J . Phys. Chem. 1989, 93, 89-94 analysis of the temperature dependence of the intervalence band moments. The model will also clearly be applicable to other systems as new data accumulate. For example, Collman et aLl9have recently reported the presence of both an intervalence band and a CTIIR absorption in a partially oxidized sample of [Os(OEP)(pyz)ln (OEP is octaethylporphyrin), and Boekelheide and co-workers20*21 have reported the synthesis of mixed-valence dimers with a two-electron difference in oxidation state of the metal atom. It would also be possible to extend our approach to more complicated cases, for example a many-mode treatment of the three-center model7**or a many-mode system in which one of the modes must be treated exactly. Acknowledgment. This work was supported in part by the National Science Foundation (P.N.S.) under Grants CHE8400423 and CHE8700754. We also acknowledge receipt of a NATO travel grant (RGO 146/87).
89
(ii) An, = f 2 , AnBza = 0: (TM)*2 =
-y'(
Kn,
+ 1) f 11P2
f
c1-)2X,*M
K,
+
7
C',
(
1
(cI-)2
K,
+
C',
F
+
1
(CI+)'
u,
+
6,'
F 1
(iii) An, = fl, An, = f l : (TM)*l.*l =
+ 1 ) f 1)'/2((2ng+ 1) 1)112+ 7 1)(Kp + €81 7 1) ~ ~ ( C , - ) ( C ~ + ) ~ X , X , M (+ ( ~ 1) ~ , f 1)'/2((2n, + 1) f 1)1/2 x -y2(C1-)3XaXBM
(K,
6',
Appendix A1
Second-Order Terms in Eq 26. Second-order contributions to the dipole strength arise for three cases as follows (D N (TM12): (i) An, = 0: Appendix A 2
Secondorder Terms in Eq 44. Second-order contributions arise as follows (D N ITMI'): (i) An, = f 2 , AnBZa= 0: (n, (K,
+
' ,€
+ 1)/2
- l)(U,
+ t,'
(TM),, = -'/zXa2M((n, f l)(n,
+ 1 f l))lI2/(2~,7 1)'
+I)
(A41 (ii) An, = fl,An, = fl:
(19) Collman, J. P.; McDevitt, J. T.; Leidner, C. R.; Y e , C. T.; Torrance, J.; Little, W. A. J . Am. Chem. SOC.1987, 109, 4606. (20) Voegeli, R. H.; Kang, H. C.; Finke, R. G.; Boekelheide, V. J . Am. Chem. Soc. 1986, 108, 7010. (21) Plitzko, K. D.; Boekelheide, V. Angew. Chem., In!. Ed. Engl. 1987, 26, 700.
(TM)*l,*l = -'/zV@4K2na + 1 f 1) x (2n, 1 f 1))'/'/[(2t,
+
T
1)(2t8 7 l ) ] (A5)
Registry No. (TCNQ)y, 523 15-68-1; (TCNQ-),, 34464-96-5.
Electronic States and Potential Energy Surfaces of ASH,:
Comparison with AuH,
K. Balasubramanian*s+and M. Z. Liao Department of Chemistry, Arizona State University, Tempe, Arizona 85287- 1604 (Received: February 8, 1988)
Complete active space MCSCF (CASSCF) followed by second-order configuration interaction (SOCI) and multireference single plus double configuration interaction (MRSDCI) which include excitations from the d shells are carried out on the two low-lying states of AgH, (,B2 and 'A,). The bending potential energy curves of the two states with bond lengths optimized for all angles are presented. The 'Bz surface contains a double minimum with acute and obtuse H-Ag-H angles. The 2Al surface contains a large barrier for the insertion of an Ag(,S) atom into Hz to form the linear 2Zg+state of AgH,. The excited Ag(,P) atom spontaneously inserts into H, to form an acute-angled weak complex of Ag with H2 and another more stable ,B2state with obtuse bending angle. The d shell correlation lowers the 'B2 obtuse-angled structure significantly. The potential energy surfaces and electronic states of AgH, are compared with those of AuH2. Relativistic mass-velccity effects are significant for AuH, in comparison to AgH,, while d correlation effects are more significant for AgH, in comparison to AuH2. The Mulliken population analyses of the electronic states of AgH, reveal considerable 5p participation. The bending potential energy surfaces of the 'B, and 'Al states of both the molecules cross, which would lead to avoided crossing of the 2E,/2components if the spin-orbit term is included. The effect of f-type polarization functions is also investigated by carrying out MRSDCI calculations which included the ten-component f functions in the basis sets.
1. Introduction The electronic properties, geometries and reactivities of transition-metal clusters are topics of intense activity in recent years. The investigation of metal atom insertion into hydrogen bonds Alfred P. Sloan Fellow; Camille and Henry Dreyfus Teacher-Scholar.
