general picture of the S potential curves of valence and Rydberg states, including all singlet and some triplet states. However, since this work is focused mainly on the states involved in direct one-photon absorption processes, 3 g/u states were omitted in these calculations. The effects of spin orbit coupling were also not accounted for in this study. Obviously, this lack of completeness in the theoretical data causes additional difficulties in the analysis of the spectroscopic data observed experimentally. Radiative lifetimes for the lowest gerade ion-pair states of Cl 2 correlating with Cl ( 3 P) Cl ( 1 S) have been measured in Ref. 12. Among the ungerade states, only the radiative lifetime of the 1 u ( 1 D) state has been estimated Furthermore, information concerning the transition dipole moments as a function of the internuclear distance is also very limited. Such a study has been carried out experimentally only for the E0 g ( 3 P 2 ) B0 u transition 23 and for four transitions from the D0 u ( 3 P 2 ) state. 24 An analysis of the experimental spectra becomes very complicated, however, if more than one transition participates in the emission spectrum, 24 and theoretical data certainly give more reliable information on the dipole moment functions in this case. Our goal in the present work is to conduct a detailed theoretical examination of the spectroscopic and radiative properties of the low-lying ion-pair states of Cl 2. For this purpose calculations of potential energy curves including the spin orbit interaction are carried out for valence and lowlying ion-pair states. The resulting theoretical curves should be considered as adiabatic in nature, and they may be mixed through nonadiabatic interactions. The influence of nonadiabatic effects radial and rotational coupling on the spectro /2001/115(20)/9298/13/$ American Institute of Physics

2 J. Chem. Phys., Vol. 115, No. 20, 22 November 2001 Ion-pair states of Cl TABLE I. Atomic transition energies. scopic and radiative properties of the ion-pair states of Cl 2 is discussed. An analysis of the valence states is given as well, since such information is necessary for understanding the radiative properties of the ion-pair states. Dipole moment functions are calculated for radiative transitions between states that correlate with the Cl ( 3 P, 1 D) Cl ( 1 S) ionic dissociation limits and the lower valence species. Radiative lifetimes of these states are obtained as well. We also give special attention to the emission spectra of the D0 u ( 3 P 2 ) state that have been observed experimentally. 24 II. THEORETICAL TREATMENT Calc./cm 1 Expt. a /cm 1 Cl ( 2 P 1/2 2 P 3/2 ) Cl ( 3 P 1 3 P 2 ) Cl ( 3 P 0 3 P 2 ) Cl* (3p 4s) ( 2 P 1/2 2 P 3/2 ) a Reference 27. The core electrons of chlorine atoms (1s 2 2s 2 2p 6 ) are described by the relativistic effective core potential RECP associated with the related (6s6p) Gaussian basis set for the 3s 2 3p 5 electrons derived from the SCF optimization of the atomic energy. 25 Two d and one f polarization functions with exponents of 1.16, 0.39, 0.75 obtained from CI energy minimization as well as two s, two p, and one d diffuse functions, with exponents of 0.06, 0.02, 0.05, 0.02, taken from Ref. 26, are added to the basis set. The resulting extended basis set together with the RECP employed underestimates the magnitude of the 2 P 3/2 2 P 1/2 spin orbit splitting of the Cl ground state. To achieve better agreement with experiment, we have scaled the RECP spin orbit operator. In varying this factor, we have attempted to reproduce the experimental results for both the neutral Cl atom ( 2 P 3/2 2 P 1/2 ) and the Cl ion ( 3 P 0 3 P 1 3 P 2 ) spin orbit splittings, 27 since the latter can be important for the calculation of the ion-pair states. The best agreement with the experimental data has been achieved with a factor of 1.04, which has then been used in the ensuing molecular calculations. The resulting spin orbit splittings for the ground and Rydberg (3p 4s) states of the Cl atom as well as for the Cl ion are given in Table I. As a first step in the theoretical treatment, molecular orbitals MOs have been obtained in the SCF calculations of the 1 g ( g 2 u 4 g 4 u 0 ) state. A few additional calculations have also been carried out in the basis of the SCF-MOs of the 3 g state, but they lead to no significant improvement in the accuracy of the excited state results, however. The resulting MOs are employed as a basis for a conventional multireference single- and double-excitation configuration interaction MRD-CI treatment 28 with a configuration selection at an energy threshold of T 0.25 E h and subsequent energy extrapolation to T 0. Calculations are carried out in the D 2h point group for the sake of technical simplicity. The correspondence between calculated molecular states in the D 2h and D h symmetry groups is given in Table II, along with TABLE II. Technical details of the MRD-CI calculations at the -S level (r 5.3a 0 ). D 2h N root N ref SAF total /SAF selected D h c p 2 /% 1 A g / g g g g g B 2u / 1 B 3u / u u B 1g / g g B 1u / u u B 2g / 1 B 3g / u u A u / u u B 2u / 3 B 3u / u u B 1g / g g B 1u / u u u B 2g / 3 B 3g / g g A u / u u 88.4 the number of roots and reference configurations for each symmetry. The number of roots is chosen so that all valence states and all ion-pair states correlating with the Cl( 2 P) Cl( 2 P) and Cl ( 3 P, 1 D) Cl ( 1 S) atomic limits, respectively, are included in the calculations. The generalized Davidson correction procedure 29 has been used to account for the influence of higher excitations on the resulting energies. The corresponding S functions are employed in the computation of the spin orbit matrix elements that are used together with the S energies to determine the state energies and electronic dipole transition moments. III. POTENTIAL CURVES A. Valence states There are 12 -S valence states dissociating into two Cl( 2 P J ) atoms see Figs. 1 and 2, and these give rise to 23 states after the inclusion of spin orbit coupling. In the Franck Condon region, r r x e r x e is the equilibrium distance of the X state, each valence state can be associated with a single dominant S component. At smaller internuclear distances, r r x e, there are multiple crossings between valence and Rydberg states that strongly change the S composition of the states as well as the electronic structure of the S states themselves. This mixing has been thoroughly analyzed on the S level by Peyerimhoff and Buenker, 19 and we shall not consider this range of internuclear distances in the present work. With increasing r, S components become strongly mixed in the states

