J. Phys. Chem. 1994,98, 5878-5890
5878
Quantum Chemical Study of the Potential Energy Curves and Electronic Transition Strengths in HCl, XeCl, and HCl Xe
+
George F. Adams and Cary F. Chabalowski' US.Army Research Laboratory, AMSRL- WT- PC, Aberdeen Proving Ground, Maryland 21 005-5066 Received: January 10, 1994; In Final Form April 6, 1994'
Potential energy curves and electronic transition strengths are calculated for selected singlet states in HCl, XeC1, and HCl Xe using effective core potentials (ECPs) with state-averaged CASSCF-CI techniques. In HCl, the maximum photoabsorption cross section for the A('II) %(lZ+) transition is calculated to be udt = 3.86 X 10-l8 cm2 for the v" = 0 band, in good agrtement with the experimental value of udf = 3.8 X 10-18 cm2. The oscillator strength for the 0-0transition in C(lII) %(lZ+)is calculated to befm = 0.175, differing by 5% from the experimental value offm = 0.185 f 0.037. The calculated oscillator strength for excitation into u' = 1 is significantly larger than the experimental values or those from previous theoretical treatments. In the XeCl, radiative lifetimes, 7 , are predicted for selected doublet excited electronic states. This study substantiates earlier theoretical predictions and compares favorably with available experimental lifetimes. In the HCl Xe system, low-lying singlet states are calculated as a function of the HC1-Xe distance with the H-C1 distance held fixed and the atoms kept collinear. A charge-transfer state is located which represents the excitation of a ?r electron into a u* antibonding orbital. This state offers a simplified model of the photoinitiated charge transfer observed in solid xenon doped with HC1, where the HCl is reported to dissociated after transfer of an electron from Xe to HCl. Other electronic states and electronic transition moments of the HC1 Xe system are analyzed and related to the isolated HC1 electronic states and transitions when possible.
+
-
-
+
+
I. Introduction In a series of papers by Apkarian and co-workers,1-3 solids composed of rare-gas (Rg) atoms doped with various halide compounds were chosen as a starting point for studying energy storage via photoinduced, charge-transfer (CT) reactions. This choice was based, in part, upon the Rg atoms providing "...the necessary conceptual simplicity to afford a detailed and rigorous description of the fundamentals of these processes."' Part of this "simplicity" is due to the absence of complex ground-state interactions. Apkarian et ai. have studied spectra of these CT transitions in liquid xenon& and in Rg ~olids~-3~5~~.* (for various Rgsystems). In thecaseof HCl insolidxenon, they demonstrated that spatially separated, long-lived, dipolaron states are produced via the r e a c t i ~ n l - ~ , ~ Xe
+ HCl + 2hv
-
Xe'(HC1)-
Xe+CI-(C)
-
+ Xe
-
-
Xe+CI-(B/C)
+H
x~,+cI-(~~F)
The only observed emission is seen from the radiative dissociation of the Xe2+C1-(421') Xe + Xe + C1+ hv + KE. The kinetic energy arises "...due to the fact that the transition terminates on a steeply repulsive ground [state] p~tential."~ In addition, they have shown the lasing capabilities of XeF in crystalline argon, creating a laser tunable over an 80-nm range in the visible region.9 Other combinations of Rg halides are expected to be likely candidates as tunable lasers in the visible, UV, and VUV spectral regions.1° Classical molecular dynamics studies by Gerber and co-workersIIJ2 have shed some light on possible mechanisms for dissociating F2,13C12,11 and HI12 in Rg solids. They found large qualitative differencesin the dissociation mechanisms as well as the dynamical pathways followed by the dissociated atoms among these three molecules. Last, George and co-workers14 have performed semiempirical (i.e.,DIM and DIIS)quantum chemical calculations on various (Xe,Cl) and (Xe,HCl) systems, predicting potential energy surfaces, permanent dipole moments, electronic transition enerAbstract published in Advance ACS Abstracts, May 15, 1994.
gies, and electric transition dipole moments. From these calculations they made assignments to the observed absorption and emission spectra, provided structural data for the complexes in thegas and solid states, and rationalized the observed bandwidths. Their findings are generally in good qualitative agreement with experiment. As LG have pointed out, there have been very few ab initio calculations on related systems. With respect to energy storage, the physical model for the long-lived, separated charges is a halide negative ion separated from the trapped, positively charged hole state which appears to be quasi-localized on Rg molecules of weakly bound Rg atoms. There is evidence suggesting that the positively charged Rg,(+) chains are linear and prefer n = 3 in the solids,3 with the Rg-Rg interatomic distance being shorter than what is seen in the neutral Rg matrix. These separated dipolaron states can exist so long as the negatively charged halide, X(-), remains separated from the Rg,(+) hole. But when the (+) holes migrate to the X(-), they rapidly form the exciplex Xez(+)X(-), releasing the exciton energy as fluorescence. The gas-phase equilibrium geometry for the XezCl exciplex in the 42I' state is predicted to have a Xe-Xe separation of 3.17 A (5.99 bohrs)" and a Cl-Xe separation of 6.41 bohrs.' The cationic self-trapped holes (STHs) reportedly migrate to the X(-) by one of two methods: either by tunneling or by "hoppingn3(due to a thermal perturbation) which stretches the Xe-Xe,(+) bond lengths to the neutral geometry, apparently increasing the energy of the R,(+) to that of an excited hole state and conducting the hole to the X(-). At a constant temperature of 12 K, the separated dipolarons for C1 in Xe have been shown to exist for longer than 30 h, with the rate-determining step to recombination being the ability of the trapped hole to tunnel.3 Schwentner, Fajardo, and ApkarianI6presented the CT process as the excitation of a positive "hole" (analogous to an electron in an atom) into a Rydberg orbit with the halide atom acting as a negatively charged "nucleus" of infinite mass. On the basis of this model, they calculate the Rydberg term values B, and the state radii r, for these Rydberg states. The progression of predicted B, energies fit quite nicely to the experimentallyderived values obtained from excitation spectra. To date, Xe has been the only Rg/halide matrix to show such a Rydberg (hole)
This article not subject to US. Copyright. Published 1994 by the American Chemical Society
Potential Energy Curves for HC1, XeCl, and HCl
+ Xe
progression spectra.16 This delocalized Rydberg “hole” description has been shown to be applicable for Xe and perhaps Kr, but not the lighter Rg atoms.16 In addition, no evidence has been seen experimentally to support a delocalized hole state for fluorine in Rg solids. Xe appears to play a special role among the rare gases in its ability to stabilize the charge separation. This dependence of the charge-transfer process and stabilization on the halogen and type of rare gas matrix warrants further theoretical study. To obtain an understanding of the microscopic processes involved in formation of the exciplex, as well as the factors determining the lifetime of the separated dipolarons, one needs detailed information about the electronic structure and molecular interactions. This report describes an ab initio study of the Rg/ halide interactions of xenon and chlorine. Quantum chemical calculations are performed on the ground and low-lying singlet excited states of HCl, XeC1, and HClXe using effective core potentials (ECPs) to represent the inner-shell electrons, stateaveraged complete active space MCSCF (SA-CASSCF), and configuration interaction (CI) calculations. The results from the HC1 and XeCl calculations are compared to experimental molecular properties as well as properties calculated in earlier ab initio studies, thus allowing one to evaluate the accuracy of the current calculations. In the HClXe system we are most interested in exploring the qualitative nature of the excited electronic states and determining if charge-transfer states exist even in these small model systems. The permanent electric dipole moments and transition electric dipole moments will also be calculated as a function of internuclear separations, i.e.,H-C1, Xe-C1, and H C C Xe. The permanent dipole moments should help identify CT electronic states, and the transition moments will offer at least a semiquantitative measure for the likelihood of populating each electronic state. These results are reported in three main parts, with each part corresponding to one of the species HCl, XeCl, and HClXe, in that order. 11. General Theoretical Considerations
All calculations were carried out in the C , point group. The atomic basis sets used are a combination of Gaussian-type atomic orbitals (AOs) and the ECPs of Wadt and Hay.I7 The Gaussian basis set on hydrogen consists of a noncontracted set of four s-type primitives18 and one p-type polarization function ( a p= 0.75),19 giving [4s,lp]. The chlorine basis contains three noncontracted s- and p-typevalence AOs with exponentsoptimized for their use with the ECPs.17 This is augmented by a negative ion function (ap = 0.049)20and a polarization function ( a d = 0.50),20 as well as a set of noncontracted Rydberg functions (a, = 0.025, a p= 0.020, a d = 0.015),20for a total basis set of [4s,5p,2d]. Likewise, the Xe basis associated with the ECPs17consists of three s- and p-type primitives which remained noncontracted and were augmented by a single polarization function ( a d = 0.25),z1 giving [3d,3p,ld]. The molecular orbitals (MOs) used as expansion vectors in the CI calculations are obtained from the SA-CASSCF calculations using the general second-order, density matrix driven MCSCF algorithm of LengsfieldSz2These MOs should be suitable for describing both the ground and excited states. The CI wave functions are generated from the symbolic matrix element, directCI method called ALCHEMY.23 Thedetails of the SA-CASSCF and CI approaches will be given in the appropriate sections. Potential energy curves (PECs) and electronic transition dipole moments are then calculated as a function of atomic positions. The vibrational wave functions corresponding to the PECs for the diatomic systems were determined by solving the radial Schroedinger equation for nuclear motion (ignoring rotational motion). Transition probabilities and radiative lifetimes are predicted based upon the above treatment. One potential weakness, especially in the HClXe calculations, is the neglect of spin-orbit (SO) interactions. But earlier theoretical work done
