3020
J . Phys. Chem. 1988, 92, 3020-3023
Full Configuration Interactlon Benchmark Calculations for TiH Charles W. Bauschlicher, Jr. NASA Ames Research Center, Mofjett Field, California 94035 (Received: June 26, 1987; I n Final Form: August 31, 1987)
Full configuration interaction (FCI) calculations have been performed for the 'F and SFstates of Ti atom and the
and
2A states of TiH. The FCI calculations are compared to approximate treatments of the correlation problem; for the 2A state,
the CASSCF/MRCI treatment agrees with the FCI results for re, we, the dipole moment, and the dipole derivative. For the '0 state, the CASSCF/MRCI approach agrees well with the FCI for re, we, and De. However, the agreement between CASSCF/MRCI and FCI treatments for the dipole moment is not as good, even when the CASSCF and MRCI reference spaces contain up to 800 CSFs. Natural orbital iterations improve the dipole moment but have a smaller effect on the other spectroscopic parameters. The CPF and MCPF methods agree well with the FCI for the 'a state, which is reasonably well described by the SCF; this is true even for the dipole moment, where a natural orbital iteration must be performed for the CASSCF/MRCI treatment. The CPF and MCPF treatments do not agree as well for the 2A state, which is not as well described by the SCF.
Introduction Accurate calculation of properties of transition-metal compounds has proven to be a very challenging The major problem in the treatment of these systems is probably due both of the need to describe the bonding which can arise from a mixture of the atomic occupation^'-^ 3dn4s2and 3dn+'4s'; the difference in the spatial extent of the 3d orbitals and the large difference in the correlation energy between these two occupations require very high levels of treatment to give a balanced de~cription.'-~ The large difference in the correlation energy between the two occupations means that the zero-order wave functions, either SCF or CASSCF, can be biased toward one of the occupations. Since the orbitals for the two occupations are different, the bias introduced by the zero-order wave functions may be sufficiently large that even a CASSCF/MRCI treatment cannot overcome it.*-3 We have found that natural orbital (NO) iterations can reduce the zero-order wave function orbital bias, since the NOS are defined at a higher level of correlation treatment.'-3 However, this procedure gave rise to questions of whether the properties should be taken from the MRCI with the lowest energy or the NO iterations should be repeated until the properties are converged. A full CI(FC1) calculation does not suffer from any orbital bias and can help to unambiguously determine what level of correlation treatment is needed to correctly describe the bonding in transition-metal compounds. In this work we compute the spectroscopic constants re, De,T,, and we, at the FCI and several levels of approximations to determine what level of treatment is required to obtain an accurate description of TiH. In addition we report the dipole moment and dipole derivative, since these can be used to interpret how well different levels of approximation are describing the mixing of the atomic asymptotes. Qualitative Features of the Bonding In the case of TiH, the bonding can arise from either the 3d34s' or the 3d24s2occupations. In the 3d34s' occupation, a 4s-Is bond is formed which is polarized toward the H. In the 3d24s2occupation, 4s-4p and 4s-3d hybridization can occur, with one hybrid bonding with the H , while the other is polarized away. The open-shell 3d orbitals that are not involved in the bonding can be coupled in several ways leading to a large number of states. (1) Walch, S. P.; Bauschlicher, C. W.; Langhoff, S. R. J . Chem. Phys 1985, 83, 5351.
(2) Chong, D.P.; Langhoff, S. R.; Bauschlicher, C. W.; Walch, S. P.; Partridge, H. J . Chem. Phys. 1986, 85, 2850. (3) Walch, S. P.; Bauschlicher, C. W. J. Chem. Phys. 1983, 78, 4597. (4) Bauschlicher, C. W.; Walch, S. P.; Langhoff, S. R. In Quantum Chemistry: The Challenge of Transition Metals and Coordination Chemistry; Veillard, A., Ed.; Reidel: Dordrecht, Holland, 1986; p 15. (5) Bauschlicher,C. W.; Walch, S. P.; Partridge, H. J . Chem. Phys. 1982, 76, 1033.
