THE JOURNAL OF CHEMICAL PHYSICS 126,

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1 THE JOURNAL OF CHEMICAL PHYSICS 126, Symmetry-adapted-cluster configuration interaction study of the doublet states of HCl + : Potential energy curves, dipole moments, and transition dipole moments Valerij S. Gurin Physico-Chemical Research Institute, Belarusian State University, Leningradskaya Street 14, Minsk, Belarus Mikhail V. Korolkov Institute of Physics, National Academy of Sciences, Independence Avenue 68, Minsk, Belarus Vitaly E. Matulis Physico-Chemical Research Institute, Belarusian State University, Leningradskaya Street 14, Minsk, Belarus Sergei K. Rakhmanov Belarusian State University, Independence Avenue 4, Minsk, Belarus Received 8 May 2006; accepted 25 January 2007; published online 30 March 2007 The electronic structure of the HCl + molecular ion has been calculated using the general-r symmetry-adapted-cluster configuration interaction SAC-CI method. The authors present the potential energy curves, dipole moments, and transition dipole moments for a series of doublet states. The data are compared with the previous CASSCF and MCSCF calculations. The SAC-CI results reproduce quite well the data available in literature and extend the knowledge on the HCl + electronic structure for several higher states. The calculated R-dependent behavior of both dipole moments and transition dipole moments for a series of bound and unbound states reveals an intricate dissociation process at intermediate distances R R e. The pronounced maxima in transition dipole moment TDM describing transitions into high electronic states X 2 3 2, X 2 3 2, , occur at different interatomic separations. Such TDM features are promising for selection of excitation pathways and, consequently, for an optimal control of the dissociation products American Institute of Physics. DOI: / I. INTRODUCTION During the last decade intensive studies of HCl molecule and HCl + ion were accomplished both experimentally 1 12 and theoretically The latter involves electronic structure calculations, spectroscopic applications, and laserdriving time-dependent processes, described by coupled Schrödinger equations as well as by semiclassical approach with hopping algorithm. 28 HCl + ion such as the classical examples H 2 and H + 2 Refs becomes a popular candidate for studies of ultrashort laser pulse control of its photochemical properties and dynamics There is a lot of information on HCl + from spectroscopy e.g., threshold photoelectron spectroscopy 2,4,5,9 11 and ab initio calculations However, even for this rather simple ion, so far there is no accurate theoretical description of the nonlinear excitation between the ground and a number of excited electronic states, and some approximations have been used to complete the data. For instance, the asymptotic behavior for dipole moments DMs and transition dipole moments TDMs has been used in Refs In the recent paper 23 it was shown that even higher electronic states at energy 5 ev can play an important role during the excitation process. In this context one of the aims of our paper is to provide the data on all necessary DMs and TDMs in the wide range of molecular bond distances. Electronic transitions at large interatomic separation can be most important for the states for which an increasing ionic bond length results in an increasing TDM. 26 We use here the advanced calculation method as compared with the previous calculations: the symmetry-adapted-cluster configuration interaction SAC-CI This method has been developed for calculations of ground and excited states of molecules and was successfully adopted for molecular spectroscopy purposes In particular, the HCl ionization spectrum has been reproduced quite successfully. 13 The SAC-CI approach includes an optimum cluster expansion to take into account configuration interaction CI due to a number of excited states, and selection of expansion terms based on symmetry provides both more physical insight and better convergence As compared with MCSCF approaches such as CASSCF, coupled-cluster singles and doubles, multireference singles and doubles configuration interaction etc., SAC-CI uses an optimized selection of the reference states to account CI of one- and multielectron excitations. We exploit the SAC-CI for our purposes because of the following features: i wide range of different electronic states are covered with the same accuracy; ii multielectron excited states can be described adequately; iii the energy gradient is calculated for any states for both one- and multielectron excited states; iv the /2007/ /124321/10/$ , American Institute of Physics

