Electronic States and Potential Energy Surfaces of LaH,

Electronic States and Potential Energy Surfaces of LaH,. Kalyan K. Das and K. Balasubramanian*.' Department of Chemistry, Arizona State University, Te...
2 downloads 0 Views 658KB Size
Download PDF
42

J . Phys. Chem. 1991, 95, 42-46

through the exciplex or directly in the encounter state. 3. i n the above discussion it has not been mentioned why the exciplex formation is preferable for the DCA-X-AS system. A plausible explanation is as fo~~ows: The energy gap between the excited singlet state and the radical pair State is so small (0.1 5 eV) that the rate of the full ET is not necessarily high enough to compete with the exciplex formation. Further investigations are in progress for clarifying this problem.

Concluding- Remarks

For the DCA-X-AL and -X-DMA systems the duced ET reaction OCCUrS directly in the encounter state between the fluorescer and the quencher' In for the DCA-X-AS system the ET reaction occurs through the exciplex formation as the primary quenching product. As a result, the heavy-atom effects on @T and aRare remarkable for the DCA-X-AS system but not for the DCA-X-AL and -X-DMA systems. It is noteworthy that the exciplex is formed even in a highly polar solvent such as acetonitrile. 2. The heavy-atom effects on aT and @R are useful to discriminate whether the excited singlet state ET reaction occurs

Acknowledgment. We are greatly indebted to Professor H. Kokubun for his interest in this work and for generous support. We are also grateful for Miss C. Iwanaga and Mr. K. Azumi for the purification of reagents and acetonitrile.

Electronic States and Potential Energy Surfaces of LaH, Kalyan K. Das and K. Balasubramanian*.' Department of Chemistry, Arizona State University, Tempe, Arizona 85287- 1604 (Received: April 9, 1990; I n Final Form: July 5, 1990)

Electronicstructures, potential energy surfaces, and one-electron properties of low-lying electronicstates of LaH2 are investigated by using the complete active space MCSCF (CASSCF) method followed by full second-order configuration interaction (SOCI) calculations. These calculations reveal that the a2D ground state of the lanthanum atom has to surmount a barrier of 21 kcal/mol for insertion into H2 to form the ,AI ground state of LaH2 [re = 2.14 A and 0, = 11 1.9OI. The first excited La(a4F) atom needs to surmount a larger barrier for insertion into H2. The doublet potential energy surfaces of LaH2 show bent minima while the quartet surfaces of LaH, have linear geometries. The 'Al ground state of LaH, is 11 kcal/mol more stable than La + H2. The bent ground state of LaH2 is found to be very ionic with a dipole moment of 3.79 D (La'H- polarity).

Introduction

I n recent several experimental and theoretical investigations were focused on reactivities of transition-metal atoms and ions with small molecules such as H2, D2, HD, and N2. Transition-metal atoms and ions are considered as useful models of regions in surfaces, and thus interactions of small clusters with molecules such as H2 and N2 would provide considerable insight into our understanding of catalysis and chemisorption processes.I3 Transition-metal hydrides are also tractable models for theoretical investigations. Armentrout and co-workers6-I0 have studied the energetics and dynamics of the reactions of transition-metal atoms (their positive ions) with H2, D2, and H D by using the guided ion beam mass spectrometry. Recently, Elkind et a1.I0 have studied the interactions of Sc+, Y+,La+, and Lu+ with H2. They measured the M+-H bond energies using the M+ + H2 MH+ + H reaction. Matrix isolation techniques have also been employed to study the spectroscopic properties of metal mono- and dihydrides.12 Theoretical studies of model reactions of M and M+ with H2 provide useful information on the nature of these types of reactions. Electronic states and potential energy surfaces of many transition-metal dihydrides have been studied extensively by Balasubramanian and c o - w o r k e r ~ ' ~using - ~ ~ CASSCF/CI methods. Recent s t ~ d i e s ' ~have - ~ ~revealed that the insertion of the metal atom and its positive ion into H2 is sensitive to the electronic state and the electronic configuration of the metal atom. For example, the 4F ground state of Rh does not insert into H2 while the excited 2F state inserts spontaneously.17 The platinum atom in its 3D3 state does not react with H2, but the IS,, state reacts easily.I8 The ground-state Au(,S) atom is found to be unreactive with H, while the Au(*P) + H2 reaction yields the ground-state A u H ~ ( ~ B , ) . ' ~ Whereas the potential energy surfaces of PtH2 and AuH, have been studied, the potential energy surfaces of other third-row transition-metal hydrides have not been studied at all.

