Spectroscopic properties and potential energy curves of GaH

JOURNAL OF MOLECULAR SPECTROSCOPY I%,4

12-420 (1989)

Spectroscopic Properties and Potential Energy Curves of GaH GYOUNG-BUMKIM AND K. BALASUBRAMANIAN’ Department of Chemistry, Arizona State University, Tempe, Arizona 85287-1604

Relativistic completeactivespaceMCSCF (CASSCF) followed by second-order configuration interaction calculations are carried out on several valence and Rydberg electronic states of GaH. The spectroscopic properties, dipole moments, and the potential energy curves of various electronic states are reported. The spectroscopic properties of 17 new electronic states are reported which are yet to be observed. The dissociation energy of the ground state is calculated to be 2.8 1 eV in excellent agreement with a corrected spectroscopic value of 2.80 eV obtained from the predissociation of the A-X system. 0 1989Academic press hc. 1. INTRODUCTION

The spectroscopic properties of heavy group III hydrides such as GaH, InH, and TlH have been the topics of many investigations (Z-II). The electronic spectra of GaH differ from those of lighter analogs such as BH and AlH in that intercombination systems occur for the heavier species. The early spectroscopic studies on GaH include those by Garton ( 1 ), Neuhaus (2, 3), and Ginter and Innes (4). In a more comprehensive articie Ginter and Battino (5) have calculated the potential curves for the third group hydrides using the Rydberg-Klein-Rees method. Poynor et al. (6) have studied the ‘II,- + X ‘2+ emission system. Kronekvist et al. ( 7) have studied the A ‘II-X’Z+ system. These authors have suggested that there should be a barrier due to some avoided crossing although the exact nature of the state undergoing avoided crossing still remains uncertain. The linewidths in the A-X system were found to increase with increasing J suggesting a tunneling effect and a small barrier prior to dissociation, Based on the predissociation of the A-X bands these authors have estimated that the dissociation energy of GaH should be less than 22 900 cm-’ or 2.84 eV. The summary of experimental works on GaH up to 1976 can be found in Ref. ( 12). The interest on Ga and As cluster hydrides also arises from recent experimental studies on reactive etching of Ga, As; by HCl ( 23). There are no theoretical calculations on the spectroscopic properties and potential energy curves of electronic states of GaH although Hurley et al. (14) have obtained R, and we values of the ground state of GaH in an attempt to gauge the relativistic effective core potentials ( RECPs). The lighter BH (II) and very heavy TlH ( 10) molecules have been studied theoretically. The objective of the present investigation is the systematic calculation of potential energy curves and spectroscopic properties of electronic states of GaH using a relativistic complete active space MCSCP (CASSCP) ’ Alfred P. Sloan fellow; Camille and Henry Dreyfus Teacher-scholar. 0022-2852189 $3.00 Copyright 0

1989 by Academic Prss. Inc.

All rights of reproduction in any form reserved.

412

SPECTROSCOPIC PROPERTIES OF GaH

413

followed by second-order configuration interaction (SGCI) methodology. We consider about 25 electronic states of GaH. 2. METHOD OF CALCULATIONS

We use the complete active space MCSCF (CASSCF)/second-order CI method to investigate the electronic states of GaH. All the calculations described here employ relativistic effective core potentials for the gallium atom. The outer 4s24p’ shells were explicitly retained in the calculations while the inner electrons were replaced by relativistic ECPs. We use the gaussian RECPs generated by Hurley et al. (14) for the gallium atom. These authors have also optimized a (3~3~) valence gaussian basis set for the 2P ground electronic state of the gallium atom. This was augmented by a set of diffuse s, p and two sets of d-type polarization functions. The exponents for the additional functions are LY, = 0.02644, cup = 0.0164, (Yd, = 0.2542, and cY,+ = 0.07077. The orbitals for CI calculations were generated using the CASSCF method. In this method the gallium valence 43, 4p, and H 1s orbitals were included in the active space. These orbitals correlated into three al, one b2, and one b, orbitals in the Cz, group. The four outer electrons of GaH were distributed in all possible ways among these five orbitals in the CASSCF method. Separate CASSCF calculations were carried out for states of different spatial and spin symmetries in the C2, group. State-averaged CASSCF calculations were carried out for states of ‘II and ‘II symmetry. The second-order CI calculations were carried out following CASSCF calculations. In these calculations all configurations in the CASSCF plus (i) configurations generated by distributing three electrons in the internal space and one electron in the external space in all possible ways and (ii) co&urations generated by distributing two electrons in the internal space and two electrons in the external space in all possible ways were included. The CASSCF and SGCI calculations were carried out using BaIasubmmanian’s (IS) modified version of ALCHEMY II2 codes to include relativistic ECPs. 3. RESULTS AND DISCUSSION