2 Gurin et al. J. Chem. Phys. 126, method is appropriate both for small molecules and for reliable calculations of large molecules. Thus, the purpose of the present work is twofold. i The SAC-CI calculation of a series of electronic doublet states of HCl + together with evaluation of DM and TDM as the most important characteristics for simulation of laser-induced dynamics and comparison with experiment. ii A comparative analysis with the data from Ref. 16, that is, most widely used during last decades for description of HCl + electronic structure. Our set of HCl + states provides more detailed data on the higher states. More data are derived also for DMs and TDMs. As compared with the treatment in Ref. 16, weuse the different calculation method that is more advanced and flexible to treat many excited states, therefore the comparison of different approaches was of great interest. The main properties of the electronic states of HCl + are described correctly within the framework of SAC-CI results. Furthermore, the results can be used for studies of the dissociation dynamics as well. The outline of the paper is as follows. Section II gives a brief description of the electronic structure calculation technique and evaluation of spectroscopic constants for the HCl + bound states. Section III A deals with the potential curves for the full set of states. In Sec. III B the calculation of spectroscopic constants is given. Sections III C and III D represent the calculated R dependencies of DMs and TDMs and Sec. IV summarizes the key points of the work. II. COMPUTATIONAL METHODS We used the SAC-CI method at the general-r level including R operators up to the third order, which takes into account the excitations up to states with S=2.5 for the ion under study. SAC-CI allows evaluation of molecular properties of interest for all states under consideration at the equal footing while many other advanced CI calculations sometimes have problems with convergence for excited states in large basis sets. For both atoms in the molecular ion HCl + we use the all-electron basis sets 6-311G with addition: for chlorine, two diffuse s and p functions with exponents s =0.06, and p =0.04, 0.01 and four d functions with d =0.7, 0.25, 0.08, and 0.02; for hydrogen, two p functions with p =1.0 and 0.3. This choice of basis was adopted from Ref. 13 where good consistence of calculations with experimental results has been shown for ionization spectrum of HCl. We have also performed additional calculations modifying this basis set by increasing the number of basis functions. This has not lead to any improvement in the results in comparison with known spectroscopic constants of HCl + see Table I. On the other hand, the simplification of the basis sets, e.g., down to 6-31G, leads to noticeable degradation of results. The parameterization of the basis with the above adjustable exponents adopted here means the optimization for calculations with these atoms at the ab initio level with CI starting from a widely used basis developed by McLean and Chandler. 43 A variation of the exponents could influence the results; however, the above values were shown to be the optimum for Cl and H atoms. 44 In Ref. 16 the other type of basis sets has been used Slater-type commonly acceptable years ago. More flexibility and extensive development of the modern Gaussian-type basis sets motivated our present choice. However, the similarity in results with both types of basis sets means the genuine feature of the ab initio calculations at the adequate level of CI treatment that should give basisinvariant results. 1s, 2s, and 2p atomic orbitals of Cl were used as frozen within the calculation step of Cl. Active space included the valence orbitals beginning from 3s- for Cl and 1s- for H, consisting of four occupied and 58 virtual orbitals. This choice of active orbitals is typical also for different molecules with 3p elements. All calculations were carried out with GAUSSIAN 03 software. 45 III. RESULTS AND DISCUSSION A. Potential curves A series of potential curves under consideration within the framework of our study includes five states of 2 symmetry, four states of 2 + symmetry, one 2, and two 2 states. They are the lowest energy states from the whole set of HCl + electronic states and are of utmost interest for simulation of the photodissociation from the ground state X 2. Three first states of 2 symmetry, three ones of 2 + symmetry, one 2, and one 2 states have been analyzed in Ref. 16 and partially the potential curves were given for 4 2 and states. The eight first states cover the lowest energy set corresponding to the dissociation limits with energy range not higher than 4 ev above the ground state. The next states are separated by the gap 5 ev, and we have restricted ourselves to several next states. The dissociation limits of this series of 12 states are given in Table II. The states located more than 4 ev higher than the ground one are of less importance for the photodissociation dynamics in the UV/vis range, but cannot be neglected and contribute also in multiphotonic processes. The potential curves calculated for 12 doublet states are presented in Figs. 1 and 2. A 2 + and X 2 states are bound in agreement with experimental data 10,11 and the calculations in Ref. 16 some states were calculated also in Refs and 17. The different dissociation limits of all states determined from the electronic configurations at large distances see Table II comprise two types of dissociation: one leading to ionized chlorine, H 0 +Cl +, and the other resulting in ionized hydrogen, H + +Cl 0. The first one with the lowest atomic state of Cl + 3 P corresponds to the decay of the ground state, X 2, and state. The higher atomic terms of Cl +, 1 D and 1 S, are resulted from the series of unbound states of different symmetries. The second type of dissociation is obtained from the bound A 2 + and 2 2 states. On the whole, this picture conforms to known data. 16,17,46 48 There is the difference in the energy values between 2 2 and A 2 + states 0.17 ev. These both have the limits H + +Cl 0 2 P, and energies of these states deviate from the spectroscopic data 0.26 ev for 2 2 against 0.41 ev in Ref. 16, Table II. Thus, the calculations are to be upgraded for the better agreement.

