J. Phys. Chem. 1988, 92, 361-364
361
Electronic States and Potential Energy Surfaces of AuH, K. Balasubramanian* and M. Z. Liaot Department of Chemistry, Arizona State University, Tempe, Arizona 85287 (Received: June 30, 1987)
Complete active space MCSCF (CASSCF) followed by second-order configuration interaction (SOCI) calculations as well as multireference singles and doubles CI (d-MRSDCI) including the d electrons of Au are carried out on the two low-lying electronic states (,B2 and ,A1) of AuH2. The bending potential energy surfaces of the ,B, and ,Al states with the bond lengths optimized for all angles are presented. The ground state of AuH, is found to be a bent ,B2 electronic state with a bending angle of 127' at the d-MRSDCI level and 128' at the CASSCF/SOCI level. The d correlation is shown to be significant, approximately 0.88 and 0.59 eV, respectively, especially for the ,B2 (bent) state. Two linear states, namely ,Eg+and ,Eu+, above the ,B2 bent ground state are found. The bending potential energy surfaces of the two states reveal that the ground state of the gold atom (,S) has to surmount a large barrier (90 kcal/mol) to insert into H2 to form the 2Eg+ linear state while the excited 2Pstate of the gold atom inserts spontaneously into H, to form the bent 2B2ground state. The AuH2 ground state is about 0.85 eV less stable than Au(,S) + H2 at the d-MRSDCI level while the atomization energy of AuH, (Le., AuH,(,B,) Au(,S) + 2 H ) is found to be 3.71 eV.
-
1. Introduction
TABLE I Valence Basis Sets of Gaussian-Type Function for Au
The electronic structure and potential energy surfaces of MH2 molecules where M is a transition metal could provide significant insight into the reactivities of the metal atom and small clusters of the atom with HZ. Such model reactions are useful in our understanding of catalytic reaction photochemical process," and hydrogenation processes of transition-metal s ~ r f a c e s . ~ Theoretical studies of gold- and silver-containing molecules such as A U H , &AgH,69 ~ A u ~ , ~ Ag2,638 , ~ , ~AuAg,a ~ , ~ Au3,I2 ~ etc., are of considerable interest in recent years for a number of reasons. First, the relativistic correction arising primarily from mass-velocity correction is significant, especially for gold-containing molecules. This is manifested in the relativistic contraction of the bond lengths in AuH and Au2. The other anomaly that is primarily attributed to mass-velocity correction is that the dissociation energy De of Au2 is larger than the corresponding value for Ag,. While the AuH diatomic has been studied extensively, there are no a b initio theoretical calculations on AuH,. On the experimental side, the related AuH2+ species has been isolated by using the field-induced surface-catalyzed reaction^.^^,^^ The AuH2+ ion was formed on metal surfaces of Au and was studied by using the pulsed-laser time-of-flight atom-probe field ion micro~cope.'~The Au atoms were found to be field evaporated dominantly as AuH2+ions. The average lifetime of AuH2+was s. found to be -6.2 X The objective of the present investigation is to carry out ab initio CASSCF (complete active space MCSCF) followed by configuration interaction calculations with and without d electrons including relativistic effects. We investigate three low-lying electronic states, namely ,Zg+, ,Xu+,and ZB2. Further, the bending potential energy surfaces of the 2B2 and zAl electronic states of AuH2 were obtained at the CASSCF level with the objective of studying the reactivities of the Au(,S) and Au(,P) atoms with H2. Theoretical studies of electronic and spectroscopic properties of molecules containing very heavy atoms have been a topic of considerable activity in recent year^.'^-^^ Section 2 outlines our method of investigation, and section 3 contains results and discussions.
2. Method of Investigations We carry out multiconfiguration self-consistent field (MCSCF) calculations followed by configuration interaction calculations with and without the d shell of the gold atom. All calculations reported here were carried out using relativistic effective core potentials with the 5dl06sl outer shell of the gold atom explicitly retained in the valence space. Ermler and Christiansen2' have recently 'Alfred P. Sloan Fellow, Camille and Henry Dreyfus Teacher-Scholar. *Permanent address: Department of Chemistry, Tsinghua University, Beijing, China.