Table I shows the dissociation relationships for the possible low-lying states of GaH and the energies of the separated atoms. The experimental atomic energies in that table am from Ref. (16). As one can see from Table I, the theoretical SOCI atomic energy separations are in very good agreement with the experimental values indicating that the basis sets and levels of electron correlation included in our calculations are quite adequate. It is somewhat surprising that even the energy separations of the Rydberg states of Ga are in very good agreement with the experimental results since our starting basis set was optimized only for the ground state of Ga. Table II shows the calculated spectroscopic properties while Fig. 1 shows the actual potential curves. The experimental spectroscopic constants are known for the X ‘Z + state and the spin-orbit components of the ‘II state. In addition the A-X system has been studied although the constants of the A state are not known. The experimental & and oe values of the ground state are 1.663 A and 1605 cm-‘, 2 The major authors of ALCHEMY II codes are B. Lengsfield, B. Liu, and M. Yoshimine.

414

KIM AND BALASUBRAMANIAN TABLE I Dissociation Relationships of Some Low-Lying States of GaH Molecular States

3il(I),

%+(I),

Atomic States

*P + 2s

0

0

(5S)2S + 2s

24345

24789

lE+(III),

(5P)2P + 2s

32395

33118

3A(I),

(4d)‘Ll + 2S

34330

34782

b+(I),

3z+(II),

1x+(11)

3r+(III),

3iI(II),

Energy of Se arated Atoms -P (cm ) Theory Exp.

h(I)

‘ll(I1) 3E+(Iv),

3ll(III),

*E+(IV),

‘II(H),

‘A(I)

respectively. As can be seen from Table II the theoretical constants are almost in exact agreement with those values for the ground state. The first excited state of GaH is a 311state which has been seen experimentally.

0.16

-

0.06

-

r z

0 04 -

m L ‘f

0.02

-

I” OW

2P+2s -002

-

-0.08

-

-0.

IO 1.0

1 2 0

I 3.0

I 4.0

I 5.0

1 60

,

I

7 0

6.0

R (ii)+ FIG, 1. The potential energy curves of several electronic states of GaH.

415

SPECTROSCOPIC PROPERTIES OF GaH TABLE II Spectroscopic Constants for GaH

state

R, iA1

T,

(cm-')

we

(cm-‘I

lE+(I)

1.662

0

1612

3n(I)

1.603

16836

1559

In

1.780

24206

3x+

1.935

39271

2245

lC’(II)

3.582

40933

447

31-

1.564

45649

1772

lE”(II)

1.747

46632

931

3n(Ir)

2.091

46737

1218

lZ’(III)

4.609

50573

219

‘A(I)

1.541

51319

1907

‘A( II)

1.553

51982

1835

lZ”(III)

1.612

52076

2192

3lT(IIl)

1.737

54243

1660

3A(I1

3.440

64415

3lT(IV)

1.813

65420

831

‘A( III)

1.615

72554

1567

3A( II)

2.039

79284

917

3A( III)

2.033

32295

956

11-

1.606

83271

1497

‘A( IV)

2.321

85703

1744

Since the spin-orbit interaction was found to be rather small, we did not include spinorbit interactions in our calculations. The calculated 12, T,, and w, values of the ‘II state are, however, in very good agreement with the experimental results. The experimental A-X system was found to be predissociated. The A state was tentatively assigned to the ‘II state and the experimental TOvalue of the A-X system obtained by Kronekvist et al. ( 7) is 22 745 cm-‘. The experimental R, value of the A state is 1.82 A. Our theoretical calculations entirely support this finding. The ‘II state has a very shallow minimum with an & value of 1.78 A in good agreement with the experimental value. The theoretical T, value is 24 206 cm-’ in comparison to an experimental value of 22 745 cm-‘. Our theoretical value is a bit high as anticipated for the level of electron correlations and basis sets included in these calculations. The experimental A state was found to be predissociated. This is consistent with the potential energy curve in Fig. 1 which has a shallow short & minimum and