The Journal of Physical Chemistry, Vol. 98, No. 23, 1994 5879 by Hay and Dunningz1 on XeCl showed that much useful qualitative and semiquantitative information can be obtained without inclusion of SO effects. 111. HCl
Calculations are performed on the-ground stat_e,R(lZ+), and the first two excited I I I states, i.e., A(III) and C(lII), and the electric dipole transition moments coupling 2 with A and There has been much experimental and theoretical interest in the photodissociation processes of HCl due to its important role in thechemistryof the earth’sstratosphere. It has also been predicted to exist in interstellar clouds in detectable amounts.24-26 Photodissociation_ is know; to occur from absorption into the A(111).27TheA(III) +X(lZ+) transition has beenfirmlyassigned to a broad absorption band occurring a t 1400-1 800 A. The broad natureof the band isconsistent with the theoretical description28-30 of the upper state as being dissociative. There are reliable e ~ p e r i m e n t a l ~estimates_of l-~~ the photodissociation (absorption) cross section for the A X(u” = 0) band, which produces the ground electronic state atoms. (Some perturbation of this repulsive state by the xenon atoms could play an important role in the photodynamics observed for HCl in solid xenon matrices.) The first boundsinglet excitedstateis thee(lII),whichis Rydberg in character. The e(lII) %(lZ+) transition is observed experimentally as an intense band system with its 0-0 vibrational band a t 1291 A. The vibrational bands appear broadened, indicating predissociation. It has been suggested that this predissociation occ11rs29 by the spin-forbidden process of crossing from the singlet C to the repulsive l3Z+ state via spin-orbit (SO) coupling(s). The potential enefgy curves for these tw? show the l3Z+ crossing the C state near the re for C. A theoretical model for photodestruction of HC1 based on the combined effects from photodissociation of A and the predissociation of by the l3Z+ state29 put the theoretical model for the photochemistry of HCl in substantially better agreement with the observed terrestrial chemistry and interstellar predictions for the abundance of HC1. Even though spin-orbit coupling could play a significant role in understanding the photochemical processes in both HCl and HClXe,, we will begin by studying only the low-lying singlet electronic states, with the inclusion of SO effects anticipated in future studies of the HCl-Xe, interactions. A. Details of Calculations. The R(lZ+) (ground state, as well as the and e(lII)excited states, are calculated over the bond length range R = 1.8-10.0 bohrs, at increments of 0.10 bohr between R = 1.80 and 3.00 bohrs, with the remaining points at R = 3.15, 3.30, 3.45, 3.60, 3.75, 3.90, 4.00, 5.00, 8.00, and 10.00 bohrs. Due to the symmetry of the molecule, only one component of each II system need be considered and the transition properties corrected by a factor of 2-when appropriate. In the C h point group, the ground state X(lZ+) belongs to the A1 irreducible repres_entation (IRREP), while the II, component of the A(llI) and C(III) states belong to the B1 IRREP. The numbers of active MOs used in the state-averaged, complete active space MCSCF (SA-CASSCF) in each IRREP are A I = 4, Bl = 1, B2 = 1, and A2 = 0, with no frozen core orbitals outside of the implicit “frozen core” due to the ECPs. The numbers of active electrons per IRREP are (2,1,1,0), respectively. The numbers of states averaged per IRREP are (2,2,2,0) with weights of w i= (2,2,1,1,1,1), respectively. In the CI calculations an implicit set of frozen core orbitals once again existed due to the use of ECPs, but no other MOs were explicitly frozen out of the electronic excitations and all virtual MOs were retained. An equivalent set of frozen core orbitals consisting of la2,2a2,3a2,4a2,1~4was used in earlier CI studies by both Bettendorff, Peyerimhoff, and Buenker28 (BPB) and van Dishoeck, van Hemert, and DalgarnoZ9(VVD) on HCl. BPB report potential energy curves for many electronic states but not
e.
-
+
5880 The Journal of Physical Chemistry, Vol. 98,No. 23, 1994
Adams and Chabalowski
TABLE 1: Reference CFSs Used in the CI Procedure for HCP A(lZ+)(IRREPAl) set 1
set 2
-
- 15.w
-
set 3 (MO indices per IRREP)
4a22r22r2 5a2607a3r,3uy al = 5-20, bl = 3-8,bz = 3-8, a2 = 1-2 4 u 2 2 f 2 f 5a16uL7a3r,3uy 4u22r:2u; 5u16u7u~3ux3ry A(’IIJ,e(lIIu)(IRREP B1) set 2 set 3 (MOs per IRREP)
set 1
-14.80
-15 10h
LI
v
4 0 . ~ 2 ~ 2u~5u26a1703r, ~ 4u22r; 2ri5 ~ ~ 6u’3u, . ~ 7
= 16, bl = 6,b2 = 6, a2
2
See section 1II.A for more details concerning the final CI expansions based on these reference CSFs.
transition properties, while VVD concentrate on fewer states but are specifically interested in the electronic transitions between these states. In the present study, the AI space contains three reference configurations including the closed-shell ground-state and two excited-state configuration state functions (CSFs) represented by the electronic excitation u u*. The two B1 reference CSFs represent 7~ u* electronic excitations. Starting with the reference CSFs given in Table 1 for the AI and Bz IRREPs, new CSFs are generated in a two-step process. The first step is to divide the MOs into three sets. Table 1 gives the MOs contained in each set. The second step is to distribute the eight valence electrons in all symmetry-allowed combinations within these three sets but restricting the electron occupancy in each set according to
-
-
A, symmetry: set 1 (6-4 electrons), set 2 (W), set 3 (0-2)
B, symmetry: set 1 (4-2 electrons), set 2 (2-6), set 3 (0-2) This scheme for generating CSFs was chosen to roughly mimic the MRD-C134scheme (excluding CSF “selection”) used by VVD and BPB. The similarity lies in the fact that this scheme generates all single and double excitations from “many” reference CSFs, these reference CSFs being generated by the electron distributions described in MO “set 1” and “set 2”. In the MRD-CI terminology the reference CSFs given in Table 1 would best be labeled as “main” CSFs, Le., the largest contributors to the electronic state wave functions. This should aid in evaluating the effectiveness of the ECPs in predicting molecular properties by facilitating comparison with the widely used and well-tested MRD-CI technique employed by VVD and BPB. This scheme generated CI expansions of 7743 and 8434 CSFs for the AI and BI IRREPs, respectively. The lowest three roots of AI and Bl symmetries were determined in the diagonalization of the CI Hamiltonian matrix, but due to the choice of reference CSFs, only the 1Al and 1,2B1 roots will be considered. The current CI expansions are larger than those used in the study by BPB, where the ground-state CI wave function contained -4100 CSFs and the excited I l l states had expansions around 4400
2
I
I
3
1
R(H-CI)
I
I
I
i
5
6
7
6
(bohr)
Figure 1. Potential energy curves for the g(lE+) ground state and the A(III) and @If) excited states as a function of internuclear distance in bohrs for HCI.
CSFs. VVD generated CI wave functions containing -3000 CSFs per IRREP. It must be noted that the MRD-CIj4method used by these two previous studies contains an extrapolation technique which effectively calculates the state energies (but not the transition moments) consistent with CI expansions on the order of 71 000 CSFs for the l X + states and 64 000 CSFs for the 1II states in the BPB study, while VVD do not report the sizes of the CSF spaces corresponding to the extrapolated energies but do report the use of extrapolation. B, ResultsandDiscussion. I. Propertiesofthe~(’X+),;i(’II), and C(’II) Electronicstates. The potential energy curves (PECs) for the three states of interest are shown in Figure 1. The molecular constants calculated from these curves are given in Table 2, along with theoretical predictions from other studies and the experimental values. The vibrational wave functions, x@), and frequencies are obtained from the potential energy curves for each state by solving numerically the radial Schroedinger equation for nuclear motion while ignoring rotational effects. Our results for the ground state, X,give re = 2.43 bohrs and we = 2983 cm-’, in good agreement with the experimental values35 of re = 2.408 bohrs and o, = 2991 cm-I. The other theoretical studies listed in Table 2 also calculate these two propertiv to be in generally good agreement with experiment. For the C(lll), the first bound I l l state, the current values for re and we are 2.62 bohrs and 2857 cm-I, while the experimental values36 are 2.55 bohrs and 2817 cm-1, respectively. The theoretical work of BPB predicts re = 2.60 bohrs and we = 2520 cm-I, and VVD predict re = 2.68 bohrs (no we reported). Even though BPBs bond length is in slightly better agreement with
TABLE 2: Molecular Constants (re au; we cm-l) for the % ( W ) and e(lII,)States from This Study, Experiment, and Other Theoretical Studies for HCI current study
MRD-CI“
theoretical treatments PNO-CIb
CEPAb
c
IC
experiment
re We r, WC re We re we re WC 2.42 2961 2.41 3034 2.42 2977 2.44 3005 2.408d 2991d (2.43)’ (g) 2857 2.60 2520 2.62 nch nc nc nc nc 2.5Y nc 28 17e (2.68)’ (g) Reference 28. Reference 39. Reference 30. Reference 35. Reference 36. f Reference 29. From their Gaussian set. 8 Not reported. nc = not calculated.
