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Spectroscopic properties and potential energy curves of GaCl
Volume
193, number
1,2,3
CHEMICAL
PHYSICS
22 May 1992
LETTERS
Spectroscopic properties and potential energy curves of GaCl Gyoung-bum
’
Kim and K. Balasubramanian
Department of Chemistry, Arizona State University, Tempe, AZ 85287-1604, Received
17 October
199 1; in final form I9 February
USA
1992
Fifteen electronic states of GaCl are investigated using relativistic ab initio complete active space MCSCF (CASSCF) followed by large-scale multi-reference configuration interaction calculations which included up to 1000000 configurations. Potential energy curves and spectroscopic constants of various electronic states are reported. Spectroscopic constants of eight new states are obtained which are yet to be observed. Calculated spectroscopic constants of GaCl are in accord with the experimental constants
for the known states.
1.. Introduction
Spectroscopic constants of group (III) monohalides and their cations are of interest [ l-81 since they can be formed in halogen-etching reactions with GaAs semiconductors. For example, Liberman et al. [ 7 ] observed GaCl molecules using a differentially pumped quadrupole mass spectrometer in the reaction of CIZ with n-type GaAs ( 110) surface under high-vacuum conditions. The GaCl molecule was one of the main desorption products which resulted from both thermal and laser-induced reactions. Reents [ 91 conducted an experiment in which the gas phase HCl etches Ga,As_; clusters primarily through loss of GaCl. Our investigation here predicts a number of spectral bands for GaCl in the visible-near-UV region. The theoretical results on the GaCl diatomic molecule reported here should therefore be of use in not only the assignment of existing spectra, but also in the prediction of new spectra which are yet to be observed. The early spectroscopic studies on GaCl include those by Miescher [ 11, Levin and Winans [ 21, Barrett and Mandel [ 31, Bartky [ 41, and Tiemann et al. [ 5 1. A summary of experimental work on GaCl up to 1976 can be found in ref. [ 61. In a more recent Correspondence to: K. Balasubramanian, Department of Chemistry, Arizona State University, Tempe, AZ 85287-1604, USA. ’ Camille and Henry Dreyfus Teacher-Scholar. 0009-2614/92/$
05.00 0 1992 Elsevier Science Publishers
spectroscopic study of monohalide cations, Glenewinkel-Meyer et al. studied GaCI+ using the ionmolecular reaction, Ga+ + CIZ+ GaCl+* + Cl [ 8 1. In their chemiluminescence spectra, a band near 4 1150 cm- ’ was attributed to the C ‘II-X ‘C+ system of GaCl. The C state was predissociated due to a curve crossing. Berkowitz and Dehmer [ lo] have recorded the photoelectron spectrum of GaCl among other group III halides. They have also considered ab initio and semi-empirical calculations on the ground state of GaCl. Although there are ab initio computations on the ground state of GaCl [ 10,111, there are no theoretical calculations on the spectroscopic properties and potential energy curves of the excited electronic states of GaCl. The objective of the present investigation is the systematic calculation of the potential energy curves and the spectroscopic properties of electronic states of GaCl using a relativistic complete active space MCSCF (CASSCF) followed by first-order configuration interaction (FOCI) calculation. In addition to this, second-order configuration interaction (SOCI) calculations, which include up to 1000000 configurations, are carried out on some of the electronic states of GaCl.
2. Method of calculation We use complete active space MCSCF (CASSCF)
B.V. All rights reserved.
109
Volume 193, number
I ,2,3
CHEMICAL
PHYSICS
followed by first-order configuration interaction (FOCI) and second-order configuration (SOCI) calculations. All the calculations described here employ relativistic effective core potentials (RECP) which include the outer 4s24p’ shells for the Ga atom and outer 3s23ps shells for the Cl atom in the valence space, respectively. We employ the Gaussian RECPs generated by Hurley et al. [ 12 ] for the gallium atom and by Patios and Christiansen [ 131 for the chlorine atom. These authors have also optimized (3~3~) valence Gaussian basis sets for the 2P ground electronic states of each atom. Each set was augmented by one set of diffuse s, p and one set of d-type polarization functions. The exponents of the additional functions are a,=O.O2644, a,=0.0164 and a,=0.20 for Ga atom, and (~~~0.06322, (u,=O.O532 and (~,=0.750 for Cl atom. The orbitals for the FOCI calculations were generated using the CASSCF method. The gallium valence 4s 4p and chlorine 3s and 3p orbitals correlate into four a,, two bz and two b, orbitals in the CzV group. Excitations from the la, orbital which is correlated into the 3s orbital of Cl atom were not allowed in the CASSCF because of its low orbital energy, but the seven remaining orbitals were included in the active space in the CASSCF. The eight outer electrons of GaCl were distributed in all possible ways among these seven orbitals in the CASSCF method. Separate CASSCF calculations were carried out for states of different spatial and spin symmetries in the CzV group. The first-order CI calculations were carried out following CASSCF calculations. In these calculations, excitations from the la, orbital were also included. All configurations in the CASSCF, plus configurations generated by distributing nine electrons in the internal space and one electron in the external space in all possible ways, were included in this step. After FOCI calculations, SOCI calculations were carried out for some states. In these calculations all configurations in the CASSCF and FOCI, plus configurations generated by distributing eight electrons in the internal space and two electrons in the external space in all possible ways, were included. The CASSCF and FOCI/SOCI calculations were carried out using Balasubramanian’s [ 141 modified version
of ALCHEMY II #’ codes to include relativistic
ECPs.
