J. Phys. Chem. 1983, 87, 3273-3279
3273
Localized Molecular Orbital Studies of Transition-Metal Complexes. 1. Simple Octahedral Complexes of General Formula (NH,),M-L, M = Sc3+, Cr', Mn', Fe2+, Co3+, or Zn2+, and L = H-, NH,, CHf, F-, CI-, or H,O Dennis S. Marynlck' and Carol M. Klrkpalrlck DepaHment of Chemistty, The University of Texas at Arllngton, Arlington, Texas 760 19 (Recelved: October 28, 1982; I n Final Form: February 22, 1983)
Localized molecular orbitals are presented for a series of simple transition-metal complexes with the formula (NH&M-L, M = Sc3+,CrO, Mn+,Fe2+,Co3+,or Zn2+,and L = H-, NH3, CHS-,F,C1-, or H20. Wave functions are calculated by using the PRDDO approximations and are localized by employing the Boys criterion. The localized orbitals in the M-L region are examined in detail. For each localized orbital, an electron density contour map is presented, along with a population analysis which includes atomic populations, hybridization, and percent delocalization. Trends in the amount of d-orbital participation, bond polarity, and inner-shell hybridization are discussed in terms of the formal charge on the metal and the d-orbital occupancies. For scandium complexes, the localized representation of ligand to metal T bonding is discussed.
Introduction It has often been noted that highly accurate quantummechanical calculations on molecular systems will not replace the need for simplified schemes and concepts, such as chemical bonds, since the molecular orbital methods produce orbitals which are delocalized over the entire molecule and do not directly represent the chemical bond. Various mathematical transformations exist which will convert these delocalized molecular orbitals into localized molecular orbitals (LMO's) without changing the total wave function or energy. Among the best known criteria for defining LMO's are those of Edmiston and Ruedenberg' (ER) and Boys.2 The ER method maximizes the orbital self-repulsion energy J J =
Y (4i(l) 4i(2)ll/rizl+i(l) ~ ( 2 ) )
i=l
while the Boys method maximizes the sum of squares (SOS) of displacements of the orbital centroids from an arbitrarily defined molecular origin. occ
SOS = C (dilQ4i)2 i=l
It can be shown that the Boys method also minimizes the orbital self-extension E
E =
E
i=l
(w)
4i(2)lri214i(l) 4 ~ 2 ) )
These two criteria yield similar LMOs for most molecules, but, because the ER approach requires a computationally difficult four-index transformation of the two-electron integrals, it has been less widely applied in recent years. The Boys approach, which requires only the easily obtainable one-electron dipole moment integrals, is computationally fast and is the method of choice of the study of LMO's in large molecules. For simple organic molecules, these methods yield LMO's which correspond closely to the chemist's traditional concepts of bonds, lone pairs, and inner shell^.^!^ (1) Edmiston, C.; Ruedenberg, K. Reu. Mod. Phys. 1963, 35, 467.
(2) Boys, S. F. In "QuantumTheory of Atoms, Molecules and the Solid
State"; Gwdin, P. O., Ed.; Academic Press: New York, 1966;pp 253-62.
(3) For a review discussing the meaning of localized orbitals, see: England, W.; Salmon, L. S.; Ruedenberg, K. Top. Curr. Chem. 1971,23, 31. 0022-36541a3120a7-3273$0 I .5010
More importantly, for complex molecules such as boron hydrides,6 carboranes? and beryllium compounds,' in which localized bonding descriptions are not always obvious, LMO calculations provide objective bonding descriptions which are often useful in understanding the molecular structure. In addition, while LMO's are not intrinsically symmetry based (individual LMOs do not in general transform as irreducible representations of the point group of the molecule), they can be used as a basis for forming symmetry-adapted orbitals which are often useful for qualitative examination of other molecular properties. Such an approach is implicit in much of the application of orbital symmetry rules to organic chemistry.8 While a large number of LMO studies on molecules containing only f i t - r o w atoms have appeared, there has been less work of this type involving atoms in the second major and almost none on transition-metal complexes.1° There are two obvious reasons for the sparsity of LMO work on transition-metal systems. First, the large size of such molecules has until recently made the calculation of suitably accurate wave functions (the starting point of any LMO calculation) very difficult and computationally expensive. Second, bonding patterns in transition-metal complexes have traditionally been interpreted in a symmetry basis, in part because of the early success of crystal and ligand field theories (both of which are symmetry based) and in part because of the widespread utilization of spectroscopic methods (which are also intrinsically symmetry based) for characterizing these complexes. In this paper, we initiate a series of LMO calculations on transition-metal complexes using the PRDDO molecular orbital approximationl1J2and the Boys2localization (4) Newton, M. D.; Switkes,E.; Lipscomb, W. N. J. Chem. Phys. 1970, 53,2645. Kleier, D. A.;Dixon, D. A.; Lipscomb, W. N. Theor. Chim. Acta 1975, 40, 33. Dixon, D. A.; Lipscomb, N. W. J.Biol. Chem. 1976,251, 5992. (5) Dixon, D. A.;Kleier, D. A.; Halgren, T. A.; Lipscomb, W. N. J. Am. Chem. SOC.1976, 98,2086. (6) Dixon, D. A.; Kleier, D. A.; Halgren, T. A.; Hall, J. H.; Lipscomb, W. N. J. A m . Chem. SOC.1977, 99,6226. (7) Marynick, D. S. J. Am. Chem. SOC.1977,99, 1436. (8)Woodward, R. B.; Hoffman, R. "The Conservation of Orbital Symmetry";Verlag Chemie: Weinheim, West Germany, 1970. (9) See, for instance: Guest, M. F. Hillier, J. H.; Saunder, V. R. J. Chem. SOC.,Faraday, Trans. 2 1972, 68, 867. (10) Qualitative discussions of LMO's in ferrocene and CoFe3-have appeared Hoffman, D. K.; Ruedenberg, K.; Verkade, J. G. In "Structure and Bonding";Dunitz, J. D., Hemmerich, P., Ibers, J. A., Jorgensen, C. K., Neilands, J. B. Reinen, D., Eds.; Springer-Verlag: West Berlin, 1977; Vol. 33, pp 57-96.
