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Spectroscopic constants and potential energy curves of GaAs, GaAs+, and GaAs−
JOURNAL
OF MOLECULAR
SPECTROSCOPY
139,405-423 (1990)
Spectroscopic Constants and Potential Energy Curves of GaAs, GaAs+, and GaAsK. BALASUBRAMANIAN’ Chemistry Department, Arizona State University, Tempe, Arizona 85287-1604
Twenty electronic states of GaAs, 12 electronic states of GaAs+, and 13 electronic states of GaA- are investigated using relativistic ab initio complete active space MCSCF (CASSCF) followed by large-scale configuration interaction calculations which included up to 700 000 configurations. Potential energy curves and spectroscopic constantsof all these states of three radicals are obtained. Spectroscopic constants of low-lying states of GaAs are in very good agreement with both experiment and all-electron results. Two nearly-degenerate states of ‘Z+, 211( 2Z+lower) symmetries are found as candidates for the ground state of GaA-. The GaA- negative ion is found to be more stable compared to the neutral GaAs (D, ( GaA-) = 3 eV). The electron affinity of GaAs is computed as 0.89 and 1.3 eV at the FOCI and SOCI levels of theory, respectively. Calculated potential energy curves of GaAs are in accord with the experimentally observed predissociation in the 3H(III)-x3S- system. 0 1990 Academic Press, Inc. INTRODUCTION
Electronic structural and spectroscopic properties of small semiconductor clusters and their ions are of considerable current interest (l-l 9). The properties of Group III-V mixed semiconductor clusters such as Ga,As,, InXPY,In,Sb,, etc., are especially interesting since GaAs semiconductors are used in fast devices. Furthermore, mixed clusters offer additional challenge for investigation as they give rise to more isomers and electronic states arising from competing atomic states of Ga vs As. As mentioned in an earlier paper by the author (IO), compared to a large literature on solid GaAs, very little information has been accumulated on GaxAsy clusters and their ions. The present author ( 10) was the first to study spectroscopic constants and potential energy curves of low-lying electronic states of GaAs and GaAs+. He found an X 3L: ground state for GaAs and an X42- ground state for GaAs+ . Following his theoretical calculations, Knight and Petty (9) confirmed the author’s prediction of a 42- ground state for GaAs+ through ESR spectroscopic study. Recently Lemire et al. (15) have carried out a spectroscopic study of diatomic GaAs. These authors confirmed the present author’s prediction of an X3X ground state. They found electronic bands attributed to 311(III)-X3Z- systems. The bands in theses systems were found to be predissociated due to crossing of a repulsive 52curve with the two excited 311curves. With the exception of 3II,,+-X3Zp system all other systems are predissociated. O’Brien et al. (1) have studied Ga,As, clusters generated by laser vaporization of GaAs crystal. Mass analysis of these clusters revealed considerable deviation from a ’ Camilleand Henry Dreyfus teacher-scholar. 405
0022-2852190 $3.00 Copyright All n&s
0
1990 by Academic
of reproduction
Press, Inc.
in any form reserved.
406
K. BALASUBRAMANIAN
binomial distribution for smaller clusters while large clusters followed the expected binomial distribution. Photofragmentation studies of Ga,As; , Si;, and Ge; have also been made (2). Ionization potentials of Ga,As, clusters exhibited even-odd alternations. After the appearance of the author’s theoretical paper (IO), Meier et al. ( 16) published an all-electron MRDCI study of GaAs and GaAs+. These authors basically confirmed the various states found earlier by the author in addition to investigating a few new states not studied before. The ground state obtained by all-electron study is also 32: _ for GaAs and 42 ~ for GaAs+ . The related AlP has also been studied (20). In the present study we obtain potential energy curves of many electronic states of GaAs and GaAs+ not obtained before. In addition, many electronic states of GaAsare studied for the first time. Further, in addition to CASSCF/first-order CI (FOCI) calculations, full second-order CI (SOCI) calculations which include up to 700 000 configurations are carried out. A larger valence (4s4p2d) basis set on both Ga and As is also employed to study the effect of additional diffuse and polarization functions on the calculated bond lengths and vibrational frequencies. METHOD
OF CALCULATIONS
We employ complete active space MCSCF (CASSCF) followed by first-order configuration interaction (FOCI) and second-order configuration interaction (SOCI) calculations which included up to 500 000 configurations for GaAs and up to 700 000 configurations for GaAs- . All calculations carried out here were made with relativistic effective core potentials ( RECPs) which included the outer 4.~~4~’ shells for Ga and the outer 4.~~4~~ shells for As in the valence space, respectively. In addition, calculations which included the outer 3 d”4s24p ’ , 3 d”4s24p3 shells for Ga and As, respectively, were also made. However, bond lengths did not change much in using either set of potentials, although if d correlations are included bond lengths shrank by O.Ol0.04 A. CASSCF calculations included all six valence electrons of GaAs in the active space. All calculations were carried out in the CzUpoint group with the GaAs diatomic oriented along the z-axis. In this orientation, we included all those orbitals of GaAs which correlated into the 4s and 4p orbitals of the separated atoms at infinite separation. Thus the active space for CASSCF included four al orbitals, two b2 orbitals, and two b, orbitals. All calculations of GaAs+ and GaAincluded seven and nine active electrons, respectively. At the CASSCF level seven, eight, and nine active electrons were distributed in all possible ways among the eight active orbitals for GaAs +, GaAs, and GaA- . We employed three types of basis sets. The smallest basis set is labelled (333~1 d) and included three sets of s functions, three sets of p functions, and one set of 6-component d Gaussian functions on each atom described before ( 10). A more extended (4s4p2d) valence Gaussian basis set was also used. The ( 3s3p 1 d) valence the Gaussian basis set was augmented by an s function with CY$= 0.02644, three p functions with cyp = 0.0164, and six d functions with old = 0.0708 for Ga; the corresponding exponents for As are a, = 0.0405, CQ,= 0.0324, and ffd = 0.115. Calculations which included 3d” core electrons were made with a (4s4p4d) basis set, where the two additional d functions were used for describing the 3 d orbitals of Ga and As.
SPECTROSCOPY
OF GaAs,
GaAs+,
AND
GaA-
407
CI calculations were made using both a first-order Cl (FOCI) method and a full second-order CI (SOCI) method. The FOCI calculations included (i) all configurations in the CASSCF and (ii) those configurations generated by distributing N - 1 electrons in the active space and 1 electron in the orthogonal external space in all possible ways, where N is the number of active electrons for various species (N = 7 for GaAs+ , N = 8 for GaAs, and N = 9 for GaAs-). The second-order CI calculations included all configurations in the FOCI and those configurations generated by distributing N - 2 electrons in the active space and 2 electrons in the external space in all possible ways. The FOCI calculations in the (4~4~2 d) basis set included up to 80 000 configurations for GaAs. The SOCI calculations included up to 500 000 configurations for GaAs and address electron 700 000 configurations for GaAs- . Thus the present calculations correlation effects to a high order compared to any previous study. All calculations described here were carried out using the author’s modified version of ALCHEMY II2 codes to include relativistic effective core potentials as described in Ref. (21). RESULTS
AND
DISCUSSION
Table I shows possible low-lying electronic states of GaAs, GaAs+, and GaAs ~. While it is now quite established that the ground states of GaAs and GaAs+ are 32and 42 -, respectively, this is not so for GaAs- . Since there are two very low-lying electronic states for GaAs of 32- and 311 symmetries arising from the 1u22023&r2 and 1a22a23an3 configurations, respectively, there are two possible candidates for the ground state of GaAs-. If the electron is attached to the P orbital of the ‘II state it would result in a 2Z+ state for GaAs-. If the electron is attached to the ?r orbital of the 32- state, it leads to a 211 state arising from the la22a23a2r3 configuration. Depending on mixing of other low-lying electronic states, either state could be a candidate for the ground state of GaAs-. In addition, high spin states such as 4Z+, 411, etc., could also be low-lying due to spin-exchange stabilization, although the 40 or r* antibonding orbital may have to be occupied in some of these high spin states. In addition, electronic states arising from Ga- + As dissociation limit could also be very low-lying since the difference in electron affinities of Ga and As atoms is only 0.5 eV (24). In this investigation most of the electronic states in Table I and a few additional high-lying electronic states for GaAs and GaAs+ are thoroughly studied. SPECTROSCOPIC
CONSTANTS
OF GaAs
Table II shows spectroscopic constants of the electronic states of GaAs lying below the 50 000 cm-’ region as obtained using a modest CASSCF/FOCI level of treatment employing a (3s3pld) basis set. Among the electronic states listed in Table II, properties of six states were obtained before ( IO). The R, values of most of the states obtained before were 0.11-o. 13 A longer due to an error in one of the ECP parameters acknowledged in an erratum published subsequently ( 10). The vibrational frequencies were also a bit smaller. M. Morse had communicated this discrepancy to the author through his experimental findings prior to the appearance of the all-electron work of Meier et al. ( 16 ) _ ’ Major authors of ALCHEMY
II codes are B. Liu, B. Lengsfield,
and M. Yoshimine.
408
K. BALASUBRAMANIAN TABLE I Dissociation
Relationship
for Low-Lying
Species
Electronic
States of GaAs, GaAs+,
States
Dissociation
GaAS
3E-,311. 4E-.411
6tiS
It+. ‘z-(2).
$3).
3E+. 3f(2).
311(3), 3A(2), 3*,
EtiS
lE+(2). ‘Z-, $2). 3f,
‘A(2).
‘*
*A, 3E+(2),
Ga(2P)
+ ADS
6a(2P)
+ ADS
Ga(2P)
+ ADS
and GaAsLimit
311(2). 3A
6aAS4
4x-
Ga+(%)
+ ADS
fhAS'
2E* 21 9 2x-
6a*(‘S)
+ ADS
t&AS+
?I. %+
Ga*(‘S)
+ ADS
GaAs+
2p+, 2E-(2). 2n(2). 2A, ‘A,
Ga(2P)
+ ADS+
Ga+(‘S)
+ ADS
4C(2), G&i+
48, 4E-
4il(2), 9’
Gab-
GO
Gal&-
Ga-(3P)
+ ADS+ ADS
The predicted ground state of GaAs is a ‘X ground state, which was recently confirmed by Lemire et al. ( 15). A very low-lying 311 state also exists for GaAs. There are three low-lying excited states of ‘II, ‘Li+, and ‘A symmetries below 8200 cm-‘. The large bond length change between the two low-lying 32- and 311 states is quite interesting but fully consistent with the results of other calculations on Gaz ( 17)) Gez ( 18)) etc. The author (25) has recently completed a comparative critical review of all main group p-block dimers and trimers containing atoms heavier than Ga. The 3Z- and 311(111) states of GaAs have been observed through the 311-X3Zsystem of jet-cooled GaAs by Lemire et al. ( 15) recently. They obtained the spectroscopic constants for the X32- and spin-orbit components of ‘II( III) states. The experimental r, of the 32;+ state is 2.548 A and that of the 311(III) state is roughly 2.662 A. The FOCI calculations employing a (3s3pld) basis set yield an r, of 2.645 A, 0.097 A larger than the experimental value. As we discuss later, SOCI calculations yield much better spectroscopic constants and when the effects of d correlations are taken into account, the bond lengths come very close (within 0.0 1 A) to experimental values.