The lowest state arising from 4s-4p bonding with the hydrogen is determined by the mixing of the 3dn4s2and 3dn+'4s1atomic occ~pations.~ For TiH this leads to the 4@ ground state with the occupation
...6a27u13a'16'
'@I
(1)
where the 6a orbital is the Ti-H bonding orbital and the 357 and 16 are Ti 3d-like orbitals. The 7a orbital is a mixture of 4s, 4p, and 3d character, since both atomic asymptotes contribute to determining its composition, Le., 3d-like from the 3d34s1asymptote and the 4s-4p hybrid polarized away from H arising from 3d24s2. The mixed-state character of the 4@ state is manifested in the Mulliken population (a 3d population of 2.40 electrons at the FCI level) and in the magnitude of the dipole moment. The bonding in the 3d34s1occupation polarizes the 4s toward the hydrogen resulting in a large dipole moment, while for 3d24s2,the polarization of the nonbonding 4s-4p hybrid orbital away from the hydrogen balances the polarization of the bonding charge distribution toward the hydrogen, resulting in a small dipole moment. Thus the dipole moment of the 4 @ state parallels the mixing of the two occupations in the wave function. On the left-hand side of the transition series, the 3d and 4s orbitals are most similar in spatial extent, and therefore the bonding arising from 4s-3d hybridization is competitive with the 4s-4p bonding. For ScH, this bonding mechanism leads to the ground state,2-6while for TiH the hybridization of the 3d and 4s orbitals in the 3d24s2occupation results in the low-lying 2A state: 'A
...6a27a216'
(2)
In this state, the 6u is the Ti-H bonding orbital, while the 7u is the nonbonding 4s-3d hybrid orbital. While both the 6u and 7a orbitals mix in some 4p character, very little Ti 3d34s' mixes into the wave function; the FCI population analyses shows 2.07 3d electrons. While the '@ state arises from a mixing of the two atomic asymptotes and the zA does not, the 2A state is actually more poorly described by the S C F than is the '@I state. Thus the 2A state is a more severe test for the single reference based approaches. Thus the separation between the 4@I and 2A states is a measure of how well the 3d-4s bonding mechanism is described relative to 4s-4p bonding.
Methods The hydrogen basis set is the Dunning (4s)/[2s] contraction,' with the exponents scaled. A set of 2p polarization functions is added (cup = 1.0). The Ti primitive basis set is the (14s 9p 5d) (6) Bauschlicher, C. W.; Walch, S. P. J . Chem. Phys. 1982, 76, 4560. (7) Dunning, T.H. J . Chem. Phys. 1970,53, 2823. Huzinaga, S. J . Chem.
Phys. 1965, 42, 1293.
This article not subject to U S . Copyright. Published 1988 by the American Chemical Society
FCI Benchmark Calculations for TiH set of Wachters,* supplemented with two functions to describe the 4p (ap= 0.15234 and 0.051 08), a diffuse 3d9 (ad = 0.072), and four 4f polarization functions (af= 2.1741,0.8696,0.3478, and 0.1391). The Ti basis set is contracted by using an atomic natural orbital (ANO) scheme.I0 Since the bonding in TiH involves a mixture of the atomic asymptotes, SF(3d34s') and 3F (3d24s2), it is important that contraction of the basis set not degrade this separation. Since the orbitals for the 3F and SFstates are quite different, they are obtained from a state-averaged S C F calculation. This is followed by a single and double C I (SDCI) calculation for each state correlating only the four valence electrons. The two SDCI density matrices are averaged and the resulting NOS used to define the A N 0 contraction. The final Ti basis set is of the form (14s 1 l p 6d 4f)/[5s 4p 