0022-3654/89/2093-0089$01.50/0
could provide considerable insight into the reactivities of small clusters with H2.I4 Further, such calculations could also provide (1) Daudey, J. P.; Jeung, G.; Ruiz, M. E.; Novara, 0. Mol. Phys. 1982, 46, 67. (2) Muller, E. W.; Tsong, T. T. Prog. Surf. Sci. 1973, 4, 1.
0 1989 American Chemical Society
Balasubramanian and Liao
90 The Journal of Physical Chemistry, Vol. 93, No. 1, 1989 TABLE I: Valence Basis Sets for Gaussian-Type Functions for Ag (3s3p4d lf/3sZp3d 1 f ) O
shell
exponential factor
contract coefficient
s
0.4981 0.1584 0.047 1
P
0.7589 0.0908 0.0283
d
2.4127 1.0153 0.4093 0.1503
0.308853 0.450434 1.o 1.o
f
0.45
1.o
1 .o 1.o 1.o -0.0287 0.29797 1.o
Reference 27. The exponent of f function from this work. models for our understanding of the reactivity of metal with hydrocarbons due to the similarity of the C-H n bond with the Hz bond and photochemical processes.’ Theoretical studies of molecules containing gold and silver atoms such as AgH, AuH, Ag,, Au,, etc., are of considerable interest.613 These species are fundamentally interesting due to large relativistic effects. The relativis’ic mass-velocity contraction of the outer s orbital of the gold atom is the primary reason for the chemical and spectroscopic difference of gold-containing molecules in comparison to silver compounds. For example, the binding energy of Aut is larger than Ag, primarily due to this mass-velocity contraction. The electronic states of AgHz and their potential energy surfaces could be quite valuable since these surfaces can reveal the differences in the reactivities of different states of the silver atom. Further, comparison of these surfaces and the nature of the electronic states of AgH, with AuH, could provide valuable insights into the contrast and similarities of the two systems. The only theoretical calculation to date is that of Novaro et al.,14 who employ a model potential S C F procedure followed by perturbational CI calculation on AgH,. There are no experimental studies on AgH2 or AuH2, although the related AuH2+ ion has been studied by using the field-induced surface-catalyzed reaction^.'^^'^ The objective of the present investigation is to carry out ab initio complete active space MCSCF (CASSCF) followed by configuration interaction calculations on AgH2 with and without correlating the d electrons and including relativistic effects. We investigate the bending potential energy surfaces of the ,B2 and ’A, states using the CASSCF method. The ,Bz surface contains a double minimum (acute and obtuse angles) which is investigated further through configuration interaction methods which include excitations from the d shells. In addition, the linear ?2,+ and 2Zg+ electronic states are investigated. These results are compared with similar calculations on AuH,. Theoretical studies of electronic structure of molecules containing heavy atoms are topics of current interest.”-26 Section 2 contains the method of calculations. (3) Ozin, G. A. Catal. Reu.-Sci. Eng. 1977, 16, 191. (4) Rulz, M. E.; Novara, 0.;Ferreira, J. M.; Gomez, R.J . Catal. 1978, 51, 108. (5) Ozin, G. A,; Mitchell, S. A,; Giaria-Prieto, J. Angew. Chem., Suppl. 1982, 369. (6) McLean, A. D. J. Chem. Phys. 1983, 79, 3392. (7) Lee, Y. S.; McLean, A. D. J. Chem. Phys. 1982, 76, 735. (8) Lee, Y. S.;McLean, A. D. In Current Aspects of Quantum Chemistry; Elsevier: New York, 1982; Vol. 21, pp 219-238. (9) Ermler, W. C.; Lee, Y. S.; Rtzer, K. S. J. Chem. Phys. 1979,70,293. (10) Lee, Y. S.; Ermler, W. C.; Pitzer, K. S.; McLean, A. D. J . Chem. Phys. 1979, 70, 288. (11) Ross, R. B.; Ermler, W. C. J . Phys. Chem. 1985, 89, 5202. (12) Balasubramanian, K.; Liao, M. 2. J. Chem. Phys. 1987, 86, 5587. (13) Balasubramanian, K.; Liao, M. 2. J . Phys. Chem. 1988, 92, 4595. (14) Novaro, 0.;Garcia-Prieto, J.; Poulain, E.; Ruiz, M. E. J . Mol. Struct. (THEOCHEM)1986, 135, 79. (15) Tsong, T. T.; Kinkus, T. J.; Ai, C. F. J . Chem. Phys. 1983,78,4763. (16) Tsong, T. T.; Kinkus, T. J. Phys. Scr. 1983, 14, 201. (17) Pitzer, K. S. Acc. Chem. Res. 1979, 12, 271. (18) Pitzer, K. S. Int. J. Quantum Chem. 1984, 23, 31. (19) Balasubramanian, K.; Pitzer, K. S. Adu. Chem. Phys. 1987, 67, 287.