SPECTROSCOPY
OF Ga4s,
409
GaAs+, AND GaAs-
TABLE II FOCI Spectroscopic Constants for GaAs
stata
re (AI
x31-
2.645
311
2.370
1,
T, (cm-‘)
re (cm-‘)
D, (W
187
1.24
996
241
1.12
2.336
5 943
280
12,
2.237
7 192
291
IA
2.582
8 232
213
lc+(II)
2.475
15 950
3ll(II)
3.055
18 900
142
32+
2.421
22 503
210
3il(iII)
2.687
22 564
187
lll(I1)
2.693
24 679
148
3f(II)
2.421
31 106
201
5ll(II)
2.818
40 352
168
=A
2.449
45 431
287
2.794
51 174
187
5Il(lII)
0
Meier et al. (16) published an all-electron study of electronic states of GaAs. They also found a 32- ground state for GaAs and a very low-lying 311 state ( T, - 0.170.24 eV) above the ground state using Hat-tree-Fock/MRDCI method. Most of the discrepancies noted by these authors between the earlier results (IO) and their allelectron results ( 16) are due to an error in one of the ECP parameters ( IO). The bond lengths in Table II are within 0.04-0.05 A of all-electron results for these states. The revised 0,s are also in much better agreement with all-electron results. It is, however, worth noting that the ‘A state has a larger o, if ‘A, CASSCF orbitals are used in calculations, while the ‘AZ orbitals yield a more reasonable w,. Hence the larger W, for the ‘A state obtained before (10) is due to the change of ‘Al orbitals due to the avoided crossing of 1a22a217r4 and 1a22~23a2~2 configurations in the CASSCF calculations. Meier et al. obtain r, = 2.60 A;, w, = 202 cm-’ for the X ‘Z- ground state of GaAs using the all-electron MRDCI method. The present calculations include electron correlations to a much higher order, compared to a restricted configuration space of less than 10 000 configurations in the MRDCI. Although the FOCI method includes most of the significant electron correlations, a full SOCI method is much superior to both the MRDCI and FOCI methods. Even at the FOCI level, the spectroscopic constants,
410
K. BALASUBRAMANIAN
GaAs
\
.a ,
2.00
I
3.00
I
4.00
I
5.00
I
6.00
R -‘& FIG. 1. Potential energy curves of low-lying electronic states of GaAs dissociating into Ga( *P) + and Ga(*P) + As(*D) limits.
r,= 2.645&we
As( 4S)
= 187 cm-‘, of the 3Z- state are in good agreement with all-electron MRDCI calculations. It is worth noting that although Meier et al. employ an allelectron method, they do not include relativistic effects, while our calculations take into account relativistic effects. Meier et al. obtain r, = 2.38 A and U, = 260 cm-’ for the 311state, while we obtain r, = 2.37 A and w, = 241 cm-’ at the FOCI level. For the ’ Z ‘( II) state, FOCI calculations starting from a CASSCF orbital set of ‘A I symmetry yield a larger w, of 420 cm-‘. However, when SOCI calculations are made using FOCI natural orbitals this discrepancy vanishes, and thus the higher w, of the iE+( II) state at the FOCI level must be due to the strong variation of the composition of CASSCF orbitals due to the avoided crossing of la22a21a4 and la22u23021s2 configurations. The D, (GaAs) obtained at the FOCI level is 1.24 eV, compared to the MRDCI value of 1.40 eV. However as we note later, SOCI calculations when corrected for dcorrelation effects yield a much better D,, in closer agreement with the value predicted by Ixmire et al. (15). Figures 1 and 2 show the actual potential energy curves of various electronic states of GaAs studied here. As seen from these figures, the repulsive ‘Z- state which dissociates into the ground state atom crosses with the 311(II) curve. This would lead to
411
SPECTROSCOPY OF GaAs., GaAs+, AND GaAs0.25
i
GaAs
4P+
2P
0.20
-z ::%
0. I5
L z 2P+2P
t W
0.10
0.05
0 2.00
5.00
4.00
3.00
6.00
R --*(%I FIG. 2. Potential energy curves for upper states of GaAs dissociating into Ga(‘P) limits.
+ As(*D),
Ga( *P)
+ As(*P), and Ga(5p *P) + A#S)
of all but 52 = O+ component of the 311-X3Z- system. An experimental spectrum obtained by Bemire et al. (15) is in full accord with this. The ‘2 + curve has a shoulder due to an avoided crossing noted before ( 10, 16). However, the double minima found in earlier calculations (10) are most probably an artifact of the erroneous ECP parameter mentioned above. The ‘2+ curve in Fig. 1 is in better agreement with all-electron results of Meier et al. ( 16 ) . All curves in this study are calculated up to dissociation unlike those of Meier et al. Meier et al. report only curves closer to the potential well. This is presumably due to the size consistency problem in the MRDCI method due to cutoff limits in the truncation of configurations. The CASSCF/FOCI/SOCI method in this sense appears to be superior to the MRDCI method. However, all second-order correlations are not taken into account in FOCI calculations and thus we also carried out full SOCI calculations, which are decisively superior to MRDCI calculations, since the largest SOCI calculations included 500 000 configurations. predissociation
Predissociation of ‘II(III),
‘II(U),
5A, ?i?‘,
and
‘A
States
As seen from Fig. 1, the repulsive 52: - curve dissociating to the ground state Ga( ‘P) + As( 4S) atoms intersects with ‘A, 3Z + , 311(III), and 311(II) curves. Similarly, as seen
412
K. BALASUBRAMANIAN
from Fig. 2, the excited ‘A state curve is intersected by the repulsive %( II) curve, dissociating into Ga( 5p)*P + AS atoms. The intersections of ?!- with excited ‘II curves are e sp ecially interesting. Lemire et al. (15) observed that the bands in the 3&-X32: -, Q-- X3X, and 3111-X3Z- systems were predissociated. Since the %state gives rise to Q = 2, O-, and 1 states, the intersection of ‘Z- with 311will cause mixing of 311~-, 311~,and 3111with the corresponding spin-orbit components of 5Z states through spin-orbit coupling. Thus the only state that can survive predissociation by the 5Z- repulsive state is the D = O+ component of 311. This is in full agreement with the experimental spectrum which revealed progressing-forming bands for 3110+-X3Z- system. Consequently both our calculated curve crossings and those of Meier et al. (16) fully support the experimental finding of predissociation of all but 311(III) O+ spin-orbit components. Experimentally no transitions are found (15) which terminate on V’> 1 for s2’ = 2 of the 311(III) state. No transitions could be found terminating on o’ > 0 for D ’ = 1 and Q ’ = O- substrates. Evidently, there is no other candidate for predissociating the 311(III) state as seen from Fig. 1. The same 5L:- state predissociates 32 + , ’ A, and 311(II) states. The predissociation in the 311(11) state, which is yet to be observed, is expected to be analogous to the observed predissociation in the 311(III)-X32- system. The 3Z+ state gives rise to Oand 1 components. Hence both of them cannot survive predissociation. However, the intersection of ‘Z- with 3Z+ occurs at a somewhat longer distance compared to the r, of 3Z+. Those vibrational levels whose classical turning points lie below the curve crossing of 52- and 3Z+ are observable. Consequently, although the two states cross, more vibrational levels are expected to be seen in the 3Z+ state compared to the 311(III) state. Similarly, the crossing of ‘A and ‘Z- occurs at even a longer distance compared to the ‘Z+-%:- curve crossing. Hence the ‘A state should have longer lifetimes compared to 3Z+, 3II( II), or 311(III) states. SOCI Spectroscopic Constants and Dissociation Energy of GaAs As mentioned before we carried out full second-order configuration interaction calculations. Such calculations are likely to yield superior results compared to any other theoretical method. Table III shows the results of our SOCI calculations for lowlying states together with experimentally known values. As seen from Table III, a full SOCI calculation which correlated all eight valence electrons yields r, = 2.60 A compared to experimental values of 2.5 16 A for the 32; state and 2.548 A for the 32L+ state. Yet there is a difference of roughly 0.08 A. However, as noted by Meier et al. (16), d correlation effects tend to shrink the bond length by 0.04-0.05 A. We also corroborate with their findings in that an r, value of 2.55 A is estimated, including d correlation correction to the SOCI results. Full SOCI calculations of all 28 electrons are beyond the scope of any theoretical method at present. The further difference between the theoretical value of 2.55 A and the experimental value should be attributed to the spin-orbit coupling effect. Lemire et al. (15) obtain an r, = 2.516 A for the X32; and an r, = 2.548 A for the X 3Z;+ state of GaAs. Hence it is evident that the spin-orbit mixing of the 3Z;+ with the ‘Z,’ state is likely to alter the bond length of the X 3Zc+ state. As seen from Table III, the second ‘Z+ state has a shorter bond length. Thus mixing of 3Z;+ with
413
SPECTROSCOPY OF GaAs, GaAs+, AND GaAs TABLE III SOCI Spectroscopic Constants and Known Experimental Constants for GaAs” Species
State
T, (cm-‘)
Ide (6’)
re (4 Theory Expt.
Theory
Expt.
Theory
Expt.
Lbob
0
0
215
214
2.54%
G&S
X31-
G&S
3il
2.38
1830
236
SaAs
‘il
2.34
6440
277
SaAs
‘I+
2.23
7768
279
&AS
'A
2.58
7874
214
GaAS
IX+(H)
2.47
14 383
321
GaAs
3n(Ir)
3.10
18 590
135
&As
3+ E
2.405
23 403
208
GaAS
3II(III) 2.68
a Experimtal
2.66
24 600
23 800
160
152
values frcm Ref. (15); experimental re value is for the 32;,
state. b An re value of -2.55 A is estimated if d correlation effects are included.