0 1983 American Chemical Society
3274
The Journal of Physical Chemistry, Vol. 87, No. 17, 1983
Marynick and Kirkpatrick
TABLE I: Transition-Metal Basis Sets' metal
state
Is
2s
3s
4sb
sc Ti V Crd Mn Fe
'D
20.279 21.242 22.204 23.169 24.130 25.092 26.055 27.017 27.980 28.942
8.168 8.642 9.116 9.591 10.060 10.532 11.003 11.474 11.945 12.415
3.195 3.428 3.656 3.848 4.098 4.322 4.542 4.760 4.977 5.192
1.175 1.233 1.286 1.263 1.376 1.427 1.474 1.518 1.562 1.604
co Ni cu Zn
3F
"F
7s
6S 'D "F 'F *D 'S
3dC
3 dC 1.6955 1.9511 2,1241 2.0068 2.4878 2.5980 2.7258 2.8553 2.9868 3.1090
(0.76395) (0.75386) (0.73643) (0.72427) ( 0 . 7 2849) (0.71883) ( 0.71 171) (0.70563) (0.70076) ( 0 . 6 93 9 5)
4.1519 4.6236 4.9598 5.0305 5.7442 6.0488 6.3695 6.6904 7.0143 7.3176
(0.36531) (0.36890) (0.38610) (0.42078) (0.39252) (0.40625) (0.41563) (0.42349) (0.42976) (0.43822)
' From ab initio atomic SCF calculations. The 2p and 3p orbitals are constrained to have the same exponent as the corresponding s orbital. The 4s and 4p orbital exponents were set to 2 . 0 for the molecular calculations (see text). The number in parentheses is the expansion coefficient from the atomic calculation, which is used directly as the contraction coefficient for the molecular calculations. The 'S state arises from orbital occupancies of 3d54s'. This basis set yields excellent metal-ligand optimized bond lengths in (CO),Cr (error = 0.01 A ) and (C,H,),Cr (error = 0 . 0 2 A ) . criterion. The PRDDO method, recently extended12 to include atoms through the first transition series, closely reproduces ab initio self-consistent field calculations with a minimum basis set of Slater orbitals, while requiring a fraction of the computational time. The PRDDO method is particularly useful here, since PRDDO computing times have a basic n3 dependence (where n is the basis set size) rather than the n4dependence typical of ab initio methods. This will result in dramatic savings in computing time for the large systems studied here and in future papers. We initiate our LMO studies by examining a series of very simple octahedral complexes of general formula (NH,),M-L, with all possible combinations of M = Sc3+, Cro,Mn+,Fe2+,Co3+,or Zn2+,and L = H-, NH3, CH,, F, Cl-, or H20. The pseudooctahedral environment provides for straightforward orbital interactions, while the relatively strong field ammonia ligands stabilize the low-spin, closed-shell states of these complexes-the simplest to analyze. For CrO, Mn+, Fez+,and Co3+(all d6 metals) we have also studied and briefly discuss the LMO's of the complexes (CO),M-NH,, which provide better models of diamagnetic complexes for chromium, manganese, and iron. Our primary interest is in how the LMO's and electron density in the M-L region change as the metal or ligand is varied. Characterization of the M-L LMO's will be accomplished with the aid of electron density contour plots and standard population analyses. Hybridization, percent delocalization, and hybrid bond angle deviations (when significantly different from zero) are also reported, as are inner-shell hybridizations and hybrid orientations. In this initial work we have deliberately focused our attention on simple ligands in which t~ bonding is expected to dominate in most instances (the exceptions being the scandium complexes with fluorine and chlorine, in which ligand to metal P bonding is important). In future papers13 we will extend our studies to include ligands which are good P acceptors (such as CO, NO+, CN-, and pyridine), different stereochemistries, and olefin complexes. Calculations
For all atoms except the transition metals, a minimum basis set was employed, with exponents given by Hehre et al.'* The transition-metal basis sets were also minimal, except that the 3d orbitals were represented by a fixedcontracted linear combination of two Slater orbitals. For (11) Halgren, T. A.; Lipscomb, W. N. J. Chem. Phys. 1973,58, 1569. (12) Marynick, D. S.;Lipscomb, W. N. Proc. Natl. Acad. Sci. U.S.A. 1982, 79, 1341.
(13) Marynick, D. S.;Kirkpatrick, C. M., work in progress. (14) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J. Chem. P h p . 1969,51, 2657. Hehre, W. J.; Ditchfeld, R.; Stewart, R. F.; Pople, J. A. Ibid. 1970, 52, 2769.