Section 3 consists of results and discussions. 2. Method of Investigation We carry out multiconfiguration self-consistent field (MCSCF) calculations followed by configuration interaction calculations with and without correlating the d shell of the silver atom. All calculations reported here were carried out using relativistic effective core potentials with the 4dI05s’ outer shell of the silver atom explicitly retained in the valence space. La John et aLZ7have recently generated analytical Gaussian fits of relativistic effective potentials for the silver atom suitable for molecular calculations. We employ these potentials together with the (3s3p4d) valence Gaussian basis set optimized by these authors for the ,S and ,P ground states of the silver atom. The three p functions were contracted to a 2p set, and the four d functions were contracted to a set of three functions with the coefficients shown in Table I. The resulting basis set for the silver atom can be described as (3s3p4d/3s2p3d). To this set, a set of ten-component f-type polarization functions was added with the exponent shown in Table I with the objective of studying the effect off functions. McLean6 has shown that inclusion of f-type functions can lead to a bond contraction of about 0.07 A in both AgH and AuH. However, it should be noted that if one includes extensive d correlation, the shifts in bond lengths due to the f-type function are small.6 The calculations that included f-type functions carry the f prefix. We employ van Duijneveldt’sZ8(5s/3s) basis set augmented by a set of p-type polarization functions for the hydrogen atom. The aP for the hydrogen atom is 0.9. The hydrogen exponents were multiplied by a scaling factor of 1.44. MCSCF calculations were made 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 AgH, molecule. Two sets of CASSCF calculations were carried out, one which did not include the d shells in the active space while the other, which we label d-CASSCF, included the d shell in the active space. The internal space of AgHz in C, symmetry without the d orbitals spans two a, and one b2 representations. These orbitals correspond to the 5s atomic orbital of the silver atom and the 1s orbitals of hydrogens at infinite separation. Distribution of the three outer electrons of AgH2 among the complete space of orbitals generates four CSF‘s in the C, group. In this CASSCF, no excitations from the d shells were 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 five a,, two bz, one b,, and one a2 orbitals. The ALCHEMY 11 codesz9were used to generate CASSCF orbitals. There is one more a, orbital than necessary in the d-CASSCF. Note that although for the ground state the four a,, two b2, one bl, and one a, orbitals correspond to the 4d and 5s orbitals of the Ag atom and 1s orbitals of hydrogens, for the excited ,B2state the active space would contain the 5p orbital since this state dissociates into Ag(2P) Hz. Thus, the exact nature of the orbitals in the active space would actually depend on the electronic state and geometry. Three types of configuration interaction (CI) calculations were performed following CASSCF. The first type of CI calculations
+
(20) Pyykko, P. Adu. Quantum Chem. 1978, 11, 353. (21) Christiansen, P. A.; Ermler, W. C.: Pitzer, K. S. Annu. Rev. Phys. Chem. 1985, 36, 407. (22) Pykkd, P. Chem. Rev., in press. (23) Balasubramanian, K. J . Chem. Phys. 1986, 85, 1443. (24) Balasubramanian, K. J . Chem. Phys. 1986, 85, 6786. (25) Balasubramanian, K. J . Phys. Chem. 1988, 92, 4595. (26) Balasubramanian, K. J. Mol. Spectrosc. 1987, 123, 228. (27) La John, L. A,; Christiansen, P. A,; Ross, R.B.;Atashroo, T.; Ermler, W. C. J. Chem. Phys. 1987, 87, 2812. (28) van Duijneveldt, F. B. IBM Res. Rep. 1971, 945. (29) The major authors of ALCHEMY II codes are B. Liu, B. Lengsfield, and M. Yoshimine.
Electronic States and Potential Energy Surfaces of AgH2
The Journal of Physical Chemistry, Vol. 93, No. 1, 1989 91
TABLE II: Geometries and Energies of Electronic States of AgH,
system AgH2 AgH2 AgH2 AgH2 M 2 S ) + H2 W 2 P ) + H2 Ag(2S) + 2H(*S)
state
r, 8,
CASSCF 8, deg
2B2
1.81 1.85 2.05 1.67
106 180 22 180
2z*+
2B2d 22*+
E'
r, A
8, deg
SOCI Eb
r, 8,
d-MRSDCI 8, deg
EC
2.47 2.59 2.98 2.92 0 3.75 4.16
1.79 1.85 2.01 1.68
104 180 23.6 180
2.41 2.61 2.60 2.96 0 3.35 4.55
1.66 1.76 1.85 1.65
112.0 180 27.5 180
1.89 2.33 2.65 2.26
0 3.98 5.12
+
'All energies in electronvolts with respect to Ag(2S) t H2(E = -38.413216 hartrees). bWith respect to SOCI energy of Ag(2S) H2 With respect to d-MRSDCI energy of Ag(2S) + H2 (-38.529 703 hartrees). dSecond minimum in the ZB2 surface
(-38.429 936 hartrees). (see Figure 1).