3 Doublet states of HCl + J. Chem. Phys. 126, TABLE I. Comparison of the calculated including the data of Table VIII of Ref. 16 and experimental spectroscopic constants for HCl + : dissociation energy D e, equilibrium distance R e, vertical transition energy X 2 A 2 +, T e, and vibrational constants e and e x e. The latter are given for both HCl + and DCl +. X 2 A 2 + Value Calc. Expt. Calc. a Calc. Expt. Calc. a D e ev b b c c 4.50 d 2.04 d 4.82 e R e a.u c c X 2 A 2 + T e ev c b d c HCl + e cm c c g h g e x e cm c c g 31.3 h 55.3 g e cm c c g h g DCl + e x e cm c c g 16.1 h 26.6 g a Reference 16. b Reference 39. c Reference 40. d Reference 41. e Reference 7. f Reference 42. g Two values from Ref. 11 are related to 2 3/2 and 2 1/2 states. h Reference ,5 2,4 2 +, and 2 2 states also appear in the second type of dissociation ionized hydrogen with neutral chlorine. These four curves are featured by the bound character at the slightly shorter 2 2 and longer 4 2,5 2, and H Cl bond and open a new series of states to be studied. Their dissociation limits are essentially higher than the previous series of states see Table II. Complete potential curves for and 2 2 states can be given in future by analysis of much more number of states because many crossings in the range R 8a 0 occur, and the exact energies of them depend on the number of states included in the CI procedure. Starting at the distance R 8 9a 0 the potential curves for all states exhibit the explicit asymptotic behavior, and the variations of energy along curves is negligible as compared with the binding energies of the states, i.e., at these distances the atoms are weakly interacting. The high fourth and fifth states reveal the worse asymptotics at these middle distances Figs. 1 and 2, however, an occurrence of both Frank- Condon region and asymptotic one is also quite evident for them. Another values under consideration in the paper, DMs and TDMs, still vary noticeably at these middle distances see Secs. III C and III D below. The collection of potential curves for the states shown in Figs. 1 and 2 are in good agreement with the data in Ref. 16, and even the feature for at R=3.0a 0 3.5a 0 is reproduced properly. The weak features for 2 2 +,3 2 +, 2, and 1 2 at R 4.5a 0 absent in the data of Refs. 16 and 48 in both studies the points have been calculated with a wider step not enough to note this weak feature in the curves. However, this nonmonotonous behavior of potential energy within the small interval is quite reproducible in our data and appear only for the unbound excited states of this series. This provides also the feature in the R dependences of DM see Sec. III C below. If to check the contributions of the basic functions into the leading electronic configurations for these

4 Gurin et al. J. Chem. Phys. 126, TABLE II. Calculated dissociation paths for 12 states of HCl +. State of HCl + Dissociation limits and their atomic terms Energy at R=20a 0. a.u. Experimental energy for states given in the column 2 ev a Calculated energy for states given in the column 2 ev b Calculated energy for states given in the column 2 ev X 2 H 0 2 S +Cl + 3 P H 0 2 S +Cl + 3 P H + +Cl 0 2 P c A 2 + H + +Cl 0 2 P c /0.97 d H 0 2 S +Cl + 1 D c 3 2 H 0 2 S +Cl + 1 D c /1.64 d 1 2 H 0 2 S +Cl + 1 D c H 0 2 S +Cl + 1 S c /3.31 d 5 2 H + +Cl 0 2 P /12.67 d 4 2 H + +Cl 0 2 D /14.50 d H + +Cl 0 2 S e 2 2 H + +Cl 0 2 P e /13.49 d H + +Cl 0 2 D e H + +Cl 0 2 S e H + +Cl 0 2 P e /12.67 d H + +Cl 0 2 D e a The zero level is assumed for H 0 2 S +Cl + 3 P Ref. 57. b This work. c Reference 16. d Reference 48, however, there are differences in assignment of the states see text. e The dissociation limits differed only by the terms of Cl 0 Ref. 58 are given in correspondence with close electronic configuration of our and 2 2 states 3s 2 3p 4 3 P 4p obtained at R=20a 0. states one can note that in the case of excited states p x,y,z functions producing outermost orbitals vary significantly between the points R=4.5a 0 and R=4.7a 0. In the series of 2 states in this region we observe avoiding crossing between 4 2 and 5 2 states see above. The potential curves for two lowest bound states are almost completely coincident in the Frank-Condon region, and the excited states have the difference less than 0.01 a.u. The deviations in the same range exist also for the asymptotic region of large R. This difference