3 9300 J. Chem. Phys., Vol. 115, No. 20, 22 November 2001 Kokh, Alekseyev, and Buenker FIG. 1. Calculated S potential energy curves of the low-lying gerade states in Cl 2. FIG. 2. Calculated S potential energy curves of the low-lying ungerade states in Cl 2. through spin orbit coupling. Valence states ultimately correlate with the three possible dissociation limits that combine the ground Cl( 2 P 3/2 ) and excited Cl( 2 P 1/2 ) states of the chlorine atom: 2 P 3/2 2 P 3/2 (0 g (2),0 u (2),1 g,1 u (2), 2 g,2 u,3 u ), 2 P 3/2 2 P 1/2 (0 g,0 g,0 u,0 u,1 g (2), 1 u (2),2 g,2 u ), 2 P 1/2 2 P 1/2 (0 g,0 u,1 u ). The calculated potential curves are plotted in Figs. 3 and 4 for states of g and u symmetry, respectively The ground state The 3p 5 electrons of two chlorine atoms give rise to the...5 m g 2 n u 2 p g 5 q u configuration of valence electrons in the Cl 2 molecule. Symmetric and antisymmetric combinations of the p z atomic orbitals AOs determine the bonding g and antibonding u MOs, respectively. Linear combinations of the p x,p y chlorine atomic orbitals with equal contributions from both atoms, in turn, form the antibonding g and bonding u MOs. The lowest strongly bound state, 1 1 g, is characterized by the most stable 2 g 4 u 4 g 0 u electronic configuration, but its contribution decreases rapidly at large internuclear distances 76%, 50% of 2 g 4 u 4 g 0 u and 10%, 35% of 0 g 4 u 4 g 2 u at r 5.0a 0 and r 7.0a 0, respectively, for example. The 1 1 g state makes the dominant contribution to the X0 g ground state, although a small admixture of 1 3 g appears at large r 3.5% at r 6a 0. As will be shown below, the latter S component has a decisive influence on the dipole moments for radiative transitions between ungerade ion-pair states and X0 g. The calculated spectroscopic constants of the X state show a clear underestimation of its bonding character. In particular, the dissociation energy D e of the computed potential is too small 2.11 ev and its equilibrium internuclear distance is too large 2.03 Å compared with the experimental values: D exp e ev and r exp e Å. 31,32 The problematics of obtaining an accurate description of the molecular properties of halogen ground states, specifically in the case of Cl 2, has been discussed in detail in numerous studies In particular, it has been demonstrated that a very important condition for accurate calculations is a sufficiently large basis set including polarization functions with higher angular momentum up to g functions. The level of correlation treatment is also of special importance for the Cl 2 closed-shell ground state. For this reason, the inclusion of triple and higher excitations might be necessary to obtain high accuracy in such calculations. In the present work, this correlation energy can be accounted for by increasing of the Cl reference space and by lowering the energy threshold in the configuration selection procedure. Our test calculations have shown that an extended basis set one d and one f function in addition to the original set and a lower-energy selection threshold (T 0.05 E h ) increase the dissociation energy value to D e 2.41 ev. Unfortunately, such an enlargement of the configuration function space and AO basis set would not allow us to include higher roots in the calculations, in particular, those roots corresponding to the ion-pair states that are of special interest in the present study. On the other hand, one can expect that the lack of accuracy in describing the bonding of the ground state does not affect the quality of excited and especially ion-pair states to the same extent. Moreover, the main effects of the deviations of the theoretical potential from the experimental one are usually observed for high vibrational levels near the dissociation

4 J. Chem. Phys., Vol. 115, No. 20, 22 November 2001 Ion-pair states of Cl FIG. 3. Calculated potential energy curves for the valence and low-lying ion-pair gerade states. FIG. 4. Calculated potential energy curves for the valence and low-lying ion-pair ungerade states. limit, whereas only the rather low vibrational levels of the ion-pair states will be of major interest in the present work. 2. Excited valence states The lowest excited -S state, 1 3 u, as well as its singlet counterpart, 1 1 u, arises from the g u excitation in the Franck Condon region. With increasing internuclear distance, their dominant configuration, g 2 u 4 g 3 u 1, is replaced by one of higher energy, g 1 u 3 g 4 u 2. The latter becomes dominant in both S states at large r 59% at r 6a 0. After inclusion of the spin orbit interaction, 1 3 u splits into four components: 2 u, 1 u, 0 u ( 2 P 3/2 2 P 3/2 ), 0 u ( 2 P 1/2 2 P 3/2 ), while 1 u generates one state, 1 u ( 2 P 3/2 2 P 3/2 ). All these states retain their single-component S character almost up to the dissociation limit. The computed potential curves of the states arising from 1 3 u are bound by ev. The difference in the dissociation energies of 2 u, 1 u, 0 u ( 2 P 3/2 2 P 3/2 ) is about the magnitude of the spin orbit matrix element 322 cm 1 at r 4.5a 0. The B0 u (1 3 u ) state correlates with the higher dissociation limit ( 2 P 1/2 2 P 3/2 ) and thus has the largest D e value. The resulting dissociation energy of the B state is 0.23 ev (D e exp 0.41 ev). 