Second-Order Meller-Plesset Perturbation Theory for Systems

Sep 1, 1994 - and second transition row systems we optimized the geometry at the modified coupled-pair functional5 (MCPF) level. That is, the geometry...
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J. Phys. Chem. 1994, 98, 9498-9502

9498

Second-Order Meller-Plesset Perturbation Theory for Systems Involving First Transition Row Metals Alessandra Ricca, Charles W. Bauschlicher, Jr.,* and Marzio R o d NASA Ames Research Center, Moffett Field, Califomia 94035 Received: June 4, 1994@

Results obtained using second-order Mprller-Plesset (MP2) perturbation theory are compared with those obtained using coupled cluster singles and doubles approach including a perturbational estimate of the connected triple excitations, CCSD(T), or the modified coupled-pair functional (MCPF) approach. For FeCO, FeCO+, FeH20+, and the states of FeC&+ derived from the Fe+ 3d64s' occupation, the MP2 geometries are found to be in good agreement with those obtained at the CCSD(T) or MCPF level. At the MP2 level the Fe-C bond lengths for the states of FeC&+ derived from the 3d7 occupation are too long relative to the MCPF or CCSD(T) results. The geometries computed at the self-consistent-field (SCF) level are quite poor for FeCO+ and all states of FeC&+. The energetics at the MP2 level, while superior to the SCF, are still significantly inferior to those obtained at the CCSD(T) or MCPF level. We find that FeC&+ has a quartet ground state with an q3 coordination.

I. Introduction The number and quality of calculations involving transition metals have increased dramatically in the past few years.' It has been found that it is even more important to include extensive correlation to obtain accurate energetics for transition metal systems than for nonmetal systems. Geometries determined at the self-consistent field (SCF) level have been found to be reasonably accurate for many covalently bonded system^.^^^ For electrostatically bonded systems with some dative bonding, the SCF can underestimate the dative bonding and lead to metal-ligand bond lengths that are too long.4 In addition to these problems with the geometry, the SCF overestimates the frequencies of intraligand modes but underestimates them for the metal-ligand modes.4 Thus, there is no simple scaling which can improve the frequencies (and hence the calculation of the zero-point energy). To avoid these limitations of the SCF geometry, in many of our previous studies' of the first and second transition row systems we optimized the geometry at the modified coupled-pair functional5 (MCPF) level. That is, the geometry was optimized at the same level of theory that was used to determine the accurate energetics. While this works well for small systems, it can clearly become prohibitively expensive for large systems. In these cases we partially optimized the geometries at the MCPF level, with the remaining parameters taken from the optimal SCF geometry. While this works reasonably well, it is still time-consuming and somewhat arbitrary in the choice of which parameters are optimized. In addition, the MCPF approach is not suitable for the calculation of vibrational frequencies except for small systems, because analytic derivatives have not been implemented. It should be noted that these problems associated with the SCF approach appear to be much more severe for the first transition row. In fact, Siegbahn and co-workers3 have found that the SCF geometries are reasonably accurate for molecules containing second transition row atoms, with only a few cases where the SCF fails. They routinely optimize the geometry at the SCF level and only compute the energetics using a correlated approach in a large basis set. Permanent address: Department of Chemistry, University of Perugia, 1-06100, Perugia, Italy. @Abstractpublished in Advance ACS Abstracts, September 1, 1994.