computational efficiency,12the exponents of the following orbitals were constrained to be equal: 2s = 2p, 3s = 3p, and 4s = 4p. All exponents and contraction coefficients were obtained from fully optimized ab initio atomic SCF calculations, except that the exponents of the 4s and 4p orbitals were taken to be 2.0. Preliminary work (see below) has shown that this value yields remarkably accurate optimized bond lengths in many different transition-metal complexes. Because transition-metal basis sets of this type have not to our knowledge been described previously and may be useful in other molecular orbital methods that constrain s- and p-orbital exponents, we list in Table I the optimized basis sets for the complete first transition series. The accuracy of our PRDDO calculations relative to ab initio calculations with the same basis set has been previously documented for 12 simple compounds containing transition-metal centers.12 Briefly, average absolute errors in total energy (0.056 au), HOMO eigenvalues (0.011 au), LUMO eigenvalues (0.014 au), Mulliken charges (0.038e), overlap populations (0.051, and dipole moments (0.280 D) are only moderately larger than the earlier first-row-atom version of PRDD0,'l while very few new empirical parameters have been introduced (none for transition-metal interactions). In addition, PRDDO has been shown to be useful15 in assessing relative conformational energies of Fe(C0)4(C2H4).The equatorially substituted trigonal bipyramidal ground-state geometry is correctly predicted, and the relative energies of several other conformers are given to within an average error of -6 kcal/mol when compared to the ab initio double-zeta results of Demuynck, Strich, and Veillard.16 Finally, PRDDO optimized metal-ligand bond lengths" agree remarkably well with experiment (average absolute error = 0.03 .&for the limited set of compounds studied to date (Cr(CO),, Cr(C6H,J2, M~I(CO)~H, Mn(CO),Cl, Fe(CO),, Fe(C5H5)2,Co(NH3):+, CO(NH~),(SCN)~+, and Ni(C5H5)(NO))using the basis sets given in Table I. Because of the large number of transition-metal complexes studied, standard geometries were adopted for all calculations except in a few instances described below. Experimental distances for Cr(CO)6,18Mn-H,l9 Fe-CH3,20 Fe-C0,20 Fe-OH2,21Fe-F,22 CO-NH,,~~ C O - O H ~Zn-0,~~ (15) Marynick, D. S.; Axe, F., in preparation. (16) Demuynck, J.; Strich, A.; Veillard, A. Nouu. J. Chim. 1977,1,217. (17) Marynick, D. S.; Kirkpatrick, C. M.;Throckmorton, L.; Axe, F., work in progress. (18) Whitaker, A,;Jeffrey, J. W. Acta Crystallogr. 1967, 23,977. The actual distance used was 0.005 A longer than that reported in this reference. (19) Kaest, H. D.; Saillant, R. B. Chem. Reu. 1972, 72, 231. (20) Goedkem, V. L.; Peng, S. J. Am. Chem. SOC.1974, 96,7826. (21) Clark, D. W.; Farrimond, M. S. J. Chem. SOC.A 1971, 2, 299. (22) Allen, G. C.; Clack, D. W. J. Chem. SOC.A 1970, 16, 2668. (23) Kalman, B. J.; Richardson, W. J . Chem. Phys. 1971, 55, 4443.
The Journal of Physical Chemistry, Vol. 87, No. 17, 1983
Localized MO Studies of Transltlon-Metal Complexes
TABLE 11: Standard Bond Distancesa metal
H-
sc3+
3.220 Cro 3.120 Mn+ 3.030 Fe 2+ 2.970 Co3+ 2.850 Zn2+ 3.210
CH,- NH, 4.185 4.170 4.080 3.930 3.810 4.180
4.118 4.100 4.010 3.863 3.740 4.110
H,O
F-
C1-
3.940 3.935 3.840 3,720 3.680 3.930
3.810 3.790 3.700 3.550 3.430 3.800
4.590 4.570 4.480 4.336 4.210 4.580
CO
TABLE 111: Metal-Hydrogen LMO's in (NH, ),M-H Complexes hybridization population
3.500 3.410 3.350 3.400
Atomic units.
complex (NH,),ScH2+ (NH,),CrH(NH,),MnH (NH,),FeH+ (NH,),CoHZ+ (NH,),ZnH+
SC3'
-L-
Zn-L-
M
H
M
delocalization,
H
% I
spl."ds.z - 0.66 1 . 3 4 ~ p O * ~ d "* ~ 0.28 1.72 sp"*6d"*7 - 0.31 1 . 6 9 ~ p ~ . ~ -d ~0 . 5*2 ~ 1 . 4 9 ~ p ~ * ~ d ~ 0.95 * * ~ 1.06 ~pO*~d'' - 0.21 1 . 7 9
Cr'
M""
6.0 6.4 7.6 8.3 6.4 12.2
co3'
Fez'
Zn"
Flgure 2. Metal-hydrogen LMO's for (NH,),M-H complexes. The contour levels for thls plot and all plots in thls paper are 0.5, 0.3, 0.1, 0.02, 0.005, and 0.002 e-/au3.
Y
unitary matrices. In all cases, convergence to a saddle point on the SOS surface was avoided. Hybridization of the metal and ligand orbitals was calculated in the usual fashion.28 Percent delocalization, defined as
L Flgure 1. Out-of-plane angle 8,Illustrated for an L,ZnOH;+
3275
complex.