32,37 It should be noted that a similar underestimation of bonding 0.18 ev is observed for all states arising from 1 3 u, since the accuracy of the bonding description is solely determined by the accuracy of the calculations at the S level. Similarly as for the X state calculations, both AO basis and configuration space extension are needed for a correct description of these dissociation energies. It should be noted, however, that the underestimation in the D e value for the B state is smaller than that for the X state 0.18 versus ev. Corresponding states of g symmetry, 1 1,3 g ( 2 g 3 u 4 g u ), result from u u excitations, which causes them to be of higher energy than the states of u symmetry. In addition, an admixture of 1 g 4 u 3 g 2 u character 54% at r 6a 0 appears at large internuclear distances, where both states are repulsive. After inclusion of the spin orbit interaction 3 g splits into four states: 2 g,1 g,0 g,0 g, whereby three of them, 2 g,1 g, and 0 g, correlate with the ground state atomic limit ( 2 P 3/2 2 P 3/2 ) and 0 g and 1 g (1 1 g ) correlate with the next dissociation limit ( 2 P 1/2 2 P 3/2 ). It is worth noting that the original diabatic curve of the 0 g ( 3 g ) state does correlate with ( 2 P 1/2 2 P 3/2 ), but it undergoes a crossing at r 5.8a 0 with the 0 g (1 3 g ) state that lies higher in the Franck Condon region and correlates with the lower dissociation limit ( 2 P 3/2 2 P 3/2 ). Finally, both states together form adiabatic potential energy curves of the 0 g (II)( 2 P 3/2 2 P 3/2 ) and 0 g (III)( 2 P 1/2 2 P 3/2 ) states, which therefore exchange their S character at r 5.8a 0. We shall use Roman numerals below to designate states within each symmetry, starting from the lowest one and omitting a number if the corresponding dissociation limit is given or a letter notation is available. The present calculations also show that some admixture of the 2 1 g state appears starting from r 5a 0, and its contribution competes with that of the 1 3 g component at intermediate internuclear distances in the 0 g (III) state and then, at r 5.8a 0,in the 0 g (IV) state. Thus, at large internuclear distances, both

5 9302 J. Chem. Phys., Vol. 115, No. 20, 22 November 2001 Kokh, Alekseyev, and Buenker the 2 1 g and 1 3 g states participate with comparable weights in 0 g (II) and 0 g (IV). Dominant electronic configurations of the following high-lying valence states in the Franck Condon region are g 1 u 4 g 4 u u, 2 g 4 u 2 g 2 u, 2 g 2 u 4 g 2 u 1 3 g,1 1 g,2 g, and 2 g 3 u 3 g 2 u 1 1 u,1 3 u,2 3 u. An admixture of the 2 g 2 u 4 g 2 u configuration reaches 40% for the 1 1 g,2 1 g,1 3 g states at r 6a 0. Diabatic 0 u components of the 1 3 u and 1 1 u intersect at r 5.5a 0 and together give rise to the 0 u (III)( 2 P 3/2 2 P 1/2 ) and 0 u (IV)( 2 P 1/2 2 P 1/2 ) adiabatic states of mixed S character. All other states show no significant changes in S composition relative to that given above for the Franck Condon region. B. Ion-pair states Ion-pair and Rydberg states of Cl 2 lie at 7.2 ev above the ground state. Ion-pair potential curves have significantly larger equilibrium distances typically r e ip 5.5a 0 and thereby cross Rydberg states typically r e Ry 3.8a 0, generally near a 0 see Figs This leads to multiple avoided crossings between ion-pair and Rydberg states of the same symmetry and to the formation of double-minimum potential curves. At r 4.5a 0, potential curves lying in the energy interval of ev belong to pure ion-pair states dissociating into Cl ( 3 P, 1 D) Cl ( 1 S) and, since these states are of major interest in the present study, we shall consider only this region of internuclear distances. The lowest ionic dissociation limit, Cl ( 3 P) Cl ( 1 S), gives rise to four triplet states: 1 3 g, 2 3 u, 2 3 u/g, and the next one, Cl ( 1 D) Cl ( 1 S), to six singlet states: 3 1 g, 1 1 u,2 1 u/g,2 1 g,1 1 u. We shall subsequently refer to these two groups of ion-pair states as first and second tiers, respectively. The energy gap between these two dissociation limits is rather large, cm 1 Ref cm 1 in our calculations, but the difference between T e values of the states of different tiers is smaller and S states of both tiers may even be mixed through spin orbit coupling, as will be discussed below. The next ionic dissociation limit, Cl ( 1 S) Cl ( 1 S), lying cm 1 above Cl ( 3 P) Cl ( 1 S), produces 1 g and 1 u states. According to the calculations of Ref. 19, these states remain significantly higher than those of the first two tiers for the entire range of internuclear distance and, therefore, they have not been included in the present calculations. 1. Electronic structure of -S states The lowest ion-pair state is gerade, 2 3 g ( 3 P)( 1 g 4 u 3 g 2 u ), whereas the corresponding ungerade counterpart, 2 3 u ( 3 P)( 1 g 3 u 4 g 2 u ) lies slightly higher in the Franck Condon region (r ip e a 0 ). The electronic configurations given above are also dominant in the singlet 2 1 u/g states correlating with the next Cl ( 1 D) dissociation limit. It should be mentioned that the n/ p occupation of the 2 n u 2 p g orbitals is obviously different for the g- and u-symmetry manifolds of both the valence and the ionpair states. This results in an inverted position of the gerade and ungerade states in the ion-pair manifold relative to that of the valence states. Specifically, a more stable configuration with the occupied bonding 4 u configuration gives rise to the u-symmetry valence states, 1 1,3 u ( 2 g 4 u 3 g 1 u ), and the g-symmetry ion-pair states, 2 1,3 g ( 1 g 4 u 3 g 2 u ), which are therefore found to be the lowest-lying among the valence and ion-pair groups, respectively. At larger internuclear distances, r 5.5a 0, a significant admixture of the 2 g 4 u 3 1 g u and 2 g 3 u 4 g 1 u electronic configurations appears, respectively, in the ion-pair 2 1,3 u and 2 1,3 g states. This leads to some lowering of the u-symmetry potentials relative to their g-symmetry counterparts with increasing internuclear distance, until they become degenerate at the dissociation limit. On the basis of the leading electronic configurations, one can separate most of the other ion-pair states correlating with Cl ( 3 P, 1 D) into two groups as follows: 2 3 g ( 3 P), 2 1 g ( 1 D)( 2 g 2 u 4 g 2 u, 2 g 4 u 2 g 2 u ) and 1 3 u, 1 1 u ( 2 g 3 u 3 g 2 u ). The former one has a dominant 2 g 2 u 4 g 2 u configuration at small and intermediate r, with an admixture of the lower-energy 2 g 4 u 2 g 2 u configuration at large r, so that at r 7a 0 both configurations give almost equal contributions. Potential curves of the and 3 1 g 1 D g 0 u 4 g 4 u 2, g 2 u 4 g 4 u u 1 D g 1 u 4 g 4 u 1 states exhibit behavior that differs significantly from that of the other ion-pair states of the first and second tiers see Fig. 5. Indeed, 3 1 g is the only ion-pair state with an empty g shell in its leading electronic configuration, resulting in the highest excitation energy at small r corresponding to the repulsive limb of the potential. At large internuclear distances, by contrast the lowest configuration, g 2 u 4 g 4 u 0, admixes and produces a rather flat attractive limb of the 3 1 g