cannot be neglected under the comparison with reference spectroscopic data for the corresponding atomic states see Table II. A comparison of the calculated data for 4 2, 5 2, 4 2 +, and 2 2 states with the previous calculations 16,48 deserves special attention as far as they are much less studied to date for HCl + and more problematic for ab initio calculations. There is no good agreement with Refs. 16 and 48 in FIG. 1. Potential energy curves for a series of 2 states of HCl + solid lines in comparison with the reference data dashed lines, plotted with the vertical shift to fit the calculated curve in the minimum point of X 2 state. FIG. 2. Potential energy curves for a series of 2 +, 2, and 2 states of HCl + solid lines in comparison with the reference data dashed lines, plotted with the vertical shift to fit the calculated curve in the minimum point of X 2 state.

5 Doublet states of HCl + J. Chem. Phys. 126, contrast with the lower states considered above. In Ref. 16 only the sketch for 4 2 and states has been presented, and evidently, the complicacy of the curves can be due to avoided crossing with the higher states. Moreover, instead of in Ref. 48 we assign it as 2 2, and the intersection between and 2 2 states is possible see Fig. 2. The difference with data in Ref. 48 appears to be also for the states of symmetry: we have obtained explicitly bound states while in Ref. 48 the features of possible minima are very weak. The values of asymptotic atomic energies Table II have also the difference in 2 3 ev as compared with our data and experimental atomic energies. A reason of these differences can be issued from details of CI procedure. Final conclusion regarding the higher states may not be drawn from the present calculations since the assignment of experimental values of energy of the asymptotic limits is also ambiguous due to complicated electronic configurations and close energies of Cl 0 2 S, Cl 0 2 P, and Cl 0 2 D terms see Table II. Comparing with the previous publications on HCl + electronic structure in particular, Refs. 16 and 48, we note that the different calculation methods were used SAC-CI against to CASSCF and MCSCF in Ref. 16 and the simpler CI approach in Ref. 48, and the basis sets are not coincident. However, the calculations with different methods can be considered as similar level of description. The earlier calculations 17,46,47 with some other approximation to treat CI have considered less number of states, but they also do not contradict our data. Thus, one can conclude from both new calculation and the reference data that the potential curves for the eight states, X 2,2 2,3 2, A 2 +,2 2 +,3 2 +, 2, and 1 2, are properly determined, and the curves for 4 2,5 2 and 4 2 +,2 2 states are also quite reliable at the present level. Corresponding wave functions may be successfully used for analysis of electronic transitions considered below. A further development of the present calculation, evidently, requires to account for the spin-orbital interaction resulting in the splitting and shifting of these states More excited states should be analyzed including the higher multiplicity and the double ionized molecular ions, HCl B. Spectroscopic constants A lot of electronic spectroscopy studies have been done for HCl + and most of them for the two lowest bound electronic states X 2 and A ,11,14 17,40,47 The spectroscopic constants constitute one criterion for applicability of the potentials derived in Sec. III A by ab initio electronic structure calculations. The values of equilibrium distance R e, dissociation energy D e, and transition energy vertical between the bound states, T e, are obtained immediately from the data on electronic structure see Table I. R e and D e fit quite well the various experimental data 7,11,39 41 and the calculations in Ref. 16. T e appears to be slightly higher than the set of experimental values, however, this deviation is not more than 7%, and the calculations in Ref. 16 also overestimate this value. Few approaches can be used to determine the values of TABLE III. Vibrational levels calculated from the potential curves for the two bound states of HCl + and DCl + with respect to the corresponding energies in Hartree at R=20a 0. X 2 A 2 + HCl + DCl + HCl + DCl vibrational constants e and e x e. One can fit e and e x e so that the Morse potential and potential curves from the