R
c
re 2.43
We
2983
Potential Energy Curves for HCl, XeCl, and HCl
TABLE 3
+ Xe
The Journal of Physical Chemistry, Vol. 98, No. 23, 1994 5881
Experimental and Theoretical Electronic Transition Properties for the Singlet 2 and theory this study van Dischoeck et a1.a Bettendorff et d b Hirst and GuestC +
-
+ -
2 Transitions of HCI ~
experiment
'&(TI) R(IZ+)
.?Eo
3.9 x 10-18 cm* d 7.9 eVg 0.37 au at r = 2.40
AE. ccc
(3.7-3.8) X cm2 7.9 eV 0.35-0.39hat r = 2.409 C(lII)
cm2f
3.8 X 8.0 eVf
7.8 eV
R(12+)
fw 0.175 0.09-0.14h 0.185 & 0.037' AEw 9.63 eV k 9.51 eV (AE,) = 9.75 eV 9.608 eVj a Reference 29. Reference 28. Reference 30. u?Z0 is maximum in the photodissociation cross section as a function of AE. e = (3.7-3.8) X 10-8 cm2,estimated from their Figure 9. f Reference 3 1. g AEe is the transition energy at maximum in U+O. * The range in values occurs from testing of different MOs as expansion vectors in their CIS,as well as combining theoretical transition moments with empiricalPECs. Reference 37. Reference 36. Not reported.
1
4.0
O 8 O 1
3.0
O.*O
0.00
-1 f t
fi_ 3
2
1
5
R(H-CI)
-
-
7
6
0 0
8
10 10
~, 3
(bohr)
Figure 2. TJe x component of the e!ectric dipole transition moments for A(lII,) X(lZ+) and e(lII,) X(l2+) as a function of internuclear
distance for HCI.
0.0
4
5
6
7
8
9
io
11
AE (eV)
Figure 3. Photodissociation _crosssecti_on(in cm2) as a function of A E for the electronic transition A(III) X(lZ+) originating in u" = 0 for +
HCI.
experiment than the current value, their we differs by -300 cm-1 from the cu_rrent value and experiment. 2. The A(1II) X ( l Z + ) Trysition. The theoretical and experimental properties for the A 2 and transitions are summarized in Table 3. The x component of the electric dipole transition moments, pe(R),us R predicted in this study is plotted in Figure 2. The explicit reference to the R dependence of p,(R) will now be dropped, and the nomenclature pe(I-J) used to define the electric dipole transition moment between states I-J. As in the VVD study, our calculations show a rapidly decreasing pe(A-X) with increasing R, especially in the region near Re. Experimentally, there is a broad absorption band with a maximum appe_aring near 8.0 eV, which is clearly assignable to the A(1II) X(lZ+) transition. The absorption represents a photodissociation-cross section,29 udt, of HCl due to excitation into the repulsive A state (see Figure 1)
-
+-
c
+-
w
-
U(AE)~,,= 1.225 X 10-23gAE (cm-') X
where g is the degeneracy of the excited electronic state and p,(A-X) is defined as
The integral in eq 1 is solved numerically. Figure 3 shows the results from our vibrational treatment where we predict the photodissociation cross section, U ~ J = Ous, AE. Our maximum uU~~-o value is calculated to be 3.86 X 10-18 cm2 at AE = 7.99 eV, in good agreement with the experimental value31 of 3.8 X 10-18cm2 at hE = 8.0 eV. In the ab initio work of VVD, they calculate uU~~=o us AE using both Gaussian and Slater AOs and different sets of MOs as expansion vectors in their CIS. Their maxima for ~ u also ~ occur ~ = at~ AE = 8.0 eV and range from -3.6 X 10-18 to -4.2 X 10-18 cm2, giving an average of -3.9 X 10-18 cm2, in close agreement with both the experimental and the current value. It is interesting to note that VVD achieved good agreement with the experimental maximum for ud,=o by averaging the results of several S C F plus CI calculations, while the present study obtained this agreement from a single set of AOs and MOs, which is most likely attributable to using MOs generated from the stateaveraged CASSCF procedure instead of an SCF. The photodissociation cross section for absorptions from the lowest four vibrational levels are shown in Figure 4, which again closely resemble those of VVD. The band patterns reflect the nodal structure of the vibrational wave functions as increases from u" = 0 to 3. 3. The~(lII)--8Trunsition. Forthec(lII)-k transition, experiment predicts Em = 9.608 eV, in good agreement with our value of 9.63 eV. The absolute value of the electric dipole
-
Adams and Chabalowski
5882 The Journal of Physical Chemistry, Vol. 98, No. 23, 1994
TABLE 4: Oscillator Strengths for the Transition for HCl this study experiment van Dishoeck et al.' v' fw X (A) fd X (A). all SlatePfw empiricalefw 0 0.175 1287 0.185 A 0.037 1290.6 0.14 0.15 0.024 1 0.0769 1245 0.0228 1247.4 0.022 (0.02-0.03y 1208.8 0.0028 0.0024 2 0.0378 1208 0.000006 3 0.0072 1176 1174.5 0.0002 a Reference 29. Reference 37. Reference 36. ThePECsanddipole moments calculated from ab initio CI using Slater PECs and dipole moments. e PEC for X obtained empirically, ref 38, and for from a RKR potential. 1 For various ab initio calculationsusing either Gaussian or Slater PECs and dipole moments. 8 Factor of 2 uncertainty.
e
At first glance it would appear that our value forfol must b_e in error, but the remainder of the data calculated here for the X and states suggests otherwise. For example, our we = 2983 cm-1 for is in excellent agreement with the experimental value of 2991 cm-1, and for the C state, our we is 2857 cm-l, differing from the experimental value of 28 17 cm-1 bx only 40 cm-I. This suggests that the shape of our PECs f0r-X and C near their minima is quantitatively accurate. For theC state, theexperiment of Tilford and Ginter36 predicts the energy separation between u' = 0 and u' = 1 to be 2700 cm-1 while this study predicts 2660 cm-I, again in excellent agreement. This_also supports the claim that the shape of the current PEC for the C state is quantitatively accurate. If this informatio? is cougled with the observation that our re values for both the X and C states are in good or better agreement with experiment than those from VVD, one might conclude that our& andfol values should be more accurate than those of VVD and offer quantitatively accurate values for both these oscillator strengths.
c
3
4
5
6
7
0
9
10
11
AE (0'4)
-
Figure 4. Photodissociation _crosssection (in cm2) as a function of A E for the electronic transition A(lII) X(lZ+) originating in v"= 0, 1,
2, 3 for HC1.
transition moment ( x component) can be seen in Figure 2 as a function of internuclear separation. The oscillator strength,fht, is defined as
&."!= 2/3gAE( a u ) l ( x , X ~ , ( X - C ) I x ~ ) ~
c
-
(3)
The oscillator strength for the 0-0 transition resulting from the vibrational analysis isfm = 0.175, differing by 5% from the experimental value& = 0.185 f 0.037,j7and well within the experimental uncertainty. VVD calculatedfmusing various PECs and dipole moments obtained from Gaussian and Slater AOs and using MOs optimized for different states, and they found values for& ranging from 0.09 to 0.14. Theirfm = 0.14 value, which differs by 24% from experiment, came_fromusing the all-Slater PECs and dipole moments with the A(1II) MOs. In the allSlater calculations they predicted thefod values for u '= 0-3. And finally, they recalculated thefoJ's with an RKRj8 potential for the C(1II) state, an empirical potential for the ground state, and used the dipole moments from their Slater calculations with the A(lII) MOs. The dipole moment curve was uniformly shifted by 0.1 bohr to smaller R H Z Ivalues because of the difference in the Re calculated from the Slater orbitals us the Re predicted by the empirically fit PEC for the ground state. This approach produced a slightly largerfm value of 0.1 5, which is 19% smaller than expected but falls within the experimental uncertainty. The experimental and theoretical predictions of fw for u' = 0-3 are collected in Table 4. The agreement between thefol value from the present study and experiment is poor, with the theory predictingfol = 0.077 and experimentfol = 0.022 (factor of 2 uncertainty). The earlier theoretical work of van Dishoeck et ai. getsf&= 0.024 for the analysis utilizingempirically derived PECs and theoretically derived dipole moments. This value is in excellent agreement with experiment. Their fw values calculated from the all-Slater theoretical treatment are quite similar to their mixed empirical-theoretical results for u' = 0-2. Overall, the present study predicts the& oscillator strength in good agrement with experiment but oscillator strengths considerably larger than experiment (or the previous theoretical study) for u' = 1-3. In comparison, the theoretical study of VVD calculate an oscillator strength in excellent agreement for u' = 1 but anfm value that differs from experiment by at least 19%.