‘Z,‘+ could result in a shorter bond length for the 32;+ component compared to the 3Z ; state. However, Lemire et al. find that 32,+ has a longer bond length than 32 7. This discrepancy is puzzling and needs further investigation. Lemire et al. find that the 32,t state is 43 cm-’ above the 32; state. This is surprising since 32;+ is likely to for other isovalent dimers such be stabilized through mixing of ‘Z,‘+. Furthermore, as Snz (25)) the 3Z;+ state is lower. Further investigation of spin-orbit states of GaAs is warranted to resolve this apparent discrepancy. When spin-orbit coupling is included both perturbation and coupling with ’ Z +( a%?) could result in a longer band length. This was the case for the isoelectronic InSb. The present SOCI w, value of 2 15 cm -’ is in remarkable agreement with a value of 214 cm-’ obtained by Lemire et al. (25). The T, value obtained in the present study of 24 600 cm-’ is in excellent agreement with the spin-orbit averaged experimental T, of 23 800 cm-‘, giving further confidence to our SOCI calculations. The r, value obtained in the present study for the 311(III) state (2.68 A) is in much closer agreement to the experimental value, compared to a value of 2.70 A obtained by Meier et al. ( 16). Furthermore, the T, value of 2 1 6 16 cm-’ obtained by Meier et al. ( 16) is much lower than our SOCI value of 24 600 cm-’ and the FOCI value of 22 564
414
K. BALASUBRAMANIAN TABLE IV FOCI Spectroscopic Constants for GaAs Using Larger (4s4p2d) Basis Sets” State
re (A)
X32-
2.65
311 *II *I+ IA
*x+(11) 3ll(II) 3n(IrI)
T, (cm-‘) 0
Ye (cm’) lffl
2.373
516
245
2.329
5 390
281
2.217
6 475
300
2.595
8 014
216
2.475
15 635
3.10
18 223
136
2.671
22 474
157
a II, (EaAs) - 1.24 eV.
cm-‘. The present SOCI T,value is in much better agreement with experiment compared to that of Meier et al. (16). However, it must be noted that the experimental value is for the 3110+state and theoretical calculations ignore spin-orbit coupling. The effect of spin-orbit coupling on o, could be as large as 10 cm-’ for some of the states which undergo spin-orbit contamination with other states. The direct FOCI De of GaAs, calculated as the energy difference at r, and 8.0 A, is 1.24 eV. However, as noted before, FOCI calculations do not include higher-order correlation effects; such effects tend to have severe impact on Descompared to other spectroscopic properties. Full SOCI calculations tend to stabilize the well, as evidenced by shortening of the bond length and increase in the w, value. A full SOCI calculation yielded a De (GaAs)= 1.5 eV. However, this value does not include the effects of 3 delectron correlations of Ga and As atoms. Meier et al. (16) estimated an increase in D, of 0.20 eV due to d correlations. Furthermore, extension of the basis set to a (4s4p2d) set leads to an improvement of 0.2 eV in D, even at the FOCI level. If the SOCI value is corrected for d correlation effects and for basis set extension we estimate D, (GaAs) = 1.9 eV. Lemire et al. ( 1.5) obtained the De(GaAs) using the third law method by calculating the partition function of GaAs through the spectroscopic constants obtained by theoretical calculations and using the measured equilibrium constants for the process: Ga (g) + &As2 (g) + GaAs (g). The spectroscopic constants of As2 are well known experimentally. The resulting Do (GaAs)= 2.09 & 0.02 eV is smaller than the value predicted before (22). Another determination of D, through the formula De = w,2/4( mexe) yielded D,, (GaAs) = 2.06 eV. This value is in excellent agreement with the study corrected for d-correlation effects and basis Table IV shows CASSCF/FOCI spectroscopic (4s4p2 d)basis set described before. In comparing
SOCI value obtained in the present set extensions. constants obtained using a larger Table IV with Table II we find that
SPECTROSCOPY
OF GaAs,
GaAs+,
AND
415
GaAs-
TABLE V FOCI Spectroscopic State
re (1)
Constants T,
for GaAs+
(m-l)
tie (cd)
4E-
2.877
0
103
22-
2.519
9 707
250
21
2.968
11 604
134
2A
2.632
13 034
141
2n(II)
2.560
18 600
293
22+
2.530
20 551
177
411
2.624
30 024
168
2ll(III)
2.907
33 854
100
4C(II)
2.566
34 070
218
4A
2.938
36 237
126
4n(Ir)
2.346
39 982
362
4r(III,
2.909
46 290
402
the FOCI results obtained using an extended (4~4~2 d) basis set are quite comparable to FOCI results obtained using a smaller (3~3~ 1d) basis set. Thus further extension of basis sets did not introduce significant changes in the FOCI results. This is comforting since we plan to investigate larger clusters containing Ga and As atoms for which extended basis set will be computationally difficult to use. SPECTROSCOPIC
CONSTANTS
OF GaAs’
Table V shows FOCI spectroscopic constants for GaAs+. In the present study, we obtain potential energy curves of more electronic states compared to our previous study ( IO) or that of Meier et al. (16). Figures 3 and 4 show potential energy curves of electronic states of GaAs+ dissociating into both Ga+ + As and Ga + As+ electronic states. The 4Z - ground state of GaAs+ was experimentally confirmed before by Knight and Petty (9). There are 14 low-lying electronic states of GaAs+ . These are of doublet and quartet spin symmetries. The FOCI r, of the X4Z ground state of (GaAs+) is 0.23 A longer than the X3Z- ground state of GaAs, implying destabilization of the Ga-As bond upon ionization. This is consistent with the bonding nature of the 3a orbital, which is a mixture of both Ga and As 4p, orbitals. Hence removal of an electron from the 30 orbital leads to lengthening of the bond. Alternatively, removal of a 7r electron leads to a ‘II state. This state has a bond length of 2.968 A. The ‘II state arises
416
K. BALASUBRAMANIAN 0.157
Go As+
2
O.lO-
: ,’ L I” -
T
0.05-
W
o-
,,, 2.00
I
3.00
I
1
4.00
5.00
1
6.00
R -(ii) FIG. 3. Potential energy curves of (GaAs)+ dissociating into Ga+( ‘S) + As(“S), Ga+( ‘S) + As(‘D) and Ga+(‘S) + As(‘P) limits.
0.30-
Go
As+
0.25E 0) ,' Is
0.20-
T W 0.15
0.10
, 2.00
3.00
, 4.00
, 5.00
, 6.00
R -di, FIG. 4. Potential energy curves of (GaAs)+ dissociating into Ga+( ‘S) + As(*P) and Ga+(‘S) + ADS
limits.
SPECTROSCOPY OF GaAs, GaAs+, AND GaAs-
417
predominantly from the lu22a23a2r configuration. Thus the longer bond length for the 211state implies that the 7~orbital is also a mixture of Ga and As orbitals. However, it must be noted that bonding in GaAs is partially ionic and orbital relaxation effects are large. In the comparison of all-electron MRDCI calculations of (GaAs)+ ( 16) with our present FOCI results a few discrepancies are worth noting. The bond lengths obtained by Meier et al. ( 16) for (GaAs)+ electronic states are about 0.1-O. 15 A longer than the FOCI values obtained in the present study. For example, Meier et al. ( 16) obtained an r, value of 3.03 A compared to 2.88 A obtained through FOCI calculations. The w, obtained by Meier et al. for the X4X- ground state is 80 cm-‘, which is also lower than the FOCI value. Similarly, the r, and U, values obtained by Meier et al. for the 211state are 3.12 A and 114 cm-’ , respectively. Our FOCI calculations yield r, = 2.97 A, w, = 134 cm-‘. For the *Z+ state Meier et al. obtained r, = 2.64 A and w, = 155 cm-‘. We obtain r, = 2.53 A and we = 177 cm-‘. However, these discrepancies are a bit narrowed when our SOCI results are compared with the results of the all-electron MRDCI method. The 0, value obtained by Meier et al. for (GaAs)+ is only 0.11 eV compared to the present FOCI D, (GaAs+) = 0.42 eV. Thus the D, value obtained by the MRDCI method is much lower compared to the CASSCF/FOCI method. In view of the disagreement between the D, value obtained by Meier et al. ( 16) and the present FOCI and SOCI values, the longer bond lengths and lower w, values obtained by Meier et al. are understandable. The most probable cause for the discrepancy would be that the MRDCI method does not take into account electron correlation effects as much as required for a relatively weakly bound GaAs+ compared to the neutral GaAs species. There are no photoelectron spectra on GaAs diatomic. It is, however, worth noting that comparable heavy group IV-VI diatomics such as PbSe, PbTe, SnSe, and PbSe were studied recently in a joint experimental-theoretical study (23). For these species a comparable theoretical method to that employed in the present investigation gave bond lengths within 0.04-0.06 A for both ionic and neutral species. The w,s were within 2.4-6% of experimental values. Theoretical IPs also came close to experimental values. This gives considerable confidence in the present results on GaAs+. The adiabatic IP of GaAs is calculated as 6.4 eV at the FOCI level and 6.85 eV at the SOCI level. Since SOCI calculations take into account higher-order correlation effects much more accurately we believe that SOCI results should be regarded as more accurate. Meier et al. (16) obtained 6.85 eV for the adiabatic ionization potential of GaAs using the MRDCI method. Although the exact experimental IP of GaAs is not known at present, we believe that the predicted IP is in the general experimental range obtained by O’Brien et al. (2). O’Brien et al. noted that even clusters have larger IPs and that odd clusters have smaller IPs. The experimental IP (GaAs) is predicted to lie between 7 and 7.5 eV. The large change in the GaAs X32- r, and (GaAs)+ X4Z;- r, implies that the Franck-Condon transition from the neutral GaAs X ( 32 -) to the GaAs+ X ( 42 ) state would fall in the repulsive side of the 42- curve. Hence the Franck-Condon factor for this transition should be smaller. Similarly the X3X --, 211transition also involves large geometry changes. This transition also falls on the repulsive side of the 211potential well. Hence the Franck-Condon factor should be small for this transition. As noted
418
K. BALASUBRAMANIAN TABLE VI SOCI Spectroscopic Constants for GaAs+ State
re (4
X4f
2.944
0
211
3.058
10 500
120
2A
2.719
12 148
135
2.598
17 126
285
2E+
2.653
18 155
138
42-(u)
2.592
33 329
210
2iT(II)
T, (cm-‘)
me (cm-5
Oe (ev)
89
0.36
by Meier et al. (16) and in our earlier paper on GaAs+, the ‘II state is a complex mixture of both 3a217r and r3 configurations. This should lead to a complex photoelectron spectrum with additional satellite peaks. The *Z+-X3X and *II(X32transitions are the most favorable from the standpoint of the Franck-Condon factor. Note that both the states involve only small changes in bond lengths compared to the neutral GaAs. Hence the vibrational overlap should be quite strong although the *II( II) and 22 + states are predicted to lie 18 000 and 20 55 1 cm -I, respectively, above the ground state of (GaAs) + . The energy separations of electronic states of GaAs+ calculated using the secondorder CI method should be considered more accurate compared to FOCI values. Table VI shows SOCI spectroscopic constants for GaAs+. As seen from Table VI, the r, value of the X42- ground state increases to 2.944 A. The o, value also decreases to 89 cm-’ in comparing the FOCI method. The FOCI D, value of 0.42 eV changes very little to the SOCI value of 0.36 eV. Since d correlation effects tended to stabilize neutral (GaAs), we predict that De (GaAs)+ - 0.6 eV. Meier et al. (16) MRDCI De (GaAs+) = 0.11 eV appears to be rather low. The energy separations predicted by the SOCI method of calculations are more accurate than those predicted by the FOCI method. Hence T, values in Table VI should be regarded as more accurate. The T, values obtained by Meier et al. (16) are in excellent agreement with our full SOCI results. The main discrepancy between our SOCI results and those of Meier et al. seems to be in the De (GaAs+) mentioned before. It seems that since, in the SOCI method, (GaAs)+ dissociates properly and because the SOCI method is more size-consistent than the MRDCI method, the SOCI De should be more accurate. Hence it would be interesting to have an experimental adiabatic IP for GaAs from which De (GaAs)+ could be calculated. If one takes IP (GaAs) to be 7.2 eV then using the formula shown below De (GaAs)+ can be estimated: D, (GaAs)+ = IP (Ga) - IP (GaAs) + De (GaAs).
If one uses De (GaAs) = 2.0 eV as estimated by Lemire et al. ( 15) in the above formula one obtains De (GaAs+) < 0.8 eV. The value obtained this way is not far from our d-correlation corrected SOCI value of 0.6 eV but is in disagreement with the MRDCI (16) value of 0.11 eV.