With this work of Siegbahn and co-workers3 in mind, we used4 second-order Mldller-Plesset perturbation theory6 (MP2) to optimize the geometry and compute the frequencies of several VI.,+,CoL+, and CuL+ systems. The results showed that MP2 performed reasonably well for the geometry and frequencies but that higher levels of correlation were required to compute accurate binding energies. While the MP2 approach is more expensive than the SCF, it is still practical to optimize the geometry and compute the frequencies at this level, because analytic second derivatives have been developed' for the MP2. In this work we extend our tests to include systems with Fe, because the Fe atom population in FeL and FeL+ can be between six and seven 3d electrons and correlation is known to be important in correctly establishing the correct mixing of these two limits. We consider FeCO and FeCO+. Both are kn0wn*3~ to bond from the Fe excited state with a 3d7 occupation because this maximizes Fe to CO 2n* donation, which is much larger for FeCO than for FeCO+. We study FeH20+, which is known1° to bond from the 3d64s1Fe+ ground state. There is very little dative bonding in this case. We also study FeC&+, where the bonding mechanism is expected to involve C& to metal The MCPF calculations of Perry and Goddard12 predict a quartet state, while Schultz and Armentrout13predict a sextet state. However, this latter prediction is based only on the trends in the experimental successive binding energies for Fe(CH&+. 11. Methods The geometries are optimized using a small basis set, and final binding energies are computed using the MCPF approach in a large basis set. The large Fe basis set is the (20s12p9d6f4g)/ [(6 f l)s(5 l)p4d2flg] described p r e v i o ~ s l ywith , ~ ~ a set of g polarization functions included. The remaining large basis sets are the augmented correlation consistent polarized valence triple-zeta sets of Dunning and c o - w o r k e r ~ .The ~ ~ small Fe set is a [8s4p3d] contraction of the (14s9p5d) primitive set developed by Wachters.16 The s and p spaces are contracted using contraction number 3, while the d space is contracted (31 1). To this basis set are added two diffuse p functions; these are the functions optimized by Wachters multiplied by 1.5. A diffuse d f ~ n c t i o nand ' ~ an f polarization (a = 1.339) are added.

+

This article not subject to US.Copyright. Published 1994 by the American Chemical Society

J. Phys. Chem., Vol. 98, No. 38, 1994 9499

Systems Involving First Transition Row Metals

TABLE 1: Computed Separation (kcaymol) and Error of Fe sD(3d64s2)-5F(3d74s1) and Fe+ 6D(3d64s1)-4F(3d7Y' Fe 5D(3d64s2)-5F(3d74s') error Fe+ 6D(3d64s1)-4F(3d7) error

UHF

MP2

MCPF

43.4 23.3 38.0 32.2

16.4 27.0 (249) 6.9 (4.4) -3.7 4.2 10.4 (7.89 -1.6 4.6 (2.0)

CCSD(T)

exptb

26.1 6.0 8.3 2.5

20.1

5.8

"The results obtained from the large basis set are given in parentheses. Reference 26. The separation including the +R correction is 31.3 kcal/mol. d The separation including the +R correction is 16.1 kcdmol.

'

TABLE 2: Summary of the FeCO+ 4Z- Result9 FeCO+ r(Fe -C) r(C-0) De De(C0rr) De(ME geo) w(bend) o(Fe-CO) o(C-0)

co

r(C-0)

UHF

MP2

MCPF

CCSD(T)