416

KIM AND BALASUBRAMANIAN

another long-range minimum separated by a very small barrier. The De calculated using the predissociation of the ‘II state should, however, be quite accurate since the predissociation energy and the energy of 2P + ‘S atoms is very close. We estimate that the De of 2.84 eV obtained using extrapolation of the predissociation of the A-Xbands should only be 0.04 eV lower yielding a corrected value of 2.80 eV. A direct theoretical SOCI De value obtained by calculating the difference in the energy of the X ‘Z+ at R, and 8.0 A is 2.8 1 eV. This value is almost in exact agreement with the experimental result. Kronekvist et al. ( 7) have noted that the observed linewidth in the A-X bands increases with increasing J. This indicates a tunneling effect. It was suggested that there should be an avoided crossing between a deep ‘II potential curve dissociating into an excited configuration and another repulsive ‘II dissociating into the ground

TABLE III Dipole Moments near Equilibrium Geometries of the Various Electronic States of GaH’ State

ve (W

lE’(I)

-0.460

3vI)

-0.221

1,

0.107

32’

2.799

lz+(II)

-1.151

3E-

-0.285

lx+‘(H)

-1.395

3ll(II)

0.239

h+(m)

0.010

‘A(11

0.572

IA

0.745

h+‘(m)

0.417

3ll(III)

0.935

3A(I)

0.221

3ll(IV)

0.684

‘A(II1)

0.117

3A(II)

0.424

3A(III) If ‘A( IV)

0.745 -0.424 0.117

. Positive polarity means positive charge on the hydrogen atom.

417

SPECTROSCOPIC PROPERTIES OF GaH TABLE IV

Contributions of Various Electronic Configurations to the SOCI Wavefunctions near the Equilibrium Geometries of the Electronic States of GaH*sb

state

Electronic Configurations

‘z+(I)

3wIl ill

‘E’(II)

1022ol3ol

(23.1%),

lgz201801 (7.1%),

10230* (10.3%)

10~20~70~ (6.8%).

3E-

1o21n* (85.6%).

lZ”(I1)

lo22011301 (15.8%), lo2201110’

2o*1n* (4.313,

lo2201601 (5.4%).

10~20’70~ (14.5%),

Io2201d

(11.4%)

10~20~130~ (5.3%),

lo’202701

3ll(II)

lo12021n1 (70.1%).

lo23011n1 (12.7%).

lo22012n1 (3.2%)

lz+(III)

10~20~60~ 117.1%). 10~20~1101 (10.7%), (9.3%).

10~20~30~ (6.5%).

‘A(I)

lo21n2 (82.1%).

lo*2016

IA

lo21n2 (38.4%),

lo12011n2 (15.2%).

IE”(II1)

10~20~130~ (22.111,

(5.1%).

lo23011101 (5.5%).

1~~20~25~ (9.5%)

lo22a11101 (16.9%),

lo2201501 (11.4%)

(5.4%),

10~20~30~ (4.7%)

3li(III)

Io22016nI (57.4%),

lo22013n1 (23.4%),

lo12021n1 (6.9%)

3A(I)

lo12oll”*

102201161 (27.91),

loI20*16l

3ll(IV)

lo2Z012n1 (35.1%). lo22013n1 (8.2%).

‘A(III)

lo22a1d 1ov

(44.8%), (7.9%).

(15.9%)

10120*261 (4.0%) lo12013011n1 (24.4%),

lo22014n1 (10.1%)

lo12013011n (3.4%)

102160116 (lI.S%),

lo*90116

10~20~26~ (8.1%)

(3.8%)

3A( II)

lo12011n2 (52.6%).

10~20~16~ (15.9%).

3A(111)

Io12011n2 (57.2%),

lo*ln*

‘z-

lo*ln13”’

Io21n16n1 (31.7%).

‘A( IV)

lo12011n2 (44.4%).

(36.2%).