0022-3654/88/2092-0361$01.50/0
shell
exponential factor
S
0.4409 0.2626 0.0617
contraction coeff 1 .o 1.o 1.o
P
0.6642 0.1073 0.0381
0.038440 0.306335 1.o
d
1.3458 0.4947 0.1664
1.o 1.o 1.o
generated analytical Gaussian fits of relativistic effective potentials for the gold atom suitable for molecular calculations. We employ these potentials together with the (3s3p3d) valence Gaussian basis set optimized by these authors for the ground state of the gold atom. The three p functions were contracted to a 2p set with the coefficients shown in Table I. The resulting basis set for the gold atom can be described as (3s3p3d/3s2p3d). McLean6 has shown that inclusion of f-type functions can lead to a bond contraction of about 0.07 8,in both AgH and AuH. However, it should be noted that if one includes extensive d correlation the shifts in bond (1) Hay, P. J. Chem. Phys. Lett. 1984, 103, 466. (2) Daudey, J. P.; Jeung, G.; Ruiz, M. E.; Novara, 0. Mol. Phys. 1982, 46, 67. (3) Ozin, G. A. Catal. Reu.-Sci. Eng. 1977, 16, 191. (4) Ozin, G. A.; Mitchell, S. A.; Giaria-Prieto, J. Angew. Chem. Suppl. 1982, 369. (5) Ruiz, M. E.; Novaro, 0.;Ferreira, J. M.; Gomez, R. J . Catal. 1978, 51, 108. (6) Mclean, A. D. J . Chem. Phys. 1983, 79, 3392. (7) Lee, Y. S.; McLean, A. D. J. Chem. Phys. 1982, 76, 735. (8) Ross, R. B.; Ermler, W. C. J . Phys. Chem. 1985, 89, 5202. (9) Lee, Y. S.; McLean, A. D. In Current Aspects of Quantum Chemistry; Elsevier: New York, 1982; Vol. 21, pp 219-238. (10) Ermler, W. C.; Lee, Y. S.; Pitzer, K. S. J . Chem. Phys. 1979, 70,293. (11) Lee, Y. S.; Ermler, W. C.; Pitzer, K. S.; McLean, A. D. J. Chem. Phys. 1979, 70, 288. (12) Balasubramanian, K.; Liao, M. Z . J . Chem. Phys. 1987, 86, 5587. (13) Tsong, T. T.; Kinkus, T. J.; Ai, C. F. J . Chem. P h y s 1983, 78,4763. (14) Tsong, T. T.; Kinkus, T. J. Phys. Scr. 1983, 1 4 , 201. (15) Pitzer, K. S. Acc. Chem. Res. 1979, 12, 271. (16) Pyykko, P. Adu. Quantum Chem. 1978, 11, 353. (17) Pitzer, K. S.Int. J . Quantum Chem. 1984, 23, 131. (18) Krauss, M.; Stevens, W. J. Annu. Rev. Phys. Chem. 1984, 35, 3 5 7 . (19) Christiansen, P. A,; Ermler, W. C.; Pitzer, K. S. Annu. Reu. Phys. Chem. 1985, 36, 407. (20) Balasubramanian, K.; Pitzer, K. S . Adu. Chem. Phys. 1987.67, 287. (21) Balasubramanian, K. J . Chem. Phys. 1986, 85, 1443. (22) Balasubramanian, K. J . Mol. Spectrosc. 1986, 123, 228. (23) Balasubramanian, K. J . Phys. Chem. 1986, 90,6786. (24) Balasubramanian, K. J . Chem. Phys. 1986, 85, 3401. (25) Balasubramanian, K.; Han, M.; Liao, M. Z. J . Chem. Phys. 1987, 86, 4979. (26) Balasubramanian, K. J . Chem. Phys., in press. (27) Ermler, W. C.; Christiansen, P. A., private communications.