IV. Xe-CI Interactions
A. Details of ConfigurationInteraction Calculations. We have calculated the PECs for the 1,222+and the 1,2211states. In the Cb point group these states transform as Z+(Al), ~ , ( B I ) and , IIy(B2), so the state symmetries included in the SA-CASSCF are 1,2A1, 1,2B1, and 1,2Bz, with the weighting scheme wi = (2,2,1,1,1,1). Dueto themolecularsymmetry, nolossofgenerality occurs by considering only the x component of the II states in the CIS,with an appropriate factor of 2 applied when necessary. All the valence electrons remained active in the CI, and the entire set of virtual orbitals was retained. The MO fillings in the two reference CSFs for the %+(AI) states are (1a2,2u2,3u2,4u1, and for l?r;,l?r:,2~$2?r$ and (1 a2,2a2,3u1,4u2,1?r~,l?r~,2?r~,2?r~) and the 211,(Bl) states are (1u2,2a2,3a2,4u2,1?r~,l?r~,2a~,2?r~) (1 u2,2a2,3~2,4u2,1?r~,l?r~,2?r~,2?r~). All single and double excitations were done from these filled orbitals into the virtual space. The final CI wave functions are then used to study the strong transitions 2211 l2II and 2*2+ 122+,as well as the weak 2% 1 2 2 + and 222+ 12II transitions, reporting lifetimes for emissions from the u' = 0 levels. This is believed to be the first report of theoretical predictions for the lifetimes of the weak transitions. Empirical spin-orbit (SO) effects are then included in a simple fashion described by Hay and Dunning21 (HD) and based upon the SO splittings in atomic C1 and Xe+. The SO corrected state energies and SO mixing coefficients are then used to obtain SO corrected PECs and electric dipole transition moments for five transitions. B. Results. 1 . Neglecting Spin-Orbit. The Xe-CI system has already been studied both theoretically1&I6 and experimentally.4w8 The current PECs without SO effects can be seen in Figure 5, and molecular constants are reported in Table 5 along with values from theoretical work by HD and available
-
- -
-
Potential Energy Curves for HCl, XeC1, and HCI -29.700
-
-29 750
-
-29 800
-
-29.850
-
+ Xe
The Journal of Physical Chemistry, Vol. 98, No. 23, 1994 5883
,-29 900 -
n v
s
y
E -29.950Y
-30.000
-30.150
-1
\
4
I 5
4
6
R(Xe-CI)
7
TABLE 5 Molecular Constants and Radiative Lifetimes for XeCl Neglecting Spin-Orbit Effects Re (4 we (cm-1) state HERE HD’ HERE HD 3.25 198 190 222+ 3.20 196 188 3.08 3.14 22n transition 222+- 12 2 +
~~
HERE 6.0
22II-12l-l
74
22n-122+ 222+-12n
50 ps
a
I
I
I
I
I
I
6
8
10
12
14
16
(bohr)
Figure 5. Potential energy curves (all units are atomic) for the 1,2(22+) and 1,2(2n) electronic states as a function of internuclear separation neglecting spin-orbit effects for XeC1.
~
4
8
R(CI-Xe)
-
-
18
(au)
Figure 6. Electric dipole transition moments, pe (in au), for the strong transitions 222+ 12E+and 22n l2nas a function of internuclear
separation neglecting spin-orbit effects for XeCl.
n = ’I2
radiative lifetimes (ns) HD exp 5.6 11.1 f0.2,b27f3c 64 131 f 10: 53 f 6c
13 ps
Reference 21. Reference 40. Reference 44.
experimental values. As can be seen in Table 5, our equilibrium bond lengths and w,)s are in reasonably good agreement with DH’s values. Figure 6 gives the electric dipole transition moments, ke, for the strong transitions as a function of R(Xe-Cl). Near the Re (6.4 bohrs) for the 222+excited state, the pe for the 2-2 transition is approximately 4.5 times greater than the n-II moment. The transition moments and PECs from this work are nearly identical to those calculated by H D when SO is ignored. Table 5 also includes the results of our vibrational analysis for the radiative lifetimes. Again, our predicted lifetimes for the strong transitions, ~ ( 2 ~ 8 + - . 1 ~ 2 +=) 6.0 ns and ~(2~l-I+l~l-I) = 74. ns, are very similar to HD’s without SO effects, i.e., 5.6 and 64. ns, respectively. In HD’s study, the SO corrections had a significant affect on these lifetimes, nearly doubling the aforementioned values. 2. IncludingSpin-Orbit. It should be kept in mind that, with the inclusion of SO effects, the term symbols 2 2 + and 211will only be approximations to the correct state descriptions due to mixing of different A components of R through the spin-orbit operator. We have included SO couplings in the same way as HD, using the empirically obtained atomic C1 and Xe+ SO coupling parameters. The inclusion of SO effects mix the 2211-222+ and 12II-lW states. The resulting wave functions for the states, in HD’s nomenclature, are
n= 3i2
Within this four-state (in zeroth-order) model, the Qo(121-13/2) and \E0(221-13/2)components of the l-I states have no other spin states with which to couple, so the energies of the I3/2 and II3/2 have been SO “corrected” by H D (and here) according to the simple formulas used by H D
E&/*) = JWZm- A,, E(113/2) = E(22n) -
(6)
where ACI = 294 cm-I and Axc+= 3512 cm-1 are the atomic SO coupling constants for the C1 and Xe+ atoms, respectively. These values were taken from HD’s Table I1 and assumed to be independent of internuclear separation. The mixing coefficients A and B, as well as the energies for the R = 1/2 states, are obtained by diagonalizing the 2 X 2 matrices E(%+)
[- f i x ,
-&A,
E(2l-I)
+ A,
1
The A, is either A c ~(for the covalent states) or Axe+(for the ionic
Adams and Chabalowski
5884 The Journal of Physical Chemistry, Vol. 98, No. 23, I994
again, our results for Re and we are seen to be very similar to those of HD when SO is included, with the current values lying slightly closer to experiment than HD's. For the I I I 1 / 2 state, our Re and we values are 3.17 A and 195 cm-I, respectively. The corresponding experimental values are 2.94 A and 195 cm-1. HD's values are 3.22 A and 188 cm-I, respectively. This similarity between the results from our study and from HD's is expected due to thenearly identical resultsobtained between the twostudies before including SO effects. The electric dipole transition moments over SO states are
-29 8500
--2
-29.9000
-30.0000
-30.0500
-30 1000
-30.1500
4 I
1
4
5
I
6
R(Xe-CI)
I
I
7
8
(bohr)
Figure 7. Potential energy curves for the six stata I I / ~ 1312, , II1/2, 11312, and IV1/20f XeClincluding thespin-orbit interactions. Seesection IV.B.2 for a detailed description of the electronic states.