-

'Camille and Henry Dreyfus Teacher-Scholar.

0022-3654/9 1 /2095-0042$02.50/0

Ab initio studies of both bare metal clusters and their reactivities are extremely difficult due to the problem of electron correlation and the large number of low-lying electronic states of different spatial and spin symmetries. Relativistic effects can be very large for these systems. Spin-orbit interactions are often quite important for very heavy metal atoms. Therefore, one has to include all these effects properly. (1) Allison, J. f r o g . Inorg. Chem. 1986, 34, 627. (2) Smalley, R. E. In Comparison of Ab Initio Quantum Chemistry with Experiment; Bartlett, R. J., Ed.; Reidel: New York, 1985; pp 53-65. (3) Powers, D. E.; Jansen, S. G.; Geusic, M. E.; Michalopoulos, D. L.; Smalley, R. E. J . Cfiem. Pfiys. 1983, 78, 2866. (4) Geusic, M. E.; Morse, M. D.; Smalley, R. E. J. Cfiem. Phys. 1985, 82, 590. (5) Morse, M. D.; Geusic, M. E.; Heath, J . R.; Smalley, R. E. J. Cfiem. Phys. 1985,82, 2293. (6) Armentrout, P. B.; Halle, L. F.; Beauchamp, J. L. J. Am. Cfiem. SOC. 1981, 103, 6501. (7) Elkind, J. L.; Armentrout, P. B. Inorg. Chem. 1986, 25, 1078. (8) Elkind. J. L.: Armentrout. P. B. J. Phvs. Cfiem. 1986. 90. 5736.6536. (9) Sunderlin, L. S.; Armentrout, P. B:J. Am. Chem. 'Soc. 1989, I l l . 3458. (10) Elkind, J. L.; Sunderlin, L. S.; Armentrout, P. B. J. Pfiys. Chem. 1989, 93, 3 I5 I . ( 1 1 ) Whetten, R. L.; Zakin, M. R.; Cox, D. M.; Trevor, D. J.; Kaldor, A. J . Chem. Phys. 1986, 85, 1697. (12) Van Zee, R. J.; Devore, T. C.; Wilderson, J. L.; Weltner, W. J . Chem. Phys. 1978, 69, 1869. (13) Knor, Z. In Catalysis: Science and Technology; Anderson, J. R., Boudart, M., Eds.; Springer: Berlin, 1982; Vol. 3, p 231. (14) Weltner, W. Jr.; Van Zee, R. J. Annu. Reu. Phys. Chem. 1984, 35, 291. (15) Balasubramanian, K.; Ravimohan, Ch. J. Phys. Chem. 1989, 93, 4490. (16) Balasubramanian, K.; Ravimohan, Ch. Chem. Phys. Lett. 1988, 145, 39. (17) Balasubramanian, K.; Liao, D. W. J . Phys. Chem. 1988, 92, 6259. (18) Balasubramanian, K. J. Chem. Phys. 1987, 87, 2800. (19) Balasubramanian, K.; Liao, M. 2. J . Phys. Chem. 1988, 92, 361. (20) Rappe, A. K.; Upton, T. H. J. Chem. Phys. 1986,85,4400. Elkind, J. L.; Armentrout, P. B. J. Phys. Chem. 1987, 91, 2037. Sanders, L.; Hanton, S.; Weisshaar, J. C. J . Phys. Cfiem. 1987, 91, 5145.