0 1 9 8 8 American Chemical Society
Balasubramanian and Liao
362 The Journal of Physical Chemistry, Vol. 92, No. 2, 1988 TABLE 11: Geometries and Energies of Electronic States of AuH2 CASSCF
SOCI
d-MRSDCI
system
state
r, 8,
8, deg
Ea
r , 8,
8, deg
Eb
AuH2 AuH, AuH2 Au(*S) + H, Au(,P) H2 A U ( ~ S ) 2Ht2S)
2B2 2Z"+
1.68 1.75 1.68
128 180 180
1.83 1.94 2.08 0 4.88 4.16
1.67 1.73 1.68
128 180 180
1.82 1.98 1.79 0 5.34 4.62
+ +
2zg+
r, 8, 1.62 1.69 1.66
8, deg 127 180 180
EC 0.85 1.44 I .73 0 4.56
) H 2 (-34.468 501 "All energies in electronvolts with respect to Au(*S) + H2 (E = -34.451796 hartree). With respect to SOCI energy of A U ( ~ S+ hartree). cWith respect to MRSDCI energy of A U ( ~ S+ ) H2 (-34.597 8097 hartree).
lengths due to the f-type function are smalL6 We employ van Duijneveldt's28 (5s/3s) basis set augmented by a set of p-type polarization functions for the hydrogen atom. The cyp for the hydrogen atom is 0.9. The hydrogen exponents were multiplied by a scaling factor of 1.44. The multiconfiguration self-consistent field (MCSCF) calculations were performed using the complete active space MCSCF (CASSCF) method. In this method, the outer electrons are distributed in all possible ways in a chosen set of internal space of the strongest occupied orbitals of the separated atoms. All calculations reported here were carried out in C, symmetry with the x axis being perpendicular to the plane of the AuH2 molecule. Two sets of CASSCF calculations were carried out, one which did not include the d shell in the active space while the other which we label d-CASSCF included the d shell in the active space. The internal space of AuH2 in C2, symmetry without the d orbitals spans 2 a, and 1 b2 representation. These orbitals correspond to the 6s atomic orbital of Au and the 1s orbitals of hydrogens at infinite separation. Distribution of the three outer electrons of AuH2 among the complete space of orbitals generates four CSF's in the C, group. In this CASSCF, no excitation from the d shells was allowed, but the coefficients of the d orbitals were allowed to relax for all geometries. The d-CASSCF included 13 electrons in the active space. The internal space of this CASSCF included 5 a l , 2 b2, 1 bl, and 1 a 2 orbitals. The ALCHEMY 11 codes29 which we use to generate CASSCF orbitals requires the three dX2,dy2, and dZ2orbitals to be treated in an equivalent way. Thus, there is one more al orbital than necessary in the d-CASSCF. Two types of configuration interaction (CI) calculations were performed following CASSCF. The first type of C I calculations carried out were second-order C I (SOCI) calculations and were done following the CASSCF without the d shell. The other type was multireference singles and doubles C I including d electrons labeled d-MRSDCI calculations. The SOCI calculations did not allow excitations from the d shell. The SOCI calculations included all configurations in the CASSCF, first-order and second-order excited C I configurations. The first-order excited C I configurations were generated by distributing two electrons in the CASSCF internal space and one electron in the orthogonal MCSCF external space in all possible ways. The second-order excited C I configurations were generated by distributing one electron in the internal space and two electrons in the external space in all possible ways. The d-MRSDCI calculations which allow excitations from the d shells included all configurations in the d-CASSCF with coefficients 20.07 for a given state as reference configurations. Single and double excitations were allowed from these reference configurations. The d-MRSDCI calculations were carried out using the orbitals generated by d-CASSCF, which included the d shells in the active space. The SOCI calculations included about lo00 configurations. The d-MRSDCI which included excitations from the d shell contained 30 OOodO 000 configurations depending on the electronic state and geometry. All the calculations reported here were carried out using one of the author's30 modified versions (28) van Duijneveldt, F. B. IBM Res. Rep. 1971, 945. (29) ?e major authors of ALCHEMY II codes are B. Lengsfield, B. Liu, and M. Yoshimine. (30) Balasubramanian, K. Chem. Phys. Lezf. 1986, 127, 5 8 5 .