1111/2,
TABLE 6 Molecular Constants and Radiative Lifetimes for XeCl Including Spin-Orbit Effects Re (A) we (cm-1) state
HERE
HDa
ex9
HERE
HD
exub
111112 IV1/2
3.17 3.12 ~ 3.08 ~
3.22 3.18 3.14
2.94
195 198
188 189 188
195
1 1 ~
transition moments ( p l ) and radiative lifetimes (7) HERE transition 111112
+
pJ
1112
79
2.85
IVl/2+11/2
2.09
II3/2-I3/2
0.98
IVlp+IIlp IIIlp- II1/2
0.49 0.88
8.8 (1
HD fie
exP 7
7
2.76
11 ( 12)k 1.94 9.6
7.4 (9.6)h 95 0.96 120 (133)h 169 0.50 180 119 0.87 140 (140)'
11.1
0.2; 27 f 3d
131 f 10; 53 f 6d
AE (ev)
--
transition
HERE HD exP 4.39 4.20 4.03c 5.73 5.53 5.251 4.05 3.76 3.63c IV1/2 5.32 5.13 IIIl/2 4.04 3.83 Reference 2 1 . b Reference 43. Reference 40. Reference 44. References 41 and 42. f p c in units of debye. 7 in units of ns. * Recalculated using experimental AE. Recalcualted using HD's AE.j References 49 and 50. Recalculated using experimental AE by the current authors. Ih/2 IV1/2 b / 2
11/2 I1/2 1312 II1/2 II1/2
-.-
-
states). X is defined as the spin-orbit splitting parameter
= [ E ( 2 p 1 / 2 ) - E('P3/2)1/3 (7) Figure 7 shows the PECs for the six states represented by eqs 5 and 6 with SO corrections to the energies included as described above. The Re and we for a selection of SO corrected states are given in Table 6. It can be seen that the SO correction has had little effect on the Re and wevalues for the 1111/2 and I V l / 2 states. Once
The results for the radiative lifetimes (including SO) are also given in Table 6. The transition dipole moments and AE's were taken in this study near the minima for the excited states. These are R = 5.80 bohrs for the II3/2, R = 5.90 bohrs for the IVI/?, and R = 6.00 bohrs for the I I I 1 / 2 state. The lifetime, T , IS calculated from the definition of the Einstein coefficient for spontaneous emission:
A=1 /= ~ 1.O63(pe(Z- J))2(AE)3X lo6 s-l
-
(9)
For the III!/z 1 1 / 2 transition, the lifetimes are 7 = (8; 1 1 ; 11,m 27 nsM) with the order being (this study; HD; experimental), respectively. The lifetimes for the 113/2 13/2transition are (95; 120; 131,@ 5 3 9 , and for the I V I p 111/2 T = (169; 180; no experiment). For the III1p I l / 2 lifetime, the current result and that of HD's are in good agreement with the more recent experiments of Inoue et al.m The lifetime for the 113/2 13!2 transition from this study lies midway between the two experimental values and is 21% smaller than the theoretical value predicted by HD. The transition moments agree to two significant digits between the two theoretical studies for the I V l / ~ IIIl2 transition (no experimental data available), so the difference between the two lifetimes is attributable to the difference in transition energies. The discrepancy between the current ~(113/2+13/2) value and that of HD is due primarily to a larger vertical A,?? predicted in the current study. Table 6 lists the five transition energies predicted by the two theoretical studies, as well as the experimental values for the 1111/2 1112, I V 1 / 2 1112, and 11312 I3/2 transitions. This study predicts a vertical transition energy (see eq 6) of AE(I1312-13/2) = 4.05 eV at Re(I13/2) = 5.80, while HD predict 3.76 eV, which is closer to the experimental value of 3.63 eV. As a general statement, the level of CI theory used in the current study should be able to generate more accurate wave
-
-
-
-
-
-
Potential Energy Curves for HCl, XeCl, and HCl
+ Xe
The Journal of Physical Chemistry, Vol. 98, No. 23, 1994 5885
TABLE 7: Reference CSFs and Total Number of CSFs Used in Defining the CI Wave Functions for HClXe orbital occunancies in reference CSFs IRREPS la1 2a1 3al 4al 5al 6a1 lbl 2bl 3bl 1b2 AI states 2 2 2 2 0 0 2 2 0 2 2 2 2 1 1 0 2 2 0 2 total CSFs 80 372 BI states
2b2
3b2
0 0 0 0 0 0 0
2
2
2
1
0
1
2
2
0
2
2 2 2
2 2 2 2
2 2 2 2
2
2 2 2
1 1 0 0
0 0 1 1
2 1 2 1
1 2 1 2
0 0 0 0
2 2 2 2
2 2 2 2
2 2 2
2
total CSFs 115 344 functions than the correlation techniques used by HD. Apparently, the higher-lying state in this study did not receive the same level of correlation correction as the lower state, even though each wave function could very well be a better description of that respective electronic state than what was produced in the CI calculations of HD. Since experimental AE's are usually fairly accurately known, one commonly used technique to predict a lifetime from theory is tocombine the theoreticalvalue for the transitiondipolemoment with the experimental AE, thus eliminating the uncertainty in T due to the transition energy. If we recalculate the lifetimes for this study and the H D study using this technique, we get T = 133 ns from this study and T = 138 ns from HD, using the electric dipole transition moments from Table 6. These are both very close to the experimental value of 131 ns predicted by Inoue et al., with the current study now being in better agreement with experiment than the H D value. The T'S for the III1p 1112, recalculated in this fashion, are T(this study) = 11.3 ns and T(HD) = 12.2 ns, to be compared with r(exp) = 11.1 ns. This again puts our value of T in better agreement with experiment than H D value, although the agreement with experiment is quite satisfactory in both cases. These calculations have shown that using effective core potentials, along with modest sized single-and-double excitation CI wave functions, one can predict electronic transition probabilities in good agreement with the experimental values. This lends credence to the prediction of such values for electronic transitions in which experiment has been unable to determine the lifetimes in these doped rare-gas systems. Our vertical transition energies are seen to be larger than the experimentally observed transition energies by -0.4 e in the 111112 1112,I V I ~ 1112, and 11312 13/2bands. This implies that our CI expansions did a better job describing the zeroth-order 122+ and 12II states than the 222+ and 22II states. Much larger (and much more costly) CIS could be done on this system, but the goal is to find out if semiquantitative results could be obtained using modest CI expansions. This would make future studies on larger HClXe, systems computationally feasible where significantly larger C I expansions, commensurate with a highly accurate CI wave function, would not be possible. The discrepancies between experiment and theory for the AE's could be attributed to deficiencies in either the zeroth-order wave functions or the very simple method used here to include spin-orbit effects. This may be answered by a morecomplete treatment of the SO interactions.
-
-
-
-
V. HCI-Xe Interactions HC1-Xe is treated as a linear system with the arrangement of atoms as written. The theoretical work of LG14bpredicted two stable ground-state structures of nearly identical energy: one with the linear arrangement used here and the other with a bent structure where Xe-C1-H forms an angle of 78'. The experimental data strongly support theexistence of two linear structures, one with the hydrogen directed away from Xe as used in this study and one with the hydrogen lying between the C1 and Xe,51-52 and no mention is made of a bent equilibrium structure. The current study uses the linear arrangement supported by both the
theoretical workof LG and experiment, thus allowing comparisons with the semiempirical results of LG.14b The atoms are coincidental with the z axis of the global coordinate system. Calculations were performed at 25 HCI-Xe separations while holding the H-Cl bond length fixed at 2.409 bohrs. This is the experimentally determined equilibrium bond length for the ground state in the gas-phase HCl molecule.3s Henceforth, R(HC1-Xe) will simply be referred to as R. All units are in bohrs unless otherwise stated. The calculations again use effective core potentials on Xe and C1 for all but the outershell electrons. MOs are obtained at each point along the PEC from SA-CASSCF calculations averaging six electronic states; Le., the two lowest-energy roots from the AI, BI, and B2 IRREPs. The weighting scheme used is wi = (2,2,1,1,1,1). The groundstate X(Z+) transforms as the A1 IRREP and the two II components, (IIJI,,), as the (B1,Bz) IRREPs, respectively. A frozen core was maintained which included the two lowest-energy MOs of A I symmetry. The number of active MOs per IRREP were then (AI = 4, B1 = 2, B2 = 2, A2 = 0), with the active electrons per IRREP being (AI = 4, BI = 4, B2 = 4, Az = 0). The use of ECPs is analogous to having a frozen core of MOs, so it must be kept in mind that the symmetry designations la,, lbl, etc., for the MOs label the lowest-energy, noncore MOs from these IRREPs. With no further freezing of orbitals, these state-averaged MOs are used as expansion vectors in multireference, single-and-double excitation C I calculations a t each point along the PECs. In the CIS, due to the axial symmetry of the system, only the II,(Bl) component of the II states is calculated. Three reference CSFs of AI symmetry were used and four of BI symmetry. The reference CSFs are listed in Table 7, along with the total number of CSFs retained per IRREP. Three roots were requested in the diagonalization of the CI Hamiltonian matrix from the Al IRREP and four from the BI. Since only singlet states are treated in this study, the spin multiplicity label will be dropped from the state labels. The typical means for describing the general characteristics of electronic states generated in CI calculations is to refer to the nature of the singly occupied MOs in the main CSFs for each state. One such use of the singly occupied MOs is in determining whether an electronic state is Rydberg, valence, or some mixture of these characters. But using state-averaged CASSCF MOs means that these orbitals, at least the ones included in the active space, are usually guaranteed to be some Rydberg-valence mixture if the states being averaged are of both characters, as it appears to be in this study. The fact that the state-averaged MOs are designed to simultaneously describe several states reduces somewhat their interpretive capabilities. Excluding the use of the MOs as indicators of Rydberg vs valence character, one can still learn much about the nature of the electronic states by inspection of the singly occupied MOs. The A I states are described in their main CSFs by single excitation from the u(4al) into either the 5al or 6al u* virtual MOs. The B1 states are described by an excitation from either the ?r(lbl) bonding or 7r(2bl) antibonding MOs into either the Sal or 6a1 u* MOs. Therefore, both the Z(Al) and II,(B1) use the same u*(5a1,6al) virtual MOs, which are mixed Rydberg-
5886 The Journal of Physical Chemistry, Vol. 98, No. 23, 1994
Adams and Chabalowski I.oc
! I
-30 2
! !
S'B,-X
!
I
0.8C
!