0 199 1 American Chemical Society

The Journal of Physical Chemistry, Vol. 95, No. 1, 1991 43

Electronic States of LaH, TABLE I: Geometries and Energies of the Low-Lying States of LaH2

SOCI

CASSCF state

E, eV

E , eV

re, A

Be, deg

(5s5p3d)

re, A

4, deg

(5s5p3d)

(5sSp3dlf)

2.158 2.225 2.277 2.200 2.339 2.207 2.322 2.3I4 2.279

111.4 120.5 180.0 102.2 180.0 122.4 180.0 180.0 180.0

0.0 0.52 0.66 0.83 0.81 1.94 2.17 2.80 3.03

2.140 2.190 2.260 2.174 2.312 2.195 2.310 2.298 2.259

1 1 1.9

0.0 0.48 0.69 0.76 0.84 1.32

0.0 0.48 0.68 0.75 0.88 1.30 1.49 3.01 3.12

119.7 180.0 102.8 180.0 119.8 180.0 180.0 180.0

1.50

2.94 3.1 1

In the present study we investigate the reactivity of the lanthanum atom with H2 in the insertion mode of collision. We obtain the potential energy surfaces of four doublet and four quartet states of LaH, arising from La(aZD) and La(a4F) by using complete active space MCSCF (CASSCF) calculations. Further, interesting regions in the potential energy surfaces such as minima, saddle points, and dissociation limits are studied by using the second-order configuration interaction (SOCI) technique. The spin-orbit interaction is also introduced by using a relativistic CI scheme for low-lying bent states of LaH,.

Method of Calculation The bent LaH, molecule was placed on the yz plane with the z axis bisecting the H-La-H bond angle. We have employed valence Gaussian basis sets and relativistic effective core potentials with spin-orbit operators for the La atom generated by Ross et aL2' Hay and WadtZ2have also generated comparable RECPs without the spin-orbit operator. The 5s25p65d16s2shells of the lanthanum atom were retained as the valence shells. We start with a Gaussian basis set of the type 5s5p3d generated by Ross et al.,' To this set, 10-component 4f functions with exponent 0.365 were added. The 4f exponent was optimized for the ground state of LaH. The addition of these diffuse functions did not change the geometries much for the electronic states of LaH,. Therefore, the geometries of various electronic states of LaH, were optimized by using the (5s5p3d) basis set while energy separations were calculated by a more extended (5s5p3dlf) basis set at the optimized geometries. For the hydrogen atoms we used scaled [5slp/3slp], Van Duijneveldt's basis set.23 Multiconfiguration S C F calculations were made using the complete active space MCSCF (CASSCF) method. The valence electrons (active electrons) were distributed in all possible ways in a configuration space spanned by a chosen set of the most important active orbitals. In the present study, excitations from the 5s25p6shells were not allowed but the coefficients of these orbitals were allowed to relax. The remaining five electrons of LaH, were distributed in all possible ways among the strongly occupied orbitals of the separated atoms which correlated into the 5d and 6s orbitals of La and Is orbitals of the hydrogen atoms at infinite separation. I n the C,, group, the active space thus consisted of four a', two b,, and one each of b, and a2 symmetries. The CASSCF calculations were carried out for the entire potential energy surfaces of eight electronic states of LaH, with the objectives of locating minima and saddle points. The bending potential energy surfaces were obtained by superposing two sets of surfaces. The small-angle surfaces were obtained from the dissociated MCSCF wave function as the input guess while the large-angle surfaces were obtained by using the MCSCF wave function of the linear geometry as the starting guess. Saddle points were located as intersections of these two surfaces. Configuration interaction calculations were carried out following CASSCF near the extrema and linear geometries located by the CASSCF method. The CI was done by using the second-order (21)R o s s , R. B.;Powers, J. M.; Atashroo, T.; Ermler, W. C.;LaJohn, L. A.: Christiansen, P. A. J . Chem. Phys., submitted for publication. (22)Hay, P. J.; Wadt, W. R. J . Chem. Phys. 1985,82, 299. (23)Van Duijneveldt, F. B. IBM Res. Rep. RJ 1971, 445.

LaH2

0

30

60

90

8 (Deqrees)