H2,%and Mn-C125 were used directly, in some cases with the appropriate correction for the ionic radii difference between high- and low-spin complexes.26 All other distances were estimated from the above distances and the relative ionic radii of the various transition-metal ions, except for the Co-CO distance, which was taken as the average of distances in several different complexes. The standard bond lengths used are listed in Table 11. To determine the proper stereochemistry for water coordination to the transition metal, we optimized the angle t9 (Figure 1) for the complexes (NH3)5S~OH23+, (NH3)5FeOH22+, and (NH3)5ZnOH2+. In each case, we found 0 = 180°, corresponding to a situation in which each lone-pair orbital makes equal contributions to the metal-oxygen bonding. This stereochemistrywas also assumed to hold for Cro, Mn+, and Co3+. The 0-H bond length and H-0-H bond angle were taken as 1.810 au and 104.5O, respectively. The assumed geometries for NH, and CH,were N-H = 1.928 au, H-N-H = log', C-H = 2.060 au, and H-C-H = 109'. Because complexes of the type (NH3)5M-L (M = CrO, Mn+,or Fe2+)are expected to have high-spin ground states, we have also studied the complexes (CO)5M-NH3 for all d6 metals. These complexes should be more realistic models of compounds with closed-shell ground states, which is a prerequisite for the Boys localization procedure. The C-0 distance in C z O was set at 2.132 au (the experimental distance in free carbon monoxide). Localization of the molecular orbitals was accomplished by the Boys criterion2 as implemented in the PRDDO pr~gram.~'Convergence was judged by the limited second-derivative test2' and, when necessary, by multiple localization calculations with different starting random (24) Ray, S.; Zalkin, A.; Templton, D. H. Acta Crystallogr. Sect. B. 1973,29,2741. (25) Green, P. T.; Bryan, R. F. J. Chem. SOC.A 1971, 10, 1559. (26) Huheey, J. E. "Inorganic Chemistry"; Harper and Row: New York, 1978. (27) Kleier, D.; Halgren, T. A.; Hall, J. H.; Lipscomb, W. N. J . Chem. Phys. 1979,61, 3905.
D = (y21(4. - 4T)2du)1'2
X
100
where 4 L is a localized orbital and $T is the same orbital with all nonlocal contributions truncated and then renormalized, was also calculated. Nonlocal contributions to a LMO are (somewhat arbitrarily) considered to be those with less than 0.2e- on any atomic center. The bond angle deviation of each hybrid orbital (defined as the angle between the maximum in electron density of the hybrid orbital and the internuclear bond axis) was calculated and is presented if it is significantly different from zero. All PRDDO calculations were carried out on an IBM 4341 computer, and the electron density contour plots were calculated on a DEC 2060 computer. The CPU time requirements for PRDDO may be illustrated with Co(NH3):+ as a typical example: integrals (5.5 min), SCF (3.2 min, 10 cycles), localization (1.9 min, 15 iterations). Results and Discussion (NI3,)Jkf-L Complexes. We consider the (NH,),M-L complexes initially since the pure u donating properties of the ammonia ligands should make the LMO's relatively easy to analyze. For each complex, we have isolated the LMO (or LMO's) which correspond to the M-L bond. These LMO's are plotted in Figures 2-9. For ease of comparison, all LMO's describing bonds to the same ligand (e.g., all metal-hydrogen LMOs, all metal-fluorine LMO's, etc.) are grouped together in the same figure. In each case, the ligand of interest is positioned along the positive z axis, making the analysis of possible orbital interactions particularly simple. With respect to the M-L bond, metal u orbitals will be the 3d,z, 4s, and 4p,, and the metal K orbitals will be 3d,,, 3dy,, 4p,, and 4p,. The 3d,, and 3d,kYz orbitals have local 6 symmetry and will not be involved to a significant extent in the bonding. Our results are, of course, invariant to the molecular orientation. The results for hydrogen (Figure 2 and Table 111) are in many ways representative of all of the simple u donors studied here. All metal-hydrogen interactions are well(28) Switkes, E.; Stevens, R. M.; Lipscomb, W. N.; Newton, M. D. J. Chem. Phys. 1969,51, 2085.
3276
The Journal of Physical Chemlstry, Vol. 87, No. 17, 1983
TABLE IV: Metal-Ammonia LMO's in (NH,),M Complexes hybridization complex (NH,),Sc'+ (NH,),Cr (NH,),Mn+ (NH,),Fe*+ (NH,),Co3+ (NH,),Zn2'
M
population
N
M
~ p O * ~ d ~spZ.O .' 0.26 sp0.8do-4 S P ' . ~ 0.07 ~ p ~ . ~S Pd' .~~ .0 .~1 0 ~ p ~ * ~ d 'S.P' ' . ~ 0 . 1 8 sp'.Od"' sp2*O 0 . 3 2 ~pO.~d' S P ' . ~ 0.18
Marynick and Kirkpatrick
Nitrogen-
delocalization,
N
%
1.77 1.96 1.94 1.86 1.72 1.86
10.0 10.5" 11.F 13.8a 10.9 13.8"
Metal
Mn
Cr
SC"
.
co *
Fe"
Figure 3. Metal-nitrogen LMO's in (NH,),M
Zn
+
complexes.
" Based on a one-center orbital; see text. TABLE V : Metal-Methyl LMO's in (NH, )5M- CH, Complexes population
hybridization complex
M
C
(NH,),SCCH,~+~ p ~ . ~sp2.O d ~ (NH,).CrCH,- sDo.7do.s (NHijiMnCH, $0*7d0.5 s p 2 . 0 (NH,),FeCH,+ sp0*8d'.6 sp'.' (NH ,) ,CoCH, '+sp's4dI2 spr ' (NH,),ZnCH,+ spO.'dO sp*.O
sc
delocalization,
M
C
%
0.55 . ~ 0.18 0.22 0.40 0.91 0.42
1.48 1.85 1.81 1.64
11.3 12.9"
1.11 1.61
.
Fe"
Mn'
Cr
Zn"
CO"
Figure 4. Metal-carbon LMO's in (NH,),M-CH3
complexes.