3. Results and discussion Table 1 shows the dissociation relationships for the possible low-lying states and the energy separations obtained by the CASSCF/FOCI method at the dissociation limits for the molecular electronic states of GaCl. The experimental atomic energy separations were taken from Moore’s table [ 15 1. The theoretical FOCI 2P+2P and ‘S+‘P energy splitting is 29934 cm-’ which is a little larger than the experimental value of 24789 cm-‘. On the other hand, the (5~) 2P+2P and 2S+2P energy splitting is a little lower than the corresponding experimental energy splitting. In general, it has been known that the FOCI method yields satisfactory agreement of such magnitude with experiment. The SOCI results are much improved. It should be noted that although our (4s4pld) basis set is adequate for the ground state, it is somewhat less satisfactory for the excited states. Table 2 shows the calculated FOCI spectroscopic properties and fig. 1 shows the potential energy curves. The experimental spectroscopic constants are known for the X ‘C+ state and the spin-orbit components of the 311 state. The experimental B 311, and A 3110+ states were found to be at 29859 and 29527 cm-‘, respectively. As seen from table 2, the theoretical FOCI T, of the 311 state is 24589 cm-‘. Our calculated FOCI transition energy for the 311-‘E+ transition, therefore, shows only fair agreement with the corresponding experimental value. However, the ” The major authors of ALCHEMY
II codes are B. Lengsfield,
B. Liu and M. Yoshimine. Table I Dissociation Molecular
relationship
of low-lying states of GaCl
states
Atomic states (Ga+CI)
Energy (cm-‘) exp. a’
FOCI ‘E+(2), 3X’(2), ix-, ‘E‘I-I(2), ‘D(2), ‘A,‘A ‘II, )rI, ‘z+, SE+ iE+(2), 3x+(2), ‘Z-, %x.‘1-1(2),311(2), ‘A, ‘A a) Averaged
110
22 May 1992
LETTERS
over J from ref.
2P+2P *Sf2P (5p)ZP+2P
[ 151.
0 29934 35007
0 24789 33118
Volume
193, number
Table 2 FOCI spectroscopic
CHEMICAL
1,2,3
constants
of GaCl
State
R,(A)
T, (cm-‘)
w, (cm-‘)
& (D)”
Ix+ ‘II ‘z+
2.208 2.177 3.636 2.835 2.844 2.858 2.870 3.268 2.203 2.948 2.205 2.443 2.082
0 24589 35884 36285 36355 37799 37813 38213 38379 52659 65977 70329 74690
381 364 46 240 269 212 256 160 359 383 377 283 371
2.03 1.80 -0.32 - 1.60 - 1.63 - 1.55 -1.51 -0.83
‘A ‘A ‘X‘Z‘Z:+(U) ‘I-I %(III) W(I1) ‘rI(II1) ‘A(I1)
‘) Positive polarity
0.20
-
0.15
-
PHYSICS
-4.50 -0.49 0.53
means Ga+Cl-.
0.10t
0.05
-
0.00
-
;i
ih m
6 w
I 1.0
I
2.0
I
1.0
/
I
I
I
I
1.0
5.0
6.0
1.0
80
A IWram)
Fig. 1. Potential
energy curves for GaCl.
SOCI results are in much better agreement. In addition, the C ‘II-X ‘E+ system has been studied although the C state was predissociated and the C-X bands were diffuse. The FOCI R, of the ground state is 2.208 8, which is in good agreement with the ex-
LETTERS
22 May 1992
perimental value r, (X ‘C+ ) =2.202 A. The FOCI o, of the ground state is, however, a little larger than the corresponding experimental o,= 365 cm-‘. The same pattern holds for the first excited state in that there is agreement between the FOCI R,= 2.177 8, and the experimental R,=2.146 8, for 311,,+, but a little discrepancy exists between the FOCI w,=364 cm-’ and the experimental we=395 cm-‘. Table 3 shows the SOCI spectroscopic constants of GaCl. The SOCI results include electron correlation effects to a greater degree compared to the FOCI results since the SOCI also includes two-electron excitations into the external space of orbitals. A critical comparison of the results of tables 2 and 3 reveals that the r, values predicted by the FOCI method are in reasonable agreement with the SOCI values except for electronic states with larger r, values. For states with larger r,s, the SOCI method yields improved results. The SOCI vibrational frequencies are closer to the experimental values. For example, the SOCI ground state w, of 364 cm-’ is extremely close to the experimental value of 365 cm-‘. The T, values are generally much improved at the SOCI level. For example, the experimental T, of the B 311’ and A3110+ states are 29859 and 29527 cm-‘, respectively, while our SOCI T, of the 311 state in the absence of spin-orbit coupling is 21994 cm- ‘. The smaller theoretical T, is primarily because the electron correlation effects of the X ‘C+ state are still not fully accounted for at the SOCI level. The D, of the X ‘Z+ ground state is computed as 4.5 eV at the SOCI level and 4.48 eV at the FOCI level. The Davidson correction to SOCI did not change the D, at all, indicating the completeness of the SOCI method. This suggests that the most possible source of the discrepancy in the De and T, of the electronic states of GaCl is due to the basis set limitation and possible 3d-electronic core-valence correlation effects. Levin and Winans [ 21 have studied the absorption spectrum of GaCl. From the experimental spectrum, they have deduced the existence of B 3111, A 3110+ and C ‘II electronic states for GaCl. A subsequent recalculation of the molecular constants of Bartky [4] has suggested voo values of 29874 and 29542 cm-‘, respectively for the B 3111 and A 3110+ states. The band head of the C-X system of GaCl was located at 40 139 cm-’ by Levin and Winans [ 21. 111
Volume 193, number 1,2,3
CHEMICAL PHYSICS LETTERS
22 May 1992
Table 3 SOCI spectroscopic constants of GaCl State
R,(A)
T, (cm-‘)
0, (cm-‘)
pc tD) =)
‘x+ ‘I-I ‘11+ 3A ‘A
2.209 2.164 3.714 2.633 2.648
0 27991 36026 39839 39842
364 370 42 217 217
2.41 1.96 -0.43 -0.31 -0.34
a) Positive polarity means Ga+CI-.