electronic structure calculations have appeared as much as possible close. For estimation of e and e x e from the experimental data the eigenenergy of Morse potential is commonly used, E v = D e + e v + 1/2 e x e v + 1/2 2, where v =0,1,2,... is corresponding vibrational level. Now we again have arbitrariness depending on what set of E v is used in the determination of e and e x e. Often for their calculation the lowermost levels are used, e.g., if v=0,1,2, then e =2 E 1 E 0 E 2 E 1, e x e = E 1 E 0 E 2 E 1 /2. Table III presents the vibrational eigenenergies for X 2 and A 2 + electronic states of H 35 Cl + = and D 35 Cl + = calculated using the Fourier grid Hamiltonian method 56 for our SAC-CI potentials interpolated on the equidistant grid in the range of 1.5a 0 R 20a 0 with step 0.01a 0. The reasonable correspondence between the vibrational eigenenergies derived with the SAC-CI potential and the Morse potential Eq. 1 has been achieved with the values e and e x e presented in Table I. Let us note that the states are calculated without the spin-orbit interaction and corresponding splitting e.g.,x 2 2 1/2 and 2 3/2. In this respect the spectroscopic constants obtained here display quite good agreement with experimental data, which are also rather scattered in particular, e x e. In theoretical calculations the essential dependence of e and e x e 1 2

6 Gurin et al. J. Chem. Phys. 126, FIG. 3. DMs as a function of the H Cl distance for a series of 2 states of HCl + and comparison with the data of Ref. 16 for X 2 dashed line. can arise from a choice of E v in Eq. 2. For example, our comparison of E v from Table III with Eq. 1 for the state A 2 + of D 35 Cl + leads to e x e =21.07 cm 1 see Table I, while the evaluation with Eq. 2 results in e x e =6.1 cm 1. This difference of almost a factor of 4 makes the application of Eq. 2 far from equilibrium distance R e unacceptable. Thus, the values of e and e x e, resulted in Table I, are rather good not only for the equilibrium points R e but also for high vibrational levels. C. Dipole moments The values of DMs were calculated by the standard procedure see, e.g., the conventions in Ref. 57 integrated into the software used. 45 In order to define the dipole moment within this approach the center of nuclear charges is taken as the origin of coordinates for dipole moments of ionic diatomics this is of importance for comparison with data of other calculations. The calculated DMs corresponding to the above potential curves are given in Figs. 3 and 4. Inthe whole, DM curves for the states under study reveal rather different behaviors. This can be associated with different pathways of HCl + dissociation. There is good consistence with calculations in Ref. 16 for the states for which the comparison is available, X 2 and A 2 +. Taking into account the whole distance range, we can compare the results with asymptotic forms calculated by the classical electrostatic formulas 26 however, in the coordinate system of center of masses. DM behave as 35/36 er for the case of dissociation to H and Cl, while the dissociation pathway with H and Cl + results in the asymptote 1/36 er. 26 In our calculated data we also see two types of asymptotic behavior; however, numerically the values are slightly different at large distances and strongly deviate from the classical estimations at short distances. Calculated DMs are increasing with distance for the bound state A 2 +, and for the excited -symmetry states, 2 2,4 2, and 5 2. That reflects the asymptotic behavior when the charge by dissociation remains at hydrogen atom, DM R 35/36 er in the center of mass coordinate system. In other words, this large DM appears as effect of large separations, but these growing curves are also nonmonotonous see Fig. 3. DM dependencies on distance for the states dissociating to Cl + and H 0, X 2, and 3 2, exhibit the pronounced maxima at about R=5a state, additively, enters the negative region and possesses the maximum at small distances. The similar extreme behavior occurs for and 3 2 +, while 2 and 1 2 states indicate the negative maxima see Fig. 4. For and states the positions of maxima are different and not coincident with the corresponding ones for the couple of states. There are several points of sign inversion of DMs for these states at short distances and the jumplike dependency for some states 3 2,5 2, and 1 2. Thus, there is