10.0 11.4 11.4 13.5
" Based on a one-center orbital. localized, two-center LMO's, with percent delocalizations ranging from 6.0% to 12.2%. Participation of d orbitals (dZz)is clearly evident for all metals except zinc. The series CrO, Mn+, Fe2+,and Co3+show a characteristic pattern of d-orbital participation-as the charge of the metal increases, donation into the vacant dzz orbital increases (the chromium and manganese complexes appear to have about equal d-orbital contributions to the M-H bond). This trend is evident from both the density maps, where the characteristic dzz orbital shape increases in extent as the metal charge increases, and from the calculated hybridizations, which show increasing d character along this series. The hybridizations of the metal range from spo.ed0,7 in (NH3)5CrH-to sp1.5d11.2 in (NH3)5CoH2+(Table 111). It is interesting to note that the ligand-metal orbital overlap Hls-dzz actually decreases along this series (from 0.19 in the chromium complex to 0.11 in the cobalt compound). The increasing d character cannot therefore be attributed directly to orbital overlap, but is more likely due to the increasing formal charge on the metal, effectively making the metal more electronegative and the bond less polar. Mulliken charges on the metal parallel the formal charges, increasing from -0.25e- in (NHJ5CrH- to 0.93e- in (NH3)5CoH2+.The increase in the participation of metal orbitals in this series can also be seen by comparing metal populations in the M-H LMO (Table 111),where the Cr-H LMO is seen to be highly polar (0.28e- on Cr) while the corresponding Co-H LMO has nearly equal populations on H and Co. Scandium behaves in a manner similar to Fez+ and Co3+. The large metal charge (3+) results in important d-orbital contributions (the hybridization is and the bond polarity is intermediate between that sp1.0d6.2 of Fe-H and Co-H). Thus, for simple u donors like H-, the d-orbital occupancy (doin Sc3+or d6 in Fez+and Co3+) has little effect on the resultant M-H LMO's. In effect, the Boys localization criterion successfully distinguishes between bonding ( u ) and nonbonding (d,) electrons, separating them cleanly in the d6 case. The zinc complex, with a d10 configuration, shows essentially no d-orbital participation in the Zn-H LMO. This is, in fact, typical of all zinc complexes studied in this paper. The 4s and 4p, orbitals on zinc dominate the metal contributions to the Zn-H bond, with the largest contribution coming from the 4s orbital (the calculated hybridization is spo.').
sc
Cr
*
Fee*
Mn
Figure 5. Metal-fluorine LMO's in (NH,),M-F
SC"
cr
Fez'
Mn'
Zn"
co *
complexes.
Zn"
GO"'
Figure 6. Combination of the metal-fluorine LMO's shown in Figure 5 plus the three lonapair LMO's on fiuorlne.
TABLE VI: Metal-Fluorine LMO's in (NH,),M-F Complexes hybridization complex
M
F
population M
(NH,),ScFZ+ sp'*od26 sp5.' 0.37 (NH,),CrF- ~ p ~ * sp3.8 ~ d ~ 0.24 * ~ (NH,),MnF spo.8do.4sp4.0 0.27 ( NH ,) ,FeF + sp0.8d'. sp"' 0 . 4 1 (NH,),CoFz+ sp'*'d6.' S P ' ~ . ' 0.75 ( N H , ) , Z n F + sp0*'do sps3 0.43
delocalization,
F
%
1.62 1.76 1.73 1.59 1.25 1.58
3.7" 4.0 5.2 5.8 4.8 9.8
" For the u type LMO. LMO's for metal-ammonia interactions (Figure 3 and Table IV) and metal-methyl interactions (Figure 4 and Table V) parallel in all respects those obtained for the metal-hydrogen bonds. Metal-CH, orbitals are uniformly less polar than the corresponding metal-NH, orbitals, in accord with simple electronegativity arguments. If we use the admittedly arbitrary but chemically reasonable criterion that an atom is not participating in a localized bonding orbital unless it contributes at least 0.2e- to the LMO, most of the metal-ammonia LMO's (CrO, Mn+, Fez+,and Zn2+) and one metal-methyl LMO (CrO) are best described as coordinated one-center lone pairs, rather than two-center M-L LMO's. Hybridization of the nitrogen in NH, and carbon in CHf is in all cases between sp1.9and sp2.'. These values are not significantly different from the hybridizations of the lone-pair orbitals in free NH, (spZ.O)and CH3( S P ~ . ~This ) . is consistent with the fact that metal binding induces only small changes in the ligand bond angles,29and (29) For instance, the optimized H-N-H angle in (NH3),Co3+is 103.9', compared with 106' for free ammonia. The corresponding angles in (H20)Jn2+and H 2 0 are 106" and llOo, respectively.
Localized MO Studies of Transition-Metal Complexes
The Journal of Physical Chemistty, Vol. 87,No. 17, 1983 3277
TABLE VII: Metal-Chlorine LMO's in (NH,),M-CI Complexes hybridization
population
complex M C1 M (NH,),ScCl'+ ~ p ~ * S~P ' d . ~ ~0.28 * ~ (NH,),CrCl' spa.8d0.3sp3.2 0.08 (NH,),MnCl spa.8da.4sp3., 0.11 (NH ,) ,FeCl' spa. d'. sp3.4 0.21 (NH,),CoCIZt sp1*0d6.Zsp4.8 0.49 (NH,),ZnCl+ sp0.*d0 sp3*, 0.22 a
C1
delocalization, %
1.71 1.92 1.89 1.79 1.52 1.78
3.8 6.Sa 8.4a 5.5 5.3 7.4
Cr"
sc3*
Mn *
Fe"
Flgure 7. Metal-chlorine LMO's in (NH,),M-CI
ZnZ'
CO"
complexes.