120

150

180

Figure 1. Bending potential energy surfaces for the low-lying states of

LaH,. CI method (SOCI). The SOCI calculations included all configurations in the zeroth-order CASSCF, configurations generated by distributing one active electron in the external space and four electrons in the active space in all possible ways, and those configurations generated by distributing two electrons in the external space and three electrons in the active space in all possible ways. The effect of the spin-orbit coupling term was studied by the relativistic CI (RCI) scheme. In this method, the spin-orbit operator is obtained as the differences of 1 + I / , and 1 - I / , potentials. Spin-orbit integrals are then transformed over the natural orbitals obtained from CASSCF/SOCI calculations. Pitzer's modified version of ARGOS codesz5were used to calculate spin-orbit integrals in Gaussian basis sets. In general, the RCI method included all low-lying electronic states that have the same symmetry in the C:, group. In the present investigation we have considered four low-lying bent doublet states of LaH,. The ,A, ground state of LaH, included ,Ala, ,B2P, ,BIB, and ,A2a reference configurations. Thus, for a given state all the important configurations were taken as reference configurations in RCI. Single and double excitations from these reference configurations were also allowed in a restricted space. Identical RCI calculations were done omitting the spin-orbit term. Differences in energies obtained with and without the spin-orbit term were then applied as corrections to the corresponding CASSCF/SOCI energies.

Results and Discussion Table I shows the equilibrium geometries and energy separations for the bent and linear minima of LaH,. Figure 1 shows the bending potential energy surfaces of eight electronic states of LaH, of doublet and quartet spin multiplicities correlating into La(a2D) and La(a4F), respectively. The ,Al state is the round state of LaH, with a bent equilibrium geometry (re= 2.14 ,e, = 11 1.9'). For the bent doublet states, the H-La-H bond angles do not change much due to higher order correlations included in the S K I method. The maximum change in the bond angle (about 3') is found in the ,Bz state while for the ,A,, ,Bi, and 2Azstates such

1

44

The Journal of Physical Chemistry, Vol. 95, No. 1, 1991

TABLE 11: Saddle Points in Various Potential Energy Curves of LaH, barrier height,' state r, A 6,deg kcal/mol 21 2.21 24

2.16 2.17 2.1 1 2.42

2.40 2.44 2.45

33 31 57

93 I10 97 108

36 40 51 52 53

5s 66

Barrier hcights were calculated with respect to the corresponding dissociation limits.

changes are less than 1 '. As seen from Table I, the La-H bond lengths contract at most 0.03 8, due to higher order correlations. In general, linear states tend to show longer bond lengths compared to bent states. The ,B1 state is only 0.48 eV above the ,Al ground state. Among the linear states, the '2: state which correlates with the ,A, bent state is the lowest in energy. The ground state is 0.68 eV more stable than the state. The quartet states do not have bent minima. The 4Au and 411ustates are highly excited states lying more than 3.0 eV above the ground state. The geometries of the electronic states of LaH, do not change significantly due to the addition of 4f functions in the basis set. However, in Table I we have shown the effects of these functions on the energy separations for all electronic states of LaH,. We may note that the energy separations are also not very sensitive to the addition of these functions. With the exception of the ,Ag and 4Au states, the changes in energies are within 0.02 eV. Thus, 4f functions do not play a very important role. Figure I shows that all the electronic states have pronounced barriers for insertions of the La atom into the H-H bond. The quartet states have larger barriers compared to the doublet states. The barrier heights for these insertions were calculated at the CASSCF level of theory. The saddle points were optimized at the CASSCF level of theory. Table I1 reports the saddle point geometries and the barrier heights with respect to their corresponding dissociation limits. All four quartet states have larger barriers for the insertion of the La(a4F) atom into Hz. The 4A, state has the largest barrier. In general, bond lengths at the saddle points of the quartet states are found to be 0.2-0.3 8, longer compared to the doublet states. This trend is expected for high-spin states since high-spin states of metal atoms do not form strong M-H bonds. For the doublet states saddle points occur at acute bond angles (20' C 8 < 110') while for the quartet states saddle point bond angles are obtuse (90' C 8 < 110'). As seen from Figure 1, the aZDground state of the lanthanum atom does not insert into H2 spontaneously. There are five different channels in which the La(a2D) atom can insert into the H-H bond. In all these channels the La atom has to surmount a barrier larger than 20 kcal/mol before forming bound states of LaH,. The ,A, ground state of LaH, is formed only after surmounting a barrier of 21 kcal/mol. In other channels, insertions of La(a2D) into H2 lead to the 2B,, ,Az, and ,B2 states of LaH, after surmounting barriers of 36, 40, and 51 kcal/mol, respectively. These barrier heights are considered as upper bounds since higher order correlations would lower these barriers by 2-5 kcal/mol. There are remarkable similarities between the doublet electronic state surfaces of YH2 and LaH,. Balasubramanian and RavimohanI6 found saddle points of ,AI, ,B,, and ,A2 states of YH, at 28', 37', and 40°, respectively. They found a barrier of 23 kcal/mol for the insertion of Y(,D) into Hz in the ,AI surface. The ,Al state is also the ground state of YH,. In the present study, we find that the ,A,, ,BI, and ,A, surfaces of LaH, are reminiscent of the corresponding surfaces of YH,. The first excited state (a4F) of the lanthanum atom arises from the 5d26s1electronic configuration. At the CASSCF level of calculation, the a4F-a2D energy separation is about 3300 cm-I, in good agreement with the experimental J-averaged splitting of 2900 cm-1.24 The La(a4F) atom is very unreactive to H, in the