strong rebuilding of the molecule at distances typical for the bound states R e, and the dissociation is accompanied by complex changes in bonding of the atoms rather than any single-bond breaking. DMs of the high-lying states of both + and symmetry fourth and fifth deserve special attention due to very featured behavior see Figs. 3 and 4. Their asymptotics correspond to the dissociation onto H + and Cl 0, but even at distances R=20a 0 the values of DMs are different for these states and do not coincide with DM of 2 2 state which is also possesses this dissociation limit. Several crossings and nonmonotonous behavior occur for R dependences of DM in the wide range of distances Figs. 3 and 4. These features of the excited states can have a great effect upon transitions with these states; however, we leave more detailed study to future publications. FIG. 4. DMs as a function of the H Cl distance for a series of 2 +, 2, and 2 states of HCl + and comparison with the data of Ref. 16 for A 2 + dashed line. D. Transition dipole moments For calculation of TDMs we also used the standard conventions 57 as well in Ref. 16 for the proper comparison. TDMs from the ground state X 2 are summarized in Figs. 5 and 6. The transitions to two nearest 2 states see Fig. 5 are well consistent with Ref. 16 apart from some deviation at very small distances, R 2a 0. Qualitatively, the behavior of TDMs for these transitions reveals pronounced maxima, and

7 Doublet states of HCl + J. Chem. Phys. 126, FIG. 5. TDMs from X 2 to the three higher states of symmetry of HCl + as a function of the H Cl distance in comparison with the data of Ref. 16 dashed lines. the maximum for the lower final state 2 2 occurs at a noticeably larger distances than for the 3 2 final one. This displacement for the maxima of TDM from the ground to different states can mean a possibility of selective excitation of this molecule to these final states: the earlier dissociation step will result in transition to 3 2, while the next steps will drive to 2 2 state. This separation of the excitation pathways is interesting for the 2 2 and 3 2 states because they correspond to different dissociation products. The fact of this selectivity means a possibility of the time-resolved control of the dissociation path of this molecular ion, as proposed in Ref. 23. Both maxima of TDM occur at the distances essentially larger than the equilibrium, R e, for the ground X 2 state, but at R=R e the values of TDMs are close to zero. Thus, most intensive transitions take place at the beginning of the predissociation steps rather than in the equilibrium stable state. At the large distances, R 12a 0, TDM for both transitions again become practically zero. Remember, the corresponding potential curves attain a plateau at smaller distances, R 8a 0, i.e., rather intensive transitions in particular, for the case X can occur even for weakly interacting ions at considerably late dissociation steps. We also present the R dependence of TDM from the ground X 2 state to 4 2 state. This TDM shows more complicated behavior see Fig. 5 and have also the maximum but at smaller distances than in the case of the transitions to 2 2 and 3 2. In particular, the value of TDM changes the sign at R 6a 0 and decreases slower with increasing of R than the corresponding TDM to 2 2 and 3 2 states. At larger separations, R 10a 0, this transition can yet noticeably contribute to a light absorption. The complicacy of this TDM R curve can be associated with the above nonmonotonous potential curves and, correspondingly, R dependence of DM for this state. That behavior of the X transition indicates also the possibility of selective excitations, and this selectivity depends strongly on R. The transition takes place at large distances where the transitions to 2 2 and 3 2 states are already negligible. It is worthwhile to note also that rather large intensities of the transitions from the ground state to three excited ones are important to motivate treating multiple states in a description of dynamics of this molecule under light excitation, while the contributions of the transitions to states of other symmetry are much weaker see below. TDMs for transitions from the ground state X 2 to the states of other symmetries show very different behavior see Fig. 6. The maximal values of these TDMs are much lower than those for the above - transitions. They