potential. As a result, the 3 1 g state has the largest equilibrium internuclear distance, r e 6a 0, among all ion-pair states of the first and second tier. On the contrary, the 1 1 u ( g 1 u 4 g 4 u 1 ) state has a relatively small equilibrium distance, r e 5a 0, since its dominant electronic configuration possesses the lowest energy among all ion-pair states at small and intermediate internuclear distances both g and u orbitals are occupied. One can see from the electronic structure of the -S states described above that, except for 3 1 g, all gerade states acquire approximately equal contributions from the low-energy electronic configurations with increasing r. As a result, to a large extent gerade states within each tier run parallel to one another at internuclear distances greater than 4.6a 0. States of u symmetry, by contrast, either have a sufficiently large admixture of low-energy electronic configurations with increasing r, as for 2 3 u, or they exhibit only

6 J. Chem. Phys., Vol. 115, No. 20, 22 November 2001 Ion-pair states of Cl FIG. 5. Calculated S potential energy curves without spin orbit coupling for the lowest ion-pair states. FIG. 6. Calculated potential curves with spin orbit coupling for the gerade ion-pair states. one dominant configuration at all r (1 3 u,1 1 u ). This behavior causes several crossings within the manifold of ungerade-states and also between gerade and ungerade states see Fig. 5. The crossing between 1 3 u and 2 3 u at r 5.9a 0 is of special importance since it leads to a mixing of -S character in the adiabatic states of 0 u and 1 u symmetries when spin orbit coupling is taken into account. 2. states of gerade symmetry After including the spin orbit interaction in the theoretical treatment, gerade states of the lowest ionic limit, 2 3 g ( 3 P) and 2 3 g ( 3 P), split, respectively, into 2 g ( 3 P 2 ) 1 g ( 3 P 2 ) 0 g ( 3 P 1 ) 0 g ( 3 P 2 ) and 0 g ( 3 P 0 ) 1 g ( 3 P 1 ). Potential curves for the resultant states are shown in Fig. 6. Since the energy gap between the 2 3 g ( 3 P) and 2 3 g ( 3 P) potentials is large in comparison with the spin orbit coupling constant, all the gerade states retain their single-component -S character. The following letter notation is usually employed in experimental studies for these states: D 2 g ( 3 P 2 ), E0 g ( 3 P 2 ), f 0 g ( 3 P 0 ), 1 g ( 3 P 2 ), and G1 g ( 3 P 1 ). Spectroscopic properties of gerade states in the first tier have been determined experimentally The main spectroscopic constants (T e,r e, e ) are given in Table III, together with the present theoretical results. As can be expected, states of the same S origin have almost equal equilibrium distances and vibrational quanta, which is also confirmed by the present calculations. Theoretical values for r e and T e are in very good agreement with experimental results, whereby even the absolute value of T e has only a small discrepancy for states arising from either the 2 3 g or 2 3 g S states 200 and 100 cm 1, respectively. One can also see from Table III that experimental splittings within both triplets are reproduced with an accuracy of better than 20 cm 1 in all cases. The discrepancies for the vibrational quanta are relatively large 8 13 cm 1, however. For a visual comparison of the calculated and experimental potentials, RKR curves of the f0 g and E0 g states are plotted in Fig. 7, along with the ab initio data. The main distinctions occur for the repulsive limbs. One can see that both theoretical potentials are too steep compared with the RKR curves, an effect that is caused mainly by the frozen core approximation ECP employed in the calculations. On the contrary, the attractive limbs of the computed potentials lie slightly lower than the experimental curves, but this effect is less pronounced. This results in some overestimation of the vibrational quanta and r e values in the present theoretical treatment. Gerade states correlating with the next Cl ( 1 D) Cl ( 1 S) dissociation limit give rise to states of three different symmetries, 2 g ( 1 g ), 1 g ( 1 g ), 0 g ( 1 g ), each of them thereby having only one dominant S component. The 1 g ( 1 D) state, v 0 6 has been studied experimentally by Ishiwata et al. 13 Some molecular parameters of the 0 g ( 1 D) state have also been estimated in the same study from the analysis of the 0 g ( 1 D) 1 g ( 1 D) heterogeneous coupling. As can be expected, T e values for these states are overestimated in the present study in comparison with those originating from 2 3 g and 2 3 g by cm 1, since correlation effects are usually better described for triplet states than for singlets. On the other hand, r e and e

7 9304 J. Chem. Phys., Vol. 115, No. 20, 22 November 2001 Kokh, Alekseyev, and Buenker TABLE III. Spectroscopic constants of the ion-pair states correlating with Cl ( 3 P, 1 D) Cl ( 1 S). a T e /cm 1 r e /Å e /cm 1 State Calc. Expt. Calc. Expt. Calc. Expt. D 2 g ( 3 P 2 ) b g ( 3 P 2 ) c (v 0 20) E0 g ( 3 P 2 ) d (v 0 23) 0 g ( 3 P 1 ) e (v 0 15) G1 g ( 3 P 1 ) b (v 0 14) f0 g ( 3 P 0 ) b (v 0 15) 0 g ( 1 D) f (v 0 50) 1 g ( 1 D) f (v 0 6) 2 g ( 1 D) u ( 3 P 2 ) g (v 0 4) 1 u ( 3 P 2 ) g (v 0 3) D0 u ( 3 P 2 ) g (v 0 3) 0 u ( 3 P 1 ) h (v 0 3) 1 u ( 3 P 1 ) h (v 0 3) 0 u ( 3 P 0 ) i (v 0 6) 0 u ( 1 D) g,j (v 40) 1 u ( 1 D) u ( 1 D) a Experimental constants are taken from the following. b Reference 11. c Reference 10. d Reference 7. e Reference 9. f Reference 13. g Reference 14. h Reference 16. i Reference 15. j Reference 20. FIG. 7. Calculated solid line and RKR points potential curves of the 0 g states correlating with Cl ( 3 P 0,2 ) Cl ( 1 S). values are in very good agreement with the experimental data see Table III. It should also be mentioned that some g-symmetry states may be perturbed because of nonzero off-diagonal elements in the rotational Hamiltonian, so-called heterogeneous interactions with the selection rule, 1. In the pure separated atom basis the interacting states should have the same dissociation limit. Indeed, strong heterogeneous perturbations have been observed experimentally, for example, for the pair of vibrational levels 1 g ( 3 P 2 ), v 2 E0 g ( 3 P 2 ), v Such an interaction has a local character since the overlap of vibrational functions between levels having v 1 is almost negligible. Longer-range perturbations arising from both 1 g ( 3 P 2 ) E0 g ( 3 P 2 ) and 1 g ( 3 P 2 ) D 2 g ( 3 P 2 ) coupling also have some influence on the rotational constants, although these effects are weaker. It has been shown experimentally, however, that some experimental results, namely doubling, cannot be explained in the framework of the pure precession approximation. 