TABLE 111: CASSCF Wave Functions of the Low-Lying States of AuH,
configuration" state
coeff
'B2 (8 = 180')
-0.972 -0.216 0.096 -0.986 0.152 0.074 0.980 -0.175 -0.092 -0.990 0.1 19 0.072 -0.974 -0.180 0.130 0.988 0.137 -0.072
(8 = 128')
'B2
2B2(8 = 60')
2
~
(e,
= 1800)
'A, (0 = 108') 2A1 (8 = 60')
lal 2 1 0 2 1 0 2 1 0 1 1 2 2 0 1 2 0 1
2a1 0 1 2 0 1 2 0 1 2 0 2 0 1 1 0 1 1 0
lb, 1 1 1 1 1 1 1 1 1 2 0 1 0 2 2 0 2 2
"Does not include the d shell. of the ALCHEMY 1 1 package ~ ~ of codes to include relativistic effective core potentials. Since the spin-orbit splitting of the ground state of the gold atom (2S)is zero, it is not necessary to include spin-orbit interaction for the low-lying states of AuH2. However, near the dissociation limit of the 2Bzstate which dissociates into A u ( ~ P ) H2('BB'), the spin-orbit interaction would become important. Since this is near the dissociation limit, we could discuss the effect of spin-orbit interaction based on the atomic splitting of the 2P state. Thus, the calculations described here do not include spin-orbit interaction.
+
3. Results and Discussions Table I1 shows the optimized geometries and energies of lowlying electronic states of AuH2 at various levels of theory. Also shown in that table are the energies of the A u ( ~ S )+ H2, A u ( ~ P ) H2, and A u ( ~ S ) 2H(2S) systems. As one can see from Table 111the ground state of AuH, is the bent *B2electronic state at the d-MRSDCI level. The best level of calculations yields a bent structure with an Au-H bond length of 1.62 A and an H-Au-H angle of 127'. The CASSCF/SOCI calculations predict the corresponding geometry to be re = 1.67 A and 0 = 1 2 8 O . Thus, the bond length is shrunk by 0.06 8,due to the inclusion of d correlation in the MRSDCI. However, the most dramatic change is in the energy of the 2B2 state which is lowered by over 50% relative to A u ( ~ S )+ H2, indicating the importance of d correlation in calculating the energies of these systems. The importance of d correlation for silver- and goldcontaining molecules was previously pointed out by McLean6 as well as Ross and Ermler.8 The CASSCF and SOCI results without the d shell are not substantially different. The SOCI brings about a bond contraction of approximately 0.01 A. The inclusion of d shells in the CI is thus much more important than inclusion of higher order correlations within the s shells. The fact that the d correlation is especially important for the 'B2 state is reflected in the second and third leading configurations of the
+
+
Electronic States and Potential Energy Surfaces of AuH,
The Journal of Physical Chemistry, Vol. 92, No. 2, I988 363
TABLE I V Mulliken Population Analysis of the I-MRSDCI Natural Orbitals of AuH2
net population
gross population
total state 'B,
'E> 2Zg+
total
Au
H
Au(s)
Au(p)
Au(d)
H(s)
Au
H
Au(s)
Au(p)
Au(d)
H(s)
overlap
10.30 10.68 10.01
1.89 1.60 2.11
0.76 0.92 0.31
0.11 0.10 0.05
9.18 9.40 9.08
1.87 1.60 2.10
10.71 11.04 10.45
2.29 1.96 2.55
1.13 1.26 0.86
0.14 0.09 0.21
9.44 9.69 9.39
2.25 1.93 2.53
0.808 0.713 0.89