3d If]. In all calculations the 3s component of the 3d functions, and the 4p component of the 4f functions have been deleted. In addition to the SCF/SDCI calculations performed for the A N 0 contraction, a CASSCF/MRCI calculation is performed for the 3Fstate. This CASSCF/MRCI treatment accounts for the 4 s - 4 ~near degeneracy by having the 4s and 4p orbitals active in the CASSCF and includes all CSFs in the CASSCF wave function as references in the MRCI calculation. FCI calculations are also reported for both the 3F and SF states of Ti atom. In this work several different zero-order reference approaches are used for TiH. In all calculations the core (the Ti 1s-3p-like) orbitals are fixed in the same form to avoid any confusion between core relaxation and correlation effects. The form of the core orbitals is defined by a CASSCF calculation at each internuclear separation. For the 4@ state, the CASSCF calculation that defines the core orbitals has an active space consisting of four a,, one b,, one b2, and one a2 orbitals, denoted [4111]. While the calculations are performed in C2, symmetry, C,, symmetry and equivalence restrictions are imposed. Therefore, one of the active a, orbitals is the 1 6 ~ 2 The . active orbitals correspond to the Ti-H bonding and antibonding orbitals, the nonbonding orbital, which is a mixture of the 4s-4p and 3du orbitals, the 3da orbitals, and 3d6 orbitals. This active space is expanded to [5111] to allow separative active orbitals for the 3du and the 4 s - 4 ~nonbonding hybrid orbital. A [5221] CASSCF wave function corresponds to having the Ti 3d, 4s and 4p, and H 1s orbitals all active. The addition of a sixth active a, orbital was found to be relatively important, and these [6111] and [6221] CASSCF wave functions represent expanding the active space outside of the usual definition of the valence orbitals (Ti 3d, 4s and 4p, and H 1s). Only a [5111] choice of active space is used for the 2A state, since there are no occupied 3da orbitals in this state. The 2A core orbitals are defined by this [5111] CASSCF calculation. The single reference correlation approaches used in this work are based upon S C F wave functions. The core orbitals are those defined in the CASSCF calculations. For the 2A state, a symmetry- and equivalence-restricted wave function corresponding to eq 2 is used. For the 4 @ state, a symmetry-broken S C F calculation using the 7 0 ' 3 ~ ~16,'' component of eq l is used to optimize the orbitals. More extensive correlation is added to the S C F reference wave functions by using the coupled pair functional (CPF) method1' or its modified formI2 (MCPF). In these calculations, as in all other correlation treatments, only five electrons are correlated. In the MRCI wave functions, all single and double excitations from all CSFs in the CASSCF reference space are included. Therefore, the MRCI calculations are denoted by the CASSCF space on which they are based; e.g., [6221]MRCI includes all single and double excitations away from all CSFs in the [6221]CASSCF wave function. In one case we select the references based upon the coefficients of the occupations in the CASSCF wave functions, where an occupation was included in the reference only if the absolute value of the coefficient of one (8) Wachters, A. J. H. J . Chem. Phys. 1970, 52, 1033. (9) Hay, P. J. J . Chem. Phys. 1977, 66, 4377. (10) Almlof, J.; Taylor, P. R. J . Chem. Phys. 1987, 86, 4070. (1 1) Ahlrichs, R.;Scharf, P.; Ehrhardt, C. J . Chem. Phys. 1985, 82, 890. (12) Chong, D. P.; Langhoff, S . R. J . Chem. Phys. 1986, 84, 5606.