Das and Balasubramanian TABLE III: Leading Configurations for the Electronic States of LaH2

configurationa la:2a,lbi (95) l a ~ l b ~ l (95) bl

state ZAI

2B,

1 u:2ug1 u: (95) la:lb:la, (94) l u : l 0 t l 6 ~ (96)

2z;

2A2

2Aa

la:lb:2b2 (94) lu;la;l?rg (95) 1 u ~ 2 u gu, l 16, (92), I u,2ug3ug I u, 16, (3) 1 u:2u8 1u, I T , (88), 1u,2u,3ug 1 u, 1 ?rg (3)

2B2

2ns 4A"

4n"

"Numbers in parentheses are in percentages. insertion mode. As seen from Figure 1, there are no bent minima in the quartet-state surfaces. The insertion of La(a4F) into the H-H bond in four possible channels can yield the 411uand 4Au states of LaH2 only after surmounting larger barriers. The largest barrier of 66 kcal/mol is noted for the 4A1surface. In the potential energy surfaces of the quartet states there exist very weak acute angle complexes La(a4F)-H2 near 8 = 10-1 5'. The depth of the potential wells forming the La(4F)-H2 complex is at the most 5 kcal/mol in the 4B, state surface at the CASSCF level of calculation. Although these complexes are not very strong, they cannot be discarded, but in a normal jet expansion experiment a product to survive it should be at least 19 kcal/mol more stable. Therefore, they are unlikely to be detected in a Smalley type of experiment. The ,A, ground-state surface of LaHz intersects the 4BI,4B,, and 4A2 surfaces at 0 = 25", while the ,A2 and ,B, surfaces intersect these quartet surfaces near 40'. These intersections may provide channels for the quartet-state atom to move to the doublet-state surfaces via the Landau-Zener surface hopping model, thereby lowering the barrier heights. Spin-orbit interactions could also facilitate the insertion of La(a4F) into H2 with lower barrier. However, the spin-orbit couplings among electronic states of different spin multiplicities near intersections are negligible. This is primarily because of large r, differences. That is, although these states cross in a one-dimensional projection of the PES,the large differences in r2 suggest that the global surfaces do not cross. Our RCI calculations are consistent with this. The energy for the reaction La(aZD) + H,

-

LaH#A,)

is calculated to be -1 1 kcal/mol at the SOCI level. The true energy of formation should be larger than 1 1 kcal/mol since higher order correlation effects and larger basis sets not considered here would stabilize the LaH2 molecule more compared to the dissociated La(*D) H2 species. However, we expect the error bars in our calculations to be within *5 kcal/mol. The error bar allows to improve the basis sets and higher order electron correlation not considered in the present study. Table 111 shows the important configurations for the low-lying states of LaH,. All the states reported here are dominated by a single configuration. The ,A, ground state is predominantly described by the la:2al Ib: (95%) configuration. The ,B, and ,A2 excited states arise from la:l b:l b, and la;lb:la, configurations, respectively. Similar configurations for the ,Al, ,B,, and 'Az states of YH, were noted by Balasubramanian and Ravimohan.16 The low-lying linear state, namely, ,2:, is described by the 1 u ~ 2 u gu{ l (95%) configuration. The highly excited quartet linear states are also found to be considerably pure. The 4Au and 411 states can be represented mainly by l ~ ~ 2 u ~ l u u(92%) l b g and Iug2ugluulxg Y (88%) configurations, respectively. Some of the saddle points in the potential energy surfaces arise from avoided curve crossing. This is confirmed by noting the

+

(24) Moore, C. E. Atomic Energy Leoels; US. National Bureau of Standards: Washington, DC, 1971. ( 2 5 ) Pitzer. R. M.; Winter, N. J . Phys. Chem. 1988, 92, 3061.