8 1
:! r\
0.60 -30.3 r\
v
J 0
z
v
c
f
F W
0.40
-30 4
0.20
0.W
1
1
1
1
1
1
1
1
1
1
1
1
4
6
8
10
12
14
16
18
20
22
24
26
R(HCI-Xe)
I
I
I
I
I
I
I
I
I
I
6
8
10
12
14
16
18
20
(au)
R(HCI-Xe)
Figure 8. Potential energy cuwes as a function of R(HC1-Xe) for the x component of the three lowest I l l electronic states belonging to the B1
IRREP in linear HClXe. See section V.A for a detailed discussion of these states. valence in character for most values of R. At R = 26.0, the 6al becomes a HC1 u antibonding orbital, and the 5al is essentially a C1 Rydberg s-type orbital. In addition, the u(4al) MO, which is doubly occupied in the ground state, is almost entirely described by Xe atomic pr orbitals for most R values. At the very short distances where R = (4.0,5.0), there is moderate contribution from the C1 s- and p-type AOs, but the Xe AOs are still dominant even at these close distances. So both the 2A1 and 3.41 electronic states arise primarily from an electronic excitation out of atomic Xe. All the R,'s reported here are determined from a simple three-point fit to a parabola. A. The Bl States. The four reference CSFs (see Table 7) for the 1,2,3BI states represent 7~ u* excitations. The 6al MO is comprised primarily of AOs on HCl for R = (4.0,5.0,6.0), with increasing Xe character going from 5.0 to 8.0, a t which point the 6al MO is essentially an even mix of HC1 and Xe AOs. The lbl and 2bl MOs are .rr bonding and antibonding in character, respectively. For 7.0 IR I 12.0, all four MOs have significant contributions from AOs on both C1 and Xe, making the three B1 states truly states of the complex and not isolated to either HCl or Xe within this range. Figure 8 contains the PECs for the electronic states of BI symmetry. It appears that the electronic states undergo significant changes in their character around R = 16.0 and again around 20.0. Figure 9 shows the absolutevalue ?f the electric dipole transition moments, M,, for the 1,2,3B1 X transitions as a function of R. These too suggest major changes taking place in the description of the electronic states around 16.0 and 20.0 bohrs. 1 . The 1B, State. The Re for this state is predict to lie at 8.98 bohrs, which is 0.62 bohr longer than the ground-state minimum. Figure 9 shows the transition moment for lB1 l A l changing rapidly in the region from R = 4.0 to 6.0. The transition moment starts out at 0.21 for R = 4.0, then apparently goes through zero (with a sign reversal) near R = 6.0, and again rises to 0.18 at R = 8.0. No attempt was made to verify the changes in sign for transition moments, since it would serve no purpose in this study. Examination of the CI coefficients for the main CSFs in the lB1 and 2Bl states shows them exchanging character going from R = 5.0 to 6.0, which probably accounts for the rapid change in the transition moment. From R = 8.0, the moment slowly rises to
-
-
-
---. I I 22
24
I 26
(au)
Figure 9. Absolute value of the electric dipole transition moment, we
(au), as a function of R(HC1-Xe) for the transitions from the ground state to thex component of the three lowest-lyingsinglet ll states belonging to the BI IRREP.
TABLE 8 Absolute Value of the Electric Dipole Transition Moment, pe, between the Singlet Ground 1Al and Excited States at Selected R(HC1-Xe) Distances kc
R=
R= R= R= R= state" 6.0b 8.0 12.0 18.0 26.0 HC1 _____~ 2Al 0.69 0.68 0.75 0.18 0.01 1.01 0.34 0.12 0.05 0.00 AI 1Bi 0.04 0.18 0.20 0.25 0.27 0.37,d0.35-0.39e 2B1 0.74 0.77 0.55 0.39 0.43 0.57,60.48C 0.42 0.29 0.19 0.08 0.00 3B1 a Transitions to the BI states represent only the a , component. b R is the distance, in bohrs, between C1 and Xe. Transition dipole moments are in au. This study for R(H-C1) = 2.40 bohrs. e Reference 29 for R(H-CI) = 2.41 bohrs. a value of 0.27 at R = 26.0, with a slight deviation from its monotonic increase occurring around R = 18.0. At R = 26.0, the transition moment apeears to be approaching the values reported for the A ( n ) X transition in HC1, Le., fi,(HCl) = (0.37(this study), 0.3543929). Table 8 reports the transition dipole moments at selected points along the PECs. It is interesting to look at the permanent dipole moment of the lB1 along the PEC. From Table 9 we see it holds rather constant at values ranging from approximately 2 to 3 D for R 1 6.0. These values are in close_agreement with our calculated value of +2.9 D for HC1 in its A ( n ) state. A look at the vertical transition energies, T, for selected R values given in Table 10 shows T decreasing from8.32eVatR = 6.0to8.04eVatR = 26.0,againinreasonable agreeme_nt with t$e T, = (7.90(this study), 7.8428) eV reported for the A ( n ) X transition in HCl. Based on the transition energies, and the permanent and transition dipole moments in the re_gion R = 8.0-20.0, the 1BI state might best be described as the A(II) state in HCl perturbed by the xenon. For R < 8.0, the xenon atom begins to have a significant effect on the properties, which is reasonable since the sum of van der Waals radii53 for C1 (1.8 A) and Xe (2.2 A) is 7.6 bohrs (4.0 A). The transition moment shown in Figure 9 appears to be strongly affected by the close proximity of the two species. The calculated properties for this state leads one to
-
-
Potential Energy Curves for HCl, XeCl, and HCl
+ Xe
The Journal of Physical Chemistry, Vol. 98, No. 23, 1994 5887
TABLE 9 Permanent Electric Dipole Moments for Each Electronic State at Selected R(HCI-Xe) Values for the Six Electronic States in This Study permanent electric dipole moments (debve)" R(bohrs) 1Al 2A1 3Al 1B1 2B1 ~ B I 4.0 5.0 6.0 6.4 7.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 26.0
-0.62 -1.40 -1.53 -1.53 -1.52 -1.50 -1.49 -1.50 -1.50 -1.51 -1.52 -1.51 -1.54
+1.55 -0.92 -0.63 +0.04 +1.11 +3.15 +7.25 +11.07 +15.53 +21.82 +37.09 +39.89 +64.49
+0.07 +11.61 +15.88 +17.36 +19.10 +21.92 +27.60 +33.20 +38.42 +43.18 +47.51 +51.76 +67.38
+1.09 f1.65 +3.09 +2.99 +2.83 +2.15 +2.35 +2.35 +2.39 +2.37 +2.22 +2.29 +2.65
+6.79 +1.00 -0.54 +0.08 +1.14 +3.19 +7.31 +11.13 +15.57 +21.85 -7.38 -10.53 -2.85
+0.10 -6.46 -12.34 -13.37 -14.17 -14.86 -15.72 -16.88 -17.57 -16.73 +37.20 +39.96 +64.52
a A positive dipole moment is defined as having the positive end of the vector pointing toward the Xe atom.
conclude that its character is that of the valence A ( n ) excited state of HC1 perturbed by the Xe. At R = 26.0 this state truly becomes localized to HCI, and so at R = 26.0 the_ 1B1 X transition can unambiguously be assigned to the A ( n ) 2 transition in HC1. 2. The 2B, State. At R = 26.0, the 2B1 is described primarily as a Cl(p,) a*(HCl) excitation, with the AOs on Xe making very little contribution to the singly occupied MOs in the main CSFs. The transition energy given in Table 10 for R = 26.0 is T = 9.93 eV, which lies reas2nably close to T, = (9.65(this study), 9.6728) for the C(n) X Rydberg transition in HCl. The calculated transition dipole moment in HCl is pe = (0.57(this study), 0.4829), to be compared with the HClXe value of pe(R=26.0) = 0.43 au. The current study predicts the permanent dipole moment for the C(n)state in HCl to be-0.74 D, compared with the current HClXe value of -2.8 at R = 26.0. Even though the value for HClXe is almost 3 times that of HC1, they are both relatively small dipole moments and both negative. The 2B1 state has the only negative permanent dipole of the three B1 states at R = 26.0. The HC1 and Xe seem to have a rather long-range interaction as can be seen in the changing permanent dipole in Table 9, as well as the transition dipole moments in Figure 9, even as R increases beyond 20 bohrs (- 10.6 A). So at R = 26.0 the 2Bl electronic state does appear to be Rydberg in its extensiveness. This, coupled with the calculated prcperties, suggests that, at R = 26.0, the 2B1 correlates with the C ( n ) t 2 Rydberg transition in HCI slightly perturbed by the Xe atom. It is now interesting to examine the rather large changes in properties as the Xe approaches the HCl. In Figure 9 the transition moment shows irregular behavior in moving from R = 26 to 16, particularly in the region R = 16-20. From the PECs in Figure 8, it appears that the 2Bl encounters avoided crossings with other B1 states in this region, explaining the peculiar behavior of the transition moments in this region. Beginning with pe = 0.3 1 au at R = 16, the transition moment increases as R decreases, reaching a maximum of pe = 0.78 au a t R = 7.0, and finally decreasing to 0.22 at R = 4.0. The vertical transition energy, T = 8.89 eV, at R = 8.0 (see Table lo), shows this transition to be separated from the lB1 lA1 transition by only 0.6: eV.-This is consjderably less than the separation between the C X and A X transitions in HCl, i.e., ATe = 1.75 eV, to which these two transitions appear to correlate at dissociation. One interpretation of this would be that_ the xenon atom preferentially stabilizes the C state over the A state in HCl. It is also worth noting the depth of the lowest minimum for this state at Re = 7.04 in Figure 8. If we define the barrier to dissociation to be AE* = TR,- TR40.0, then AE* = 1.65 eV (37.9 kcal/mol), which is a fairly sizable barrier to dissociation. The permanent dipole moment is calculated to be +3.2 D at R = 8.0, similar to the lB1
--
-
-
-
+-
-
TABLE 1 0 Vertical Transition Energies in eV as a Function of R(HC1-Xe) Relative to the Ground State l A 1 R (au) 4.0 5.0 6.0 6.425 7.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 26.0
2A1 5.56 7.86 8.60 8.71 8.80 8.90 9.09 9.34 9.67 10.09 10.81 10.82 11.47
AI 7.27 9.62 10.81 11.12 11.42 11.82 12.40 12.76 13.03 13.28 13.86 13.81 14.48
HC1 a
1Bi 7.57 8.28 8.32 8.28 8.25 8.23 8.22 8.22 8.23 8.22 8.07 8.20 8.04 7.90' 7.84b
~ B I 8.41
8.70 8.75 8.78 8.82 8.89 9.08 9.34 9.68 10.12 9.96 10.47 9.93
~ B I 10.80 10.17 10.39 10.48 10.59 10.70 10.79 10.85 10.86 10.78 10.84 10.84 14.53
9.65" 9.67b
This study. Reference 28.