10 It means that weak heterogeneous interactions between states having different with a selection rule of 1, for example, between f0 g ( 3 g ) and 1 g ( 3 g ) and between G1 g ( 3 g ) and E0 g ( 3 g ), should occur as well. 3. states of ungerade symmetry As has been mentioned above, the 1 3 u ( 3 P) and 2 3 u ( 3 P) potential curves intersect at r 6a 0. Moreover, the 3 1 u ( 1 D) undergoes a crossing with both 1 3 u ( 3 P) and 2 3 u ( 3 P) at r 4.3a 0 and r 4.85a 0, respectively. Thus, all three of the aforementioned -S states participate in the formation of the 0 u ( 3 P 2 ), 0 u ( 3 P 0 ), 0 u ( 1 D) potential curves, and the 2 3 u and 2 3 u states together give rise to the 1 u ( 3 P 2 ) and 1 u ( 3 P 1 ) adiabatic states Fig. 8. Inthe experimental studies the following letter notation has been proposed: 0 u ( 3 P 2 ), 1 u ( 3 P 2 ), and 0 u ( 3 P 0 ). However,

8 J. Chem. Phys., Vol. 115, No. 20, 22 November 2001 Ion-pair states of Cl FIG. 9. Calculated solid line and RKR points Refs. 15 and 16 potential curves of the 0 u ( 3 P 0 ) and 0 u ( 3 P 1 ) states. FIG. 8. Calculated potential curves with spin orbit coupling for the ungerade ion-pair states. strong mixing between these states makes such assignments rather ambiguous. 3,14,17 In the present calculations we treat the adiabatic curves and, therefore, the total atomic angular momentum of Cl at the dissociation limit seems to provide a more appropriate notation and will be used below to identify the ungerade states. Only the 2 u ( 3 P 2 ) and 0 u ( 3 P 1 ) states are composed solely of 2 3 u since they are unique in the 2 u and 0 u manifolds, except for the 2 u ( 1 D) state, which lies significantly higher and has no influence on 2 u ( 3 P 2 ). Potential curves of the 2 u ( 3 P 2 ) and 0 u ( 3 P 1 ) states have almost equal equilibrium distances and vibrational quanta see Table III. Ithas also been observed experimentally 16 that the 2 u ( 3 P 2 ) and 0 u ( 3 P 1 ) states are mixed heterogeneously with the 1 u ( 3 P 2 ) and 1 u ( 3 P 1 ) states, respectively. In order to extract an RKR potential for the 0 u ( 3 P 1 ) state from the experimental spectroscopic data, a diagonalization procedure has been employed in Ref. 16 off-diagonal terms include rotational coupling with the 1 u ( 3 P 1 ) state. The resulting RKR potential is given in Fig. 9, together with the theoretical curve. There is a rather small distinction in the shapes of the potential curves, as can be seen from the r e and e values as well Table III. The 0 u,1 u ( 3 P 2 ) states have an almost pure 2 3 u character up to the crossing point at r 6.0a 0, whereas the 1 u ( 3 P 1 ) state and the 0 u ( 3 P 0 ) state at energies cm 1 have a dominant 2 3 u character in the same range of internuclear distance. At r 6a 0 the potential curves of the 1 3 u and 2 3 u states lie rather close to each other the energy gap is about 500 cm 1, leading to comparable contributions of both S components in the resulting states. In particular, the lowest 0 u ( 3 P 2 ) state, which is 96% 2 3 u at r 5.3a 0, becomes predominantly 2 3 u at r 6a 0, although it still has a 34% 2 3 u component, even at r 7a 0. The same holds for the 1 u ( 3 P 2 ) 1 u ( 3 P 1 ) pair. At higher energy, the 3 1 u state becomes heavily involved in the formation of the 0 u ( 3 P 2 ), 0 u ( 3 P 0 ), and 0 u ( 1 D) states as well. This leads to the appearance of a shoulder on the repulsive branch of the 0 u ( 3 P 2 ) and 0 u ( 3 P 0 ) potential curves at r 4.3a 0 and 4.8a 0, respectively; see Figs. 4 and 8 and to the formation of a steep repulsive branch of 2 3 u character in the 0 u ( 1 D) state. It should be emphasized that as a result vibrational levels of these 0 u,1 u states cannot be described properly by the usual Dunham series, so that the vibrational frequencies given in Table III are averaged values. One can expect that since the computed adiabatic 0 u ( 3 P 2,0 ) and 1 u ( 3 P 2,1 ) states change their S character, the derivatives of their electronic wave functions with respect to r should be nonzero near the crossing of the original diabatic curves, and, therefore, that these adiabatic states should be mixed via radial coupling. Such effects must have some influence on the vibrational energies and wave functions of the states involved in such interactions. Indeed, anomalous behavior of the vibrational energies, which is evidence of strong homogeneous mixing, has been observed experimentally for the 0 u ( 3 P 0,), 0 u ( 3 P 2 ), 1 u ( 3 P 2 ), and 0 u ( 1 D) states. 14,15 In particular, several pairs of locally perturbed levels have been found: 0 u ( 3 P 0 ),v 1 0 u ( 3 P 2 ),v 8, 0 u ( 3 P 0 ),v 5 0 u ( 3 P 2 ),v 13, 0 u ( 3 P 0 ),v 9 0 u ( 3 P 2 ),v 18, 0 u ( 3 P 0 ),v 15 0 u ( 3 P 2 ),v The situation becomes more complicated, however, because of the heterogeneous coupling of the 0 u ( 3 P 2 ), 1 u ( 3 P 2 ), and 2 u ( 3 P 2 ) states. All these perturbations preclude a straightforward derivation of the RKR curves from the experimental spectroscopic data. An attempt to carry out a deperturbation analysis for the low vibrational

9 9306 J. Chem. Phys., Vol. 115, No. 20, 22 November 2001 Kokh, Alekseyev, and Buenker levels of 0 u ( 3 P 0 ) has been made in Ref. 15, however. Only a homogeneous interaction between the 0 u ( 3 P 0 ) and 0 u ( 3 P 2 ) states and indirectly a 0 u ( 3 P 2 ) 1 u ( 3 P 2 ) heterogeneous interaction have been accounted for in this case. By eliminating the local homogeneous and heterogeneous interactions, the low vibrational levels up to v 6 of the 0 u ( 3 P 0 ) state have been described by a Dunham series and even a type of RKR potential has been constructed for these levels. It is worth noting that the experimental RKR curve and the present calculated adiabatic potentials are in reasonably good agreement Fig. 9. Spectroscopic constants, namely T e, r e, and e, estimated from the experimental data for most of the ungerade 3 P J states are summarized in Table III. The 0 u, 1 u states correlating with the lowest ionic dissociation limit have smaller r e and e values than those with higher dissociation