The Journal of Physical Chemistry, Vol. 92, No. 11, 1988 3021 of its component spin couplings was above 0.01, which we denote MRCI(O.01). In addition to using the CASSCF orbitals, we have performed natural orbital (NO) iterations; no change in the MRCI reference space is made when the N O iterations are performed. Full symmetry and equivalence restrictions are imposed in the NOS, just as in the CASSCF optimization. For the effect of higher excitations on the separations in the MRCI calculations, we use the multireference analogue of the DavidsonI3correction, namely, AEsD (1 - CRCR2),where AEsD is the difference between the energy of the reference CSFs and the MRCI, and the CRare the coefficients of the reference configurations in the MRCI wave function. The addition of the Davidson correction is denoted +Q. These approximate treatments are compared to the FCI results. The re and we values are determined by fitting the three points nearest the minimum, with a spacing of 0.05 a. between the computed points, to a quadratic in l / r , while the dipole moment and dipole derivative at re are determined from a fit of the dipole moment to a quadratic in r. The dipole moments are computed as expectation values. The FCI calculations have been performed by using a modified version of the Knowles and Handy FCI programI4 which has been interfaced into the MOI.ECULE-SWEDEN1s'16 codes. All FCI calculations were performed on the NAS CRAY 2. The remaining calculations were performed on the NASA Ames CRAY XMP/48. The CASSCF/MRCI calculations were performed by using the MOLECULE-SWEDEN codes, and the Blomberg and Siegbahn" code was used for the C P F and MCPF calculations.
Results and Discussion The data associated with the contraction of the Ti basis set is summarized in Table I. The state-averaged S C F 3F - S Fseparation is similar (0.1 eV) to that obtained with separate S C F optimizations, but the total energies for each state show a larger error (0.3-0.4 eV) as a result of the state averaging. The fact that the optimal orbitals for the two states are significantly different is illustrated by the error in the separation that arises if either individual state orbitals are used. The addition of correlation reduces the sensitivity of the state separation to the orbital basis, with the state-averaged approach being in good agreement with the separation computed with each state using its own orbitals. The state-averaged approach seems to represent a good compromise for determining the correlation-based A N 0 contraction. The contraction to [5s 4p 3d If] represents a somewhat better than double { plus polarization basis set. This contraction is sufficiently compact to allow the FCI treatment, without affecting the relative treatment of the 3F and SF atomic states. While the contraction does not introduce any sizable errors, it is interesting to note that into an SCF/SDCI separation using average S C F orbitals differs from the FCI by almost 0.1 eV. Part of this error comes from the importance of 4s2 4p2 excitation in 3F. The inclusion of the Davidson correction reduces the error. If the 4s-4p near degeneracy is added in the CASSCF/MRCI treatment, the error is further reduced, leading to our best separation which is in error with the FCI by only 0.018 eV (see Table I); this separation is computed by using separately optimized orbitals for each state and the CASSCF/MRCI description of the 3F state. Therefore, it would appear that an accurate treatment of the atomic separations does not imply a level of treatment that would be prohibitively expensive for TiH. It should be noted that the core orbitals vary slightly with the level of the valence treatment. As a result of the differences in the core orbitals, the CASSCF/MRCI total energy is lower than the FCI using the state-averaged S C F orbitals. The difference in the FCI total energies between the state-averaged and 'F
-
(13) Langhoff, S . R.; Davidson, E. R. Inf. J . Quanfum Chem. 1974,8, 61. (14) Knowles, P. J.; Handy, N. C. Chem. Phys. Left. 1984, 1 1 1 , 315. See also Siegbahn, P. E. M. Chem. Phys. Lett. 1984, 109, 417.
(15) MOLECULE is a vectorized Gaussian integral program written by J. Almlof. (16) SWEDEN is a vectorized SCF-MCSCF-direct CI-conventional CICPF-MCPF program, written by P. E. M. Siegbahn, C. W. Bauschlicher, Jr., B. Roos, P. R. Taylor, A. Heiberg, J. Almlof, S . R. Langhoff and D. P.Chong. (17) Blomberg, M. R. A,; Siegbahn, P. E. M., private communication.