TABLE 111: Effect of f-Type Functions on the Geometries and Energy SeDarations of Electronic States of AeH, with f functions without f functions
f-MRSDCI state
r.,
1.672 1.736 1.660
2B2 22"+ 2zg+
d-MRSDCI
A 8.. dea E , eV re, 8, 8.. deg E. eV 113 180.0 180.0
W 2 S ) + H2
1.87 2.16 2.49
0.0"
1.66 1.76 1.65
112 180 180
1.89 2.33 2.26 O.Ob
"Absolute MRSDCI energy of Ag(2S) + Hz with f-type functions is -38.664714 hartrees. bAbsolute MRSDCI energy of Ag(2S) + H2 without f-type functions is -38.529 703 hartrees.
0
40.0
00.0
120.0
160.0
9Figure 1. Bending potential energy curves of 2B2and 2AI states of AgH2.
carried out were second-order C I (SOCI) calculations and were done following the CASSCF without the d shell. The other type was multireference single and double 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 and first-order and second-order excited C I configurations. The first-order 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 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 configurtions in the d-CASSCF with coefficients 10.07 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 1000 configurations. The d-MRSDCI which included excitations from the d shell contained 27 000-50000 configurations depending on the electronic state and geometry. All the calculations reported here were carried out using one of the author's30 modified version of ALCHEMY 1 1 package ~ ~ of codes to include relativistic effective core potentials. Similar methods of CASSCF, SOCI, and MRSDCI calculations were employed on AuH2 in an earlier in~estigation.'~ The results on AuH2 are compared here with the present results on AgH2.
(30) Balasubramanian, K. Chem. Phys. Lett. 1981, 127, 5 8 5 .
Another set of MRSDCI calculations which we label fMRSDCI included the ten-component f-type functions in the basis set. The basis set employed in the f-MRSDCI is (3s3p4dlf/ 3s2p3dlf). Thus, f-MRSDCI calculations are more accurate than the d-MRSDCI calculations. The inclusion of the ten f functions increased the configuration count in the C I for the 2B2 state to 84 979 and for the 2A, state to 60 180. The ground-state spin-orbit splitting of the 2S silver atom is zero. The contributions from spin-orbit interaction can arise only through mixing of the 5p and 4d orbitals of the silver atom in the molecular states of AgH2. We find that the 4d shell is nearly full in most of the electronic states of AgH2 although the 4p contribution is nonnegligible. The spin-orbit contributions to the low-lying electronic states of both AgH2 and AuH2 are discussed in a qualitative manner using the atomic 5p112-5p312 and 6p1/2-6p3/2 splittings of Ag and Au, respectively.
3. Results and Discussion
In Table 11, we show the calculated geometries and their energies for various electronic states of AgH2 and the Ag(2S) H2, Ag(2P) H2 dissociation energies. Figure 1 shows the bending potential energy surfaces of the 2Al and 2B2electronic states of AgH2. The ground state of the AgHz molecule is found to be the bent 2B2 electronic state with an obtuse bending angle at all levels of theory (CASSCF, SOCI, and MRSDCI). The Ag-H bond lengths and the bending angle are, however, sensitive to electron correlation and especially d correlation. The d-MRSDCI calculations which include single and double excitations from the d shells shorten the Ag-H bond length by almost 0.13 %, in comparison to SOCI calculations which included excitations from the s shells of silver and hydrogen atoms but not from the d shell. Thus, d correlation effects are quite significant for AgH2. The separation of the 2B2ground state with respect to Ag(2S) H 2 is also consistently lowered as one includes correlation corrections and d correlations. The 2Zu+ linear state is the state above the 2B2 obtuse angle minimum. The SOCI calculation does not change the Ag-H bond lengths in this state, while excitations from the d shell bring about a bond contraction of 0.09 A for this state. The linear 'Zg+ electronic state has the shortest Ag-H bond length (1.65 A). The
+
+
+
92
The Journal of Physical Chemistry, Vol. 93, No. 1, 1989
Balasubramanian and Liao
TABLE I V Geometries and Energies of Electronic States of A d z d
system AuH2 AuH~ AuH~ Au(%) + H2 AU(~P)+ H2 A u ( ~ S )+ 2H(2S)
state 2B2
22*+ 2Z8+
r, 8, 1.68 1.75 1.68
CASSCF 8, deg 128 180 180
SOCI E' 1.83 1.94 2.08 0 4.88 4.16
r, A 1.67 1.73 1.68
8, deg
Eb
128 180 180
1.82 1.92 1.79 0 5.34 4.62
r, 8, 1.62 1.69 1.66
d-MRSDCI 8, deg 127 180 180
Et 0.85 1.44 1.73 0 4.56
'All energies in electronvolts with respect to A U ( ~ S )+ H2 ( E = -34.451 796 hartrees). bWith respect to SOCI energy of A U ( ~ S + ) H2 With respect to MRSDCI energy of A u ( ~ S )+ H2 (-34.597 809 7 hartrees). dFrom ref 13.