2.139 1.098 -29.0 3.9

1.880 1.145 26.6 25.0

1.922 1.136 20.0 (25.8') 24.6 (27.8') 19.8

1.910 1.140 23.1 25.6 23.0

264 243 2522

321 405 2153

1.108

1.146

1.139

1.143

The final Fe basis set is of the form (14sllp6dlf)/[8~6p4dlfl. o e 2432 2110 The hydrogen basis set is the scaled (4s)/[2s] set of Dunning The results for free CO are given for comparison. The bond lengths and Hay,'* supplemented with a diffuse s (0.071) and three p are in A. The harmonic frequencies are in cm-l. The dissociation (1.2, 0.40, and 0.13) functions. The diffuse s and p functions energy (in kcdmol) is given with respect to Fe+ 6D(3d64s1). The are added to describe the polarizability of C a . The C and 0 dissociation energies computed using the MP2 geometries are given basis sets in CO and 0 basis set in H20 are [4s3p] contractions as De(MP2 geo). The results in parentheses are for the large basis set. The result including the +R correction is 20.9 kcdmol. The result of the (9s5p) primitive set optimized by Huzinaga.lg A d including the +R correction is 31.2 kcdmol. polarization function is added; the exponents are 0.75 for carbon and 0.85 for oxygen. The s space is contracted (5211). A makes the results much worse, because the relativistic effects smaller [3s2p] contraction18of the same C primitive set is used stabilize the states with a 3d6 occupation relative to those with for CH4. In addition, the C d function is not included in the a 3d7 occupation. FeCI&+ calculations. Only the pure spherical harmonic comIn Table 2 we summarize the results for the 42- state of ponents of the basis functions are used in all calculations. FeCO+. This state arises from the excited 4F state of Fef. We The orbitals are optimized at the SCF level. Correlation is first note that the UHF geometry and binding energy differ added using the MP2 approach, the MCPF method, and the significantly from the three treatments that include electron coupled-cluster singles and doubles approachz0 including a correlation. The MP2 binding energy is slightly larger and the perturbational estimate of the connected triple excitationsz1 r(Fe-C) is slightly shorter than those obtained at the MCPF or [denoted CCSD(T)]. The MP2 and CCSD(T) approaches are CCSD(T) levels. The UHF has a smaller r(C0) and higher based on a spin-unrestricted SCF (or unrestricted Hartree-Fock, CO frequency than those at the correlated levels. However, by UHF) wave function, while the MCPF calculations are based comparison with the results for free CO, it is clear that a large on a spin-restricted SCF wave function. In these calculations part of the UHF problem arises from the description of CO and only the valence electrons are correlated. not in describing the Fe-CO bonding. In all cases the r(C0) The most important relativistic effects, the mass velocity and is slightly shorter and the CO frequency is higher than in the Darwin terms, are included using fist-order perturbation theoryz2 free CO. This is due to the CO+ character that mixes into the for the MCPF results in the large basis set. The inclusion of wave function, and free CO+ has a shorter bond length and this term is denoted by S R . higher frequency than free CO. The shift in frequency at the The geometries were optimized and the vibrational frequenUHF level is larger than at the MP2 level. This combined with cies computed at the SCF and MP2 level using analytic second the longer Fe-C bond and lower Fe-CO frequency suggests derivatives. The CCSD(T) and MCPF geometries were optithat the UHF is underestimating the Fe to CO 2x* donation. mized using only the energies. The MCPF calculations were performed using the SEWARD-SWEDEN program s y ~ t e m * ~ , ~ This ~ donation weakens the C-0 bond and strengthens the Fe-C bonding. while the remaining calculations were performed using Gaussian 9LZ5 The calculations were performed using the NASA Ames The Fe atom has the occupation 3d013d?t'3ddz to maximize Central Computer Facility CRAY C90 or Computational the Fe to CO 2n* donation. At the UHF level the 4C- state of Chemistry IBM RISC Systed6000 computers. FeCO+ is computed to lie above the ground state asymptote (Fe+ 6D plus CO lX+). This arises because of the large error 111. Results and Discussion at the UHF level in the 4F-6D Fe' separation. In order to minimize the effect of the error in the atomic 4F-6D separation As noted above, the bonding in the FeL and FeL+ systems on the calculation of the dissociation energy, we compute the can involve those occupations with either six or seven Fe 3d binding energy with respect to Fe+ 4F plus CO 'E+and correct electrons. Therefore, we first consider the Fe 5D(3d64s2)this to the ground state asymptote using the experimental 4F5F(3d74s1) and Fe+ 6D(3d64s1)-4F(3d7) separations at the 6D Fe+ separation; this corrected value is denoted D,(cor). This different levels of theory considered in this work; the results results in an improvement, but the UHF value is still signifiare summarized along with experimentz6 in Table 1. Because cantly smaller than the other three. Also note that this correction it is well-knownz7that states with different 3d occupations have improves the agreement between the MP2 and MCPF or CCSDlarge differential correlation effects, it is not surprising to find (T) levels of theory. Thus, most of the overbinding at the MP2 errors of more than 20 kcal/mol at the UHF level. Adding level arises because of the error in the 4F-6D separation in Fe+ correlation at the MP2 level of theory leads to a smaller error and not in the description of the Fe-CO bonding. The current with the opposite sign. The higher level MCPF and CCSD(T) MCPF results are very similar to those reported previously8 results are in good agreement with each other and in good using a slightly different Fe basis set. Using the MP2 geometry agreement with experiment. The MCPF and CCSD(T) apresults in only a very small error in the binding energies proaches do not lead to an overshoot of the differential computed at the MCPF or CCSD(T) levels of theory. correlation effects and hence have an error with the same sign Using the large basis set increases the binding energy by as the UHF. The MCPF results in the big basis set are in better almost 6 kcal/mol. If the +R correction is added, the binding agreement with experiment. However, adding the +R correction

Ricca et al.