invert the sign but absolute value remains less than 0.1 a.u. in some range of R R e. At larger distances these TDMs are approaching zero, being negative. TDM between bound states X 2 and A 2 + see Fig. 6 decreases from the value around 0.3 a.u. crossing the zero line at about R=4 a.u. This behavior is in good consistence with the data of Ref. 16 and the experimental ones given in Refs. 47, 59, and 60 for the distances R 4a 0 the deviation of our points from the other data is not more than the range of different referenced sources. The transitions to the two next states, and 3 2 +, show the R dependence with low maxima in the range of R R e, and these TDMs invert the sign at the shorter distances. Qualitatively, this behavior is similar to the corresponding data in Ref. 16, however, they slightly deviate numerically. The transitions from X 2 to 1 2 and 2 + states exhibit another behavior. They both are very small and increase only in the range of shortest distances see Fig. 6. These curves are not in full agreement with Ref. 16, however, the deviations are not strong. We also calculate TDMs from some excited 2 states not considered earlier in order to get a more complete picture see Fig. 7. Both TDMs from the 2 2 state have comparatively large maxima and different signs. But at R R e they are close to zero. The asymptotic behavior of TDM is very different from the other above transitions e.g., from X 2, it is not equal to zero even for very large distance, and at R=13a 0 it becomes nearly constant and equal to 0.6 a.u. 2 2 state dissociates to H + +Cl 0 see Table II. We can assume that this asymptotic TDM corresponds to the transition between electronic states of Cl atom 2 P and 2 D terms. The two maxima occur in the R dependence of TDM from 3 2 to 4 2. Notice that the transitions from the excited states, 2 2 and 3 2, appear more complicated than from the ground one, X 2, and the selection of the maximum intensities can be done in dependence on R. Regarding the photofragmentation phenomenon these transitions are of importance as well as the transitions from the ground state. When the photofragmentation dynamics is described with the time-dependent Schrödinger equation e.g., in Ref. 23 the terms with transitions from excited states should be added to complete the picture. The corresponding transitions are quite accessible taking into account the high power of laser beam in the experiments on resonance enhanced multiphoton ionization spectroscopy REMPI, 2,29 resulting in noticeable occupancy of 2 2 by transitions from X 2. Thus contributions of the transitions from 2 2 and 3 2 into photofragmentation are not negligible since the maxima of these TDMs are observed at the distances in the range of

8 Gurin et al. J. Chem. Phys. 126, FIG. 6. TDMs from X 2 to a series of 2 + states, 2, and 1 2 states of HCl + as a function of the H Cl distance in comparison with the data of Ref. 16 dashed lines. Plots a e are given separately for each final state. maximal transitions from X 2. They are to lead to the higher states of Cl + or Cl 0 and to the more complicated full picture of photofragmentation. A similar discussion can concern also possible contribution of the excited states of other symmetries. Thus, the analysis of TDMs for a series of dipole transitions for HCl + from the ground state X 2 performed here shows the qualitative correspondence with previous available data obtained with the other calculation method and confirms the possibility of easy selection of different final states in the R dependencies. IV. CONCLUSIONS Within the framework of the SAC-CI approach we have calculated a series of electronic states of HCl + and presented potential curves, dipole moments, and transition dipole moments for the ground state and eleven excited ones. A comparative analysis with the data of Ref. 16 has been done throughout the paper when discussing new results, and the good reproducibility and agreement were shown. New data were added for more extended set of states and transitions. The following conclusions can be summarized.