The theoretical T, of the ‘II state is 38379 and 40709 cm-‘, respectively, at the FOCI and SOCI levels of theory, although at the SOCI level we found that the ‘II state is much shallower. Consequently, our computed energy separations of the electronic states of GaCl fully support the previous assignments. Levin and Winans [ 21 found that the C ‘H-X ‘C+ system was predissociated. The most probable state causing predissociation of the C state was considered as the ‘A state based on qualitative selection rules in the absence of spin-orbit coupling. As seen from fig. 1, both 3C+ and ‘A curves cross the ‘II curve. Although the 3C+ and ‘A states are not repulsive, they exhibit minima only at long range. Consequently both states are possible candidates for predissociation. The spin-orbit coupling effect on Ga is not negligible. Therefore, predissociation can occur through spinorbit coupling. Note that the 3C+ state yields Q= Oand 1 states in the presence of the spin-orbit operator. The Q= 1 component of 3Ec+ can interact with ‘II,. The ‘A state gives only an Q= 2 state, which cannot interact with ‘II,. Hence predissociation by ‘A can occur only through non-adiabatic rotationally induced effects rather than spin-orbit coupling. Consequently, we suggest that the 3Cf (Q= 1) component can predissociate C ‘II, through spin-orbit coupling. Levin and Winans [ 2 ] have deduced the 0, of GaCl through the predissociation of the C system as 4.99 eV, in reasonable agreement with our SOCI value of 4.5 eV. Continuous absorption at 41200 cm-’ and near 47600 cm- ’ were experimentally found [ 61. The first continuous absorption at 41200 cm-’ could be due to many closely spaced excited states with shallow minima close to each other as shown in fig. 1. Since there are no definitive analyses of the observed continua, it is hard unambiguously assign these spectra, 112
although our calculations reveal the existence of several electronic states in this region. The second roots of II symmetry, ‘II (II) and 311(II), are found to be repulsive while the third roots, ‘II(II1) and 311(111), have minima. The ‘A(I1) state is quite mixed with Rydberg states. The T, of ‘x+(11) is below that of C ‘II and it has 8.1% of lo22023021n32nk Rydberg character. Tables 2 and 3 also show the dipole moments of the various electronic states of GaCl. The SOCI dipole moments are more accurate compared to the FOCI values. For example, the pL,of the ground state increases by 0.4 D in going from the FOCI to the SOCI level of theory. As seen from tables 2 and 3, several excited states have the opposite polarity of p, (Ga-Cl+ ) compared to the ground state, indicating charge transfer in the electronic transitions from the ground state to these excited states. Table 4 shows the compositions of the electronic states of GaCl as revealed by the contributions of various electronic configurations. As seen from table 4, the contributions of Rydberg electronic configurations in several excited states are rather large. The computed T, values of such states reported in table 2 are not expected to be very accurate since the basis set was optimized for the ground state atoms although they are augmented with diffuse functions and polarization functions. The ground state arises from the closed-shell configuration lo22023a2 1n4 with an appreciable amount of the lo22021~42x2 configuration (3.7%). The ionic character of the GaCl bond is confirmed by the lo22023021rt4 configuration in which the 1~ molecular orbital is predominantly Cl (3~). The first excited state, ‘II, has a predominant (94.4%) configuration of 10~20~30’ 1rr427r’, which results from an electron excitation from the 30 MO to the 27t MO.
Volume 193, number Table 4 Contributions GaCl
CHEMICAL
1,2,3
of various electronic
configurations
PHYSICS
to the wavefunctions
of the FOCI electronic
‘z+ )II 3x+
lo22023a21~4(91.8%), lo22021x42n2(3.7%) lo22023a’ln42a’(94.4%), lo220’3021x42x’(0.5%) l~2023~lrc’2n’(91.8%), lo22a21rr’2x3(l.6%), lo220’30240’lrr4(0.9%), lr+2024~la32r’( 1.5O/o) lo220230Zln32a’(91.5%), lo22023021n32n’(4.3%) lo22023~ln32n’(93.8%), lo22021x327t3(2.1%), 10~20~3o’l~~2n’~(O.6%) lo22023021a32~‘(83.8%), lo22023alx3n~(9.3%), lo22021n32n3(l.4%) lo22023~la32z’(83.7%), lo22023021rc3xk(9.5%), lo22021x32n3(l.4%) lo22023021a’2x’(66.2%), lo22023021x3rc~(8.10/o), lo220230240’ln32n’(4.00/o), lo220’3u24u’lx4(3.5%), lu22~30’40~lx32x’(2.8%) lc?2u23u’ln42~‘(91.6%), ld2u’3u’4u’ln42x’(l.8%), lc?2u’3u14u’lx42r’(0.8%) lo22u’3u21n42r’(79.5%), lu22u’3u’4u’ln42x’(9.4%), lu22u’3u21x32x2(0.8%) lu22u’3u’ln32x3(43.9%), lu22u21x42n2(40.1%), lu’2u23u’lrr32r3(8.1%) lu22u’3&lx42x’(58.5%), lu22u24u’la42n’(7.0%), lu22u23u’lrt32n2(6.8%), lu22u’3u21x32x2(6.1%), lu22u23u’ln42n’(2.1%), 1~~2o~3~1~~~~(2.0%) lu22dln42a2(50.0%), 1u22u’3u’1x42x2(30.4%), lo22u230’ln46k(3.4%), lu’2~3u’lx42x2(2.6%), lu22u’3u’ln42~‘~~( 1.5%) lu22u217r42n’x~( 1.4%), lu22u’3~ln4S~( 1.3%) lo22&~32x3( 1.2%)