9500 J. Phys. Chem., Vol. 98, No. 38, 1994

TABLE 3: Summary of the FeCO W Result@ FeCO r(Fe -C)

r(c-0)

De De(C0rr) D,(MP2 geo) w(bend) o(Fe-CO) w(C-0)

co

r(C-0) we

UHF

MP2

MCPF

1.981 1.119 -50.8 -27.5

1.954 1.150 2.3 -1.4

1.898 1.158 -7.0(-2.3') -0.1 (2.1')

266 296 2218

178 425 2352

1.108 2432

1.146 2110

CCSD(T) 1.899 1.159 -7.0 -1.0 -7.4 414 2020

1.139

1.143 2138

The bond lengths are in A. The harmonic frequencies are in cm-l. The dissociation energy (in kcdmol) is given with respect to Fe 5D(3d64sZ).The values in parentheses are computed using the large basis set. The result including the +R correction is -5.9 kcdmol. The result including the +R correction is 5.3 kcaymol.

energy is very similar to that obtained with the small basis set. However, as the De(corr) results show, this is a result of the f R increasing the error in the 4F-6D atomic separation. The +R increases the binding energy at the De(C0rr) level. The difference between the CCSD(T) and MCPF results in the small basis set suggests that the MCPF D,(corr) results are too low by 1 kcal/mol. Thus our best DOvalue is obtained by adding 1 kcal/mol to the De(COrr) computed with the big basis and the MP2 frequencies; this value of 30.7 kcal/mol is in excellent agreement with the experimental valuez8 of 31.3 f 1.8 kcaU mol. In addition to bonding from the excited state of Fe+, it is possible to bond from the 6D(3d64~1)ground state. The occupied 4s orbital will yield a larger Fe-CO repulsion than in the 4C- state, and the Fe-CO n bonding will be weaker for the state derived from 6D as there are only three 3dn electrons for donation to the CO 2n* orbital. However, there is no atomic promotion energy for the 6D derived state. Previous calculations8 have established the ground state of FeCO+ to be 42-; however, it is of interest to ask what level of theory is required to determine the ground state. At the UHF level, the 6D derived state is bound by 7.1 kcdmol compared with -29.0 for the 4Z- state. The MP2 result of 14.0 kcaymol is very similar to the CCSD(T) result of 13.3 kcal/mol. So while the UHF level of theory incorrectly predicts the ground state, already at the MP2 level the correct ground state is predicted. Also note that the UHF level leads to an Fe-CO bond distance that is 0.17 A too long, which is slightly smaller than the 0.26 8, error found for the 4Z- state. This is probably a result of the smaller Fe 3d to CO 2n* donation for the state derived from the 3d64s1 occupation. The next system that we consider is the a5Z- state of FeCO. This state is derived from the Fe 5F(3d74s1)excited state. Relative to the 4Z- state of FeCO+, this adds an electron to the Fe 4s orbital. The results for this system, summarized in Table 3, are somewhat different from those for FeCO+. We first note that the UHF geometry is in much better agreement with the MCPF than found for FeCO+. Apparently, the Fe to CO donation is sufficiently large that an underestimation of the effect at the UHF level (see the very small binding energy even at the De(corr)level) does not lead to the very long Fe-C bond length as for FeCO+. The MP2 is overbound as found for FeCO+. The MCPF and CCSD(T) results are in good agreement, and the use of the MP2 geometry leads to only a small error in De. The UHF and CCSD(T) approaches show an increase in the r(C-0) distance and decrease in we as expected for this bonding mechanism, Le., metal to CO 2n* donation. The MP2