limits, 0 u ( 3 P 0 ) and 1 u ( 3 P 1 ). Furthermore, states that have the same S character, such as the 0 u ( 3 P 2 ) 1 u ( 3 P 2 ), and 0 u ( 3 P 0 ) 1 u ( 3 P 1 ) pairs, also have very similar r e and e values. It can be seen that the agreement between theoretical and experimental T e values is fairly good, with discrepancies not exceeding cm 1, and this is consistent with the accuracy of the ab initio curves for the homogeneously unperturbed gerade states. Theoretical values for equilibrium internuclear distances are also in quite good accord with the experimental data. Experimental and theoretical values for vibrational quanta are in quite good agreement errors less than 12 cm 1, except for the 0 u ( 3 P 0 ) and 1 u ( 3 P 1 ) states. It should be mentioned in this context that the experimentally observed vibrational levels for the 1 u ( 3 P 1 ) state are quite irregular, a clear indication of strong homogeneous perturbations from the near-lying levels of the 1 u ( 3 P 2 ) state. The energy separation between v 0 3 neighboring vibrational levels the only ones that have been observed in experiment are 293, 307, and 274 cm Therefore, it seems very likely that the vibrational quantum for the 1 u ( 3 P 1 ) state derived from these spectroscopic data ( e 312 cm 1 ) is overestimated. This conclusion is supported by the smaller e value for the 0 u ( 3 P 0 ) state 284 cm 1 obtained from the deperturbation analysis, since it agrees better with the calculated value of 255 cm 1. The underestimation of the computed e values for the homogeneously unperturbed 0 u ( 3 P 1 ) and 2 u ( 3 P 2 ) states is also quite surprising since some overestimation should be expected by analogy with the gerade states. On the other hand, the RKR potential of the homogeneously unperturbed 0 u ( 3 P 1 ) state Fig. 9 demonstrates that such discrepancies do not significantly exceed the analogous differences for the gerade state. Among states correlating with the next dissociation limit, only 1 u ( 1 D) has been observed experimentally since it can be populated in direct excitation from the X0 g state ,38 As has been described above, an avoided crossing between the 2 3 u and 1 1 u states near the latter s potential minimum leads to the formation of the adiabatic 0 u ( 3 P 0 ) and 0 u ( 1 D) potential curves. Thus, the attractive branch of 0 u ( 1 D) corresponds to an almost pure 1 1 u state, whereas the repulsive part has a dominant 3 u character. One can expect that strong radial coupling between the 0 u ( 1 D), 0 u ( 3 P 0 ), and 0 u ( 3 P 2 ) states should occur and therefore cause notable distortions in the emission spectra similar to those that take place for the ion-pair states of ClF. 39 In terms of the adiabatic approximation, this implies that vibrational energies are irregular as has been observed experimentally 14,38 and emission spectra, even from the low vibrational levels of the 0 u ( 1 D) state will borrow shortwavelength intensity corresponding to transitions at small internuclear distances from the near-lying vibrational levels of the 0 u ( 3 P 0 ) state higher vibrational levels of the 0 u ( 1 D) state may also be mixed with those of the 0 u ( 3 P 2 ) state. Since the 1 1 u 1 1 g transition is dominant in emission from all three 0 u upper states to the X state, we can also expect that nonadiabatically mixed 0 u ( 1 D) and 0 u ( 3 P 0 ), 0 u ( 3 P 2 ) states will produce emission spectra that are similar to those originating from the diabatic curve of the ion-pair 1 1 g state. Indeed, the theoretical value of e 370 cm 1 is much larger than the experimental one, e cm 1, which has been obtained from an analysis of the emission spectra from several excited vibrational levels (v 39 40). On the other hand, the experimental e value is close to that of the ab initio 1 1 u state 260 cm 1. This implies, therefore, that the diabatic S basis is actually more appropriate for an analysis of the strongly nonadiabatically perturbed 0 u ( 1 D) state and that we should refer to it as 1 1 u ( 1 D) rather than 0 u ( 1 D) in discussing its radiative properties. Furthermore, there are several experimental T e values varying from cm 1 Ref. 20 to cm 1 Ref. 14 the theoretical value is cm 1. Since some overestimation of the energy of the singlet states relative to triplets can be expected, a discrepancy between the theoretical and experimental T e values about 1000 cm 1 seems quite reasonable. Higher-lying 2 u ( 1 D) and 1 u ( 1 D) states, correlating to the next dissociation limit, are spanned by the 2 1 u and 1 1 u parents, respectively. Their spectroscopic constants are also given in Table III, but to our knowledge there are no experimental data for these states. Both are singlets and, therefore, one can expect that their T e values are overestimated up to 800 cm 1, similar to the singlet gerade states. IV. TRANSITION DIPOLE MOMENTS, EMISSION SPECTRA, AND LIFETIMES OF THE LOW-LYING ION- PAIR STATES A. States of g symmetry correlating with Cl 3 P 0,1,2 As has been discussed above, each gerade ion-pair state of the first tier is spanned by a single -S parent. This simplifies the structure of radiative transitions from these states. In particular, the strongest transitions from the lowest gerade ion-pair states, originating from the 2 3 g state E0 g, 1 g,0 g ( 3 P 1 ),D 2 g, occur to the corresponding components of the valence 1 3 u state B0 u,a1 u,b0 u,a 2 u, as may be seen in Figs. 10 and 11. Dipole moments for transitions to other valence states as 1 u (II V), 0 u (II IV), and 2 u (II) are very small and increase smoothly with an internuclear distance up to r 7a 0, also owing to the 1 3 u admixture that appears in