Electronic States of LaH,

The Journal of Physical Chemistry, Vol. 95, No. I, 1991 45

leading configurations of the CASSCF/CI wave functions at different bending angles along the surface. The saddle point at B = 24' of the 2A, state arises due to the avoided crossing of the la:2all b: configuration with the la:2ai3al configuration. At 0 < 30°, the 2A, state is dominated by la:2a:3aI, while at 8 > 30°, the state is predominantly described by the la:2a, 1 b: configuration. At the saddle point, these two configurations mix strongly. Similar avoided crossings occur for the 2Bl,2B2,and 2A2states. Near 0 = 30°, the potential energy curve of the ,B, state arising from the 1 ai1 b21b configuration undergoes an avoided crossing with the 2 B I (la12a, 1 4 1b,) surface. The saddle point in the 2A2state surface is due to the avoided crossing of 2A2(la:l b:la2) and 2A2(.la:2afl a2) configurations. For the 2B2 state, the dominant configuration for 0 > 60' is lay1 b:2b2 (90%), while for 0 60", the state is predominantly la:2a:I b2 (90%). The saddle points of the quartet surfaces are broader compared to the doublet surfaces. For the 4BI,4B2,and 4A2states the saddle points are natural barriers while the saddle point in the 4A, surface is due to an avoided crossing. We noted that the 4A,(la:l b 1 b, la,) surface undergoes avoided crossing with the 4Al(la,2al 1 b22b2)surface near 6 = 1 IO0. Although there occurs no avoided crossing in the 4B,state, there is a strong mixing of the la:2a,lb21a2 (60%) configuration with l a 1 2 a l l b ~ l b(32%) l at the saddle point geometry. The appearance of saddle points in the potential energy surfaces can be analyzed from orbital interactions between the metal orbitals and the hydrogen Is orbitals. Analyses of the natural orbitals of the * A I ground state show that the la, orbital at the equilibrium geometry is strongly bonding with respect to La(6s) and H2( 1 up)orbitals. The singly occupied 2a, orbital is a mixture of La(6s), La(6p), and La(5d) orbitals with a substantially reduced contribution from H(ls). The doubly occupied 1b2orbital is a bonding combination of La(6pJ La(5dy,) + [H,(ls)-H2(ls)]. At acute bond angles (0 < 25'), the 2A, state has the dominant configuration 1 a:2a;3al in which the la, orbital is almost the same as before with smaller bonding character. But the 2al orbital is antibonding with respect to La(6s) and H2(1u ) while the 3al orbital is a pure La( 5d+2) orbital. As the bond angle increases relative to the La(a2D) + H2 dissociation limit, the energy increases due to the substantial repulsive interaction in the 2al orbital. Once the bond angle is larger than 25', the leading configuration of the 2A, state becomes la:2allb: where the repulsive interaction in 2al is diminished and the bonding interaction in 1 b2 is increased. Near the saddle point (8 = 30') the ,B, state is predominantly described by la:2a:lb,. The l a , orbital is again a bonding combination of La(6s) and H 2 ( l a ) while the 2a, orbital is of antibonding character. The sin& occupied lb, orbital is a nonbonding La(Sd,,) orbital. Once the saddle point is crossed, the lail b:l b, configuration becomes the dominant one and the l a , orbital becomes more binding. The 1b2 orbital is now doubly occupied and a bonding orbital made of La(da) and H2(1u,). Therefore, the total energy is decreased because of the enhanced bonding interactions in the la, and 1 b2 orbitals. Similar situations are also noted near the saddle points of the 2B2and 2A2states. The nature of interactions of the orbitals near the saddle points of quartet surfaces does not change much. The potential energy surfaces of these states are broad over 100-1 30" bond angles. The leading configuration of the 4Al state for 0 > 1 IO" is la:2al 1b22b2 in which the 2a, orbital is essentially a mixture of La(6s) and La(5d). The 1 b2 orbital is a bonding combination of La(6pY)with H2( 1 u,) while the 2b2 orbital is characterized by the La(5dY,) orbital. For small-angle surfaces (0 < 1 IOo) the state is dominated by the I a:l b21 b, I a2 configuration where the nature of interactions in the Ib2 orbital does not alter much. The singly occupied lbl and la2 orbitals are basically nonbonding La(5d) orbitals. As a result, there occurs no significant change in the interaction among the orbitals due to the avoided crossing between 4A,( I a:2a, 1 b22b2)and 4Ai( 1 a:l b21b, 1 a2) surfaces. Mulliken population analyses of the natural orbitals obtained from the SOCl calculations are reported in Table IV. The total gross population of the lanthanum atom is less than 3.0 for all