(-34.468 501 hartrees).
re value of this state is not altered much by d correlation. Thus, d correlation effects are not as signfiicant for this state in comparison to the ,B2 obtuse minimum. As seen from Figure 1, the ,BZ surface has a second small angle minimum before dissociation. As one can see from Table 11, this minimum occurs a t a H-Ag-H bond angle of 27.5O at the MRSDCI level of theory. The d correlations shorten the Ag-H bond length accompanied by an increase in the bond angle; thus, d correlations stabilize the complex. The second minimum in AgH, arises from the formation of a complex of Ag(2P) with H2. The AgH, linear 2Zg+state which dissociates into Ag(,S) H2is 2.26 eV less stable in comparison to Ag(%) H2. The 2B2 bent state is, however, about 2.0 eV more stable than Ag(,P) H2 dissociation. The atomization energy of the ,B2 obtuse minimum (Le., the energy required for the process AgHZ(,B2) Ag(,S) + 2H(2S)) is calculated to be about 75 kcal/mol. Table I11 compares the MRSDCI geometries and energies of electronic states of AgH2 obtained with and without the f-type functions in the basis sets. As one can see from that table, the Ag-H bond lengths change by only 0.01 A for the 2B2and ,Zg+ states. For the 2&+ state the Ag-H bond lengths contract by 0.02 A. Thus, the effect of f-type functions on the MRSDCI geometries is not large. The energy separations with respect to the Ag(%) H 2 dissociation limit are a bit more sensitive to the addition of f-type functions. As one can see from Table 111, the 2Zu+linear state is lowered by 0.17 eV with respect to the Ag(2S) H2 dissociation due to the addition of f-type polarization functions. The state, on the other hand, goes up by 0.23 eV in comparison to the separation obtained without the f-type functions. The energy separation of the ,Bz ground state changes by only 0.02 eV due to the addition o f f functions. Thus, the energy separations of the linear 2Zg+and 2Zu+states are influenced more by f functions. Table IV shows the results of a similar calculation on AuH, carried out earlier by Balasubramanian and Liao.I3 For AuH, also, the ground state is a ZBzstate with an obtuse angle geometry. The obtuse angle of 127' is somewhat larger than the corresponding angle for AgH,. The metal-H bond lengths are shorter for AuHz for most of the states except for the linear state for which Au-H bond length is 0.01 A longer. Usually, the bond lengths increase for isoelectronic heavier systems in comparison to the lighter systems of the same group. In contrast, we find that the Au-H bond is shorter than the Ag-H bond. This shortening is largest for the linear 2Zucstate (0.07 A). This is attributed to relativistic mass-velocity corrections which shrink the inner s orbitals of the core. This is, in turn, manifested in the valence s due to core-valence orthogonality. The shrinking of 'the outer 6s orbital of the gold results in a shorter Au-H bond in comparison to the Ag-H bond. The other striking contrast between AgH2 and AuH2 is the relative stabilities of the electronic states. The separations of the electronic states of AuH2 with respect to Au(,S) H2 are substantially smaller in comparison to the corresponding separations for AgH,. For example, the ground state of A u H ~ ( ~ B is ~0.85 ) eV above Au('S) + H2, while the ,B2 state of AgH, is 1.89 eV above Ag(,S) Hz. Similar behavior is found for the linear 2Zu+ and ,Zg+ states. This implies that AuH2 electronic states are more stable than the corresponding states of AgH,. This is further justified by the fact that the atomization energy of AuH, is 85
+ +
+
TABLE V: CASSCF-CI Wave Functions of the Low-Lying States of AeH, and AuH?
configuration" 2
~
AuH2 (e, = 1800)
0.972 0.216 -0.096 ,B2 (8 = 128') -0.986 0.152 0.074
-
+
+
+
+
2B2 (8 = 60') 0.980 -0.175 -0.092
2Al (6' = 180') -0.974 0.119 0.072 2Al (6' = 108') -0.180 -0.974 0.130 2Al (8 = 60') 0.988 0.137 -0.072
AgH2 2B2 ( 8 = 180')
lal
2al
1b2
0.960 0.255 -0.1 19 2B2 (8 = 120') -0.970 -0.221 0.102 2B2 (8 = 106') 0.971 -0.216 -0.099 2B2 (6' = 60') 0.973 0.209 -0.098 2B2 (6' = 22') 0.997 -0.069 ,Al (8 = 180') -0.987 0.122 0.103 2A, (8 = 102O) -0.524 0.508 0.491 -0.475 2AI (6' = 60') -0.973 0.216 0.082
2 1 0
0 1 2
1 1 1
2 1 0
0 1 2
1 1 1
2 1 0
0 1 2
1 1 1
2 1 0
0
1 1 1
2 0
0 2
1 1
1 2 1
2 1 2
0 0 0
0
1 2 1
2 0 0 2
1 2 1
2 0 1
1 2
0 1 1 0
0 2 2
Does not include the d shell.