SPECTROSCOPY
OF GaAs,
GaAs+,
AND
419
GaAs
TABLE VII FOCI Spectroscopic State
‘e (A)
Constants
1, (cm--‘)
for GaAsre (cm-‘)
*2+
2.282
0
291
28
2.429
936
242
471
2.957
11 788
137
*z+(II)
2.493
17 705
201
2il( II)
2.808
17 863
169
*tJ
2.839
20 608
116
2n(III)
2.854
22 746
149
42+
2.538
11 457
193
411
2.957
11 806
137
4A
2.591
15 394
169
4L-
2.69
17 897
143
27 239
86
4C(II)
3.49
SPECTROSCOPIC
CONSTANTS
0, (ew
2.65
OF GaAs
Table VII shows the FOCI spectroscopic constants of GaAs- . Figure 5 shows the actual potential energy curves of seven electronic states of GaAs- . As mentioned before, attachment of an electron to the ?r orbital of the neutral X32- state of GaAs ( 1a22a23a2r2) should lead to a ‘II state for GaAs-, while attachment of an electron to the rr orbital of the 311 ( la22a23an3) state should result in a 2Z’ state for GaAs-. Both the ‘Z’ and 211 electronic states of GaAs- are very favorable candidates for the ground state as they are within 936 cm -’ of each other. A striking feature of the potential energy curves of GaAs- and the spectroscopic constants listed in Table VII is that GaAs- is much strongly bound compared to the GaAs neutral radical. This strengthening of bonding is accompanied by a significant reduction in the Ga-As bond length for the negative ion ( Ar, = -0.36 A). This trend is approximately the opposite of the bond elongation upon ionization of GaAs ( Ar, = +0.23 A). The vibrational frequency of the 2.Z+ state is considerably larger than the neutral X3X state. However, the w, of the ‘II state is very close to the corresponding w, of the 311 state of GaAs neutral radical. The r, of the 211 state of GaAs- is also remarkably close to the r, value of the 311 state. The next excited state of GaAs- is a 411 state among the states investigated here. We did not study other states such as 22-. However, since the *2- state arises from la22a23a24a?r2 or 1c22a23ax3a* configuration, we expect it to be repulsive or to
420
K. BALASUBRAMANIAN
-0. IO<, I
2.00
I
3.00
I
4.00
I
5.00
I
6.00
R --(A, FIG. 5. Potential energy curves for low-lying electronic states of (C&As ) ~.
exhibit very weakly-bound long range bonding since the 4a antibonding orbital or the a* antibonding orbital must be occupied to form a ‘Z- state. The Ga-( 3P) + AS and Ga( *P) + As-( 3P) asymptotes are expected to be within only 0.5 eV of each other as estimated from electron affinities of these atoms (24). This is anticipated since electron affinities of Ga and As are similar. At the FOCI level of theory, however, attachment of an electron to Ga appears to be more favorable near the dissociation region compared to As since the high-spin 4S ground state of As is destroyed upon attaching an electron while attaching an electron to Ga leads to a 3P state. Thus FOCI calculations do not yield correct dissociation behavior for GaAs -. However, near the well the potential energy curves are more reasonable at the FOCI level. This is not surprising since the level of the basis set (3s3pld) and the level of inclusion of electron correlations are not really adequate for computation of electron affinities. The adiabatic EA (GaAs) calculated at the FOCI level is 0.9 eV. However, FOCI calculations are not expected to yield reliable electron affinities since electron affinities tend to be very sensitive to higher-order electron correlation effects, as mentioned above. The SOCI electron affinity of GaAs is 1.3 eV. Allowing for further corrections to d correlation effects we predict that EA (GaAs) = 1.4 f 0.2 eV. The FOCI 0, (GaAs-) is calculated as 2.65 eV, considerably larger than the corresponding value for neutral GaAs. This is consistent with the shorter bond length and larger w, for GaAs- compared to the neutral GaAs diatomic. Since FOCI calculations underestimated 0, (GaAs) we believe that the SOCI D, (GaAs-) of 3 eV is more reliable (see Table VIII). There are no experimental values for Des of Ga,As;
SPECTROSCOPY
421
OF GaAs, GaAs+, AND GaAs TABLE VIII
SOCI Spectroscopic State
Re (A)
2x+
2.268
21
2.426
Constants
for GaAs0, (cm-‘)
0, (ev)
0
303
3.00
797
216
T, (cm-‘)
ions. It would be interesting to find the binding energies of Ga,As; ions. We anticipate the estimated D, (GaAs- ) to be more accurate than the EA (GaAs) since, in obtaining EA, neutral GaAs energy is compared with the energy of GaAs-, while D, (GaAs-) is obtained by finding the difference of the energies at the well and dissociation limits. We find 12 bound electronic states for (GaAs)- below the 22 000 cm-’ region. There are not this many bound states below 20 000 cm-’ for (GaAs)+ or neutral (GaAs). This is, however, consistent with the large binding energy of (GaAs)- and that Gap + As and Ga + As- asymptotes are only 0.5 eV apart. Lineberger and co-workers (26-27) have carried out a number of electron-detachment spectroscopic studies of negative ions of clusters. Hence photoelectron spectroscopy of (GaAs)- could directly yield the EA (GaAs) . Such experimental studies would certainly be of interest in view of both experimental and theoretical interest in Ga,As, clusters and their ions. We hope that the present theoretical study may provide some impetus for such experimental investigations. Table VIII shows full SOCI spectroscopic constants of the two lowest-lying electronic states of GaAs-. In comparing properties listed in Tables VII and VIII, we find that r, of the *Z+ state shrinks by 0.014 A due to higher-order correlation effects in the SOCI method. The w, value of the *Z4 state also accordingly increases at the SOCI level. The 211-2Zf energy separation does not change significantly even at the SOCI level. The main difference between the FOCI and SOCI method is that D, (GaAs-) is much improved to 3 eV at the SOCI level. Dipole Moments
Dipole moments of electronic states of GaAs and their ions should be of interest to experimentalists investigating microwave and Stark spectra of these species. Since the equilibrium bond lengths ( re) of electronic states of GaAs are 0.03-0.05 A longer than experimental values, dipole moments could be in larger errors compared to experimental results. Table IX shows the calculated full SOCI dipole moments of lowlying electronic states of GaAs. The positive polarity of dipole moments in Table IX implies Ga+As- polarity of bonds. The pe value of the X 32- ground state of GaAs is 1.34 D. Meier et al. (16) obtain a value of 1.47 D using the MRDCI method. We find that dipole moments of electronic states of GaAs vary as a function of internuclear distance. Furthermore, be values are more sensitive to extension of basis sets and additional electronic correlation effects such as d-correlation effects. Hence we believe that the error bars for dipole moments
422
K. BALASUBRAMANIAN TABLE IX Dipole Moments of Low-Lying Electronic States of GaAs and GaAsSpecies GaAS
6aAs GaAs
G&IS &AS GaAs GaAs-
&As-
State X3X--
Pe @Ia 1.34
311
1.61
lo %+
1.73
lA lI+(II) 2x+ 211
2.25 0.97 0.61 5.95 5.7
a Positive polarity means Ga+As- polarity; dipole manents were calculated at the SIJCIre using a full SIX1 method; dipole manents of ions are calculated using 6a as the origin of the dipole operator.
calculated in both theoretical studies could be as large as kO.3 D. The dipole moment of the ‘Z+ state is large (Ga+As-). This is consistent with the large mixing of la22g23a21a2 configuration with la22a21?r4 configuration in this state. Dipole moments of charged species are gauge-dependent. The dipole moments of GaAs- states in Table 9 are reported using Ga as the center of the dipole moment operator. The large positive dipole moment of GaAs- suggests more negative charge on As. Mulliken’s population analyses of the X3X ground state of GaAs reveal that the gross population on Ga and As are 2.76 and 5.24, respectively. This is consistent with the Ga+ As- polarity of bonds described above. The 2Z+ state of (GaAs)- is comprised of gross populations of 3.486 and 5.5 14, on Ga and As, respectively. This means that the negative charge is almost equally shared but there is more electronic charge on As compared to Ga. This is consistent with the electron affinities of the two atoms. Note that the experimental electron affinities of Ga and As atoms reveal that As has 0.5 eV greater electron affinity than Ga (24). CONCLUSION
In this investigation we computed spectroscopic constants and potential energy curves of 20 electronic states of GaAs, 12 electronic states of GaAs+ , and 13 electronic states of GaAs- using complete active space MCSCF (CASSCF) followed by full second-order configuration interaction (SOCI) calculations. The d-correlation corrected spectroscopic constants of the X3Z- ground state of GaAs (r= = 2.55 A, w, = 2 I5 cm-‘) are in excellent agreement with the constants obtained in a recent laserspectroscopic study (Expt: r, = 2.548 A; w, = 214 cm-‘). The calculated potential energy curves of GaAs are consistent with experimentally observed predissociation in the 311(III)-X3Z- system. Spectroscopic constants of many other electronic states of
SPECTROSCOPY
OF GaAs, GaAs+,
AND GaAs-
423
GaAs are predicted which are yet to be observed. The IP (GaAs) and EA ( GaAs) are computed as 6.9 and 1.3 eV, respectively, at a full SOCI level of theory. Two closelyspaced electronic states of 2Z+ and 211symmetries are found for (GaAs)), of which the ‘Z + state is the lowest. The D, (GaAs-) is computed as 3 eV at the SOCI level of theory. Eleven bound electronic states of (GaAs)- lying 27 000 cm-’ above the ground state are found. The spectroscopic constants of the X*Z ’ ground state of (GaAs)) are r, = 2.268 A, w, = 303 cm-‘, and D, = 3 eV. ACKNOWLEDGMENT This research was supported by the National Science Foundation under Grant CHE88 18869. RECEIVED:
October 10, 1989 REFERENCES
1. S. C. O’BRIEN, Y. LIU, Q. L. ZHANG, F. K. TITTEL, R. F. CURL, AND R. E. SMALLEY,J. Chem. Phys. 84,4074-4079 (1986). 2. Y. LIU, Q. L. ZHANG, F. K. TII-~EL, R. F. CURL, AND R. E. SMALLEY,J. Chem. Php. 85,7434-7441 (1986). 3. M. L. MANDICH,W. D. REENTS,JR., AND V. E. BONDYBEY,in “Atomic and Molecular Clusters” (E. Bernstein, Ed.), Elsevier, in press. 4. K. BALASUBRAMANIAN, Chem. Rev., in press. 5. R. E. SMALLEY,in “Cluster Spectroscopy” (E. R. Bernstein. Ed.), Elsevier, in press. 6. J. C. PHILLIPS, Chem. Rev. 86,619-634 (1986). 7. V. E. BONDYBEY,W. D. REENTS,AND M. L. MANDICH,unpublished results. 8. M. RASANEN,C. A. HEIMBROOK,G. P. SCHWARTZ,AND V. E. BONDYBEY,J. Chem. Ph_vs. 85,86-92 (1986). 9. L. KNIGHT AND J. T. PETTY, J. Chem. Phys. 88,48 l-482 ( 1988). 10. K. BALASUBRAMANIAN, .I. Chem. Phys. 86, 3410-3413 (1987); Erratum, in press. 11. K. BALASUBRAMANIAN, Chem. Phys. Lett. 150,71-77 (1988). 12. K. BALASUBRAMANIAN, J. Chem. Ph.vx 87, 3518-3521 (1987). 13. K. BALASUBRAMANIAN, J. Mol. Spectrosc. 121, 465-473 (1987). 14. W. J. REENTS,J. Chem. Phys. 90,4258-4264 (1989). 15. G. W. LEMIRE,G. A. BISHEA,S. A. HEIDECKE,AND M. D. MORSE, J. Chem. Phys., in press. 16. U. MEIER, S. D. PEYERIMHOFF,P. J. BRUNA, AND F. GREIN, J. Mol. Spectrosc. 134,259-280 ( 1989). 17. K. BALASUBRAMANIAN, J. Phys. Chem. 85,3401-3406 ( 1986). 18. K. BALASUBRAMANIAN, J. Mol. Spectrosc. 123, 228-236 ( 1987). 19. K. BALASUBRAMANIAN, AND J. Q. LI, J. Chem. Phys. 88,4979-4986 ( 1988). 20. U. MEIER, S. D. PEYERIMHOFF,P. S. BRUNA, S. R. KARNA, AND F. GRIEN, Chem. Phys., in press. 21. K. BALASUBRAMANIAN, Chem. Phys. Lett. 127,585-589 (1986). 22. G. DEMARIA, L. MALASPINA,AND V. PIACENTE..I. Chem. Phys. 52, 1019 ( 1970). 23. L.S. WANG,B.NIU,Y.T. LEE,D.A.SHIRLEY,ANDK.BALASUBRAMANIAN. J. Chem.Phys., in press. 24. H. HOTOP,AND W. C. LINEBERGER, J.Chem. Eng. Ref: Data 14,731-741 ( 1985 ). 25. K. BALASUBRAMANIAN, Chem. Rev., in press. 25. K. BALASUBRAMANIAN, AND K. S.PITZER, J. Chem. Phys. 78, 321-327 (1983). 26. D. G. LEOPOLD,J. Ho, AND W. C. LINEBERGER,J. Chem. Phys. 86, 17 15-1720 ( 1987). 27. K. M. ERVIN, J. Ho, AND W. C. LINEBERGER,J. Chem. Phys. 89,4514 (1988).