‘rI(III) ‘A(I1)
configurations
(the percentage
The 3E- and ‘A states, which are possible candidates for the predissociation of the C state, are predominantly 102202302 1x32n’, but the 102202 17r327r3configuration and some other configurations also make non-negligible contributions. The C state itself is predominantly 10220230’ 17~~2~’ near the equilibrium geometry but 10~20’30~ 1x42x’ at longer distances. Hence the C state has a very shallow minimum. It should be noted that the ‘C- and ‘Z+ (II) states contain considerable amounts of Rydberg character (9.5% and 8. I%, respectively). The electronic configurations contributing to the 3C- (II) state are 43.9% 10~20’30 1x32x3 and 40.1% 102202 17c42x2.This suggests that this state undergoes
Table 5 Mulliken population
‘z+
geometries
Electronic
‘II ‘II(R) 3X-(11)
311 3z+ 3A ‘A
near the equilibrium
State
)A ‘A ‘Z‘Z‘I;+(H)
States
22 May 1992
LETTERS
analysis near equilibrium
Net population,
geometries
of contributions)
an avoided crossing. This avoided crossing is responsible for the rather unusual shape of the potential energy curve of the 3X- (II) state (fig. 1). The ‘II(II1) and ‘A(I1) states are composed of many configurations, which include some Rydberg configurations as seen from table 4. Table 5 shows the Mulliken population analyses of the low-lying electronic states of GaCl after SOCI calculation. The ‘Z+ ground state has a strong ionic character with the polarity Ga+Clsince the total gross population of the gallium atom is below 3.0. This is consistent with its dipole moment. The overlap populations of the four excited states are close to zero which corroborates the smaller W,S of the cor-
of the SOCI electronic
state of GaCl
Gross population,
total
states of
Overlap
total
Ga
Cl
Ga(s)
Ga(p)
Ga(d)
Cl(s)
Cl(p)
Cl(d)
Ga
Cl
Ga(s)
Ga(p)
Ga(d)
Cl(s)
Cl(p)
Cl(d)
2.61 2.83 3.03 3.02 3.02
7.13 7.01 7.00 6.99 6.99
2.09 1.33 1.87 1.86 1.86
0.43 1.40 1.07 1.07 1.07
0.04 0.04 0.02 0.02 0.02
1.98 1.98 1.94 1.94 1.94
5.08 4.96 4.95 4.95 4.95
0.06 0.06 0.10 0.10 0.10
2.74 2.91 3.02 3.01 3.01
7.26 7.09 6.98 6.99 6.99
1.90 1.30 1.89 1.88 1.88
0.70 1.48 1.08 1.07 1.07
0.14 0.13 0.06 0.06 0.06
1.89 1.88 1.94 1.94 1.94
5.29 5.13 4.94 4.94 4.94
0.08 0.08 0.11 0.10 0.10
0.26 0.16 -0.02 -0.01 -0.01
113
Volume 193, number
1,2,3
CHEMICAL
PHYSICS
responding states. The distinct singlet and triplet states of A symmetry, ‘A and 3A, have identical populations since their energy curves and spectroscopic properties are almost the same. The Ga(4p) character is significantly larger in the ‘n state. The contribution of Ga(d) functions in the ground state is significant (0.14) indicating that the polarization effects have a significant contribution for the ionic ground state.
4. Summary In this theoretical calculation we studied fifteen low-lying electronic states of GaCl. The spectroscopic properties and the potential energy curves of these states were calculated using the CASSCF/ FOCI/SOCI method. The results are consistent with the experimental observations [l-6] for known states. Our computations also predict the spectroscopic constants of some electronic states which are yet to be observed.
Acknowledgement This research was supported
114
in part by the US Na-
LETTERS
tional Science Foundation
22 May 1992
grant CHE88 18869.
References [ 1 ] E. Miescher and M. Wehrli, Helv. Phys. Acta 6 ( 1933) 458; 7 (1934) 331. (21 F.K. Levin and J.G. Winans, Phys. Rev. 84 ( 195 1) 431. [ 31 A.H. Barrett and M. Mandel, Phys. Rev. 109 ( 1958) 1572. [4] I.R. Bartky, J. Mol. Spectry. 6 ( 1961) 275. [ 5) E. Tiemann, M. Grasshoff and J. Hoeft, Z Naturforsch. 27a (1972) 753. [6] K.P. Huber and G. Herzberg, Spectroscopic constants of diatomic molecules (Van Nostrand Reinhold, New York, 1979). [ 71 V. Liberman, G. Haase and R.M. Osgood Jr., Chem. Phys. Letters 176 (1991) 379. [8] Th. Glenewinkel-Meyer, A. Kowalski, B. Miiller, Ch. Ottinger and W.H. Breckenridge, J. Chem. Phys. 89 ( 1988) 7112. [9] W.D. Reents Jr., J. Chem. Phys. 90 (1989) 4258. [IO] J. Berkowitz and J.L. Dehmer, J. Chem. Phys. 57 ( 1972) 3194. [ 111 K. Balasubramanian, J.X. Tao and D.W. Liao, J. Chem. Phys. 95 ( 199 1) 4905. [ 12 ] M.M. Hurley, L.F. Patios, P.A. Christiansen, R.B. Ross and W.C. Ermler, J. Chem. Phys. 84 ( 1986) 6840. [ 131 L.F. Patios and P.A. Christiansen, J. Chem. Phys. 82 (1985) 2664. [ 141 K. Balasubramanian, Chem. Phys. Letters 127 ( 1986) 585. [ 151 C.E. Moore, Tables of atomic energy levels, NRDRS-NBS, Circular No. 467 (US GPO, Washington, 197 1).