TABLE IV: Mulliken Population Analyses for the Electronic States of LaH, gross populations .~ overlap state La(tota1) H(tota1) La@) La(p) La(d) H(s) population

t

+

~

2A,

2.38 2.37 2.39 2.46 2.36 2.45 2.49 2.82 2.88

2.62 2.63 2.61 2.54 2.64 2.55 2.51 2.18 2.13

0.74 0.14 0.89 0.21 0.22 0.18 0.27 0.87 0.85

0.27 0.28 0.49 0.20 0.48 0.70 0.56 0.10 0.16

1.37 1.95 1.01 2.05 1.66 1.58 1.66 1.85 1.86

2.61 2.62 2.60 2.53 2.62 2.53 2.50 2.17 2.11

1.09 1.13 1.14 1.13 1.15 1.15 1.17 0.62 0.64

electronic states of LaH2 considered here, indicating La+H- POlarity of La-H bonds. With the exception of the highly excited 4Auand 4rIu states, about 0.6 electronic population is transferred from the lanthanum atom to the two hydrogen atoms of LaH,. There is a significant loss of the electron density from the 6s orbital of the lanthanum atom. The La(6p) populations are considerably larger for most of the low-lying states. The 5d orbitals of the lanthanum atom also gain significant amounts of electron density. Although the 2A1ground state of LaH, arises from the a2D(5di6s2) configuation, there is significant electron transfer from the 6s orbital to the 6p and 5d orbitals. In the ground state of LaH,, the La-H bond is composed of 31% La(6s), 11% La(6p), and 58% La(5d) at the equilibrium geometry. Therefore, there is a strong dsp mixing through the contamination of the 5d16s2,5d26s1,and 5d'6s16p' configurations of the lanthanum atom. The first excited 2B, state has an unusually low La(6s) population. The La(5d) population of this state is nearly 2.0 while the La(6p) population is comparable to that of the ground state. Thus, the mixing of different configurations of La is very large. For the low-lying linear state (2Zz) the La(6p) population is 1.01. Thus, the participation of the 6p orbital in the La-H bonding is significantly large. The La-H bonds for this state have 37% La(6s), 21% La(6p), and 42% La(5d) characters. The La(6p) population of the 2rIgstate is also large. For these two doublet linear states, the overlap of the La(6p,,) orbital with H2(1 a,) along the internuclear axis is stronger. The excited 4Auand 411ustates have relatively low La(6p) populations. The La-H bonds for these two states have about 30% La(6s), 4% La(6p), and 66% La(5d) characters. Consequently, the La atom almost retains the 5d26s' configuration in these two quartet states. The overlap populations of all the doublet states are above 1 .O while for the two quartet linear states they are 0.63. As seen from the Mulliken populations, the bent states of LaH, exhibit complex spd hybridizations. For example, the 2B2 and 2B, states have similar bond angles (0, 122.4', 120.5'), but their Mulliken populations are so.2p0.7d1.6 and so,lp0,3d2.0, respectively. Effective spd hybridization as depicted by Mulliken populations determines geometries, but there is no one-one correspondence between the bond angle and Mulliken population as seen from 2B2and 2BI states. The geometries of bent states are also determined by the participation ofthe dX24orbital. (The linear molecule is oriented along they axis.) In general, for the low-spin bent states participation of the d,~-~2orbital plays a roll in the determination of 0,. The high-spin states form linear equilibrium geometries while the low-spin states form bent minima. This is primarily because of the fact that the low-spin state of the La atom can form bond pairs with the H( Is) electrons while the high-spin state is primarily nonbonding. Consequently, the bent minima are formed through the La(d,z-,2), La( d,~~~2+,2), La(6p), and La( 6s) hybridization in the low-spin states, while effective orbital overlap in the high-spin states is achieved primarily through the La(da), La(6s), and H( Is) orbitals. The most effective overlap of La(da), La(6s), and H(1s) is achieved for the linear geometry; consequently, high-spin states are linear while many low-spin states are bent. The La-H bond lengths of the linear high-spin states are longer than the La-H bond lengths in the bent states. For example, the 4A, linear state has a re 2.298 A while the 2AI ground state