Based on a one-center orbital.
thus little or no rehybridization. Metal-fluorine LMO's are shown in Figures 5 and 6 and Table VI. Fluorine is the first ligand in this study which has more than one lone pair available for metal coordination. In all cases, however, simple u LMO's similar to those found for the ammonia and methyl complexes are obtained. These are the orbitals plotted in Figure 5. Because fluorine has occupied nonbonding orbitals of local a symmetry, the possibility of ligand to metal a bonding exists. To investigate this possibility, we have plotted in Figure 6 the electron density associated with the sum of the three lone-pair LMO's on fluorine plus the M-F LMO. These plots clearly show ligand to metal donation for scandium (the only do complex studied here) but not for any other metal. This indicates that a donation into the vacant metal 4p orbitals (which is available to all the metals studied here) is not important, while donation into vacant a type d orbitals (available only for scandium) is an important part of the description of the Sc-F bonding interaction. This a type interaction is manifest in the LMO's by three equivalent delocalized lone-pair orbitals on fluorine with an average hybridization of percent delocalization of 14.0, and population of 1.92e- (F) and 0.08e- (Sc). These three lone-pair orbitals form a basis for both u and a donation to the metal, but the observed delocalization is almost exclusively into d, type orbitals. The Boys criterion, therefore, yields an LMO description of the Sc-F bond which to a large extent displays u-a separability, in marked contrast to Boys LMO's for simple organic molecule^.^ Because the extent of the a bonding would be expected to depend strongly on the Sc-F bond distance used, we have investigated the effects of varying the S c F distance on the calculated LMO's. As the Sc-F bond length is decreased to about 3.4 au, the LMO pattern changes. One lone-pair LMO is now found along the bond axis pointing away from the metal, while three equivalent bonding LMO's point toward the metal flanking the Sc-F bond axis. These three LMO's again form a basis for u and a bonding to the metal, with all three orbitals contributing equally to the bonding. Thus, u-a separation is destroyed. This is not unexpected since, as the Sc-F bond distance is decreased, the amount of a bonding increases and eventually the Boys criterion (maximizing the sum of the squares of the distances between orbital centroids) will force m r mixing. A similar study of the LMO's
Cr'
Sc"'
Mn *
Fe +
Co?'
Zn"
Flgure 8. Metal-oxygen LMO's in (NH3),M-OHp complexes in the HOH plane. Both oxygen lone-pair orbitals are shown.
Cr
Sc3'
Mn *
Fe *
Zr?'
C03'
Flgure 9. Metal-oxygen LMO's in (NH,),M-OH, complexes in the lone-pair plane. Both oxygen lone-pair orbitals are shown.
of (NH3)5ZnF+,in which a bonding of this type is not important, showed no change in the LMO's at any reasonable Zn-F distance (all calculations yielded one u LMO pointing toward the zinc and three equivalent and welllocalized lone-pair orbitals on fluorine). In summary, weak ligand to metal a bonding results in LMO's with good u-r separability, while stronger a interactions will yield equivalent orbitals. The exact orbital description obtained will depend on the amount of a bonding, but any LMO description of this kind of interaction will require at least three LMO's, and possibly four. The LMO's obtained from the (NH&M-Cl complexes are shown in Figure 7 and Table VII. In Figure 7, the small coefficients of the Is, 2s, and 2p orbitals on chlorine have been zeroed to remove the inner-shell nodal structure and simplify the plots. The metal-chlorine LMOs are very similar to those obtained for the metal-fluorine complexes, the major difference being a slightly smaller electron population on the metals in the M-Cl LMO. The eight electron interactions (including the bonding LMO and the three chlorine lone pairs) are not shown but are similar in all respects to those of fluorine (Figure 6). Again, a significantly shorter S d 1 bond distance (in this case -3.8 au) will force a change in the LMO pattern of the scandium complex similar to that observed for fluorine, but the LMO description of the Zn-Cl bond is essentially invariant with respect to the bond distance. LMO's for the (NH3),M-OH2 complexes are shown in the HOH plane in Figure 8 and in the plane perpendicular to HOH (the lone-pair plane) in Figure 9 (see also Table
TABLE VIII: Metal-Water LMO's in (NH,),M-OH, Complexes population
hybridization
M
0
SP'.,d4. Ida SP'. 'do. sP'.ado*8
sp2.3 spl" sp1.9 sp2.1 spZ.4 spa1
complex (NH,),ScOH," (NH,),CrOH, (NH,),MnOH,' (NH,),FeOHZ2+ (N H 3 ) , C o 0 H z 3 + (NH,),ZnOHZ2+
SP'.
8Pl.l
spl.'do
Averages of the two M - 0 LMO's.
delocalization,a
M
0
%
0.12
1.90 2.00 1.98 1.95 1.91 1.95
13.1
0.04 0.05 0.08 0.12 0.07
Degrees, oxygen hybrid only.