kcal/mol while the corresponding value for AgH, is 75 kcal/mol. The Ag(,P) atom forms a weak acute angle complex with H2. A corresponding minimum for AuH2 in the 2B2electronic state could not be found. This could be explained in part by comparing the atomic M(2S)-M(2P;d10p) splittings. For gold, the 2S-2P splitting is about 40 000 cm-' while this is about 30 000 cm-I for silver. In fact, the first excited state of silver is 2P while the first excited state of gold atom is a 2D state arising from the 5d96s2 configuration. This reverse ordering in gold is attributed to relativistic mass-velocity contraction which lowers the 6s orbital of the gold atom. The silver Ag(,P) state is thus energetically not very high to form a loose complex with Hz while for gold the ,P state is so high in energy that it forms a repulsive curve in this region. The bending potential energy curves of the 2B2and ,A, electronic states of the AuH, molecule were obtained in ref 13. In comparing the surfaces of AgH, with AuH2, we note that the small barrier and the second minimum are absent in AuH,. The ,Al surfaces of both the molecules contain a barrier to the insertion of the metal atom with H2 to form MHz. This barrier is calculated to be about 137 kcal/mol for AgHz although we consider this as considerably high since this was obtained using the CASSCF method which ignores d correlation and higher order correlations
The Journal of Physical Chemistry, Vol. 93, No. 1, 1989 93
Electronic States and Potential Energy Surfaces of AgH,
TABLE VI: Mulliken Population Analysis of the d-MRSDCI Natural Orbitals of AgH2 and AuH2
net population
gross population
total AgH2
M
H
M(s)
M(p)
M(d)
H(s)
M
H
M(s)
M(p)
M(d)
H(s)
'BZa 2Bj
10.35 10.70 10.59 10.13
1.56 1.72 1.53 1.59
0.32 0.075 0.49 0.26
0.12 0.68 0.06 0.20
9.78 9.995 9.91 9.56
1.55 1.67 1.52 1.59
10.90 10.99 11.03 10.77
2.10 2.01 1.97 2.23
0.59 0.13 0.79 0.43
0.31 0.87 0.17 0.54
10.00 9.995 10.07 9.79
2.08 1.97 1.95 2.20
1.08 0.58 0.89 1.27
10.30 10.68 10.01
1.89 1.60 2.11
0.49 0.68 0.38
0.11 0.10 0.05
9.45 9.64 9.31
1.87 1.60 2.10
10.71 11.04 10.45
2.29 1.96 2.55
0.85 1.02 0.63
0.14 0.09 0.21
9.72 9.93 9.62
2.25 1.93 2.53
0.808 0.713 0.89
2Zu+ 2Zgt
AuH2
2B24 2Zut 2Zg+
a
total
state
overlap
Obtuse angle minimum. *Acute angle minimum for AgH2.
from the s shell. As noted before, the d correlation effects are quite high for AgH, and thus the barrier could be lowered. In any event, a CASSCF calculation of the same level gave a barrier height of 92 kcal/mol for AuH,. While the difference in the barrier heights of the two molecules (45 kcal/mol) would certainly be lowered by d correlations, it is noted that the barrier for the Hz would be smaller than the correinsertion of A U ( ~ S into ) sponding barrier for the insertion of Ag(2S) into H2. The separation of the 2B2minimum with obtuse angle geometry for AgH2 is much smaller with respect to Ag(2P) + H2 in comparison to the corresponding separation for AuH? This separation is 2.09 eV for AgHz in comparison to 4.4 eV for AuH,. The 2B2 surface of AuH, has no barrier, implying that the Au(,P) atom would insert spontaneously into H2 to form the bent 2B2AuH, molecule (obtuse angle geometry). For AgH2 (Figure l ) , the insertion of Ag(2P) into H2 is again spontaneous but it forms a weak complex and a AgH2 2B2molecule with an obtuse angle geometry separated by a small barrier. Thus, in both cases the metal atom in the ,P state inserts spontaneously into H2 while the 2S state has to surmount a large barrier. The 2B2 and 2Al bending surfaces of both AgH, and AuH, cross. This crossing occurs at 0 = 47' for AgH2 and I9 = 60' for AuH2. In the presence of the spin-orbit term, the ,Al and ,B2 states correlate into the same ,E1/, state in the C k double group. This would imply an avoided crossing of the two states, the first component designated as ,E1/,(I) and the second comonent designated as 2E1/2(II). The magnitude of the coupling of the two components would depend on the amount of spin-orbit mixing. The spin-orbit effects are larger for gold than for silver. If one looks at the two surfaces in the double group, the barrier in the 2El/2(I)surface would occur at 0 = 47O for AgH, and I9 = 60° for AuH, and would be much shorter. Conversely, the 2El/2(II) component would have a large barrier. Next, we discuss the effect of spin-orbit interaction on the electronic states of AgH2 and AuH,. First, the separation of the ,AI and ,B2 states at long distances should correspond to the metal (2S-2P) atomic splitting. This splitting is calculated to be 30 245 cm-' at the CASSCF level for AgH2 and 38 553 cm-I at the same level for AuH,. The CI separations are somewhat higher primarily due to the fact that only double-{ quality basis is employed for p while triple-{quality is employed for d and s. The experimental atomic (4dI05p) 2Pl/2and ,P3 states of Ag with respect to the ground state lie at 29 552 a n d 30 473 cm-', re~pectively.~'The corresponding states for Au are at 37 359 and 41 174 cm-', re~ p e c t i v e l y . ~The ~ (5d96s2)2D5/2,2D3,2states are much lower for gold. Their energies are 9161 and 21 435 cm-', respectively. The corresponding states for Ag are at 30242 and 34714 cm-', respectively. The spin-orbit effects would be most significant for the 2B2surface in the near dissociation limit since this dissociates into M(2P) H,. The spin-orbit contribution would be negligible for the 2Al state in the near-dissociation limit since this state dissociates into M(,S) H2 for which the spin-orbit splitting is zero. The spin-orbit contribution would certainly be important at the crossing of the ,Al and ,B2 states. Mixing of the two
,
+
+
(31) Moore, C . E. Table ofAtomic Energy Levels; US.National Bureau of Standards: Washington, DC, 1971.