193, number
1,2,3
CHEMICAL
PHYSICS
22 May 1992
LETTERS
Spectroscopic properties and potential energy curves of GaCl Gyoung-bum
’
Kim and K. Balasubramanian
Department of Chemistry, Arizona State University, Tempe, AZ 85287-1604, Received
17 October
199 1; in final form I9 February
USA
1992
Fifteen electronic states of GaCl are investigated using relativistic ab initio complete active space MCSCF (CASSCF) followed by large-scale multi-reference configuration interaction calculations which included up to 1000000 configurations. Potential energy curves and spectroscopic constants of various electronic states are reported. Spectroscopic constants of eight new states are obtained which are yet to be observed. Calculated spectroscopic constants of GaCl are in accord with the experimental constants
for the known states.
1.. Introduction
Spectroscopic constants of group (III) monohalides and their cations are of interest [ l-81 since they can be formed in halogen-etching reactions with GaAs semiconductors. For example, Liberman et al. [ 7 ] observed GaCl molecules using a differentially pumped quadrupole mass spectrometer in the reaction of CIZ with n-type GaAs ( 110) surface under high-vacuum conditions. The GaCl molecule was one of the main desorption products which resulted from both thermal and laser-induced reactions. Reents [ 91 conducted an experiment in which the gas phase HCl etches Ga,As_; clusters primarily through loss of GaCl. Our investigation here predicts a number of spectral bands for GaCl in the visible-near-UV region. The theoretical results on the GaCl diatomic molecule reported here should therefore be of use in not only the assignment of existing spectra, but also in the prediction of new spectra which are yet to be observed. The early spectroscopic studies on GaCl include those by Miescher [ 11, Levin and Winans [ 21, Barrett and Mandel [ 31, Bartky [ 41, and Tiemann et al. [ 5 1. A summary of experimental work on GaCl up to 1976 can be found in ref. [ 61. In a more recent Correspondence to: K. Balasubramanian, Department of Chemistry, Arizona State University, Tempe, AZ 85287-1604, USA. ’ Camille and Henry Dreyfus Teacher-Scholar. 0009-2614/92/$
05.00 0 1992 Elsevier Science Publishers
spectroscopic study of monohalide cations, Glenewinkel-Meyer et al. studied GaCI+ using the ionmolecular reaction, Ga+ + CIZ+ GaCl+* + Cl [ 8 1. In their chemiluminescence spectra, a band near 4 1150 cm- ’ was attributed to the C ‘II-X ‘C+ system of GaCl. The C state was predissociated due to a curve crossing. Berkowitz and Dehmer [ lo] have recorded the photoelectron spectrum of GaCl among other group III halides. They have also considered ab initio and semi-empirical calculations on the ground state of GaCl. Although there are ab initio computations on the ground state of GaCl [ 10,111, there are no theoretical calculations on the spectroscopic properties and potential energy curves of the excited electronic states of GaCl. The objective of the present investigation is the systematic calculation of the potential energy curves and the spectroscopic properties of electronic states of GaCl using a relativistic complete active space MCSCF (CASSCF) followed by first-order configuration interaction (FOCI) calculation. In addition to this, second-order configuration interaction (SOCI) calculations, which include up to 1000000 configurations, are carried out on some of the electronic states of GaCl.
2. Method of calculation We use complete active space MCSCF (CASSCF)
B.V. All rights reserved.
109
Volume 193, number
I ,2,3
CHEMICAL
PHYSICS
followed by first-order configuration interaction (FOCI) and second-order configuration (SOCI) calculations. All the calculations described here employ relativistic effective core potentials (RECP) which include the outer 4s24p’ shells for the Ga atom and outer 3s23ps shells for the Cl atom in the valence space, respectively. We employ the Gaussian RECPs generated by Hurley et al. [ 12 ] for the gallium atom and by Patios and Christiansen [ 131 for the chlorine atom. These authors have also optimized (3~3~) valence Gaussian basis sets for the 2P ground electronic states of each atom. Each set was augmented by one set of diffuse s, p and one set of d-type polarization functions. The exponents of the additional functions are a,=O.O2644, a,=0.0164 and a,=0.20 for Ga atom, and (~~~0.06322, (u,=O.O532 and (~,=0.750 for Cl atom. The orbitals for the FOCI calculations were generated using the CASSCF method. The gallium valence 4s 4p and chlorine 3s and 3p orbitals correlate into four a,, two bz and two b, orbitals in the CzV group. Excitations from the la, orbital which is correlated into the 3s orbital of Cl atom were not allowed in the CASSCF because of its low orbital energy, but the seven remaining orbitals were included in the active space in the CASSCF. The eight outer electrons of GaCl were distributed in all possible ways among these seven orbitals in the CASSCF method. Separate CASSCF calculations were carried out for states of different spatial and spin symmetries in the CzV group. The first-order CI calculations were carried out following CASSCF calculations. In these calculations, excitations from the la, orbital were also included. All configurations in the CASSCF, plus configurations generated by distributing nine electrons in the internal space and one electron in the external space in all possible ways, were included in this step. After FOCI calculations, SOCI calculations were carried out for some states. In these calculations all configurations in the CASSCF and FOCI, plus configurations generated by distributing eight electrons in the internal space and two electrons in the external space in all possible ways, were included. The CASSCF and FOCI/SOCI calculations were carried out using Balasubramanian’s [ 141 modified version
of ALCHEMY II #’ codes to include relativistic
ECPs.