11.6 10.9 11.2 12.8 11.2
bond angle deviationasb 59.3 61.5 60.5 60.0 60.0 60.0
3278
The Journal of Physical Chemistry, Vol. 87,
No. 17, 1983
VIII). Both of these plots represent four-electron interactions, corresponding to both oxygen lone-pair orbitals. All oxygen-metal LMO's in these complexes are best described as delocalized lone pairs on oxygen, rather than two-center orbitals. The plots in the HOH plane (Figure 8) show the typical pattern of u donation found for all the ligands studied here, except that noticeable delocalization onto the hydrogens can now be seen. This delocalization is also found for an isolated water molecule and does not represent a new feature induced by coordination to the metal. In the lone-pair plane (Figure 9 ) , the two oxygen lone-pair orbitals form a basis for u and a bonding. Again, scandium clearly shows this ligand to metal a bonding, while the other metals do not. Water therefore acts as an anisotropic ?r donor, donating in the lone-pair plane, but not in the molecular plane. Inner-Shell Hybridization in (NH3)&f-L Complexes. The question of how the inner shells (especially the n = 3 shell) of the transition metals are represented in a localized framework is particularly important when the complexes contain good a-accepting ligands and metal to ligand back-bonding is expected. This is not the case for the simple (NH3)5M-L complexes studied here; however, we wish to discuss the inner-shell hybridizations found for these simple a-bonding complexes in order to lay the groundwork for future d i s c ~ ~ ~ iofo LMO's n ~ l ~ in complexes with many different a-accepting ligands, including CO, NO+, CN-, and pyridine. The discussion that follows will focus exclusively on the n = 3 shell. In all cases the Boys criterion cleanly separates the n = 3 shell from the n = 2 and n = 1 shells. For scandium, all complexes have inner-shell hybrids with hybridization very close to sp3 (varying from sp2., to sp3.3and averaging sp3.0). The orientation of the hybrids is only weakly coupled to the octahedral field of the ligands. On the average, the inner-shell hybrids make an angle of 33O with the nearest ligand-metal bond axis.3o The inner-shell hybrids of the de complexes all have approximately sp3d3 hybridization, with the minimum d-orbital contribution being sp3.0d2.3for one hybrid in (NH,),CrH-, and the maximum being sp2.gd3.soccurring once in (NH&,COCH~~+ and once in (NH,),COOH~~+. The average hybridization is sp3.0d2.9, and this average is essentially independent of the specific ligand and nearly independent of the metal (the average hybridizations range from sp3*0d2.8 for chromium to sp3.0d3.0for cobalt). The inner shells tend to avoid the metal-ligand bond axes, the average minimum angle between an inner-shell hybrid and a metal-ligand axis being 50° (the range is 43-55'). This angle is reasonably close to the maximum possible angle of -55O which would be obtained if a hybrid pointed directly toward the center of an octahedral face. The zinc complexes (d'O) have nine inner-shell hybrids and average sp3.0d5.'hybridization. The average angle between the hybrids and the nearest zinc-ligand axis is -32O, significantly smaller than that of the de complexes. The nine hybrids must, of course, lie closer to the ligand on the average than the seven hybrids in the d6 case.
-
(30) If we approximate the ligands by points with octahedral symmetry, and the inner shella by sets of four, seven, or nine points (depending on the d-orbital occupancy),then the Boys criterion of maximizing the sum of the squares of the distances between orbital centroids (or points in our example) is indeterminate, in that this s u m is invariant with respect to the relative orientation of the hybrid points and ligand points. This is true even if the hybrid pointa do not form a perfect solid. The method becomes determinate only when the octahedral ligand field and the hybrid centroids are distorted from high symmetries such as Td or Oh. Of course, none of the molecules studied here have perfect octahedral symmetry, so a discussion of inner-shell hybrid orientation remains valid.
Marynick and Kirkpatrick
TABLE IX: Metal-Ammonia LMO's in (CO),M-NH, Complexes hybridization population complex M N M (CO),CrNH, ~ p ~ * sp1s9 ~ d ~0.17 ' ~ (CO),MnNH, sp'*Od"' sp'.' 0.18 (CO),FeNH,'' sp1*od1.6 sp1.9 0.24 (CO),CONH,~+sp1.'d3.* spa' 0.61
delocalization,"
N
%
1.86
13.gb
1.85 1.78
14.7' 11.4 11.5
1.61
All electron populations on the cis carbonyls are less Based o n a one-center orbital. than 0.010e. a
Cr
Mn +
Fe"
GO''
Figure 10. Metal-nitrogen LMO's in (CO)&!-NH3 complexes.
In summary, for non-?r-bonding ligands, the Boys criterion separates shells quite well, but within a shell all subshells are mixed to form hybrids with approximately the same amount of s, p, and d character. This situation is expected to change significantly when one or more aaccepting ligands are introduced. (CO)&f-NH3 Complexes. It is important to establish that our qualitative LMO results are independent of the model complexes employed, particularly for (NH,),M-L complexes (M = CrO, Mn+, and Fe2+),which would not be expected to have closed-shell ground states. For this reason, we have studied complexes of formula (CO),MNH,. These complexes have uniformly larger HOMOLUMO gaps and should be well described at the single determinate level.31 We will limit our discussion here to the LMOs in the M-NH3 region. A future publication will deal with the metal-carbonyl bonds.13 The M-N LMO's in the (CO)&M-NH3complexes (Figure 10 and Table IX) are quite similar to those of the corresponding pentaammonia complexes. The principal difference is that there is slightly more u electron density donated from the ligand to the metal in the carbonyl complexes, particularly for chromium and manganese and to a lesser extent for iron. These metals back-bond to the carbonyls to a significant extent. For instance, the d, population of (C0),CrNH3 is calculated to be 4.29e-, while that of (NH3)&r is 5.79e-. The significantly lower d, population in (CO)&CrNH3is a direct manifestation of metal to ligand back-bonding. This results in an increase in the effective positive charge on the metal, making it better able to compete with the ligand for the u type lone-pair electrons. This effect is greatest for CrO and decreases steadily as the formal metal charge is increased, until the effect is barely noticeable for Co3+. Clearly the 3+ formal charge on cobalt inhibits back-bonding (if we compare the d, populations in CO(NH,),~+(5.99e-) and (CO),CONH~~+ (5.85e-) with those of the corresponding chromium complexes listed above, it is clear that a backbonding effects are much smaller for cobalt). Similar trends are evident in other (CO),M-L complexes not discussed here.32 (31) Correlation contributions have recently been shown to be small in CI(CO)~. Sherwood, D. E.; Hall,M. B. Inorg. Chem. 1983, 22, 93. (32) Other (Cod M-L complexes, particularly those with L = H-, CH,-, and F,show direct donation from the M-L u bond to cis carboxyl r* orbitals. Such effects have been observed previously (Fenske,R. F.; DeKock, R. L. Inorg. Chem. 1972,9,1053) and w i l l be discussed in detail for these complexes in a subsequent p~b1ication.l~
J. Phys. Chem. lW3, 87,3279-3282
Conclusions The localized orbitals of these simple transition-metal complexes provide for a conceptually straightforward analysis of such fundamental bonding concepts as hybridization, bond polarity, and delocalization. These studies can be particularly useful when comparing a series of isoelectronic or isostructural complexes, as was presented in this paper. The question of whether or not the localized framework will be useful for describing more complicated metal-ligand interactions, especially metalligand a bonding, is currently under study. Acknowledgment. This work was supported by The Robert A. Welch Foundation (Grant Y-743), the Research Corp. and the Organized Research Fund of The University of Texas at Arlington.