unfortunately shows an increase in the CO vibrational frequency relative to free CO. This is not what is observed in experiment,2gwhere the CO fundamental in FeCO decreases by 153 f 15 cm-' relative to free CO. The analogous CCSD(T) decrease in the harmonic frequency is 118 cm-', which suggests that we are underestimating the Fe to CO 2n* donation. Also consistent with this is the underestimation of the Fe-CO frequency at the CCSD(T) level, where the computed harmonic frequency of 414 cm-' is smaller than the experimental fundamental of 460 f 15 cm-'. The MP2 Fe-CO frequency is in good agreement with the CCSD(T). The MP2 bending frequencies are in good agreement with the rather uncertain experimental result of 180 & 60 cm-I. We should note that optimizing the geometry and computing vibrational frequencies with all electrons correlated does not change the MP2 results significantly. Thus, the poor MP2 vibrational frequencies are not a result of mixing of the Fe 3s and 3p orbitals with the valence orbitals. Thus, while the MP2 geometry is acceptable, the vibrational frequencies are disappointing. The failure of the MP2 to yield accurate vibrational frequencies in a case where the CCSD(T) is in good agreement with experiment is not unique to transition metal systems. For 03, the CCSD(T) agrees30well with experiment for all three modes, while the MP2 is in error3l by more than 1000 cm-l for the asymmetric stretch. Smaller, but still significant, errors in the MP2 asymmetric NO2 stretch for ClONO2 have been reported;3z this is also a case where the CCSD(T) is accurate. To see whether the errors in the MP2 approach were related to the unrestricted wave function, the FeCO calculations were repeated using an RHF zeroth-order wave function and the z-averaged MP2 approach,33 denoted ZAPT2, which were computed using SEWARDRITAN.z3%34 The Fe-C bond length (1.806 A) is too short and the C-0 bond length (1.169 A) too long. That is, the ZAFT2 has errors of the opposite sign and are larger than those obtained using the UHF-based MP2. The ZAPT2 C-0 stretching frequency (1929 cm-l) is in much better agreement with the CCSD(T) result than the UHF-based MP2 method, but the Fe-CO stretch (489 cm-') is in somewhat worse agreement. Clearly, neither second-order perturbation approach works very well for this system. In the large basis set the MCPF+R De(corr) value is 5.3 kcaV mol. This increase in De with improved treatment is consistent with the vibrational frequencies that suggested that we were underestimating the De in the smaller basis set. The agreement between the CCSD(T) and MCPF suggests that the correction of higher levels of correlation treatment should be rather small. Using the CCSD(T) stretch and MP2 bending frequencies for the zero-point energy, leads to our best DOvalue of 4.4 kcal/ mol. To this we add on the experimentalz9 a5Z--X3Zseparation (3.2 kcdmol), yielding our best value for the ground state dissociation energy of 7.6 kcaymol. This is slightly larger than our previousg estimate of 5 kcaVmol because we underestimated the a52--X32- separation. Our best value of 7.6 kcaumol is in good agreement with the recent experimental results 9.9 f 3.729and 7.5 f 3.5 kcaVm01.~~(Note that we have reduced the experimentalvalues by 0.6 kcaVmol to correct the 298 K values to 0 K.) We consider FeH20+ as an example of bonding from the 6D ground state of Fe+. The leading attractive term is charge dipole. Mixing in of the 3d7 occupation as well as metal-toligand donation is expected to be small for this case. Thus, the bonding in this system is expected to be well described at the UHF level. The results, summarized in Table 4, confirm this expectation. The geometry and binding energies at all levels of theory are in good agreement. The largest differences are

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Systems Involving First Transition Row Metals

TABLE 4: Summary of the FeH20+ 6A1Result9 FeHzO+ r(Fe-0) r(0-H) L(H-0-H) De o(Fe-0 stretch) w(Fe out-of-plane rock) o(Fe in-plane rock) o(HOH bend) o ( 0 - H s stretch) o ( 0 - H a stretch) HzO 40-H) L(H-0-H) o(HOH bend) ~ ( 0 - Hs stretch) o ( 0 - H a stretch)

UHF

MP2

MCPF

CCSD(T)

2.150 0.951 107.4 29.7 325 409 549 1784 4024 4110

2.126 0.972 106.4 31.7 333 323 5 17 1675 3750 3851

2.121 0.970 106.6 32.1 (34.p)

2.119 0.972 106.5 32.2

0.944 106.1 1747 4129 4233

0.965 0.964 103.5 103.8 1654 3837 3956

0.966 103.6

"The results for free HzO are given for comparison. The bond lengths are in A. The harmonic frequencies are in cm-'. The dissociation energy (in kcdmol) is given with respect to Fef 6D(3d64s1). The value in parentheses is computed using the large basis set. The value including the +R correction is 33.9 kcaymol.