3. Results and discussion Table 1 shows the dissociation relationships for the possible low-lying states and the energy separations obtained by the CASSCF/FOCI method at the dissociation limits for the molecular electronic states of GaCl. The experimental atomic energy separations were taken from Moore’s table [ 15 1. The theoretical FOCI 2P+2P and ‘S+‘P energy splitting is 29934 cm-’ which is a little larger than the experimental value of 24789 cm-‘. On the other hand, the (5~) 2P+2P and 2S+2P energy splitting is a little lower than the corresponding experimental energy splitting. In general, it has been known that the FOCI method yields satisfactory agreement of such magnitude with experiment. The SOCI results are much improved. It should be noted that although our (4s4pld) basis set is adequate for the ground state, it is somewhat less satisfactory for the excited states. Table 2 shows the calculated FOCI spectroscopic properties and fig. 1 shows the potential energy curves. The experimental spectroscopic constants are known for the X ‘C+ state and the spin-orbit components of the 311 state. The experimental B 311, and A 3110+ states were found to be at 29859 and 29527 cm-‘, respectively. As seen from table 2, the theoretical FOCI T, of the 311 state is 24589 cm-‘. Our calculated FOCI transition energy for the 311-‘E+ transition, therefore, shows only fair agreement with the corresponding experimental value. However, the ” The major authors of ALCHEMY
II codes are B. Lengsfield,
B. Liu and M. Yoshimine. Table I Dissociation Molecular
relationship
of low-lying states of GaCl
states
Atomic states (Ga+CI)
Energy (cm-‘) exp. a’
FOCI ‘E+(2), 3X’(2), ix-, ‘E‘I-I(2), ‘D(2), ‘A,‘A ‘II, )rI, ‘z+, SE+ iE+(2), 3x+(2), ‘Z-, %x.‘1-1(2),311(2), ‘A, ‘A a) Averaged
110
22 May 1992
LETTERS
over J from ref.
2P+2P *Sf2P (5p)ZP+2P
[ 151.
0 29934 35007
0 24789 33118
Volume
193, number
Table 2 FOCI spectroscopic
CHEMICAL
1,2,3
constants
of GaCl
State
R,(A)
T, (cm-‘)
w, (cm-‘)
& (D)”
Ix+ ‘II ‘z+
2.208 2.177 3.636 2.835 2.844 2.858 2.870 3.268 2.203 2.948 2.205 2.443 2.082
0 24589 35884 36285 36355 37799 37813 38213 38379 52659 65977 70329 74690
381 364 46 240 269 212 256 160 359 383 377 283 371
2.03 1.80 -0.32 - 1.60 - 1.63 - 1.55 -1.51 -0.83
‘A ‘A ‘X‘Z‘Z:+(U) ‘I-I %(III) W(I1) ‘rI(II1) ‘A(I1)
‘) Positive polarity
0.20
-
0.15
-
PHYSICS
-4.50 -0.49 0.53
means Ga+Cl-.
0.10t
0.05
-
0.00
-
;i
ih m
6 w
I 1.0
I
2.0
I
1.0
/
I
I
I
I
1.0
5.0
6.0
1.0
80
A IWram)
Fig. 1. Potential
energy curves for GaCl.
SOCI results are in much better agreement. In addition, the C ‘II-X ‘E+ system has been studied although the C state was predissociated and the C-X bands were diffuse. The FOCI R, of the ground state is 2.208 8, which is in good agreement with the ex-
LETTERS
22 May 1992
perimental value r, (X ‘C+ ) =2.202 A. The FOCI o, of the ground state is, however, a little larger than the corresponding experimental o,= 365 cm-‘. The same pattern holds for the first excited state in that there is agreement between the FOCI R,= 2.177 8, and the experimental R,=2.146 8, for 311,,+, but a little discrepancy exists between the FOCI w,=364 cm-’ and the experimental we=395 cm-‘. Table 3 shows the SOCI spectroscopic constants of GaCl. The SOCI results include electron correlation effects to a greater degree compared to the FOCI results since the SOCI also includes two-electron excitations into the external space of orbitals. A critical comparison of the results of tables 2 and 3 reveals that the r, values predicted by the FOCI method are in reasonable agreement with the SOCI values except for electronic states with larger r, values. For states with larger r,s, the SOCI method yields improved results. The SOCI vibrational frequencies are closer to the experimental values. For example, the SOCI ground state w, of 364 cm-’ is extremely close to the experimental value of 365 cm-‘. The T, values are generally much improved at the SOCI level. For example, the experimental T, of the B 311’ and A3110+ states are 29859 and 29527 cm-‘, respectively, while our SOCI T, of the 311 state in the absence of spin-orbit coupling is 21994 cm- ‘. The smaller theoretical T, is primarily because the electron correlation effects of the X ‘C+ state are still not fully accounted for at the SOCI level. The D, of the X ‘Z+ ground state is computed as 4.5 eV at the SOCI level and 4.48 eV at the FOCI level. The Davidson correction to SOCI did not change the D, at all, indicating the completeness of the SOCI method. This suggests that the most possible source of the discrepancy in the De and T, of the electronic states of GaCl is due to the basis set limitation and possible 3d-electronic core-valence correlation effects. Levin and Winans [ 21 have studied the absorption spectrum of GaCl. From the experimental spectrum, they have deduced the existence of B 3111, A 3110+ and C ‘II electronic states for GaCl. A subsequent recalculation of the molecular constants of Bartky [4] has suggested voo values of 29874 and 29542 cm-‘, respectively for the B 3111 and A 3110+ states. The band head of the C-X system of GaCl was located at 40 139 cm-’ by Levin and Winans [ 21. 111
Volume 193, number 1,2,3
CHEMICAL PHYSICS LETTERS
22 May 1992
Table 3 SOCI spectroscopic constants of GaCl State
R,(A)
T, (cm-‘)
0, (cm-‘)
pc tD) =)
‘x+ ‘I-I ‘11+ 3A ‘A
2.209 2.164 3.714 2.633 2.648
0 27991 36026 39839 39842
364 370 42 217 217
2.41 1.96 -0.43 -0.31 -0.34
a) Positive polarity means Ga+CI-.