3279
Registry No. (NH3)$cH2+,86307-91-7; (NH3)&rH-,8630792-8; (NH3I6MnH, 86307-93-9; (NH3)6FeH+,86307-94-0; (NH3)6CoH2+,86307-95-1; (NH&ZnH+, 86307-96-2; (NH&Sc3+, 86307-97-3; (NH&Cr, 86307-98-4; (NH3)6Mn+,86307-99-5; (NH3I6Fe2+, 15365-76-1; (NH3)&03+,14695-95-5; (NH3)sZn2+, 28074-39-7; ( N H ~ ) ~ S C C H 86308-00-1; ~ ~ + , (NH3)&rCH3-,8630886308-03-4; 01-2; (NH&MnCH3, 86308-02-3; (NH3)6FeCH3+, (NH3)&oCH32+,86308-04-5; (NH3)&CH3+, 86308-05-6; (NH3)&F2+,86308-06-7; (NH3)&rF-,86308-07-8; (NH3),MnF, 86308-08-9; (NH3)6FeF+, 75455-93-5; (NH3)&oF2+,15392-06-0; (NH&ZnF+,86308-09-0; (NH3)6S~12+, 86362-04-1;(NH3)&rC1-, 86308-10-3; (NHS)&nC1, 86308-11-4; (NH3)$eC1+, 34157-33-0; ( N H ~ ) & O C ~14970-14-0; ~+ (NH3)6ZnC1+, 86308-12-5; (NH3)6ScOH$+:86308-13-6; (NH&CrOH2,86308-14-7; (NH3)6MnOH2,86308-15-8; (NH3)$eOH,2+,75456-09-6; (NH&CoOH;+, 14403-82-8; (NHJ&OH$+, 86308-16-9; (CO)&rNH3,15228-27-0; (CO)&nNH3+, 45000-26-8; (CO)6FeNH32+,86308-17-0; (CO)&oNH:+, 86308-18-1.
Ab Initio Computation of the Enthalpies of Some Gas-Phase Hydration Reactions Jane! E. Del Bene;
Howard D. Mettee,
Department of Chemlstry, Youngstown State Un/versl@', Youngstown, Ohio 44555
Michael J. Frlsch, Brlan T. Luke, and John A. Pople Department of Chemlstty, Carnegle-Mellon University, Pittsburgh, Pennsylvanle 152 13 (Recelved: November 8, 1082; In Final Form: February 22, 1983)
Gas-phase reaction energies have been computed by means of ab initio SCF MO calculations with electron correlation computed by Merller-Plesset perturbation theory. Combined with computed vibrational, rotational, and translational energies, these give room temperature enthalpies in agreement with experimental data for the hydration reactions X + H20 HzOX, where X = H+, Li+, and HzO. The effect of full deuteration on the enthalpies of these reactions is predicted.
-
Introduction It has long been held that thermodynamic properties such as e8 can, in principle, be calculated by ab initio quantum mechanical methods. Modern theoretical chemistry has now reached a level of sophistication where this can be done for gas-phase acid-base reactions in small systems, with an accuracy comparable to that of experiment. Such a comparison of theoretical results with experimental AEP@values requires that electron correlation be included in large basis set calculations of electronic energies at optimized geometries, and that differences in zero-point vibrational energies between reactants and products be evaluated. In addition, a number of other terms arising from differences in translational, rotational, and vibrational energies between reactants and products at 298 K, and the PV work term which relates AH and AE, must also be included. In this paper, we present ab initio calculated enthalpies for three gas-phase hydration reactions HzO + H+ H30+ (1) H 2 0 + Li'
--
HzO + H2O
HzOLiC (HZO),
(2)
(3) and evaluate these results by comparison with experimental data. Enthalpies for the corresponding fully deuterated reactions are also predicted. For these reactions
(4) a z g d
AE?
+ A(AE,)2D8 + AE: + A(AEJZg8 +
+ AE?" (5)
with the following definitions: AE: is the computed difference in the electronic energies of reactants and product at 0 K, including the correlation energy correction to the Hartree-Fock energy, A(AE,)298 is the change in the electronic energy difference between 298 K and 0 K. (This term is negligible for reactions 1-3.) AE,O is the difference between the zero-point vibrational energies of reactants and product at 0 K. A(AEv)298 is the change in the vibrational energy difference between 298 and 0 K. (This term arises primarily from thermal population of new low-frequency vibrational and hindered rotational modes which may appear in the product.) AErm is the difference in rotational energies of reactants and product. (Classically, this is equal to (-1/2)RT for each degree of rotational freedom lost due to complex formation. This approximation is valid for any polyatomic molecule at room temperature.') (1) G. N. Lewis and M. Randall, 'Thermodynamics", revised by K. S. Pitzer and L. Brewer, McGraw-Hill, New York, 1961.
0 1983 American Chemical Soclety