3022 The Journal of Physical Chemistry, Vol. 92, No. 11, 1988
Bauschlicher
TABLE I: The Computed Ti 3F(3d24s2)-sF(3d34s1) Separation (Total Energies in E")
E(REF) E(CI) Uncontracted 14s 1 Ip 6d 4f
E(CI+Q)
E(FC1)
average SCF orbitals 3d34s' 3d24s2 A9 eV 3d34s1SCF orbitals 3d34s1 3d24s2 A, eV 3d24s2SCF orbitals 3d34s' 3d24s2 A, eV each state its own SCF orbitals A, eV
-848.360 656 -848.377 278 0.452
-848.41 1756 -848.442 034 0.824
-848.414660 -848.447 854 0.903
-848.372 08 1 -848.342 161 -0.814
-848.412 325 -848.435 175 0.622
-848.413 568 -848.446 923 0.908
-848.303 963 -848.392670 2.414
-848.407 187 -848.445 284 1.037
-848.422 365 -848.449 598 0.741
0.560
0.897
0.980
Contracted (14s l l p 6d 4f)/[5s 4p 3d lfl average SCF orbitals 3d34si 3d24s2 A, eV 3d34s1SCF orbitals 3d34s' 3d24s2 A, eV 3d24s2SCF orbitals 3d34s1 3d24s2 A, eV 3d24s2CASSCF orbitals 3d34s' 3d24s2 A, eV each state, its own orbitals A? eVY A, eVb
-848.360 563 -848.377 266 0.455
-848.408 214 -848.438 806 0.832
-848.4 IO 900 -848.444 313 0.909
-848.409 193 -848.443 257 0.927
-848.371 772 -848.343 189 -0.778
-848.408 566 -848.432 397 0.648
-848.409 688 -848.443 089 0.909
-848.409672
-848.304 246 -848.392 571 2.403
-848.404 109 -848.442023 1.032
-848.418 886 -848.446 090 0.740
-848.306 772 -848.423 885 3.188
-848.403 376 -848.444 367 1.115
-848.416990 -848.444 826 0.757
0.566 1.418
0.9 10 0.974
0.991 0.956
-848.444 8 15
0.956
'SCF orbitals are used for the 3F state. bCASSCF/MRCI description is used for the 3F state. CASSCF orbitals shows that there is 0.04 eV associated with the description of the inner-shell orbitals. This core relaxation effect with level of treatment is avoided in the TiH calculations by using a single set of core orbitals for each state. The dipole moment and total energies for the 4@ state at 3.40 a. and the zA state at 3.30 a. are summarized in Table 11; these bond lengths are close to the FCI optimized values. The 49S C F dipole moment is 12 smaller than the FCI. Inclusion of correlation using either the CPF or MCPF methods improves p, with the CPF being a bit better. For p, the [4111]CASSCF is a$oorer level of treatment than the SCF, and the inclusion of correlation in the MRCI treatment improves the result, but it is only slightly better than the S C F and worse than either the MCPF or C P F values. If one natural orbital iteration is performed, the energy is decreased and the dipole moment is improved. Five NO iterations leads to a total energy which is lower than that by using the CASSCF orbitals but slightly higher than after the first NO iteration. While the total energy appears to be converging to a value slightly higher than the lowest obtained in the NO iterations, the p has converged to the FCI value. In the [4111]MRCI wave function there are important CSFs (absolute value of coefficient greater than 0.05) which involve u orbitals outside the active space. These important CSFs outside the reference space are eliminated in the NO iterations, but it is of interest to determine what CASSCF level is required to eliminate important CSFs in the MRCI wave function outside the CASSCF wave function. Increasing the u active space to [5 11 11 improves the CASSCF and MRCI p slightly; however, the active must be expanded to [6111] to eliminate the important CSFs outside the reference space, but even at the [6111]MRCI level, w still does not agree with the FCI. While expanding the number of u orbitals eliminates the important CSFs outside the reference space, the NOS suggest that the 4n orbital is more important than the added u orbitals. The [4221] treatment is used to test the possibility that a missing u-T