TABLE 5: Summary of the FeC&+ Result9 Fef 3d64s' $ r(Fe-C) De De(MP2 geo) Fe+ 3d64s1q3 r(Fe-C) De De(MP2 geo) Fe+ 3d7 $ r(Fe-C) De De(MP2 geo) Fe+ 3d7v3 r(Fe-C) 0, De(MP2 geo) De(corr)

UHF

MP2

2.880 3.5

2.690 7.3

MCPF

CCSD(T)

2.694 7.6 7.6

[2.690]

2.572 8.0 (10.7b) 8.0

[2.573] 8.4

2.516 -8.7

2.386 5.7 4.3

2.292 3.5 1.7

2.607 -13.8

2.386 -8.4

18.5

-10.0

2.162 6.5 (12.3') 4.5 11.1 (14.3d)

2.124 4.4 1.8 6.9

2.753 4.13

2.573 7.8

8.1

The Fe-C bond length is in A. The dissociation energy (in kcaV mol) is given with respect to Fe+ 6D(3d64s1). The values in square brackets are taken from the MP2 and not optimized. The values in parentheses are computed using the large basis set. bThe value computed using the +R correction is 10.8 kcaymol. The value computed using the +R correction is 5.8 kcaymol. dThe value computed using the +R correction is 16.1 kcdmol.

does not have C3"symmetry because of Jahn-Teller distortion, but the effect is very small, so that the Fe-H distances are essentially the same. Thus the use of symmetry by Perry and Goddard'* is justified. As a computational point, we note that the potential energy surface for the r3 structures is so flat that we were forced to compute the second derivatives at every point in the UHF and MP2 geometry optimization. Because of the number of degrees of freedom, the flat potential energy surface, and the small distortion from the free CH4 geometry, only the Fe-C distance was optimized in the MCPF and CCSD(T) calculations. We first consider bonding from the 3d64s1occupation of Fe+, which leads to a sextet state. The binding energies for the r2 and q3 geometries are very similar. In both cases, the MP2 and MCPF are in excellent agreement. In fact, the agreement was so good we did not optimize the geometry at the CCSD(T) level. The UHF geometry is significantly inferior to the MP2. That is the FeC&+ results are more similar to those for FeCO+ than for FeH20f. Thus, donation either from the metal to the ligand or ligand to the metal appears to be underestimated at the UHF level and results in metal-ligand bond lengths that are too long. The MP2, MCPF, and CCSD(T) binding energies are all in reasonable agreement. The results for the states derived from the 3d7 occupation, which give rise to a quartet state, are very different from those derived from the 3d64s1 occupation. Namely, both the UHF and the MP2 approaches yield Fe-C distances that are too long. For this case the MCPF and CCSD(T) are only in reasonable agreement for the geometry. In addition, the CCSD(T) shows that the MCPF approach yields a binding energy that is slightly too large. The MCPF D,(corr) value for the 3d7 derived state is larger than for the 3d64s1state, thus supporting a quartet state, while the reverse is true for the CCSD(T) results. The big basis set MCPF result for the sextet state is 2.7 kcaY mol larger than in the small basis set. The effect of improving the basis set is about twice as large (5.8 kcdmol) for the quartet state. Thus, at the MCPF level the De value for the quartet state is larger than for the sextet state. If the error in the Fe+ 4F-6D separation and +R effects are accounted for, the quartet state is 5.4 kcdmol below the sextet state. The CCSD(T) results suggest that the MCPF calculations are biased toward the 3d7 configuration by 2.5 kcdmol. Thus, even after applying a correction for higher levels of correlation the MCPF would still predict that the ground state is a quartet state. Perry and Goddard12 also predicted a quartet ground state for FeCH4+. The MP2 zero-point contribution to the binding energy is -0.003 and -1.27 kcal/mol for the quartet and sextet states, respectively. Our best estimate for the quartet state DOvalue is 13.6 kcdmol, which is computed by correcting the MCPF+R result with the difference between the CCSD(T) and MCPF results in the small basis set. The best estimate for the sextet state, computed in an analogous manner, is 9.9 kcal/mol. Both results are in reasonable agreement with the experimental result13 of 13.7 f 0.8 kcaYmol. A comparison with the experimental results therefore suggests that the ground state of FeC&+ is a quartet derived from the 3d7 occupation. Thus, we favor the assignment of Perry and Goddard that the ground state is a quartet.