OF MOLECULAR
SPECTROSCOPY
139,405-423 (1990)
Spectroscopic Constants and Potential Energy Curves of GaAs, GaAs+, and GaAsK. BALASUBRAMANIAN’ Chemistry Department, Arizona State University, Tempe, Arizona 85287-1604
Twenty electronic states of GaAs, 12 electronic states of GaAs+, and 13 electronic states of GaA- are investigated using relativistic ab initio complete active space MCSCF (CASSCF) followed by large-scale configuration interaction calculations which included up to 700 000 configurations. Potential energy curves and spectroscopic constantsof all these states of three radicals are obtained. Spectroscopic constants of low-lying states of GaAs are in very good agreement with both experiment and all-electron results. Two nearly-degenerate states of ‘Z+, 211( 2Z+lower) symmetries are found as candidates for the ground state of GaA-. The GaA- negative ion is found to be more stable compared to the neutral GaAs (D, ( GaA-) = 3 eV). The electron affinity of GaAs is computed as 0.89 and 1.3 eV at the FOCI and SOCI levels of theory, respectively. Calculated potential energy curves of GaAs are in accord with the experimentally observed predissociation in the 3H(III)-x3S- system. 0 1990 Academic Press, Inc. INTRODUCTION
Electronic structural and spectroscopic properties of small semiconductor clusters and their ions are of considerable current interest (l-l 9). The properties of Group III-V mixed semiconductor clusters such as Ga,As,, InXPY,In,Sb,, etc., are especially interesting since GaAs semiconductors are used in fast devices. Furthermore, mixed clusters offer additional challenge for investigation as they give rise to more isomers and electronic states arising from competing atomic states of Ga vs As. As mentioned in an earlier paper by the author (IO), compared to a large literature on solid GaAs, very little information has been accumulated on GaxAsy clusters and their ions. The present author ( 10) was the first to study spectroscopic constants and potential energy curves of low-lying electronic states of GaAs and GaAs+. He found an X 3L: ground state for GaAs and an X42- ground state for GaAs+ . Following his theoretical calculations, Knight and Petty (9) confirmed the author’s prediction of a 42- ground state for GaAs+ through ESR spectroscopic study. Recently Lemire et al. (15) have carried out a spectroscopic study of diatomic GaAs. These authors confirmed the present author’s prediction of an X3X ground state. They found electronic bands attributed to 311(III)-X3Z- systems. The bands in theses systems were found to be predissociated due to crossing of a repulsive 52curve with the two excited 311curves. With the exception of 3II,,+-X3Zp system all other systems are predissociated. O’Brien et al. (1) have studied Ga,As, clusters generated by laser vaporization of GaAs crystal. Mass analysis of these clusters revealed considerable deviation from a ’ Camilleand Henry Dreyfus teacher-scholar. 405
0022-2852190 $3.00 Copyright All n&s
0
1990 by Academic
of reproduction
Press, Inc.
in any form reserved.
406
K. BALASUBRAMANIAN
binomial distribution for smaller clusters while large clusters followed the expected binomial distribution. Photofragmentation studies of Ga,As; , Si;, and Ge; have also been made (2). Ionization potentials of Ga,As, clusters exhibited even-odd alternations. After the appearance of the author’s theoretical paper (IO), Meier et al. ( 16) published an all-electron MRDCI study of GaAs and GaAs+. These authors basically confirmed the various states found earlier by the author in addition to investigating a few new states not studied before. The ground state obtained by all-electron study is also 32: _ for GaAs and 42 ~ for GaAs+ . The related AlP has also been studied (20). In the present study we obtain potential energy curves of many electronic states of GaAs and GaAs+ not obtained before. In addition, many electronic states of GaAsare studied for the first time. Further, in addition to CASSCF/first-order CI (FOCI) calculations, full second-order CI (SOCI) calculations which include up to 700 000 configurations are carried out. A larger valence (4s4p2d) basis set on both Ga and As is also employed to study the effect of additional diffuse and polarization functions on the calculated bond lengths and vibrational frequencies. METHOD
OF CALCULATIONS
We employ complete active space MCSCF (CASSCF) followed by first-order configuration interaction (FOCI) and second-order configuration interaction (SOCI) calculations which included up to 500 000 configurations for GaAs and up to 700 000 configurations for GaAs- . All calculations carried out here were made with relativistic effective core potentials ( RECPs) which included the outer 4.~~4~’ shells for Ga and the outer 4.~~4~~ shells for As in the valence space, respectively. In addition, calculations which included the outer 3 d”4s24p ’ , 3 d”4s24p3 shells for Ga and As, respectively, were also made. However, bond lengths did not change much in using either set of potentials, although if d correlations are included bond lengths shrank by O.Ol0.04 A. CASSCF calculations included all six valence electrons of GaAs in the active space. All calculations were carried out in the CzUpoint group with the GaAs diatomic oriented along the z-axis. In this orientation, we included all those orbitals of GaAs which correlated into the 4s and 4p orbitals of the separated atoms at infinite separation. Thus the active space for CASSCF included four al orbitals, two b2 orbitals, and two b, orbitals. All calculations of GaAs+ and GaAincluded seven and nine active electrons, respectively. At the CASSCF level seven, eight, and nine active electrons were distributed in all possible ways among the eight active orbitals for GaAs +, GaAs, and GaA- . We employed three types of basis sets. The smallest basis set is labelled (333~1 d) and included three sets of s functions, three sets of p functions, and one set of 6-component d Gaussian functions on each atom described before ( 10). A more extended (4s4p2d) valence Gaussian basis set was also used. The ( 3s3p 1 d) valence the Gaussian basis set was augmented by an s function with CY$= 0.02644, three p functions with cyp = 0.0164, and six d functions with old = 0.0708 for Ga; the corresponding exponents for As are a, = 0.0405, CQ,= 0.0324, and ffd = 0.115. Calculations which included 3d” core electrons were made with a (4s4p4d) basis set, where the two additional d functions were used for describing the 3 d orbitals of Ga and As.
SPECTROSCOPY
OF GaAs,
GaAs+,
AND
GaA-
407
CI calculations were made using both a first-order Cl (FOCI) method and a full second-order CI (SOCI) method. The FOCI calculations included (i) all configurations in the CASSCF and (ii) those configurations generated by distributing N - 1 electrons in the active space and 1 electron in the orthogonal external space in all possible ways, where N is the number of active electrons for various species (N = 7 for GaAs+ , N = 8 for GaAs, and N = 9 for GaAs-). The second-order CI calculations included all configurations in the FOCI and those configurations generated by distributing N - 2 electrons in the active space and 2 electrons in the external space in all possible ways. The FOCI calculations in the (4~4~2 d) basis set included up to 80 000 configurations for GaAs. The SOCI calculations included up to 500 000 configurations for GaAs and address electron 700 000 configurations for GaAs- . Thus the present calculations correlation effects to a high order compared to any previous study. All calculations described here were carried out using the author’s modified version of ALCHEMY II2 codes to include relativistic effective core potentials as described in Ref. (21). RESULTS
AND
DISCUSSION
Table I shows possible low-lying electronic states of GaAs, GaAs+, and GaAs ~. While it is now quite established that the ground states of GaAs and GaAs+ are 32and 42 -, respectively, this is not so for GaAs- . Since there are two very low-lying electronic states for GaAs of 32- and 311 symmetries arising from the 1u22023&r2 and 1a22a23an3 configurations, respectively, there are two possible candidates for the ground state of GaAs-. If the electron is attached to the P orbital of the ‘II state it would result in a 2Z+ state for GaAs-. If the electron is attached to the ?r orbital of the 32- state, it leads to a 211 state arising from the la22a23a2r3 configuration. Depending on mixing of other low-lying electronic states, either state could be a candidate for the ground state of GaAs-. In addition, high spin states such as 4Z+, 411, etc., could also be low-lying due to spin-exchange stabilization, although the 40 or r* antibonding orbital may have to be occupied in some of these high spin states. In addition, electronic states arising from Ga- + As dissociation limit could also be very low-lying since the difference in electron affinities of Ga and As atoms is only 0.5 eV (24). In this investigation most of the electronic states in Table I and a few additional high-lying electronic states for GaAs and GaAs+ are thoroughly studied. SPECTROSCOPIC
CONSTANTS
OF GaAs
Table II shows spectroscopic constants of the electronic states of GaAs lying below the 50 000 cm-’ region as obtained using a modest CASSCF/FOCI level of treatment employing a (3s3pld) basis set. Among the electronic states listed in Table II, properties of six states were obtained before ( IO). The R, values of most of the states obtained before were 0.11-o. 13 A longer due to an error in one of the ECP parameters acknowledged in an erratum published subsequently ( 10). The vibrational frequencies were also a bit smaller. M. Morse had communicated this discrepancy to the author through his experimental findings prior to the appearance of the all-electron work of Meier et al. ( 16 ) _ ’ Major authors of ALCHEMY
II codes are B. Liu, B. Lengsfield,
and M. Yoshimine.
408
K. BALASUBRAMANIAN TABLE I Dissociation
Relationship
for Low-Lying
Species
Electronic
States of GaAs, GaAs+,
States
Dissociation
GaAS
3E-,311. 4E-.411
6tiS
It+. ‘z-(2).
$3).
3E+. 3f(2).
311(3), 3A(2), 3*,
EtiS
lE+(2). ‘Z-, $2). 3f,
‘A(2).