-

-

46

The Journal of Physical Chemistry, Vol. 95* No. 1, 1991

TABLE V: Dipole Moments for the Bent Minima of LaH2 state

fi,

D

3.79 5.42 4.72 7.42

TABLE VI: Effect of Spinarbit Coupling Term on Low-Lying States of LaH2 state'

2Al~ 2AI 2Bln

energy, cm-'

0 24 3880

'

state'

2B, 2A2a 2A2

energy, cm-l 3896 6017 6073

state'

2B2 2B2(u

energy, cm-I 10509 10574

'Spin-label a represents the inclusion of spin-orbit coupling.

-

has an r, 2.14 A. There are several factors which contrast the bond lengths. The primary factor is that La(du) + La(6s) overlap with H( Is) is considerably smaller in the linear geometry compared to the La(d6) La(du) La(6s) overlap with H(1s) in the bent geometry. This corroborates with the La-H overlap Mulliken populations in Table IV. For example, the La-H overlap is 1.09 in the ,A, state compared to 0.62 for the linear 4Au state. The La-H overlaps are also much smaller for the 4rIustate. The above discussions on LaH, then suggest a trend for other systems such as HfH2, TaH,, etc. The low-spin state of the metal atom is expected to be more reactive than the high-spin state. The low-spin state of the metal atom is likely to form bent electronic states while with shorter M-H bonds compared to high-spin states which tend to form linear MH2 molecules with longer M-H bonds. On this basis for example, we predict that H M 2 should have a bent 'A, ground state. Dipole moments were calculated from the SOCI density and property matrices for the bent states of LaH,. Table V shows the dipole moments of four doublet states of LaH2 at their equilibrium geometries. All four states exhibit strong La'Hpolarities. For the ground state of LaH, the dipole moment is

+

+

Das and Balasubramanian 3.79 D. The 2A2state shows the largest dipole moment. Since the bond lengths calculated here could be up to 5% in error due to the use of effective core potential approximations and the neglect of higher order correlation not included in CASSCF/SOCI, we expect some inaccuracies in the calculated dipole moments. The strong La+H- polarities of the La-H bonds are quite consistent with the Mulliken populations shown in Table IV. The contributions of the spin-orbit coupling term to the doublet bent states of LaH, are shown in Table VI. The geometries of these states do not change much due to the addition of the spin-orbit term. The effect on the energy separations is also small. The ground state (,Ala)is stabilized only by 24 cm-'. The largest spin-orbit splitting of 65 cm-] is found in the ,B2 state. Conclusion CASSCF/SOCI calculations show that the ground state of LaH, is of ,AI symmetry and is 11 kcal/mol more stable than the La(a2D) dissociation limit. The present investigation also reveals that the La(a2D) ground state and the La(a4F) excited state do not insert into the H-H bond spontaneously. In order to form LaH, in the ,A1 ground state, the La(a2D) atom has to surmount a barrier of 21 kcal/mol. The insertion of the La(a4F) atom into H2 requires more than 50 kcal/mol energy before forming the 4Au and 411u states of LaH,. The Mulliken population analyses show considerable dsp hybridization and large ionic character of LaH, with the La atom carrying the positive charge. The large dipole moments support the strong La+H- polarities of the La-H bonds. The spin-orbit coupling term does not play an important role in changing the geometries and energy separations of the low-lying bent states of LaH2. Acknowledgment. This work was supported by the office of the Basic Energy Sciences Division of the U.S. Department of Energy under Grant DE-FG02-86-ER-13558. K.K.D. thanks North Bengal University, Darjeeling 734430, India, for providing a leave of absence. The authors thank the two referees for many invaluable comments which improved the presentation of this manuscript.