state and much too small to be considered as an electron-transfer state. In summary, for the region R = 6.0-20.0 the main CSFs for 2B1 show it to be a state composed of electron density from both C1 and Xe, hence having no counterpart in the isolated Xe or HCl. But at the largest R value treated here, R = 26.0, the 2B1 state becomes a ?r u* transitiop loccted primarily on the HCl and roughly correlates with the C X Rydberg transition in HCl slightly perturbed by the xenon. 3. The 3B1 State. At R = 26.0, this state is predicted to lie 14.53 eV above the ground state. Neither this study nor the earlier theoretical studies on HC128329 reported excited electronic states at such high transition energies, but even if such high-lying states had been reported, the 3B1 could not be associated with any HCI state due to its description in its main CSF. This CSF, with CI coefficient c2 = 0.88, represents an electronic promotion from MO l b l into 5al, where lbl is essentially the Xe(p,) A 0 and 5al is essentially the Cl(s-Rydberg) AO. This state then represents an ionic or electron-transfer state of n symmetry. One can substantiate this claim by examining the permanent dipole moments given in Table 9. Its value at R = 26.0 is +64.5 D, which obviously makes this a very polar state. But if we look at the transition dipole moment (Table 8) at R = 26.0, we see that there is essentially zero probability for this electron transfer to occur. The excitation probability does increase as R decreases, such that at R = 16.0 the transition moment is calculated to be 0.18 au, and the transition energy has dropped to 11 eV, while the permanent dipole moment still remains very large, but of opposite sign a t -16.73 D. This change in sign of the permanent dipole moment in going from R = 18.0 to 16.0 indicates a radical change in the character of the 3B1 state, supporting the earlier statement that the PECs for the B1 states show avoided crossings with one another in this region. For distances around R = 8.0, the state is still seen to be quite polar in nature with a dipole moment of -1 4.9 D. It is interesting that the positive end of the dipole vector now points toward the hydrogen atom and not the xenon. This would suggest electron transfer from the chlorine (or HCl) toward the xenon. A look at the main CSFs for the 3B1 over the entire PEC shows that this state, like the 2B1, is truly a state that exists due to the complex. The large and relatively steady decrease in the absolute magnitude of the transition moment from R = 6.0 to R = 14.0 supports the claim that the 3B1 state does not correlate closely with any state in the isolated species over any part of the PEC. For R > 16, the state appears to be a C T state, and for R < 16, it more closely resembles a highly polarizable, diffuse (possibly Rydberg) state. B. The AI States. All the A1 states calculated here are predicted to be bound, although theground state l A l is predicted to have a barrier to dissociation of only -0.035 eV calculated from Re = 8.36. The semiempirical calculations of LG14b
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+
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Adams and Chabalowski
The Journal of Physical Chemistry, Vol. 98, No. 23, 1994 -30.20
-30 3
-30.25
-30 4
-30.30
r\
J 0
3
0
v
v
Z -30.5
Z -30.35
P
P I
[I
K
W
W -30 6
-30.40
-30 7
-30.45
-30 8 1 I
5I
6I
7I
8I
R(HCI-Xe)
Figure 10. Potential energy curves as a function of R(HCI-Xe) for the
three lowest )E+electronic states belonging to the A I IRREP in linear HCIXe. See section V.B for a detailed discussion of these states.
TABLE 11: Calculated 4 ' s for HCIXe' state De (eV) state De (eV) 1'Al 2lA1
0.035 2.1
3lA1 1'Bl
3.6 b
state
De(eV)
2lB1 3lB1
0.93
1.1
a De = E(Re) - E(R=26.0), with Re being the HCI-Xe minimumenergy separation for this state. Has a barrier to dissociation of 0.02 eV at R = 16.0 bohrs, but predicted to be unbound by definition of De given in footnote a.
predicted a R,(HCl-.Xe) of 7.22 with a H-Cl bond length of 2.41 bohrs in the linear HClXe ground-state complex. The potential well, however, is predicted to be very shallow and broad as previously noted by LG and supported by this work as shown in Figure 10. On the basis of the level of theory used here, it is not possible to conclude whether or not the ground state is indeed bound. No efforts were made to correct for the basis set superposition error due to the qualitative nature of this study. The calculated De)s for all the states are listed in Table 11. Both the 2 and 3Al states are described primarily by electronic promotions from the 4al M O of u symmetry comprised almost entirely of atomic pz density on the Xe atom into the 5al and 6al u* MOs. These are the same u* MO's involved in the .rr u* excitations describing the main CSFs in the B1 states. 1 . The2Al State. Thedominant CSFin the2Al wave function for R = 6.0-16.0 is a 4al 5al single excitation. The square of the CI coefficient for this CSF is constant at cz = 0.86 over this region. This represents an electron promoted from a MO comprised essentially of the Xe(p,) atomic orbitals into the 5al u* MO. Table9showsthat thepermanentelectricdipolemoment of the 2Al state is nearly identical with the 2B1 state for R 1 6.4-16.0, and Figure 11 shows the two PECs to be essentially degenerateover theregion R = 8.0-16.0. Thesimilarities between these two states can be rationalized in terms of the sum of the van der Waals radii for C1 + Xe, which is predicted to be 7.6 bohrss3 for the electronic ground state of HClXe. As C1 approaches Xe along the z axis, the electron clouds for the two atoms should begin penetrating one another around 7.6 bohrs. To a rough approximation, outside this distance the 4al M O can be thought of as a perturbed Xe(p,) atomic orbital. In the 2Bl state, the electronic excitation arises primarily from the 1bl(.rr,) MO, which is described predominantly by the Xe(px) atomic
-
-
9I
10 I
1I1
12 I
13 I
14 (
(au)
Figure 11. Potential energy curves as a function of R(HCI-Xe) for the 2A1 and 2B1 electronic states in linear HClXe. See section V.B.1 for a
discussion of these PECs. orbital for R > 8.0. Thus, if the spherical symmetry of the xenon atom is only moderately perturbed by HCl, an excitation out of the 4alMO (Le.,Xe(p2) AO) should be nearly indistinguishable from an excitation out of the lbl(.rr,) M O (i.e.,Xe(px) AO) as is the case for the 2B1 state. (The reader is reminded that both the A1 and B1 states are characterized by excitations into the same two u* MOs.) Hence, the PECs for the 2Al and 2Bl begin to split apart (Figure 11) for distances less than the sum of van der Waal's radii, which is near -8 bohrs. Between R = 5.5 and 7.0, the 2Al acts as if it is being preferentially stabilized over the 2B1 state by the approach of the CI and Xe atoms. The permanent dipole moment in the region R = 8.0-16.0 (+3.2 and +21.8 D at R = 8.0and 16.0, respectively) is too small for this to be considered a charge-transfer state; however, one might interpret it as a Rydberg state polarized by the electronegativity of the C1 atom. The transition moment remains large and rather constant (Figure 12), with values of fii = 0.69 au a t R = 6.0 to 0.57 a t R = 16.0. The fact that the transition moment remains both constant and large over such a distance also supports the interpretation of this as a Rydberg state. For values of R L 10.0, the 5al(u*) has a significantly larger contribution from the Xe s-type AOs than any AOs on HC1. For these larger separations, the state resembles a Xe p2 u(s) Rydberg state of the xenon atom strongly perturbed by the HC1. In the region R = 18.0-20.0, there are apparently avoided crossings occurring among the AI excited states as reflected in the PECs (Figure lo), permanent dipole moments, and transition dipole moments (Figure 12). Finally, at R = 26.0, the wave function is described by a CSF representing an electron promoted from the Xe(p2)AOs into the Rydberg u(s) M O comprised almost entirely of C1 s-type AOs. The permanent dipole moment is +64 D, which is roughly the value of unit positive and negative charges separated by 26 bohrs. This now appears to be a charge-transfer state; however, the probability for reaching this state from the ground state is practically zero due to a vanishing transition dipole moment. 2. The 3AI State. The 3AI resembles a true charge-transfer state. This is substantiated by the value of the permanent dipole moment. At R = 8.0, the dipole is predicted to be +21.9 D, while
-
Potential Energy Curves for HCl, XeCl, and HCl
+ Xe
The Journal of Physical Chemistry, Vol. 98, No. 23, 1994 5889 This type of state, a t least in the region R * 6.0-8.0, could serve as a model for studying the charge-transfer excitation in solid xenon matrices doped with HCl as reported by Apkarian and co-workers.'" As mentioned in the Introduction, the Cl-Xe distance has been estimated to be -6.4 bohrs in the gas phase 42r state of the charge-transfer exciplex Xe2Cl. These calculations predict a large probability of charge transfer in the 3A1 for R = 6.0-8.0 based upon the calculated transition dipole and permanent dipole moments. This might then be followed by dissociation of HC1 from a weakened u bond due to the H-Cl u* antibonding character of the 6a1 M O which plays a major role in describing the 3A1 state.