correlation effect is requiring the expansion of the u active space. While the [4221]MRCI p is superior to the [511 l]MRCI result, there are still important CSFs involving u orbitals outside the active space. Expansion of the active spaces to [5221] and [6221] further improves the dipole moment, becoming superior to the MCPF. The [6221]MRCI treatment, which has no important CSFs outside the reference space still has 2% error in p; this is large for a five-electron treatment that includes all single and double excitations from 800 reference CSFs. If NO iterations are performed for the [6221]MRCI treatment, p coverages to the FCI value. Probably due to the large reference space, the convergence of p with NO iteration is faster than for the [411 l]MRCI. It is interesting to note that selecting the reference CSFs, based upon a threshold of 0.01 in the CASSCF wave function, doubles the error in p for the [6221]MRCI treatment. The 'A state is more difficult to describe at the S C F level, and the convergence to the FCI result is different. The S C F level p is even poorer than for the 4@ state. While the CPF and MCPF approaches improve p, the error is much larger than for the 40 state. The [SlllICASSCF treatment is superior to the SCF, reducing the error to that of the CPF and MCPF approaches, and when more extensive correlation is added in the MRCI calculation, p is in excellent agreement with the FCI. An NO iteration has almost no effect on the dipole moment. For both the *A and 4@ states, the addition of the Davidson correction results in an energy below the FCI. This is very common for multireference approaches correlating eight or fewer electrons. The computed spectroscopic constants as a function of level of approximation are summarized in Table 111. For the 49state, the S C F bond length is 0.1 1 a,, too long. There are modest errors in the other computed properties. The MCPF or CPF results are in significantly better agreement with the FCI calculations. The [4111]CASSCF has errors as large as the SCF; however, the [411 l]MRCI results for re, we, and De are as good as, or slightly superior to, the MCPF and C P F values. This is different from
The Journal of Physical Chemistry, Vol. 92, No. 1 1 , 1988 3023
FCI Benchmark Calculations for TiH TABLE II: Total Energy and Dipole Moment for TiH as a Function of Level of Correlation Treatment, in EH and au, Respectively
energy 4@ at 3.40 a.
~1
SCF CPF MCPF [4111]CASSCF [4111]MRCI [4111]NOCI(l) [4111]NOCI(2) [4111]NOCI(3) [4111]NOCI(4) [4111]NOCI(5) [5111]CASSCF [5111]MRCI [611 IICASSCF [6111]MRCI [4221]CASSCF [422 11MRCI [5221]CASSCF [5221] MRCI [6221]CASSCF [622 11MRCI [6221]NOC1(1) [6221]NOCI(2) [6221]NOCI(3) [6221]MRCI(0.01) FCI
-848.948608 -849.014417 -849.013 741 -848.973 608 -849.016098 -849.016491 -849.016485 -849.016479 -849.016478 -849.016477 -848.979067 -849.016441 -848.979 906 -849.016 876 -848.981 933 -849.016614 -848.987 194 -849.016 960 -848.988 702 -849.017 366 -849.017 545 -849.017 545 -849.017 545 -849.017039 -849.017913
0.8145 0.9248 0.8600 0.7607 0.8252 0.8943 0.9135 0.9184 0.9197 0.9200 0.7779 0.8437 0.7570 0.8904 0.7614 0.8551 0.7793 0.8764 0.7971 0.9002 0.9183 0.9190 0.9191 0.8813 0.9207
SCF CPF MCPF [5111]CASSCF [511 l]MRCI [5111]NOCI FCI
=A at 3.30 a,, -848.896665 -849.006223 -849.005 621 -848.967 31 1 -849.006 221 -849.006 245 -849.006 950
0.9712 0.4617 0.5050 0.5034 0.6059 0.6053 0.6076
TABLE 111: Summary of the Spectroscopic Constants" for TiH and *A
4@
4@
energy + Q" SCF CPF MCPF [4111]CASSCF [4111]MRCI [4111]MRCI+Q [4111]NOCI [411 l]NOCI+Q [622 11CASSCF [622 11MRCI [622 11MRCI+Q [6221]NOCI [6221]NOCI+Q FCI
-849.018 573 -849.018 382 -849.018401 -849.018408 -849.018410 -849.01841 1 -849.018 501 -849.018 440
3.494 3.387 3.387 3.544 3.381 3.376 3.385 3.375 3.445 3.380 3.377 3.380 3.378 3.380
1521 1562 1569 1413 1559 1571 1564 1572 1529 1576 1572 1568 1574 1572