‘*
*A, 3E+(2),
Ga(2P)
+ ADS
6a(2P)
+ ADS
Ga(2P)
+ ADS
and GaAsLimit
311(2). 3A
6aAS4
4x-
Ga+(%)
+ ADS
fhAS'
2E* 21 9 2x-
6a*(‘S)
+ ADS
t&AS+
?I. %+
Ga*(‘S)
+ ADS
GaAs+
2p+, 2E-(2). 2n(2). 2A, ‘A,
Ga(2P)
+ ADS+
Ga+(‘S)
+ ADS
4C(2), G&i+
48, 4E-
4il(2), 9’
Gab-
GO
Gal&-
Ga-(3P)
+ ADS+ ADS
The predicted ground state of GaAs is a ‘X ground state, which was recently confirmed by Lemire et al. ( 15). A very low-lying 311 state also exists for GaAs. There are three low-lying excited states of ‘II, ‘Li+, and ‘A symmetries below 8200 cm-‘. The large bond length change between the two low-lying 32- and 311 states is quite interesting but fully consistent with the results of other calculations on Gaz ( 17)) Gez ( 18)) etc. The author (25) has recently completed a comparative critical review of all main group p-block dimers and trimers containing atoms heavier than Ga. The 3Z- and 311(111) states of GaAs have been observed through the 311-X3Zsystem of jet-cooled GaAs by Lemire et al. ( 15) recently. They obtained the spectroscopic constants for the X32- and spin-orbit components of ‘II( III) states. The experimental r, of the 32;+ state is 2.548 A and that of the 311(III) state is roughly 2.662 A. The FOCI calculations employing a (3s3pld) basis set yield an r, of 2.645 A, 0.097 A larger than the experimental value. As we discuss later, SOCI calculations yield much better spectroscopic constants and when the effects of d correlations are taken into account, the bond lengths come very close (within 0.0 1 A) to experimental values.
SPECTROSCOPY
OF Ga4s,
409
GaAs+, AND GaAs-
TABLE II FOCI Spectroscopic Constants for GaAs
stata
re (AI
x31-
2.645
311
2.370
1,
T, (cm-‘)
re (cm-‘)
D, (W
187
1.24
996
241
1.12
2.336
5 943
280
12,
2.237
7 192
291
IA
2.582
8 232
213
lc+(II)
2.475
15 950
3ll(II)
3.055
18 900
142
32+
2.421
22 503
210
3il(iII)
2.687
22 564
187
lll(I1)
2.693
24 679
148
3f(II)
2.421
31 106
201
5ll(II)
2.818
40 352
168
=A
2.449
45 431
287
2.794
51 174
187
5Il(lII)
0
Meier et al. (16) published an all-electron study of electronic states of GaAs. They also found a 32- ground state for GaAs and a very low-lying 311 state ( T, - 0.170.24 eV) above the ground state using Hat-tree-Fock/MRDCI method. Most of the discrepancies noted by these authors between the earlier results (IO) and their allelectron results ( 16) are due to an error in one of the ECP parameters ( IO). The bond lengths in Table II are within 0.04-0.05 A of all-electron results for these states. The revised 0,s are also in much better agreement with all-electron results. It is, however, worth noting that the ‘A state has a larger o, if ‘A, CASSCF orbitals are used in calculations, while the ‘AZ orbitals yield a more reasonable w,. Hence the larger W, for the ‘A state obtained before (10) is due to the change of ‘Al orbitals due to the avoided crossing of 1a22a217r4 and 1a22~23a2~2 configurations in the CASSCF calculations. Meier et al. obtain r, = 2.60 A;, w, = 202 cm-’ for the X ‘Z- ground state of GaAs using the all-electron MRDCI method. The present calculations include electron correlations to a much higher order, compared to a restricted configuration space of less than 10 000 configurations in the MRDCI. Although the FOCI method includes most of the significant electron correlations, a full SOCI method is much superior to both the MRDCI and FOCI methods. Even at the FOCI level, the spectroscopic constants,
410
K. BALASUBRAMANIAN
GaAs
\
.a ,
2.00
I
3.00
I
4.00
I
5.00
I
6.00
R -‘& FIG. 1. Potential energy curves of low-lying electronic states of GaAs dissociating into Ga( *P) + and Ga(*P) + As(*D) limits.
r,= 2.645&we
As( 4S)
= 187 cm-‘, of the 3Z- state are in good agreement with all-electron MRDCI calculations. It is worth noting that although Meier et al. employ an allelectron method, they do not include relativistic effects, while our calculations take into account relativistic effects. Meier et al. obtain r, = 2.38 A and U, = 260 cm-’ for the 311state, while we obtain r, = 2.37 A and w, = 241 cm-’ at the FOCI level. For the ’ Z ‘( II) state, FOCI calculations starting from a CASSCF orbital set of ‘A I symmetry yield a larger w, of 420 cm-‘. However, when SOCI calculations are made using FOCI natural orbitals this discrepancy vanishes, and thus the higher w, of the iE+( II) state at the FOCI level must be due to the strong variation of the composition of CASSCF orbitals due to the avoided crossing of la22a21a4 and la22u23021s2 configurations. The D, (GaAs) obtained at the FOCI level is 1.24 eV, compared to the MRDCI value of 1.40 eV. However as we note later, SOCI calculations when corrected for dcorrelation effects yield a much better D,, in closer agreement with the value predicted by Ixmire et al. (15). Figures 1 and 2 show the actual potential energy curves of various electronic states of GaAs studied here. As seen from these figures, the repulsive ‘Z- state which dissociates into the ground state atom crosses with the 311(II) curve. This would lead to
411
SPECTROSCOPY OF GaAs., GaAs+, AND GaAs0.25
i
GaAs
4P+
2P
0.20
-z ::%
0. I5
L z 2P+2P
t W
0.10
0.05
0 2.00
5.00
4.00
3.00
6.00
R --*(%I FIG. 2. Potential energy curves for upper states of GaAs dissociating into Ga(‘P) limits.
+ As(*D),
Ga( *P)
+ As(*P), and Ga(5p *P) + A#S)
of all but 52 = O+ component of the 311-X3Z- system. An experimental spectrum obtained by Bemire et al. (15) is in full accord with this. The ‘2 + curve has a shoulder due to an avoided crossing noted before ( 10, 16). However, the double minima found in earlier calculations (10) are most probably an artifact of the erroneous ECP parameter mentioned above. The ‘2+ curve in Fig. 1 is in better agreement with all-electron results of Meier et al. ( 16 ) . All curves in this study are calculated up to dissociation unlike those of Meier et al. Meier et al. report only curves closer to the potential well. This is presumably due to the size consistency problem in the MRDCI method due to cutoff limits in the truncation of configurations. The CASSCF/FOCI/SOCI method in this sense appears to be superior to the MRDCI method. However, all second-order correlations are not taken into account in FOCI calculations and thus we also carried out full SOCI calculations, which are decisively superior to MRDCI calculations, since the largest SOCI calculations included 500 000 configurations. predissociation
Predissociation of ‘II(III),
‘II(U),
5A, ?i?‘,
and
‘A
States
As seen from Fig. 1, the repulsive 52: - curve dissociating to the ground state Ga( ‘P) + As( 4S) atoms intersects with ‘A, 3Z + , 311(III), and 311(II) curves. Similarly, as seen
412
K. BALASUBRAMANIAN
from Fig. 2, the excited ‘A state curve is intersected by the repulsive %( II) curve, dissociating into Ga( 5p)*P + AS atoms. The intersections of ?!- with excited ‘II curves are e sp ecially interesting. Lemire et al. (15) observed that the bands in the 3&-X32: -, Q-- X3X, and 3111-X3Z- systems were predissociated. Since the %state gives rise to Q = 2, O-, and 1 states, the intersection of ‘Z- with 311will cause mixing of 311~-, 311~,and 3111with the corresponding spin-orbit components of 5Z states through spin-orbit coupling. Thus the only state that can survive predissociation by the 5Z- repulsive state is the D = O+ component of 311. This is in full agreement with the experimental spectrum which revealed progressing-forming bands for 3110+-X3Z- system. Consequently both our calculated curve crossings and those of Meier et al. (16) fully support the experimental finding of predissociation of all but 311(III) O+ spin-orbit components. Experimentally no transitions are found (15) which terminate on V’> 1 for s2’ = 2 of the 311(III) state. No transitions could be found terminating on o’ > 0 for D ’ = 1 and Q ’ = O- substrates. Evidently, there is no other candidate for predissociating the 311(III) state as seen from Fig. 1. The same 5L:- state predissociates 32 + , ’ A, and 311(II) states. The predissociation in the 311(11) state, which is yet to be observed, is expected to be analogous to the observed predissociation in the 311(III)-X32- system. The 3Z+ state gives rise to Oand 1 components. Hence both of them cannot survive predissociation. However, the intersection of ‘Z- with 3Z+ occurs at a somewhat longer distance compared to the r, of 3Z+. Those vibrational levels whose classical turning points lie below the curve crossing of 52- and 3Z+ are observable. Consequently, although the two states cross, more vibrational levels are expected to be seen in the 3Z+ state compared to the 311(III) state. Similarly, the crossing of ‘A and ‘Z- occurs at even a longer distance compared to the ‘Z+-%:- curve crossing. Hence the ‘A state should have longer lifetimes compared to 3Z+, 3II( II), or 311(III) states. SOCI Spectroscopic Constants and Dissociation Energy of GaAs As mentioned before we carried out full second-order configuration interaction calculations. Such calculations are likely to yield superior results compared to any other theoretical method. Table III shows the results of our SOCI calculations for lowlying states together with experimentally known values. As seen from Table III, a full SOCI calculation which correlated all eight valence electrons yields r, = 2.60 A compared to experimental values of 2.5 16 A for the 32; state and 2.548 A for the 32L+ state. Yet there is a difference of roughly 0.08 A. However, as noted by Meier et al. (16), d correlation effects tend to shrink the bond length by 0.04-0.05 A. We also corroborate with their findings in that an r, value of 2.55 A is estimated, including d correlation correction to the SOCI results. Full SOCI calculations of all 28 electrons are beyond the scope of any theoretical method at present. The further difference between the theoretical value of 2.55 A and the experimental value should be attributed to the spin-orbit coupling effect. Lemire et al. (15) obtain an r, = 2.516 A for the X32; and an r, = 2.548 A for the X 3Z;+ state of GaAs. Hence it is evident that the spin-orbit mixing of the 3Z;+ with the ‘Z,’ state is likely to alter the bond length of the X 3Zc+ state. As seen from Table III, the second ‘Z+ state has a shorter bond length. Thus mixing of 3Z;+ with
413
SPECTROSCOPY OF GaAs, GaAs+, AND GaAs TABLE III SOCI Spectroscopic Constants and Known Experimental Constants for GaAs” Species
State
T, (cm-‘)
Ide (6’)
re (4 Theory Expt.
Theory
Expt.
Theory
Expt.
Lbob
0
0
215
214
2.54%
G&S
X31-
G&S
3il
2.38
1830
236
SaAs
‘il
2.34
6440
277
SaAs
‘I+
2.23
7768
279
&AS
'A
2.58
7874
214
GaAS
IX+(H)
2.47
14 383
321
GaAs
3n(Ir)
3.10
18 590
135
&As
3+ E
2.405
23 403
208
GaAS
3II(III) 2.68
a Experimtal
2.66
24 600
23 800
160
152
values frcm Ref. (15); experimental re value is for the 32;,
state. b An re value of -2.55 A is estimated if d correlation effects are included.