10~30~120~ (4.1%)

(7.6%)

Io120ZlIa1

10*20126l (7.0%).

lo1202601 (5.0%)

lo22a11201 (9.3%)

Io12021301 (5.9%).

(40.7%),

10~20~50~ (4.2%)

1o12o11n* (4.2%)

(8.5%),

Io230160’

l

102202 (IO.?%),

(8.3%).

lo21n12ni

10~20~26~ (9.9%)

lo21n12n1 (3.0%) lo21n15n1 (8.5%).

lo12011n2 (4.9%)

(25.8%)

The order of orbitals comer from FOCI and some of these are Rydberq orbitals.

b Numbers in parentheses repretent the percentages of contributions.

418

KIM AND BALASLJBRAMANIAN

state configuration. Our theoretical calculations do not support such an avoided crossing although it was found that the ‘II state arising from 1a2a2 In mixes more with ‘II (1 a220 1r) at short distance than at long distance. The origin of the short-range minimum appears to be due to this mixing but it is not so large to call this an avoided crossing. This appears to be the reason for the fact that the short-range minimum is shallow and thus the A state is predissociated. Our calculations also support the prediction by Kronekvist et al. ( 7) that the 3Z+ state must be repulsive. This state has not been seen experimentally for this reason. Table III shows the calculated dipole moments of various electronic states of GaH. As can be seen from that table the ‘E+ state has some ionic character with the positive

TABLE V Mulliken Population Analysis near Equilibrium Geometries of the Electronic States of GaH Net population State

Gross population

Total

Total

Ga

H

5+(I)

2.55

3JUI) ill

Ga(s)

Ga(p)

Ga(d)

0.83

2.07

0.68

0.05

2.72

0.70

1.52

1.34

2.99

0.83

1.98

1.18

3+ z

3.23

1.19

2.25

Ga

Overlap H

Ga(s)

Ga(P)

Ga(d)

2.86

1.14

1.78

0.99

0.09

0.62

0.04

3.02

0.98

1.47

1.51

0.04

0.58

0.06

3.08

0.92

1.73

1.30

0.05

0.18

1.12

0.09

3.02

0.98

1.92

0.91

0.1a

-0.42

lLC( II)

2.54

1.13

3.06

0.24

0.23

2.71

2.29

2.60

0.28

-0.17

0.33

3z-

2.93

0.56

1.00

2.01

0.04

3.19

0.81

1.09

2.07

0.03

0.51

Y(II)

2.92

0.68

4.09

0.33

0.49

3.12

0.88

3.03

0.49

-0.40

0.40

3Il(IIJ

2.93

0.96

1.49

1.54

0.74

2.98

1.02

1.18

1.68

0.13

0.11

lE+(III)

3.00

0.99

1.09

1.99

0.03

3.01

0.99

0.94

1.99

0.08

0.01

IA(I)

2.85

0.54

1.04

1.81

0.16

3.15

0.85

1.11

1.89

0.15

0.60

0.57

1.07

1.75

0.19

3.16

0.84

1.10

1.83

0.23

0.56

‘A(I1)

2.88

lE+‘(III)

2.87

0.68

1.79

1.29

0.09

3.09

0.91

1.60

1.44

0.06

0.46

3lT(III)

2.94

0.72

1.84

1.31

0.04

3.11

0.89

1.64

1.46

0.00

0.34

3A(I)

3.01

0.94

1.74

0.90

0.60

3.04

0.96

1.58

0.91

0.55

0.05

3ll( IV)

3.01

0.71

1.78

0.57

0.89

3.15

0.85

1.61

0.67

0.88

0.27

‘A(II1)

2.89

0.61

1.65

0.64

0.86

3.14

0.86

1.54

0.80

0.80

0.49

3A( II)

3.02

0.78

1.38

1.43

0.40

3.12

0.88

1.23

1.53

0.37

0.20

3A(III)

3.20

0.66

1.28

2.00

0.1.1

3.27

0.73

1.13

2.07

0.07

0.14

b-

3.00

0.49

1.10

2.03

0.04

3.26

0.74

1.14

2.09

0.02

0.51

‘A( IV)