9 Doublet states of HCl + J. Chem. Phys. 126, ACKNOWLEDGMENTS The authors acknowledge financial support for this work from the INTAS grant INTAS-Belarus The authors would like to especially thank Professor M. Ehara for helpful discussion on SAC-CI implementation and Professor K.-W. Weitzel and Professor N. V. Korolkova for reading the manuscript, valuable comments, and stimulating discussion. FIG. 7. TDM from 2 2 to the two higher states of symmetry a and from 3 2 to 4 2 state b of HCl The potential energy curves calculated for HCl + with the SAC-CI method reproduce well both the experimental data available and previous calculations at the compatible theory level. DMs demonstrate correct asymptotic behavior for the different dissociation pathways of HCl +, and some states reveal the pronounced maxima at the distances approximately twice larger than the equilibrium. TDMs of - type transitions attain considerable large values at the distances larger than R e and vanish upon further separation of the atoms except transition. The transitions from the ground state X 2 to the states of other symmetries +,, and have much lower intensity with maxima either close to R e 2 2 +, 3 2 +, and 1 2 or at the lower distances A 2 + and. This behavior of TDM as a function of R and type of the states means the possibility of selective excitation of HCl + and proper control of its dissociation. With the new data for the higher states this circumstance became more evident. The SAC-CI technique provides the adequate level of electronic structure calculations of HCl +. The results may be used for simulation of dynamics under laser pulse excitation with inclusion of the calculated dipole moment data analysing a competition between possible channels of excitation see discussion in Ref M. Michel, M. V. Korolkov, and K.-M. Weitzel, J. Phys. Chem. A 108, M. Michel and K.-M. Weitzel, ChemPhysChem 5, M. Alagia, F. Biondini, B. G. Brunetti, P. Candori, S. Falcinelli, M. Moix Teixidor, F. Pirani, R. Richter, S. Stranges, and F. Vecchiocattivi, J. Chem. Phys. 121, Q. J. Hu, T. C. Melville, and J. W. Hepbum, J. Chem. Phys. 119, R. F. Fink, F. Burmeister, R. Feifel, M. Bässler, O. Bjömeholm, L. Karlsson, C. Miron, and M.-N. Piancastelli, Phys. Rev. A 65, F. Burmeister, S. L. Sorensen, and O. Björneholm et al., Phys. Rev. A 65, M. Michel, M. V. Korolkov, and K.-M. Weitzel, Phys. Chem. Chem. Phys. 4, M. Michel, M. V. Korolkov, M. Malow, K. Brembs, and K.-M. Weitzel, Phys. Chem. Chem. Phys. 3, A. Holzwarth, M. Penno, and K.-M. Weitzel, Mol. Phys. 97, M. Penno, A. Holzwarth, and K.-M. Weitzel, J. Phys. Chem. A 102, A. J. Yencha, A. J. Cormack, R. J. Donovan, A. Hopkirk, and G. C. King, Chem. Phys. 238, ; and references therein. 12 S. Svensson, L. Karlsson, P. Baltzer, B. Wannberg, U. Gelius, and M. Y. Adam, J. Chem. Phys. 89, M. Ehara, P. Tomasello, J. Hasegawa, and H. Nakatsuji, Theor. Chem. Acc. 102, B. A. Hess, C. M. Marian, and S. D. Peyerimhoff, in Modern Electronic Structure Theory, edited by D. R. Yarcony World Scientific, Singapore, 1995, Pt. 1, pp A. D. Pradhan and A. Dalgarno, Phys. Rev. A 49, A. D. Pradhan, K. P. Kirby, and A. Dalgarno, J. Chem. Phys. 95, H. J. Werner, P. Rosmus, W. Schaetzl, and W. Meyer, J. Chem. Phys. 80, M. V. Korolkov and K.-M. Weitzel, J. Phys. Chem. A 110, M. V. Korolkov and K.-M. Weitzel, Chem. Phys. Lett. 336, L. M. Andersson, F. Burmeister, H. O. Karlsson, and O. Goscinski, Phys. Rev. A 65, M. Kivilompolo, A. Kivimäki, H. Aksela, M. Huttula, and S. Aksela, J. Chem. Phys. 113, M. Korolkov, K.-M. Weitzel, and S. D. Peyerimhoff, Int. J. Mass. Spectrom. 201, M. V. Korolkov and K.-M. Weitzel, J. Chem. Phys. 123, J. T. Paci and D. M. Wardlaw, J. Chem. Phys. 120, J. T. Paci, D. M. Wardlaw, and A. D. Bandrauk, J. Phys. B 86, A. Conjusteau, A. D. Bandrauk, and P. B. Corkum, J. Chem. Phys. 106, P. Dietrich and P. B. Corkum, J. Chem. Phys. 97, R. Gill, R. Yanagawa, and M. Thachuk, J. Chem. Phys. 113, J. H. Posthumus, Rep. Prog. Phys. 67, A. Giusti-Suzor, F. H. Mies, L. F. DiMauro, E. Charron, and B. Yang, J. Phys. B 28, A. D. Bandrauk, E. Aubanel, and J. M. Gauthier, in Molecules in Laser Fields, edited by A. D. Bandrauk Dekker, New York, J. T. Paci and D. M. Wardlaw, J. Chem. Phys. 119, H. Nakatsuji, in Computational Chemistry: Reviews of Current Trends, edited by J. Leszczynski World Scientific, Singapore, 1997, Vol H. Nakatsuji and K. Hirao, J. Chem. Phys. 68, H. Nakatsuji, Bull. Chem. Soc. Jpn. 78, H. Nakai, Y. Ohmori, and H. Nakatsuji, J. Chem. Phys. 95, K. Kuramoto, M. Ehara, and H. Nakatsuji, J. Chem. Phys. 122, M. Ehara, Y. Ohtsuka, H. Nakatsuji, M. Takahashi, and Y. Udagavwa, J.

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