1.900 2.031 2.008 1.933 2.040 2.038 2.050 2.036 1.766 2.037 2.059 2.041 2.058 2.054
0.861 0.920 0.855 0.823 0.820
0.501 0.351 0.368 0.434 0.382
0.889
0.364
0.815 0.893
0.402 0.357
0.91 1
0.359
0.913
0.359
2A
-849.018664
~
-849.018 627
SCF CPF MCPF
-849.018 480 -849.018458 -849.018475 -849.018477 -849.018 704
~~
r, we T, P dclldr 3.203 2113 11405 0.899 0.724 3.362 1421 1767 0.464 0.015 3.336 1492 1772 0.513 0.207
relative to [4111] treatment [5111]CASSCF [5111]MRCI [5111]MRCI+Q [511l]NOCI [511 l]NOCI+Q relative to [6221] treatment [511 IICASSCF [ 5 11 11MRCI [511 l]MRCI+Q [5111]NOCI [511 l]NOCI+Q FCI *A
-849.007 562 -849.007 566
3.409 3.310 3.306 3.310 3.306
1387 1564 1569 1561 1566
1465 0.547 0.383 2169 0.609 0.341 2422 2250 0.609 0.341 2380
3.308 1566
4614 2449 240 1 2476 2398 2410 0.610 0.342
"The units for re, we, De, T,, p, and dp/dr are a,, cm-', eV, cm-', au, and aula,,, respectively.
" Indicates that the Davidson correction has been added. and dp/dr, where the MCPF and C P F are superior. The addition of the Davidson correction has only a small effect. While the NO iteration improves the dipole moment and its derivative, it makes only a small change in re, we, or De. Expanding the CASSCF active space to [6221] improves re, but De becomes significantly smaller since the important atomic excitation 4s2 4pz lowers the energy of the separated system. Addition of more extensive correlation results in an excellent bond length and we, but De is only as good as in the [4111]MRCI calculation. The [6221]MRCI + Q results yield a bond length that is too short and a De that is too large. As for the [4111]MRCI treatment, the NO iteration makes only a small change in re, De, and we, but improves p. The S C F description of the 2A state has a bond length that is too short by as much as the S C F was too long for the 4 @ state. Te is very poor since the zA state is so poorly described by a single configuration. The C P F and MCPF treatments overshoot on all properties, with the C P F dp/dr being much too small. Overall the CASSCF is only a little better than the SCF. However, the addition of more extensive correlation brings the calculated results into excellent agreement with the FCI; this includes T, if the 2A results are compared to the superior [6221] treatment of the 4 @ state. Performing an NO iteration has almost no effect on any property. The addition of the Davidson correction also has .a very small effect on the results. p
--+
Conclusions The C P F or MCPF approaches do quite well for the 4@ state of TiH, even though this state is a mixture of the 3d24s2and 3d34s1 atomic asymptotes. However, they do not perform as well for the 2A state, which arises from only the 3d24s2occupation but has 3d involvement in the bonding and is not as well described at the S C F level as the 4 @ state. For p the performance of the CASSCF/MRCI results is reversed; it does very well for the 2A state, but even when the active space is expanded outside the normal valence definition (Le., Ti 3d, 4s, 4p, and H Is), the dipole moment is only brought into agreement with the FCI by natural orbital iterations. Even though the [4111]MRCI or [6221]MRCI treatments do not reproduce the FCI dipole moment, they do quite well for the other spectroscopic constants. It therefore appears that, for energy-related quantities, the CASSCF/MRCI approach should work well for transition-metal systems, but that for properties it is best to perform at least one natural orbital iteration and preferably iterate to convergence on the property. Once the natural orbital iteration is performed, the CASSCF/MRCI results are superior to those obtained at the MCPF or C P F levels. Acknowledgment. Part of this work was performed under a grant of computer time provided by the N A S Facility. Registry No. TiH, 13776-99-3.