‘Z,‘+ could result in a shorter bond length for the 32;+ component compared to the 3Z ; state. However, Lemire et al. find that 32,+ has a longer bond length than 32 7. This discrepancy is puzzling and needs further investigation. Lemire et al. find that the 32,t state is 43 cm-’ above the 32; state. This is surprising since 32;+ is likely to for other isovalent dimers such be stabilized through mixing of ‘Z,‘+. Furthermore, as Snz (25)) the 3Z;+ state is lower. Further investigation of spin-orbit states of GaAs is warranted to resolve this apparent discrepancy. When spin-orbit coupling is included both perturbation and coupling with ’ Z +( a%?) could result in a longer band length. This was the case for the isoelectronic InSb. The present SOCI w, value of 2 15 cm -’ is in remarkable agreement with a value of 214 cm-’ obtained by Lemire et al. (25). The T, value obtained in the present study of 24 600 cm-’ is in excellent agreement with the spin-orbit averaged experimental T, of 23 800 cm-‘, giving further confidence to our SOCI calculations. The r, value obtained in the present study for the 311(III) state (2.68 A) is in much closer agreement to the experimental value, compared to a value of 2.70 A obtained by Meier et al. ( 16). Furthermore, the T, value of 2 1 6 16 cm-’ obtained by Meier et al. ( 16) is much lower than our SOCI value of 24 600 cm-’ and the FOCI value of 22 564
414
K. BALASUBRAMANIAN TABLE IV FOCI Spectroscopic Constants for GaAs Using Larger (4s4p2d) Basis Sets” State
re (A)
X32-
2.65
311 *II *I+ IA
*x+(11) 3ll(II) 3n(IrI)
T, (cm-‘) 0
Ye (cm’) lffl
2.373
516
245
2.329
5 390
281
2.217
6 475
300
2.595
8 014
216
2.475
15 635
3.10
18 223
136
2.671
22 474
157
a II, (EaAs) - 1.24 eV.
cm-‘. The present SOCI T,value is in much better agreement with experiment compared to that of Meier et al. (16). However, it must be noted that the experimental value is for the 3110+state and theoretical calculations ignore spin-orbit coupling. The effect of spin-orbit coupling on o, could be as large as 10 cm-’ for some of the states which undergo spin-orbit contamination with other states. The direct FOCI De of GaAs, calculated as the energy difference at r, and 8.0 A, is 1.24 eV. However, as noted before, FOCI calculations do not include higher-order correlation effects; such effects tend to have severe impact on Descompared to other spectroscopic properties. Full SOCI calculations tend to stabilize the well, as evidenced by shortening of the bond length and increase in the w, value. A full SOCI calculation yielded a De (GaAs)= 1.5 eV. However, this value does not include the effects of 3 delectron correlations of Ga and As atoms. Meier et al. (16) estimated an increase in D, of 0.20 eV due to d correlations. Furthermore, extension of the basis set to a (4s4p2d) set leads to an improvement of 0.2 eV in D, even at the FOCI level. If the SOCI value is corrected for d correlation effects and for basis set extension we estimate D, (GaAs) = 1.9 eV. Lemire et al. ( 1.5) obtained the De(GaAs) using the third law method by calculating the partition function of GaAs through the spectroscopic constants obtained by theoretical calculations and using the measured equilibrium constants for the process: Ga (g) + &As2 (g) + GaAs (g). The spectroscopic constants of As2 are well known experimentally. The resulting Do (GaAs)= 2.09 & 0.02 eV is smaller than the value predicted before (22). Another determination of D, through the formula De = w,2/4( mexe) yielded D,, (GaAs) = 2.06 eV. This value is in excellent agreement with the study corrected for d-correlation effects and basis Table IV shows CASSCF/FOCI spectroscopic (4s4p2 d)basis set described before. In comparing
SOCI value obtained in the present set extensions. constants obtained using a larger Table IV with Table II we find that
SPECTROSCOPY
OF GaAs,
GaAs+,
AND
415
GaAs-
TABLE V FOCI Spectroscopic State
re (1)
Constants T,
for GaAs+
(m-l)
tie (cd)
4E-
2.877
0
103
22-
2.519
9 707
250
21
2.968
11 604
134
2A
2.632
13 034
141
2n(II)
2.560
18 600
293
22+
2.530
20 551
177
411
2.624
30 024
168
2ll(III)
2.907
33 854
100
4C(II)
2.566
34 070
218
4A
2.938
36 237
126
4n(Ir)
2.346
39 982
362
4r(III,
2.909
46 290
402
the FOCI results obtained using an extended (4~4~2 d) basis set are quite comparable to FOCI results obtained using a smaller (3~3~ 1d) basis set. Thus further extension of basis sets did not introduce significant changes in the FOCI results. This is comforting since we plan to investigate larger clusters containing Ga and As atoms for which extended basis set will be computationally difficult to use. SPECTROSCOPIC
CONSTANTS
OF GaAs’
Table V shows FOCI spectroscopic constants for GaAs+. In the present study, we obtain potential energy curves of more electronic states compared to our previous study ( IO) or that of Meier et al. (16). Figures 3 and 4 show potential energy curves of electronic states of GaAs+ dissociating into both Ga+ + As and Ga + As+ electronic states. The 4Z - ground state of GaAs+ was experimentally confirmed before by Knight and Petty (9). There are 14 low-lying electronic states of GaAs+ . These are of doublet and quartet spin symmetries. The FOCI r, of the X4Z ground state of (GaAs+) is 0.23 A longer than the X3Z- ground state of GaAs, implying destabilization of the Ga-As bond upon ionization. This is consistent with the bonding nature of the 3a orbital, which is a mixture of both Ga and As 4p, orbitals. Hence removal of an electron from the 30 orbital leads to lengthening of the bond. Alternatively, removal of a 7r electron leads to a ‘II state. This state has a bond length of 2.968 A. The ‘II state arises
416
K. BALASUBRAMANIAN 0.157
Go As+
2
O.lO-
: ,’ L I” -
T
0.05-
W
o-
,,, 2.00
I
3.00
I
1
4.00
5.00
1
6.00
R -(ii) FIG. 3. Potential energy curves of (GaAs)+ dissociating into Ga+( ‘S) + As(“S), Ga+( ‘S) + As(‘D) and Ga+(‘S) + As(‘P) limits.
0.30-
Go
As+
0.25E 0) ,' Is
0.20-
T W 0.15
0.10
, 2.00
3.00
, 4.00
, 5.00
, 6.00
R -di, FIG. 4. Potential energy curves of (GaAs)+ dissociating into Ga+( ‘S) + As(*P) and Ga+(‘S) + ADS
limits.
SPECTROSCOPY OF GaAs, GaAs+, AND GaAs-
417
predominantly from the lu22a23a2r configuration. Thus the longer bond length for the 211state implies that the 7~orbital is also a mixture of Ga and As orbitals. However, it must be noted that bonding in GaAs is partially ionic and orbital relaxation effects are large. In the comparison of all-electron MRDCI calculations of (GaAs)+ ( 16) with our present FOCI results a few discrepancies are worth noting. The bond lengths obtained by Meier et al. ( 16) for (GaAs)+ electronic states are about 0.1-O. 15 A longer than the FOCI values obtained in the present study. For example, Meier et al. ( 16) obtained an r, value of 3.03 A compared to 2.88 A obtained through FOCI calculations. The w, obtained by Meier et al. for the X4X- ground state is 80 cm-‘, which is also lower than the FOCI value. Similarly, the r, and U, values obtained by Meier et al. for the 211state are 3.12 A and 114 cm-’ , respectively. Our FOCI calculations yield r, = 2.97 A, w, = 134 cm-‘. For the *Z+ state Meier et al. obtained r, = 2.64 A and w, = 155 cm-‘. We obtain r, = 2.53 A and we = 177 cm-‘. However, these discrepancies are a bit narrowed when our SOCI results are compared with the results of the all-electron MRDCI method. The 0, value obtained by Meier et al. for (GaAs)+ is only 0.11 eV compared to the present FOCI D, (GaAs+) = 0.42 eV. Thus the D, value obtained by the MRDCI method is much lower compared to the CASSCF/FOCI method. In view of the disagreement between the D, value obtained by Meier et al. ( 16) and the present FOCI and SOCI values, the longer bond lengths and lower w, values obtained by Meier et al. are understandable. The most probable cause for the discrepancy would be that the MRDCI method does not take into account electron correlation effects as much as required for a relatively weakly bound GaAs+ compared to the neutral GaAs species. There are no photoelectron spectra on GaAs diatomic. It is, however, worth noting that comparable heavy group IV-VI diatomics such as PbSe, PbTe, SnSe, and PbSe were studied recently in a joint experimental-theoretical study (23). For these species a comparable theoretical method to that employed in the present investigation gave bond lengths within 0.04-0.06 A for both ionic and neutral species. The w,s were within 2.4-6% of experimental values. Theoretical IPs also came close to experimental values. This gives considerable confidence in the present results on GaAs+. The adiabatic IP of GaAs is calculated as 6.4 eV at the FOCI level and 6.85 eV at the SOCI level. Since SOCI calculations take into account higher-order correlation effects much more accurately we believe that SOCI results should be regarded as more accurate. Meier et al. (16) obtained 6.85 eV for the adiabatic ionization potential of GaAs using the MRDCI method. Although the exact experimental IP of GaAs is not known at present, we believe that the predicted IP is in the general experimental range obtained by O’Brien et al. (2). O’Brien et al. noted that even clusters have larger IPs and that odd clusters have smaller IPs. The experimental IP (GaAs) is predicted to lie between 7 and 7.5 eV. The large change in the GaAs X32- r, and (GaAs)+ X4Z;- r, implies that the Franck-Condon transition from the neutral GaAs X ( 32 -) to the GaAs+ X ( 42 ) state would fall in the repulsive side of the 42- curve. Hence the Franck-Condon factor for this transition should be smaller. Similarly the X3X --, 211transition also involves large geometry changes. This transition also falls on the repulsive side of the 211potential well. Hence the Franck-Condon factor should be small for this transition. As noted
418
K. BALASUBRAMANIAN TABLE VI SOCI Spectroscopic Constants for GaAs+ State
re (4
X4f
2.944
0
211
3.058
10 500
120
2A
2.719
12 148
135
2.598
17 126
285
2E+
2.653
18 155
138
42-(u)
2.592
33 329
210
2iT(II)
T, (cm-‘)
me (cm-5
Oe (ev)
89
0.36
by Meier et al. (16) and in our earlier paper on GaAs+, the ‘II state is a complex mixture of both 3a217r and r3 configurations. This should lead to a complex photoelectron spectrum with additional satellite peaks. The *Z+-X3X and *II(X32transitions are the most favorable from the standpoint of the Franck-Condon factor. Note that both the states involve only small changes in bond lengths compared to the neutral GaAs. Hence the vibrational overlap should be quite strong although the *II( II) and 22 + states are predicted to lie 18 000 and 20 55 1 cm -I, respectively, above the ground state of (GaAs) + . The energy separations of electronic states of GaAs+ calculated using the secondorder CI method should be considered more accurate compared to FOCI values. Table VI shows SOCI spectroscopic constants for GaAs+. As seen from Table VI, the r, value of the X42- ground state increases to 2.944 A. The o, value also decreases to 89 cm-’ in comparing the FOCI method. The FOCI D, value of 0.42 eV changes very little to the SOCI value of 0.36 eV. Since d correlation effects tended to stabilize neutral (GaAs), we predict that De (GaAs)+ - 0.6 eV. Meier et al. (16) MRDCI De (GaAs+) = 0.11 eV appears to be rather low. The energy separations predicted by the SOCI method of calculations are more accurate than those predicted by the FOCI method. Hence T, values in Table VI should be regarded as more accurate. The T, values obtained by Meier et al. (16) are in excellent agreement with our full SOCI results. The main discrepancy between our SOCI results and those of Meier et al. seems to be in the De (GaAs+) mentioned before. It seems that since, in the SOCI method, (GaAs)+ dissociates properly and because the SOCI method is more size-consistent than the MRDCI method, the SOCI De should be more accurate. Hence it would be interesting to have an experimental adiabatic IP for GaAs from which De (GaAs)+ could be calculated. If one takes IP (GaAs) to be 7.2 eV then using the formula shown below De (GaAs)+ can be estimated: D, (GaAs)+ = IP (Ga) - IP (GaAs) + De (GaAs).