d-CASSCF of this state which include excitations from the d shell. For the linear geometries, we found two states within 0.3 eV, namely the and ,Z,+ states. The ,B2 bent structure correlated into ,Eu+and is lower than the state which correlates into ,Al bent geometry. The 2Ey+-2Egf splitting is about 0.14 eV at the CASSCF level and 0.19 at the d-MRSDCI level. Thus, these two states are nearly degenerate. The bond length of the ,Eu+ state contracts much more than the ,Eg+state due to inclusion of the d shells in the C I calculations. As one can see from Table 11, the best level of theory, namely d-MRSDCI, predicts that the ground state of AuH2, ,B2, is 0.85 H2 system. The atomization energy of eV above the Au(,S) the ground state of AuH, (i.e., energy for the reaction AuH2(,B2) Au(,S) 2H(,S)) is calculated to be about 85 kcal/mol. The nonrelativistic De of AuH was calculated by McLean6 to be 2.02 eV. However, relativistic corrections are quite significant for AuH and thus the De should be larger. In any case, AuH2(,B2) is more stable than AuH with respect to dissociation to individual atoms. Figure 1 shows the bending potential energy surface of the ,B2 and ,Al electronic states of AuH,. The Au-H bond distances were optimized for every angle. The surfaces in Figure 1 were obtained at the CASSCF level without excitations from the d shell. As one can see from Figure 1, the ,Al surface has a large barrier for the insertion of the Au(?S) atom into H2. At the CASSCF levels of calculations this barrier is calculated to be about 4.4 eV. However, as noted before, the d correlation can lower this barrier significantly. Since the barrier was found at a bending angle of 108O, one could estimate the effect of d correlation based on the d-MRSDCI lowering of the ,Eg+state with respect to Au(IS) Ha. The ,Eg+state is lowered about 0.35 eV with respect to CASSCF by d correlation. Thus, the barrier in the ,A, state should be lowered by at least this amount due to d correlation not included in the CASSCF. Also, the saddle point in Figure 1 could shift in geometry and position due to d correlation. Thus, a barrier of 4 eV or 92 kcal/mol is only an upper bound for the insertion of Au(,S) into H, to form AuH2(,Eg+). It is comforting to note that d correlation effects are not as significant for the ,Al state as they are for the ,B2 state. The bending potential energy surface of the ,B2 state has no barrier in contrast to the ,Al surface. The 2B2surface dissociates H2 as expected. Thus, the bent into the excited A U ( ~ Patom ) ground state is considerably more stable than the dissociated species. Consequently, the Au(,P) excited atom will insert into H2 spontaneously to form the AuH2(,B2) ground state while the Au(,S) atom would be unreactive with H,. Siegbahn, Blomberg, and B a ~ s c h l i c h e rhave ~ ~ carried out CASSCF/CI calculations on the bending potential energy surface of the ,AI state of CuH2. These authors have found a barrier of 89 kcal/mol for the insertion of Cu(,S) into H2 to form CuH, (?Zg+). The barrier height in CuH2 is thus similar to the barrier height of AuH,. The striking contrast between CuH, and AuH, is that the linear ,ZU+ is lower than the 22g+ state for AuH, while this is 60 kcal/mol above the ,Eg+ground state of CuH, although Siegbahn et aL3, did not optimize the geometry of the ,E,,+state. Further, Siegbahn et al. have not studied the bending surface of the ,B2 state to compare the ,B2 bent minimum of AuH, with CuH, (if there is one). The splitting of the ,B2 and ,Al states at the dissociation limit should correspond to the gold ,S2P atomic splitting. This splitting +
-
+
+
+
+
(31) Moore, C . E. Table of Atomic Energy Leuels; US.National Bureau of Standards: Washington, DC, 1971. (32) Siegbahn, P. E. M.; Blomberg, M. R. A,; Bauschlicher, Jr., C. W. J. Chem. Phys. 1984, 81, 1373.