10 J. Chem. Phys., Vol. 115, No. 20, 22 November 2001 Ion-pair states of Cl FIG. 10. Calculated dipole transition moments connecting the E0 g ( 3 P 2 ), 1 g ( 3 P 2 ) states and low-lying valence states and the experimental dipole moment function for the E0 g B0 u transition Ref. 24. FIG. 11. Calculated dipole transition moments connecting the 0 g ( 3 P 1 ), 2 g ( 3 P 2 ) states and low-lying valence states. FIG. 12. Calculated dipole transition moments connecting the f0 g ( 3 P 0 ), G1 g ( 3 P 1 ) states with low-lying valence states. valence states at large r. Sharp changes in the behavior of the dipole moment functions of the 0 g ( 3 P 1 ) 0 u (II) and 0 g ( 3 P 1 ) 0 u (III) transitions at 5.5a 0 are caused by the interchange of 3 u and 1 u character in the valence 0 u (II III) states. The only dipole moment function determined experimentally, namely for the E0 g B0 u transition, 23 agrees quite well with that calculated see Fig. 10. The dipole transition moments from the f0 g and G1 g states Fig. 12 that originate from 2 3 g are smaller than those for states with 2 3 g character, since there is no valence S state that can cause parallel transitions to the 3 g state with intensities comparable to that of the 2 3 g 1 3 u transition. The largest dipole moments corresponding to f 0 u (1 3 u ) and G 1 u (1 3 u ) are produced by a small admixture of 2 3 g to the upper states 8% and 6% for the f and G states, respectively, at r 5.5a 0. Experimental radiative lifetimes taken from Ref. 12 and calculated from the present dipole moment functions for the gerade states (v 0) are summarized in Table IV. Except for the f and G states, all computed lifetimes are in excellent agreement with the experimental data. Unlike other gerade states, the f and G species have relatively long radiative lifetimes, which have been found to be comparable to the nonradiative lifetimes due to collision-induced processes under the experimental conditions of Ref. 12. Since radiative lifetimes calculated for both the G1 g and f0 g states are somewhat larger than the experimental values see Table IV, one can speculate that this discrepancy may at least partly be caused by an underestimation of the collision rate constants in the experimental study. 12 This problem deserves some special analysis. B. States of u symmetry correlating with Cl 3 P 0,1,2 and the 1 u 1 D state Computed dipole moment functions for parallel transitions from the ungerade ion-pair states correlating with Cl ( 3 P J ) are given in Figs Emission spectra for two upper ungerade states have been studied experimentally, namely for 0 u ( 3 P 2 )(v 1,2,3) 24 and 1 u ( 1 D) (v 30) 20,38 a letter notation D has been introduced for the 0 u ( 3 P 2 ) state in Ref. 24 and we shall use it below. In TABLE IV. Radiative lifetimes of the ion-pair states correlating with Cl ( 3 P, 1 D) Cl ( 1 S), v 0. State Calc. /ns Exp. D 2 g ( 3 P 2 ) a 1 g ( 3 P 2 ) a E0 g ( 3 P 2 ) a 0 g ( 3 P 1 ) a G1 g ( 3 P 1 ) a f0 g ( 3 P 0 ) a 2 u ( 3 P 2 ) 15 D0 u ( 3 P 2 ) 27 1 u ( 3 P 2 ) u ( 3 P 2 ) 16 1 u ( 3 P 1 ) 17 b 0 u ( 3 P 0 ) 18.7 b 14.0 e 1 u ( 1 D) c, 2.11 d a Reference 13. b Radiative lifetime obtained in the adiabatic approximation; after including nonadiabatic effects, this value should increase for the vibrational levels participating in nonadiabatic interactions see the text. c Reference 21. d Reference 22 is averaged over v e Reference 4.

11 9308 J. Chem. Phys., Vol. 115, No. 20, 22 November 2001 Kokh, Alekseyev, and Buenker FIG. 13. Calculated dipole transition moments connecting the D0 u ( 3 P 2 ), 1 u ( 3 P 2 ) states with low-lying valence states. FIG. 15. Calculated dipole transition moments connecting the 0 u ( 3 P 1 ), 2 u ( 3 P 2 ) states with low-lying valence states. Ref. 24, dipole moment functions for all parallel transitions from the D state and potential curves for three 0 g repulsive valence states have been obtained from the analysis of emission spectra. Since the interpretation of the resulting dipole moments and the assignment of the observed lower valence states encountered some difficulties, we shall consider these results more thoroughly on the basis of the theoretical data obtained in the present study. As one can see from Fig. 16, experimental and ab initio D0 u ( 3 P 2 ) X transition moments are in quite good agreement. Their increase at large internuclear distances results from some admixture of the 3 g to the X0 g state. In addition to the X state, there are three repulsive 0 g valence states that correlate with the three possible dissociation limits, 0 g (II)( 2 P 3/2 2 P 3/2 ), 0 g (III)( 2 P 3/2 2 P 1/2 ) and 0 g (IV) ( 2 P 1/2 2 P 1/2 ). Corresponding experimental and calculated dipole moments for transitions from the D state are shown in Fig. 17 by solid and dotted lines, respectively. Only the function for the D 0 g (IV) transition is in good agreement with experimental results. The 0 g (IV) state is derived mainly from 1 g, but has some admixture of 3 g whose contribution increases with r and causes the increase in the dipole moment function. The shapes of the experimental dipole moments for the D 0 g (II) and D 0 g (III) transitions and their relative values differ significantly from our results. In particular, in the experimental study the most intense transition has been assigned to the valence state correlating with the lowest dissociation limit, 0 g (II), whereas the D 0 g (III) emission is thought to have an almost negligible contribution to the total spectrum see Fig. 4 of Ref. 24. According to the present calculations Fig. 17, however, the most intense transition, at least at long wavelengths, should be D 0 g (III), whereas the D-0 g (II) emission is significantly weaker. This disagreement can most likely be attributed to the mixed -S character ( 3 g 3 g ) of the valence 0 g (II,III) states in the range of internuclear distances analyzed in the experimental study. This mixing results from an avoided crossing between the adiabatic 0 g (II) and 0 g (III) states near the internuclear distance corresponding to the right turning point (r 3.1 Å) of the upper vibrational levels observed in the experimental study. Moreover, since both lower states have very similar energies at this point, their contributions might be difficult to distinguish in the total emission spectrum. In order to examine this assumption, we calculated the sum of the two ab initio dipole moments for the D 0 g (II,III) transitions. The resulting curve is very similar in shape and relative intensity to the experimental dipole moment function assigned to D 0 g (II) in Ref. 24 see Fig. 17. Since the emission ascribed to the D 0 g (III) transition is of quite low intensity and therefore has only a minimal influence on the final spectrum, its elimination can neither significantly change the fitted total emis- FIG. 14. Calculated dipole transition moments connecting the 0 u ( 3 P 0 ), 1 u ( 3 P 1 ) states with low-lying valence states. FIG. 16. Calculated and experimental Ref. 23 dipole transition moments for the D0 u ( 3 P 2 ) X transition.