If one uses De (GaAs) = 2.0 eV as estimated by Lemire et al. ( 15) in the above formula one obtains De (GaAs+) < 0.8 eV. The value obtained this way is not far from our d-correlation corrected SOCI value of 0.6 eV but is in disagreement with the MRDCI (16) value of 0.11 eV.
SPECTROSCOPY
OF GaAs,
GaAs+,
AND
419
GaAs
TABLE VII FOCI Spectroscopic State
‘e (A)
Constants
1, (cm--‘)
for GaAsre (cm-‘)
*2+
2.282
0
291
28
2.429
936
242
471
2.957
11 788
137
*z+(II)
2.493
17 705
201
2il( II)
2.808
17 863
169
*tJ
2.839
20 608
116
2n(III)
2.854
22 746
149
42+
2.538
11 457
193
411
2.957
11 806
137
4A
2.591
15 394
169
4L-
2.69
17 897
143
27 239
86
4C(II)
3.49
SPECTROSCOPIC
CONSTANTS
0, (ew
2.65
OF GaAs
Table VII shows the FOCI spectroscopic constants of GaAs- . Figure 5 shows the actual potential energy curves of seven electronic states of GaAs- . As mentioned before, attachment of an electron to the ?r orbital of the neutral X32- state of GaAs ( 1a22a23a2r2) should lead to a ‘II state for GaAs-, while attachment of an electron to the rr orbital of the 311 ( la22a23an3) state should result in a 2Z’ state for GaAs-. Both the ‘Z’ and 211 electronic states of GaAs- are very favorable candidates for the ground state as they are within 936 cm -’ of each other. A striking feature of the potential energy curves of GaAs- and the spectroscopic constants listed in Table VII is that GaAs- is much strongly bound compared to the GaAs neutral radical. This strengthening of bonding is accompanied by a significant reduction in the Ga-As bond length for the negative ion ( Ar, = -0.36 A). This trend is approximately the opposite of the bond elongation upon ionization of GaAs ( Ar, = +0.23 A). The vibrational frequency of the 2.Z+ state is considerably larger than the neutral X3X state. However, the w, of the ‘II state is very close to the corresponding w, of the 311 state of GaAs neutral radical. The r, of the 211 state of GaAs- is also remarkably close to the r, value of the 311 state. The next excited state of GaAs- is a 411 state among the states investigated here. We did not study other states such as 22-. However, since the *2- state arises from la22a23a24a?r2 or 1c22a23ax3a* configuration, we expect it to be repulsive or to
420
K. BALASUBRAMANIAN
-0. IO<, I
2.00
I
3.00
I
4.00
I
5.00
I
6.00
R --(A, FIG. 5. Potential energy curves for low-lying electronic states of (C&As ) ~.
exhibit very weakly-bound long range bonding since the 4a antibonding orbital or the a* antibonding orbital must be occupied to form a ‘Z- state. The Ga-( 3P) + AS and Ga( *P) + As-( 3P) asymptotes are expected to be within only 0.5 eV of each other as estimated from electron affinities of these atoms (24). This is anticipated since electron affinities of Ga and As are similar. At the FOCI level of theory, however, attachment of an electron to Ga appears to be more favorable near the dissociation region compared to As since the high-spin 4S ground state of As is destroyed upon attaching an electron while attaching an electron to Ga leads to a 3P state. Thus FOCI calculations do not yield correct dissociation behavior for GaAs -. However, near the well the potential energy curves are more reasonable at the FOCI level. This is not surprising since the level of the basis set (3s3pld) and the level of inclusion of electron correlations are not really adequate for computation of electron affinities. The adiabatic EA (GaAs) calculated at the FOCI level is 0.9 eV. However, FOCI calculations are not expected to yield reliable electron affinities since electron affinities tend to be very sensitive to higher-order electron correlation effects, as mentioned above. The SOCI electron affinity of GaAs is 1.3 eV. Allowing for further corrections to d correlation effects we predict that EA (GaAs) = 1.4 f 0.2 eV. The FOCI 0, (GaAs-) is calculated as 2.65 eV, considerably larger than the corresponding value for neutral GaAs. This is consistent with the shorter bond length and larger w, for GaAs- compared to the neutral GaAs diatomic. Since FOCI calculations underestimated 0, (GaAs) we believe that the SOCI D, (GaAs-) of 3 eV is more reliable (see Table VIII). There are no experimental values for Des of Ga,As;
SPECTROSCOPY
421
OF GaAs, GaAs+, AND GaAs TABLE VIII
SOCI Spectroscopic State
Re (A)
2x+
2.268
21
2.426
Constants
for GaAs0, (cm-‘)
0, (ev)
0
303
3.00
797
216
T, (cm-‘)
ions. It would be interesting to find the binding energies of Ga,As; ions. We anticipate the estimated D, (GaAs- ) to be more accurate than the EA (GaAs) since, in obtaining EA, neutral GaAs energy is compared with the energy of GaAs-, while D, (GaAs-) is obtained by finding the difference of the energies at the well and dissociation limits. We find 12 bound electronic states for (GaAs)- below the 22 000 cm-’ region. There are not this many bound states below 20 000 cm-’ for (GaAs)+ or neutral (GaAs). This is, however, consistent with the large binding energy of (GaAs)- and that Gap + As and Ga + As- asymptotes are only 0.5 eV apart. Lineberger and co-workers (26-27) have carried out a number of electron-detachment spectroscopic studies of negative ions of clusters. Hence photoelectron spectroscopy of (GaAs)- could directly yield the EA (GaAs) . Such experimental studies would certainly be of interest in view of both experimental and theoretical interest in Ga,As, clusters and their ions. We hope that the present theoretical study may provide some impetus for such experimental investigations. Table VIII shows full SOCI spectroscopic constants of the two lowest-lying electronic states of GaAs-. In comparing properties listed in Tables VII and VIII, we find that r, of the *Z+ state shrinks by 0.014 A due to higher-order correlation effects in the SOCI method. The w, value of the *Z4 state also accordingly increases at the SOCI level. The 211-2Zf energy separation does not change significantly even at the SOCI level. The main difference between the FOCI and SOCI method is that D, (GaAs-) is much improved to 3 eV at the SOCI level. Dipole Moments
Dipole moments of electronic states of GaAs and their ions should be of interest to experimentalists investigating microwave and Stark spectra of these species. Since the equilibrium bond lengths ( re) of electronic states of GaAs are 0.03-0.05 A longer than experimental values, dipole moments could be in larger errors compared to experimental results. Table IX shows the calculated full SOCI dipole moments of lowlying electronic states of GaAs. The positive polarity of dipole moments in Table IX implies Ga+As- polarity of bonds. The pe value of the X 32- ground state of GaAs is 1.34 D. Meier et al. (16) obtain a value of 1.47 D using the MRDCI method. We find that dipole moments of electronic states of GaAs vary as a function of internuclear distance. Furthermore, be values are more sensitive to extension of basis sets and additional electronic correlation effects such as d-correlation effects. Hence we believe that the error bars for dipole moments
422
K. BALASUBRAMANIAN TABLE IX Dipole Moments of Low-Lying Electronic States of GaAs and GaAsSpecies GaAS
6aAs GaAs
G&IS &AS GaAs GaAs-
&As-
State X3X--
Pe @Ia 1.34
311
1.61
lo %+
1.73
lA lI+(II) 2x+ 211
2.25 0.97 0.61 5.95 5.7
a Positive polarity means Ga+As- polarity; dipole manents were calculated at the SIJCIre using a full SIX1 method; dipole manents of ions are calculated using 6a as the origin of the dipole operator.
calculated in both theoretical studies could be as large as kO.3 D. The dipole moment of the ‘Z+ state is large (Ga+As-). This is consistent with the large mixing of la22g23a21a2 configuration with la22a21?r4 configuration in this state. Dipole moments of charged species are gauge-dependent. The dipole moments of GaAs- states in Table 9 are reported using Ga as the center of the dipole moment operator. The large positive dipole moment of GaAs- suggests more negative charge on As. Mulliken’s population analyses of the X3X ground state of GaAs reveal that the gross population on Ga and As are 2.76 and 5.24, respectively. This is consistent with the Ga+ As- polarity of bonds described above. The 2Z+ state of (GaAs)- is comprised of gross populations of 3.486 and 5.5 14, on Ga and As, respectively. This means that the negative charge is almost equally shared but there is more electronic charge on As compared to Ga. This is consistent with the electron affinities of the two atoms. Note that the experimental electron affinities of Ga and As atoms reveal that As has 0.5 eV greater electron affinity than Ga (24). CONCLUSION
In this investigation we computed spectroscopic constants and potential energy curves of 20 electronic states of GaAs, 12 electronic states of GaAs+ , and 13 electronic states of GaAs- using complete active space MCSCF (CASSCF) followed by full second-order configuration interaction (SOCI) calculations. The d-correlation corrected spectroscopic constants of the X3Z- ground state of GaAs (r= = 2.55 A, w, = 2 I5 cm-‘) are in excellent agreement with the constants obtained in a recent laserspectroscopic study (Expt: r, = 2.548 A; w, = 214 cm-‘). The calculated potential energy curves of GaAs are consistent with experimentally observed predissociation in the 311(III)-X3Z- system. Spectroscopic constants of many other electronic states of
SPECTROSCOPY
OF GaAs, GaAs+,
AND GaAs-
423
GaAs are predicted which are yet to be observed. The IP (GaAs) and EA ( GaAs) are computed as 6.9 and 1.3 eV, respectively, at a full SOCI level of theory. Two closelyspaced electronic states of 2Z+ and 211symmetries are found for (GaAs)), of which the ‘Z + state is the lowest. The D, (GaAs-) is computed as 3 eV at the SOCI level of theory. Eleven bound electronic states of (GaAs)- lying 27 000 cm-’ above the ground state are found. The spectroscopic constants of the X*Z ’ ground state of (GaAs)) are r, = 2.268 A, w, = 303 cm-‘, and D, = 3 eV. ACKNOWLEDGMENT This research was supported by the National Science Foundation under Grant CHE88 18869. RECEIVED:
October 10, 1989 REFERENCES
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