The theoretical T, of the ‘II state is 38379 and 40709 cm-‘, respectively, at the FOCI and SOCI levels of theory, although at the SOCI level we found that the ‘II state is much shallower. Consequently, our computed energy separations of the electronic states of GaCl fully support the previous assignments. Levin and Winans [ 21 found that the C ‘H-X ‘C+ system was predissociated. The most probable state causing predissociation of the C state was considered as the ‘A state based on qualitative selection rules in the absence of spin-orbit coupling. As seen from fig. 1, both 3C+ and ‘A curves cross the ‘II curve. Although the 3C+ and ‘A states are not repulsive, they exhibit minima only at long range. Consequently both states are possible candidates for predissociation. The spin-orbit coupling effect on Ga is not negligible. Therefore, predissociation can occur through spinorbit coupling. Note that the 3C+ state yields Q= Oand 1 states in the presence of the spin-orbit operator. The Q= 1 component of 3Ec+ can interact with ‘II,. The ‘A state gives only an Q= 2 state, which cannot interact with ‘II,. Hence predissociation by ‘A can occur only through non-adiabatic rotationally induced effects rather than spin-orbit coupling. Consequently, we suggest that the 3Cf (Q= 1) component can predissociate C ‘II, through spin-orbit coupling. Levin and Winans [ 2 ] have deduced the 0, of GaCl through the predissociation of the C system as 4.99 eV, in reasonable agreement with our SOCI value of 4.5 eV. Continuous absorption at 41200 cm-’ and near 47600 cm- ’ were experimentally found [ 61. The first continuous absorption at 41200 cm-’ could be due to many closely spaced excited states with shallow minima close to each other as shown in fig. 1. Since there are no definitive analyses of the observed continua, it is hard unambiguously assign these spectra, 112
although our calculations reveal the existence of several electronic states in this region. The second roots of II symmetry, ‘II (II) and 311(II), are found to be repulsive while the third roots, ‘II(II1) and 311(111), have minima. The ‘A(I1) state is quite mixed with Rydberg states. The T, of ‘x+(11) is below that of C ‘II and it has 8.1% of lo22023021n32nk Rydberg character. Tables 2 and 3 also show the dipole moments of the various electronic states of GaCl. The SOCI dipole moments are more accurate compared to the FOCI values. For example, the pL,of the ground state increases by 0.4 D in going from the FOCI to the SOCI level of theory. As seen from tables 2 and 3, several excited states have the opposite polarity of p, (Ga-Cl+ ) compared to the ground state, indicating charge transfer in the electronic transitions from the ground state to these excited states. Table 4 shows the compositions of the electronic states of GaCl as revealed by the contributions of various electronic configurations. As seen from table 4, the contributions of Rydberg electronic configurations in several excited states are rather large. The computed T, values of such states reported in table 2 are not expected to be very accurate since the basis set was optimized for the ground state atoms although they are augmented with diffuse functions and polarization functions. The ground state arises from the closed-shell configuration lo22023a2 1n4 with an appreciable amount of the lo22021~42x2 configuration (3.7%). The ionic character of the GaCl bond is confirmed by the lo22023021rt4 configuration in which the 1~ molecular orbital is predominantly Cl (3~). The first excited state, ‘II, has a predominant (94.4%) configuration of 10~20~30’ 1rr427r’, which results from an electron excitation from the 30 MO to the 27t MO.
Volume 193, number Table 4 Contributions GaCl
CHEMICAL
1,2,3
of various electronic
configurations
PHYSICS
to the wavefunctions
of the FOCI electronic
‘z+ )II 3x+
lo22023a21~4(91.8%), lo22021x42n2(3.7%) lo22023a’ln42a’(94.4%), lo220’3021x42x’(0.5%) l~2023~lrc’2n’(91.8%), lo22a21rr’2x3(l.6%), lo220’30240’lrr4(0.9%), lr+2024~la32r’( 1.5O/o) lo220230Zln32a’(91.5%), lo22023021n32n’(4.3%) lo22023~ln32n’(93.8%), lo22021x327t3(2.1%), 10~20~3o’l~~2n’~(O.6%) lo22023021a32~‘(83.8%), lo22023alx3n~(9.3%), lo22021n32n3(l.4%) lo22023~la32z’(83.7%), lo22023021rc3xk(9.5%), lo22021x32n3(l.4%) lo22023021a’2x’(66.2%), lo22023021x3rc~(8.10/o), lo220230240’ln32n’(4.00/o), lo220’3u24u’lx4(3.5%), lu22~30’40~lx32x’(2.8%) lc?2u23u’ln42~‘(91.6%), ld2u’3u’4u’ln42x’(l.8%), lc?2u’3u14u’lx42r’(0.8%) lo22u’3u21n42r’(79.5%), lu22u’3u’4u’ln42x’(9.4%), lu22u’3u21x32x2(0.8%) lu22u’3u’ln32x3(43.9%), lu22u21x42n2(40.1%), lu’2u23u’lrr32r3(8.1%) lu22u’3&lx42x’(58.5%), lu22u24u’la42n’(7.0%), lu22u23u’lrt32n2(6.8%), lu22u’3u21x32x2(6.1%), lu22u23u’ln42n’(2.1%), 1~~2o~3~1~~~~(2.0%) lu22dln42a2(50.0%), 1u22u’3u’1x42x2(30.4%), lo22u230’ln46k(3.4%), lu’2~3u’lx42x2(2.6%), lu22u’3u’ln42~‘~~( 1.5%) lu22u217r42n’x~( 1.4%), lu22u’3~ln4S~( 1.3%) lo22&~32x3( 1.2%)