components can be induced by the spin-orbit term as both states correlate into ,Eli2 in the double group. We estimate that this mixing would be much larger for AuH, than for AgH, from a simple comparison of the atomic spin-orbit splittings for the two atoms. For the linear limit, the ,Bz state correlates to the 22u+ state while 2A1correlates to the ,Zg+ state. Thus, the two states cannot mix. The ,Eg+ state would correlate to a (1 /2)g state while the 2.Zut state would correlate to a (1/2)u state for the linear geometry. An accurate treatment of spin-orbit effects of the electronic states of both AgH, and AuH, using the recently developed relativistic CI method for p o l y a t ~ m i c swould ~ ~ be the topic of a future investigation. Next, we consider the nature of bonding in the low-lying states of AgH2 and compare with AuH,. First, we compare the CASSCF-CI wave functions of the ,B2 and 2Al states of AgH, and AuH, for various geometries in Table V. As seen from Table V, the leading configuration has a consistently larger coefficient for AuH2 in comparison to AgH2, implying that correlation effects are much larger for AgH, in comparison to AuH2. The worst case is near the saddle point of the ,Al state which is a mixture of four configurations for AgH2 while it is still predominantly described by one configuration for AuH2. This would imply that the calculated barrier height for AgH, is only an estimate since higher order correlations could be quite significant. Table VI shows the Mulliken population analysis of the various electronic states of AgHz and AuH? The ALCHEMY 11 codes which we use carry out Mulliken population analysis on a basis set of six-component d functions. Thus, the ds++z component which corresponds to the s component is included in the d. A code was developed by one of the authors (K.B.) to extract the x2 + y 2 z2 population from the d and add it to the s. Table VI shows the corrected d and s populations. The population analysis of AgH, state reveals that the gross metal population is largest for the ,ZU+ and smallest for the ,Eg+state. The reduced metal populations for the ,B2 and 2Eg+states imply ionic character of the M-H bond with the polarity (M+H-). For AgH,, the d population is nearly 10.0 except for the ,Zgt state for which the d population is considerably smaller. The p population of all the states of AgH2 is quite large, indicating that the participation of the 5p orbital is quite significant. For the ,B2 acute minimum, the p population is, in fact, larger than the s population primarily because this corresponds to a weak complex of Ag(,P) with H,. A striking contrast between the Mulliken populations of AgH, and AuH, is that the p population is considerably larger for AgH, while the s population is considerably larger for AuH2. The d populations of the electronic states of AuH, are also somewhat smaller than 10.0. The overall gross populations of the two molecules indicate that the Au-H bond is much more ionic with the polarity (Au+H-) in comparison to the Ag-H bond since the gross metal population is much smaller in AuH2. The calculated dipole moments of the two bent 2B2minima are 2.4317 and 1.568 D with the obtuse minimum having a larger dipole moment than the acute minima. The dipole moment of the 2Bz (obtuse minimum) of AuH, is calculated to be 1.250 D. The smaller dipole moment in AuH2 is primarily because the
+
(32) Balasubramanian, K. J . Chem. Phys., in press.
J . Phys. Chem. 1989, 93, 94-101
94
Au-H bond is shorter than the corresponding bond length in AgH2. 4. Conclusion
In this investigation, we carried out complete active space MCSCF followed by second-order C I and MRSDCI calculations which included d correlation for 2B2and 2A1states of AgH2. For the 2B2state of AgH2, two minima were found one with a short bond angle and the oth& with a large angle. The bending potential energy curves of 2B2and 2Al states of AgH2 were obtained and compared with AuH The ZAlsurface has a large barrier to the insertion of the metdl 2S state into H 2 while the excited 2P state of the metal atom inserts into H2 almost spontaneously. The barrier to the insertidn of M(2S) into H2 was found to be larger for Ag than Au. The AuH2 electronic states were found to be
more stable than AgH2 mainly due to the relativistic mass-velocity contraction of the outer s orbital of the gold atom. The same effect resulted in shorter M-H bonds in AuH,. The 2B2and 2Al surfaces cross at 8 = 47" and 8 = 60" for AgH2 and AuH2, respectively, implying an avoided crossing of the 2E1/2states when spin-orbit coupling is included. The metal-hydrogen bonding was found to be more ionic for AuH2 than AgH2 The Mulliken population analysis of both the molecules revealed that the p population is considerably higher for AgH2 while the s population was found to be higher for AuH2. Acknowledgment. This research was supported by the U S . Department of Energy under Grant No. DEFG02-86-ER13558. The authors thank the two referees for their invaluable comments. Registry No. AgH2, 102502-37-4.