-
4
6
6
10
12
14
R(HCI-Xe)
16
I8
20
22
24
26
(au)
Figure 12. Absolute value of the electric dipole transition moment, p , (in au), as a function of R(HC1-Xe) for the transitions from the ground state to the two lowest-lying excited states belonging to the A1 IRREP.
two unit point charges of opposite sign separated by 8.0 bohrs would have a dipole moment of +20.3 D. The Re is predicted to be 5.35, in good agreement with the bond length for the "4i" ionic state calculated to be Re = 5.52 by LG.14b It should be noted that their HCl bond length was allowed to vary in their optimization and was predicted to be 2.99 bohrs, which is 0.58 bohr longer than the fixed bond length of R(HC1) = 2.41 used here. The vertical transition energy at R = 5.0 is T = 9.62 eV, while Te = 10.86 eV calculated with Re = 5.35 for the 3A1. This can be compared to Last and George's value of T , = 8.43 eV taken between the analogous minimum-energy structures. At R = 5.0, this state is primarily described by a CSF defined as a single excitation 4al 6a1, u* state. This represents an electronic excitation from the Xe pr atomic AOs into a M O localized mostly on the HCl and having H-Cl u-antibonding character. This would suggest a longer bond length for the H-CI in this state, consistent with the results of Last and George. To explore this the C1-Xe distance was fixed at R = 5.35 and the H-Cl distance varied. The result from fitting to a parabola gives a 3A1 minimum-energy H-Cl bond length of R = 2.874. Next, the H-Cl separation was held fixed at this new value and the Xe-Cl distance varied, predicting a new Re(3A1) of 5.62 and a corrected T , of 10.20 eV. This is still considerably above the value reported by LG of 8.43 eV. It is not obvious why there remains a 1.77-eV discrepancy between the T, of LG and this study, since LG also neglected SO effects in their DIM calculations.14b Returning to the original R(HC1) fixed at 2.41, the 3A1 state is seen to rise in energy as the HCl-Xe separation increases, becoming the highest-lying vertical transition calculated in this study with T = 11.82 eV a t R = 8.0. The transition energy steadily increases (excepting$ R = 20.0, see Table 10) to 14.48 eV at R = 26.0. The 3Al- X transition is calculated to be very intense for R I7.0. The transition dipole moment drops rapidly from a value of pe = 2.17 au at R = 4.0 to p, = 0.0 at R = 10.0 (see Figure 12). Along with the changing p,, the character of the 6al M O changes from one arising from density on HCl to one with contributions from all three atoms as R goes from 6 to 16. In the region of avoided crossings around R = 18-20.0, the transition moment is seen to be small and finally drops to essentially zero at R = 26.0.
-
-
VI. Conclusion Our results on the A(lII) %(lZ+) and C(lII) %('E+) transitions in HCl showed the ability of the ECPs, in conjunction with SA-CASSCFand CI treatments, to quantitatively reproduce experimentally observed properties in HCl. Perhaps the most notable results from the HCl study, besides substantiating the effectiveness of using ECPs, a_rethe oscillator strengths& and fol calculated for theelectronicC('lI) +%(lZ+) transition. Earlier theoretical results predicted, as a best value,fm = 0.15, while experiment givesfm = 0.185 f 0.037, a 19% discrepancy but lying within the experimental uncertainty. The current value is f00 = 0.175 or a 5% discrepancy with experiment. The fol= , 0.077 value from this study, representing an excitation from X(u "=O) into C(u'= l), differs substantially from the experimental value off01 = 0.022 (factor of 2 uncertainty), which agrees well with the earlier theoretical prediction off01 = 0.024. Since our t_ransitio_nenergies and values for the other properties of both the C and X states appear to be in very good agreement with experiment, the currentfol= 0.077 valueought to begiven serious consideration. These values for transition strengths become important when using HCl emission intensities to determine HCl concentrations in the stratosphere or in interstellar clouds. It has been shown that much insight into the XeCl interactions can be achieved through the combination of effective core potentials and wave functions obtained from state-averaged MCSCF and CI calculations. The results on XeCl compare favorably with earlier ab initio work by Hay and Dunning21 as well as experimental results. This study helps substantiate HD's earlier work which was based upon much smaller CI wave function expansions. It is clear from both HD's study and this work that the spin-orbit corrections are indispensable in attaining quantitative accuracy in predicting transition energies and transition strengths in future studies of rare gas/halide interactions. The results of the HCl-Xe calculations have produced much insight into the fundamental natureof the excited electronic states in this system. The 1 and 2Bl states are predicted to look like molecular HCI states perturbed by the Xe atom at values of R(HC1-Xe) Less than 10. At dissociation these states closely resemble the A(lII) and C(lII) states of HCl plus a ground-state Xe atom. In contrast, the 3Bl state shows characteristics associated with the HClXe molecule as a whole, represented by an electron promotion of r(XeC1) u(HC1Xe). At separations of R(HC1-Xe) > 16, it has the permanent dipole moment expected for a transfer of charge from Xe to HC1, but for R(HC1-Xe) < 16, it has a dipole of opposite sign and smaller in magnitude than what is expected for a CT state, perhaps indicating a polarized Rydberg state. The 2Al state also shows characteristics associated with the entire HClXe molecule. This state also appears to be a Rydberg state. The 3Al state is quite interesting since it clearly represents a charge-transfer state over the entire R(HC1-Xe) range, with a transfer of an electron from the Xe atom to an antibonding a(HC1) MO, just as predicted from the experiments of Apkarian and co-workers3 in the halogen-doped xenon (and other rare gas) matrices. The probability for excitation into this C T state is enhanced by a substantial transition dipole moment in the region
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5890
The Journal of Physical Chemistry, Vol. 98, No. 23, 1994
R(HC1-Xe) = 6-8, which includes the predicted equilibrium bond length (Re= 6.4) for Xe-CI in the 4Tcharge-transfer state of the gas-phase Xe2Cl exciplex.
References and Notes (1) Fajardo, M. E.; Apkarian, V. A. J . Chem. Phys. 1986,85, 5660. (2) Fajardo, M. E.; Apkarian, V. A. J. Chem. Phys. 1988,89, 4102. (3) Fajardo, M. E.; Apkarian, V. A. J. Chem. Phys. 1988,89,4124. (4) Wiedeman, L.; Fajardo, M. E.; Apkarian, V. A. Chem. Phys. Lett. 1987, 134, 5 5 . ( 5 ) Okada, F.; Wiedman, L.; Apkarian, V. A. J . Phys. Chem. 1989,93, 1267. (6) Fajardo, M. E.; Apkarian, V. A.; Moustakas, A,; Krueger, J.; Weitz, E. J. Phys. Chem. 1988, 92, 351. (7) Fajardo, M. E.; Apkarian, V. A. Chem. Phys. Lett. 1987,134, 51. (8) Kunttu, H.; Feld, J.;Alimi, R.; Becker, A.; Apkarian, V. A. J . Chem. Phys. 1990, 92,4856. (9) Katz, A. I.; Feld, J.; Apkarian, V. A. Opt. Lett. 1989, 14, 441. (10) Schwentner, N.; Apkarian, V. A. Chem. Phys. Lett. 1989,154,413. (1 1) Gerber, R. B.; Alimi, R.; Apkarian, V. A. Chem. Phys. Lett. 1989, 158,257. Alimi, R.; Brokman, A.; Gerber, R. B. J . Chem. Phys. 1989,91, 1611. (12) Alimi, R.; Gerber, R. B.; Apkarian, V. A. J . Chem. Phys. 1989,89, 174. (13) Alimi, R.; Gerber, R. B.; Apkarian, V. A. J . Chem. Phys. 1990,92, 3551. (14) (a) Last, I.; George, T. F. J . Chem. Phys. 1987,87,1183. (b) Last, I.;George, T. F. J . Chem. Phys. 1988,89,3071; 1987,86,3787. Last, I.; Kim, Y. S.; George, T. F. Chem. Phys. Lett. 1987,138,225. Last, I.; George, T. F.; Fajardo, M. E.; Apkarian, V. A. J . Chem. Phys. 1987,87, 5917. (15) Stevens, W. J.; Krauss, M. Appl. Phys. Lett. 1982, 41, 301. (16) Schwentner, N.; Fajardo, M. E.; Apkarian, V. A. Chem. Phys. Lett. 1989,154, 237. (17) Wadt, W. R.; Hay, P. J. J . Chem. Phys. 1985,82, 284. (18) van Duijneveldt, F. B. IBM Research Report RJ 945, No. 16437, 1971. (19) Frisch, M. J.; Pople, J. A.; Binkley, J. S. J . Chem. Phys. 1984, 80, 3265. (20) Dunning, T. H.; Hay, P. J. In Methods of Electronic Structure Theory: Modern Theoretical Chemistry; Schaefer 111, H. F., Ed.; Plenum Press: New York, 1977; Vol. 3, Chapter 1. (21) Hay, P. J.; Dunning, T. J . Chem. Phys. 1978, 69, 2209. (22) Lengsfield, B. H. J. Chem. Phys. 1982, 77,4073. (23) Liu, B.; Yoshimine, M. J. Chem. Phys. 1981, 74, 612. (24) Jura. M. Astronhvs. J. Lett. 1974. 190. L33. (25) Dalgarno, A.; db Jbng, T.; 0ppenheimer;M.; Black, J. H. Astrophys. J . Lett. 1974, 192, L37.
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