‘rI(III) ‘A(I1)
configurations
(the percentage
The 3E- and ‘A states, which are possible candidates for the predissociation of the C state, are predominantly 102202302 1x32n’, but the 102202 17r327r3configuration and some other configurations also make non-negligible contributions. The C state itself is predominantly 10220230’ 17~~2~’ near the equilibrium geometry but 10~20’30~ 1x42x’ at longer distances. Hence the C state has a very shallow minimum. It should be noted that the ‘C- and ‘Z+ (II) states contain considerable amounts of Rydberg character (9.5% and 8. I%, respectively). The electronic configurations contributing to the 3C- (II) state are 43.9% 10~20’30 1x32x3 and 40.1% 102202 17c42x2.This suggests that this state undergoes
Table 5 Mulliken population
‘z+
geometries
Electronic
‘II ‘II(R) 3X-(11)
311 3z+ 3A ‘A
near the equilibrium
State
)A ‘A ‘Z‘Z‘I;+(H)
States
22 May 1992
LETTERS
analysis near equilibrium
Net population,
geometries
of contributions)
an avoided crossing. This avoided crossing is responsible for the rather unusual shape of the potential energy curve of the 3X- (II) state (fig. 1). The ‘II(II1) and ‘A(I1) states are composed of many configurations, which include some Rydberg configurations as seen from table 4. Table 5 shows the Mulliken population analyses of the low-lying electronic states of GaCl after SOCI calculation. The ‘Z+ ground state has a strong ionic character with the polarity Ga+Clsince the total gross population of the gallium atom is below 3.0. This is consistent with its dipole moment. The overlap populations of the four excited states are close to zero which corroborates the smaller W,S of the cor-
of the SOCI electronic
state of GaCl
Gross population,
total
states of
Overlap
total
Ga
Cl
Ga(s)
Ga(p)
Ga(d)
Cl(s)
Cl(p)
Cl(d)
Ga
Cl
Ga(s)
Ga(p)
Ga(d)
Cl(s)
Cl(p)
Cl(d)
2.61 2.83 3.03 3.02 3.02
7.13 7.01 7.00 6.99 6.99
2.09 1.33 1.87 1.86 1.86
0.43 1.40 1.07 1.07 1.07
0.04 0.04 0.02 0.02 0.02
1.98 1.98 1.94 1.94 1.94
5.08 4.96 4.95 4.95 4.95
0.06 0.06 0.10 0.10 0.10
2.74 2.91 3.02 3.01 3.01
7.26 7.09 6.98 6.99 6.99
1.90 1.30 1.89 1.88 1.88
0.70 1.48 1.08 1.07 1.07
0.14 0.13 0.06 0.06 0.06
1.89 1.88 1.94 1.94 1.94
5.29 5.13 4.94 4.94 4.94
0.08 0.08 0.11 0.10 0.10
0.26 0.16 -0.02 -0.01 -0.01
113
Volume 193, number
1,2,3
CHEMICAL
PHYSICS
responding states. The distinct singlet and triplet states of A symmetry, ‘A and 3A, have identical populations since their energy curves and spectroscopic properties are almost the same. The Ga(4p) character is significantly larger in the ‘n state. The contribution of Ga(d) functions in the ground state is significant (0.14) indicating that the polarization effects have a significant contribution for the ionic ground state.
4. Summary In this theoretical calculation we studied fifteen low-lying electronic states of GaCl. The spectroscopic properties and the potential energy curves of these states were calculated using the CASSCF/ FOCI/SOCI method. The results are consistent with the experimental observations [l-6] for known states. Our computations also predict the spectroscopic constants of some electronic states which are yet to be observed.
Acknowledgement This research was supported
114
in part by the US Na-
LETTERS
tional Science Foundation
22 May 1992
grant CHE88 18869.
References [ 1 ] E. Miescher and M. Wehrli, Helv. Phys. Acta 6 ( 1933) 458; 7 (1934) 331. (21 F.K. Levin and J.G. Winans, Phys. Rev. 84 ( 195 1) 431. [ 31 A.H. Barrett and M. Mandel, Phys. Rev. 109 ( 1958) 1572. [4] I.R. Bartky, J. Mol. Spectry. 6 ( 1961) 275. [ 5) E. Tiemann, M. Grasshoff and J. Hoeft, Z Naturforsch. 27a (1972) 753. [6] K.P. Huber and G. Herzberg, Spectroscopic constants of diatomic molecules (Van Nostrand Reinhold, New York, 1979). [ 71 V. Liberman, G. Haase and R.M. Osgood Jr., Chem. Phys. Letters 176 (1991) 379. [8] Th. Glenewinkel-Meyer, A. Kowalski, B. Miiller, Ch. Ottinger and W.H. Breckenridge, J. Chem. Phys. 89 ( 1988) 7112. [9] W.D. Reents Jr., J. Chem. Phys. 90 (1989) 4258. [IO] J. Berkowitz and J.L. Dehmer, J. Chem. Phys. 57 ( 1972) 3194. [ 111 K. Balasubramanian, J.X. Tao and D.W. Liao, J. Chem. Phys. 95 ( 199 1) 4905. [ 12 ] M.M. Hurley, L.F. Patios, P.A. Christiansen, R.B. Ross and W.C. Ermler, J. Chem. Phys. 84 ( 1986) 6840. [ 131 L.F. Patios and P.A. Christiansen, J. Chem. Phys. 82 (1985) 2664. [ 141 K. Balasubramanian, Chem. Phys. Letters 127 ( 1986) 585. [ 151 C.E. Moore, Tables of atomic energy levels, NRDRS-NBS, Circular No. 467 (US GPO, Washington, 197 1).