Resonant Two-Photon Ionlzation Spectroscopy of Jet-Cooled p-Dichlorobenzene Eric A. Rohlfing* Combustion Research Facility, Sandia National Laboratories, Livermore, California 94550
and Celeste McMichael Rohlfing Theoretical Division, Sandia National Laboratories, Livermore, California 94550 (Received: March 18, 1988)
This paper reports resonant two-photon ionization (R2PI) with reflectron time-of-flight mass spectrometry on jet-cooled p-dichlorobenzene (p-DCB) performed to study both the mechanism of multiphoton ionization/dissociation (MPID) at high laser intensities and the IB2u-IAgexcitation spectrum at low laser intensities. Ionization via the 5; band at 274.10 nm under MPID conditions produces almost no C6H4Cl+. This observation demonstrates that dissociation of the parent ion at the three-photon level is too slow to compete with the higher energy processes that produce small fragments via additional photon absorption. However, absorption of one visible photon (548.20 nm) from the three-UV-photon level dramatically increases the rate of dissociation of the parent ion to form C6H4C1+.A comparison of one- and two-color R2PI spectra (where the second color is 266 nm) allows us to bracket the adiabatic ionization potential (IP) for p-DCB as 8.90 eV IIP 5 8.95 eV, in good agreement with previous measurements. High mass selectivity enables us to measure chlorine isotope shifts for 26 vibrational bands in the first 1100 cm-' of the 'B,-'A, R2PI spectrum. All-electron ab initio molecular orbital calculations are performed on the ground state of p-DCB to determine theoretical chlorine isotope shifts that, after appropriate scaling to the excited state, are compared to the observed isotope shifts. This procedure allows a straightforward assignment of almost all of the observed vibrational bands and gives vibrational frequencies for 11 modes in the excited state.
I. Introduction The trace detection of chlorinated aromatics is currently a topic of great interest because of the widespread presence of these species in the environment and their potential toxic and/or carcinogenic effects on man. Recently we have examined the use of resonantly enhanced multiphoton ionization (REMPI) in conjunction with time-of-flight mass spectrometry (TOF MS) to achieve sensitive and isomerically selective detection of jet-cooled chlorinated aromatics such as the mono- and dichlorinated naphthalenes' and the dichlorobenzenes.2 Free-jet expansion cooling is necessary to achieve species and isomer selectivity for these polyatomic molecules via their SI-So absorption spectra. Mass-selective REMPI has some decided advantages over fluorescence detection. First, the quantum yield of fluorescence for highly chlorinated aromatics is very small because of facile intersystem crossing from SI to low-lyirig triplet states. REMPI can be used effectively in such systems because the ionization rate can be made comparable (1) Rohlfing, E. A,; Chandler, D. W. In Advances in Laser Science I t , Optical Science and Engineering Series 8; Lapp, M.,Stwalley, W. C., Kenney-Wallace, G. A. Eds.;American Institute of Physics: New York, 1987; p 618. (2) Rohlfing, E. A,, submitted for publication in Int Symp. Combust., 22nd.
0022-3654/89/2093-O094$01.50/0
to the rate of intersystem crossing. Second, REMPI/TOF M S provides both an optical spectrum and a mass spectrum, and this two-dimensional aspect greatly enhances species selectivity in complex mixtures. In this paper we present results obtained as part of our investigation into the applicability of REMPI/TOF M S to chlorinated aromatics. The molecule under study is p-dichlorobenzene (p-DCB), which serves as a prototypical example of chlorinated aromatics while remaining simple enough to make detailed spectroscopic assignments and also to understand the mechanisms of multiphoton ionization/dissociation (MPID). It is known that the quantum yield and lifetime of fluorescence from p-DCB at the Sl-So origin are 0.042 and 1.7 ns, respecti~ely.~Thus, p D C B is a good test of the effectiveness of REMPI on a molecule that undergoes fairly rapid intersystem crossing. The specific REMPI ionization scheme that we employ is resonant two-photon ionization (R2PI also known as 1+1 REMPI) that is implemented either as one-color R2PI in which one laser performs both the excitation and ionization steps or two-color R2PI in which a second laser ionizes the electronically excited molecule. A high-resolution TOF M S of the reflectron type4" is used to provide mass analysis of (3) Shimoda, A,; Hikida, T.; Mori, Y. J . Phys. Chem. 1979, 83, 1309.
0 1989 American Chemical Society