3.08

0.74

1.18

1.98

0.09

3.17

0.83

1.04

2.03

0.08

0.19

SPECTROSCOPIC PROPERTIES OF GaH

419

charge on the metal atom. It is interesting to note that the dipole moment of the A state has opposite sign in comparison to the ground state. Table IV shows the important configurations in the SGCI wavefunctions of the electronic states of GaH. As can be seen from Table IV, most of the electronic states have predominant contributions from the leading configuration. The excited states of ‘Z+ symmetry, however, are quite mixed. In fact, the ‘Z+( II) and ‘Z+(III) states undergo avoided crossings leading to double minima. The ‘Z ‘( II) state is dominated by many Rydberg configurations at short distance. The first (short r,) minimum of the ‘Z+( II) state (‘Z+‘(R)) is thus a Rydberg minimum. At very long distances this state becomes predominantly 1a22a3a, 1u22u2, and 1u23u2. Similarly, the ‘Z+( III) state has substantially different character at short and long distances. The singlet and triplet excited states of A and II symmetry also are quite mixed in character. AscanbeseenfromFig. 1 theexcitedstatesofGaH,especiallythe ‘Z+(II), ‘X+(111), and 311(III) states, have very interesting features. All these states have double minima separated by barriers in their potential energy surfaces. As described above, these multiple minima are attributed to avoided crossings. Table V shows the Mulliken population analyses of the low-lying electronic states of GaH. As can be seen from this table the ‘2’ ground state is a bit ionic with the polarity Ga+H- since the total gross population of the gallium atom is below 3.0. Most of the ionization comes from a partial loss of the 4s electron to hydrogen since the gross p population of Ga is close to 1.0. The gross s and p populations of other excited states reflect the participation of the various Rydberg orbitals of the metal atom. 4. CONCLUSION

In this investigation we carried out CASSCF/SGCI calculations on several valence and Rydberg states of GaH. The spectroscopic constants and potential energy curves of these states are reported. The experimental constants for the X, a, and A states are in very good agreement with the calculated results. Our calculations predict the spectroscopic properties of some 17 additional electronic states which are yet to be observed. The potential energy curves of the excited ’ Z + states contain double minima separated by barriers. The dissociation energy obtained by extrapolating the predissociated AX bands (~2.84 eV) is corrected to 2.80 eV using our calculations. The corrected value is in excellent agreement with our theoretical value of 2.81 eV. The Mulliken population analyses and the nature of various electronic states of GaH are reported. ACKNOWLEDGMENT This research was

supportedin part by the National Science Foundation under Grant CHE8520556.

RECEIVED: November 17, 1988 REFERENCES 1. GARTON, Proc. Phys. Sot. London Sect. A 64,509 (1951). 2. H. NEUHAUS, Nature (London) 180,433-434 (1957).

420

KIM AND BALASUBRAMANIAN

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(1967).

5. M. L. GINTERAND R. BATTINO,f. Chem. Phys. 23,3222-3229 (1967). 6. P. C. POYNOR,K. K. INNES,AND M. L. GINTER, J. Mol. Specfrosc. 23,237-241 (1967). 7. M. KRONEKVIST,A. LANGERQUIST,AND H. NEUHAUS,J. Mol. Spectrosc. 39, 516-518 (197 I). 8. T. LARSSONAND H. NEUHAUS,Ark. Fys. 23,461-469 (1963). 9. T. LAR%,ONAND H. NEUHAUS,Ark. Fys. 31,299-305 (1966). 10. P. A. CHRISTIANSEN AND K. BALASUBRAMANIAN, J. Chem. Phys. 76,5087-5092 (1982). II. R. J. BLINTAND W. A. GODDAR III, Chem. Phys. 3.297-316 (1974). 12. K. P. HUBERAND G. HERZBERG,“Spectroscopic Constants of Diatomic Molecules,” Van Nostrand, Princeton, NJ, 1979. 13. W. D. REENTS,JR., submitted for publication.

14. M. M. HURLEY, L. F. PACIOS,P. A. CHRISTIANSEN, R. B. Ross, AND W. C. ERMLER, J. Chem. Phys. 84,6840-6853 (1986). 15. K. BALASUBRAMANIAN, Chem. Phys. Lett. 127, 585-589 (1986). 16. C. E. MOORE,“Tables of Atomic Energy Levels,” National Bureau of Standards, Cir. No. 467, Washington, DC, 1971.