:0 1 2 0 . a, c b
-t 0
I
0080.
t/ 0
Z O O 400 600 800 1000 1200 1400 1600 1800
e+ Figure 1. Bending potential energy surfaces of the *A, and 'B2 of AuH'. The Au-H bond distances were optimized for all bending angles. The 2B2 surface has a bent minimum (0 = 127') at the MRSDCI level of calculations. The energies in electronvolts are readily obtained by multiplying the hartree atomic units by 27.21.
is found to be 38 553 and 43 069 cm-l at the CASSCF and CI levels, respectively. The higher value at the CI level reflects the fact that we have only a double-{quality basis to describe the 6p orbital while the 6s and 5d orbitals are described at a higher level of accuracy. Note that these calculations do not include spin-orbit interaction. The experimental separations of the (5d106p)2Plj2 and (5d106p)2P3/2 states of the gold atom from the ground state are 37 358 and 41 174 cm-I, re~pectively.~'If one takes a spinweighted average of the two states, one obtains a , S Z P splitting of 39 902 cm-', which is in reasonable agreement with our calculated results. Note that the 2P1,2-2P3,2 splitting of the gold atom is 3816 cm-'. The bending potential energy surfaces in Figure 1 cross at about 8 = 60°. This would mean that the ZB2state could dissociate into Au(,S) + H2through the ,Al channel available at this angle via Landau-Zener-type processes. Table I11 shows the leading configurations in the CASSCF wave function of the electronic state of AuH, for vzrious bending angles. As one can see, two configurations are important for both the ,B2 and 2Al electronic states. For the ,B2 state these configurations correspond to 1a:lb: and la\2a1lb;. For the ,A1 state, the corresponding configurations are l b i l a l and lai2a:. Near the saddle point of the ,Al state three CSF's become important, as one can see from Table 111. It should be noted that the second and third leading configurations of the d-CASSCF of the ,B, state are different from those in Table I11 which do not include the d shell. The second and third important CSF's in the ,B2 state (bent) involve excitations from the d shell. The leading configuration of the bent 2B, state has a coefficient of 0.978 in the d-CASSCF and 0.953 in the d-MRSDCI. Table IV shows the Mulliken population analysis of the lowlying states of AuH2 for linear and bent geometries. The ALCHEMY codes include the d$+,,2+2population in the d population since the population analysis was carried out on a six-component
364
J . Phys. Chem. 1988, 92, 364-367
basis of d functions. We wrote a code to find the population contribution to the dX2+,,z+,zcomponent and subtracted this from the total d population and added this to the s population. Table IV shows the d population without the x2 + y 2 + z2 component. As one can see from that table, the bent 2B2ground state of AuH2 is ionic with Au+H- polarity. The dipole moment of the bent 2B2 state is calculated to be 1.259 D at the d-MRSDCI levels of calculation. The dipole vector points in the +Z direction. The 2Ze+state has greater hydrogen population and less gold population, indicating greater ionic character although the dipole moment cancels out since this state is linear. The bent 2B2state has greater Au-H overlap population than the linear structure (22,+), indicating enhanced Au-H bonding in the bent state. The 2&,+ state, however, has a total Au gross population of 11.04, indicating that the charge separation is insignificant for this state. The d population of the various states is another property of considerable interest for transition metal hydrides. Only in the 2Zu+state is the d shell near complete (9.69 e). For the 2B2bent and 2Zg+linear states the d population deviates quite a bit from a closed-shell population. The contribution of the p orbital of Au is relatively small for the 22,,+state, as one can see from Table
IV, but somewhat more important for the 2Ze+ and 2B2states. 4. Conclusion In this investigation, we carried out CASSCF/CI calculations of low-lying electronic states of AuH2 with and without d correlation. The ground state of AuH2 was found to be a 2B2state with a bent structure, re(Au-H) = 1.62 A and Oe = 127’. Two linear states, namely 2Ze+and 2Zu+,were found within 0.3 eV, state being the lower of the two. The d correlation was the 22u+ found to be of considerable importance in calculating the energies but somewhat less important for the geometries. The bending potential energy surfaces of the 2B2and 2A1states are studied. These surfaces reveal that the excited A U ( ~ Patom ) would insert B ~ ) the A u ( ~ S )atom spontaneously into H2to form A u H ~ ( ~ while has to surmount a large barrier (