found for the harmonic frequencies of the intra-water modes. However, the effect of correlation on the frequencies of these modes is also found for the free H2O. The results in the large basis set are very similar to those in the small basis set, and the +R effect is very small because the Fe+ is 3d64s1at both equilibrium and infinite separation. Our De in the large basis set is 1.4 kcdmol smaller than that reported previously. lo Apparently, the smaller basis set used previously lead to a slight overestimation of the binding energy. Our best DOvalue comes from the MCPF in the large basis set corrected with the MP2 zero-point energy; this yields 32.5 kcal/mol. This is in good agreement with the experimental values 30.6 & l.2,13 IV. Conclusions 32.8 f 4,36 and 28.8 f 3 kcaYm01.~~ For the Fe-containing compounds studied in this work, the The final system that we consider is FeCH4+, which is summarized in Table 5 . Previous work has s h ~ w n that ' ~ ~ ~ ~geometries computed at the MP2 level of theory are in better agreement with those computed at the MCPF or CCSD(T) levels electrostatics favor an v3 structure, but C& to metal donation than those computed at the UHF level. However, for the quartet favors an v2 structure. The C& geometry is only slightly state of FeC&+, the MP2 Fe-C distance is 0.26 A too long. distorted from that in free C& so we only report the Fe-C We have also found that for FeCO the MP2 shift in the CO distance. The v2 structure has C;?" symmetry. The v3 structure

9502 J. Phys. Chem., Vol. 98, No. 38, 1994

frequency relative to free CO has the wrong sign when compared with the CCSD(T) results. In general, the energetics at the MP2 level are in reasonable agreement with the MCPF and CCSD(T), with the one exception being the quartet state of F e C b + . We conclude that the MP2 can supply reasonable geometries and vibrational frequencies for many f i s t transition row containing systems but that some caution must be used as we have found some cases where the MP2 results differ from higher levels of correlation treatment. We conclude that the ground state of FeCH4+ is a quartet state with q3 coordination. Acknowledgment. We thank T. J. Lee and L. A. Barnes for helpful discussions. A.R. acknowledges an NRC fellowship. References and Notes (1) The application of ab initio electronic structure calculations to molecules containing transition metal atoms. Bauschlicher, C. W.; Langhoff, S. R.; Partridge, H. In Modem Electronic Structure Theory; Yarkony, D. R., Ed.; World Scientific Publishing: London, in press. (2) Sodupe, M.; Bauschlicher, C. W.; Langhoff, S. R.; Partridge, H. J . Phys. Chem. 1992,96,2118. Rosi, M.; Bauschlicher, C. W. Chem. Phys. Lett. 1990,166, 189. Bauschlicher, C. W.; Langhoff, S. R. J . Phys. Chem. 1991, 95, 2278. (3) Siegbahn, P. E. M.; Svensson, M. Chem. Phys. Lett. 1993, 216, 147. (4) Maitre, P.; Bauschlicher, C. W. J . Phys. Chem. 1993, 97, 11912. (5) Chong, D. P.; Langhoff, S. R. J . Chem. Phys. 1986,&4,5606. Also see: Ahlrichs, R.; Scharf, P.; Ehrhardt, C. J. Chem. Phys. 1985, 82, 890. (6) Pople, J. A.; Binkley, J. S.; Seeger, R. Int. J . Qwntum Chem. Symp. 1976, 10, 1. (7) Handy, N. C.; Amos, R. D.; Gaw, J. F.; Rice, J. E.; Simandiras, E. D. Chem. Phys. Lett. 1985, 120, 151. (8) Barnes, L. A.; Rosi, M.; Bauschlicher, C. W. J . Chem. Phys. 1990, 93, 609. (9) Barnes, L. A.; Rosi, M.; Bauschlicher, C. W. J. Chem. Phys. 1991, 94, 2031. (10) Rosi, M.; Bauschlicher, C. W. J . Chem. Phys. 1989,90,7264;1990, 92, 1876. (11) Perry, J. K.; Ohanessian, G.; Goodard, W. A. J. Chem. Phys. 1993, 97, 5238. (12) Perry, J. K.; Goodard, W. A. These calculations are described in the PhD. thesis of J. K. Perry, Califomia Institute of Technology, 1993. (13) Schultz, R. H.; Armentrout, P. B. J . Phys. Chem. 1993, 97, 596.

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