12 J. Chem. Phys., Vol. 115, No. 20, 22 November 2001 Ion-pair states of Cl FIG. 17. Calculated dashed lines and experimental Ref. 26 solid lines transition moments connecting D0 u ( 3 P 2 ) with repulsive valence states. sion spectrum nor the dipole moment functions and potential curves for the other two transitions derived in Ref. 24. Therefore, all results except for those regarding the 0 g (III) state and the assignment of the 0 g (II,III) states obtained in the experimental study are still valid. Dipole moment functions for transitions from the 0 u ( 3 P 0 ) state show more complicated behavior. In particular, the dipole moment of the 0 u ( 3 P 0 ) X transition is very large at small internuclear distances since the ion-pair state gains 1 u character in this region. At larger internuclear distances up to r 6a 0, the 0 u ( 3 P 0 ) state has a dominant 3 u component and at r 6a 0 has a mixed 3 u 3 u character. Since the 3 g 3 u transition is almost twice as strong as 3 u 3 g, a change of the S character ( 3 g / 3 g ) of the lower valence 0 g (II,III) states has a significantly stronger influence on the dipole moments of transitions from 0 u ( 3 P 0 ) Fig. 14 than from 0 u ( 3 P 2 ) Fig. 13 at r 6a 0. Specifically, the maximal, value of the 0 u ( 3 P 0 ) 0 g (II) dipole moment corresponds to an almost pure 3 g 3 u transition, whose intensity changes abruptly at the point of the avoided crossing of the valence states. A similar situation occurs for the 0 u ( 3 P 0 ) 0 g (III) transition. In the 1 u manifold, the dominant transitions at short and intermediate internuclear distances are 1 u ( 3 P 2 ) 1 u (III) and 1 u ( 3 P 1 ) 1 u (I,II), which correspond to transitions between the dominant -S components, 3 u 3 g and 3 u 3 g, respectively. At r 6a 0, the mixed -S character ( 3 g 3 u ) of the 1 u ( 3 P 2 ) and 1 u ( 3 P 1 ) states leads to some averaging of the magnitudes of the dipole moments. Furthermore, the 2 u ( 3 P 2 ) and 0 u ( 3 P 1 ) states have a single dominant 3 u S component, and, therefore, their transition moments Fig. 15 are quite similar to those of the gerade states. Calculated lifetimes for the ungerade ion-pair states (v 0) are given in Table IV. They correspond to the pure adiabatic approximation and, therefore, are strictly valid only for the nonadiabatically 2 u ( 3 P 2 ) and 0 u ( 3 P 1 ) unperturbed states and for low vibrational levels of the D0 u ( 3 P 2 ) and 1 u ( 3 P 2 ) states. For higher vibrational levels of the D0 u ( 3 P 2 ) and 1 u ( 3 P 2 ) states and for 0 u ( 3 P 0 ) 1 u ( 3 P 1 ), the actual radiative lifetimes should be averaged over those of homogeneously interacting vibrational levels as, for example, for D0 u ( 3 P 2 ), v 8 and 0 u ( 3 P 0 ), v 1. In general, the actual lifetimes of the perturbed vibrational levels of the 1 u ( 3 P 2 ) and D0 u ( 3 P 2 ) states should be smaller than shown in Table IV. A radiative lifetime has been measured experimentally for the 1 u ( 1 D) state 3.0 ns Ref. 21, 2.11 ns Ref. 22. As has been discussed above, the dominant transition in this case is 1 1 u 1 1 g, which gives a calculated lifetime of 1.2 ns for the 1 u ( 1 D) state. Considering that the actual value should be somewhat larger because of the interaction with other diabatic states ( 3 u, 3 u ), this result is in reasonably good agreement with the available experimental values 2.11 and 3.0 ns. A radiative lifetime of 14 ns reported in Ref. 4 probably corresponds and 0 u ( 3 P 0 ), v 0 state, and it agrees quite well with our calculated result 18.7 ns for this state. V. CONCLUSION Potential energy curves of the Cl 2 valence and ion-pair states Cl ( 3 P, 1 D) Cl ( 1 S) and dipole moment functions of the ion-pair valence transitions have been obtained in spin orbit CI calculations. The nature of the ion-pair states has been analyzed in the range of internuclear distances up to the crossing region between ion-pair and Rydberg states. It has been shown that gerade ion-pair states possess an almost pure single-component S character. The situation is different for the ungerade states, however. The S potential curves of ungerade ion-pair states correlating with Cl ( 3 P, 1 D) undergo several intersections that produce a mixed S character for the resultant adiabatic 0 u,1 u states. In particular, in the low-energy range the adiabatic 0 u ( 3 P 2 ) 0 u ( 3 P 0 ) and 1 u ( 3 P 2 ) 1 u ( 3 P 1 ) pairs of states have a mixed 3 u 3 u character. This fact makes nonadiabatic radial coupling quite important between states of the same symmetry, as has actually been observed in experiment via some irregularity in the vibrational energy spacings. 14 Nevertheless, calculated spectroscopic properties for all adiabatic states correlating with Cl ( 3 P J ) have been found to be in reasonably good agreement with the available experimental data. Furthermore, crossings between 1 u ( 1 D) and 3 u, 3 u ( 3 P) at higher energy lead to some distortions in the 0 u ( 3 P 2 ) and 0 u ( 3 P 0 ) potentials and to the formation of a very narrow adiabatic 0 u ( 1 D) potential with a vibrational quantum of about 370 cm 1, which is significantly larger than cm 1 determined experimentally. 14,20 It is noteworthy that the assignment of the vibrational levels in the experimental study has been made on the basis of an analysis of the emission spectra that is dominated by the most intense 1 u ( 1 D) X transition. Indeed, the experimental e value is very close to the vibrational quantum of the pure 1 u ( 1 D) state calculated in the present study, 260 cm 1. Therefore, a diabatic S potential for the 1 u ( 1 D)