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Theoretical electron densities in transition metal dihydrides
Journal of Molecular Structure (Theochem) 545 (2001) 111±118
www.elsevier.nl/locate/theochem
Theoretical electron densities in transition metal dihydrides James A. Platts* Department of Chemistry, Cardiff University, P.O. Box 912, Cardiff CF10 3TB, UK Received 9 December 2000; revised 30 January 2001; accepted 31 January 2001
Abstract Analysis of the DFT calculated electron density distributions of the ®rst-row transition metal (TM) dihydrides are reported. Nickel dihydride was used to assess the effects of basis set and exchange-correlation functional on calculated density properties, leading to the conclusions that diffuse basis functions and gradient-corrected functionals accurately describe the essential features of NiH2. These calculations indicate a remarkably high degree of covalent character in the Ni±H bond, as measured by most density properties, although the Laplacian of the density and the electron localization function (ELF) apparently show `closed-shell' interaction. Subsequent B3LYP/6-31111G(f,p) studies of the ground states of the 10 ®rst-row TM dihydrides were performed, and similarities and trends across this series examined. The M±H bond becomes less polar and more covalent across the row, as expected on the basis of electronegativity. We go on to show that several simply calculated electron density properties, notably those at the M±H bond critical point, also recover this trend. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Electron density; Atoms in molecules; Transition metal; Hydride; Density functional
1. Introduction The nature of bonding in transition metal (TM) compounds is of great current interest: see Ref. [1] for an excellent recent review. The use of density functional theory (DFT) [2] and effective core or pseudopotential methods [3] has expanded the scope of computational studies of TM compounds to cover a great many systems of genuine chemical interest [4]. Numerous models of bonding in such compounds have been proposed, including orbital overlap methods such as the Natural Bond Orbital (NBO) scheme [5], donor±acceptor models including Dewar±Chatt± Duncanson [6,7] and Charge Decomposition Analysis
* Tel.: 144-2920-874950; fax: 144-2920-874030. E-mail address: [email protected] (J.A. Platts).
(CDA) [8], and Morokuma's Energy Decomposition Analysis (EDA) [9]. Bader's Atoms in Molecules (AIM) theory [9,10] is increasingly popular in elucidating bonding and structure in organic molecules [11], and more recently has been applied to a number of problems in TM bonding [12±15]. AIM uses the electron density and its gradient vector ®eld to partition real space into discrete atomic basins: speci®c trajectories of 7r can be used to rigorously identify bonds and interatomic surfaces [10]. With this de®nition of distinct atoms in place, atomic properties such as populations, energies, and multipoles can be obtained by integrating the appropriate property density over the atom. A particular advantage of this approach is that such atoms individually obey the virial theorem [16], meaning that the total atomic energy can be determined from the atomic kinetic energy. Bonding properties are conveniently
0166-1280/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0166-128 0(01)00392-X
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J.A. Platts / Journal of Molecular Structure (Theochem) 545 (2001) 111±118
Table 1 NiH2 1A1 properties with various theoretical models (all properties in atomic units unless otherwise stated, all calculated using the 631111G(f,p) basis set) Method Ê) rN±H (A H±N±H (8) a rc 7 2r c q(H) AIM E(H) m (H) q(Ni) AIM E(Ni) m (Ni) Bond order a
a
QCISD
B3LYP
B3PW91
BLYP
B1LYP
MPW1PW91
LSDA
HF
± ±
1.426 84.5 0.152 0.059 20.149 20.602 0.189 0.298 21508.231 0.194 1.090
1.419 81.4 0.153 0.057 20.141 20.596 0.190 0.282 21508.192 0.247 1.083
1.434 81.6 0.147 0.071 20.119 20.597 0.182 0.239 21508.304 0.132 1.092
1.428 86.2 0.151 0.058 20.164 20.605 0.188 0.327 21508.174 0.189 1.090
1.419 82.4 0.154 0.054 20.151 20.598 0.192 0.302 21508.293 0.254 1.084
1.430 45.7 0.145 0.177 20.030 20.559 0.205 0.060 21506.254 0.249 0.867
1.546 114.5 0.119 0.145 20.478 20.652 0.092 0.955 21506.458 0.089 0.896
0.147 0.096 20.153 20.617 0.167 0.306 21506.706 0.135 ±
Calculated at the B3LYP geometry.
summarised by electron density properties at the (3, 21) or `bond' critical point, the minimum on the line of maximal electron density joining two bonded nuclei [17]. In this study, we will apply the AIM methodology to a series of TM dihydrides, with the aim of exploring the bonding and observing trends across the 1st row of TM's. TM hydrides have long been used as model ligands in computational studies [18], their small size lending themselves to accurate calculations. Dihydrides are of particular interest, since they are the simplest example of a s-bond coordinating directly to a metal centre [19], and also can be considered as (simplistic) models of H2 adsorbed on metal surfaces [20]. The hydride ligand has no possibility of acting as either a p-donor or acceptor, thereby simplifying considerations of its bonding. Through a detailed AIM study of the ®rst-row TM dihydrides, we hope to discover properties that allow characterisation of bonding modes, which should prove useful in subsequent studies of more complex ligands. 1.1. Computational details All calculations were carried using the gaussian98 package [21] on EPSRC's Columbus central facility. The bulk of the calculations were at the B3LYP/631111G(f,p) level [22±25], but for NiH2 several other basis sets, namely 6-31G(f), [26] 6-311G, 6311 1 G(f), 6-31111G(3f,3p) [27], and the effective core potential basis sets LANL2DZ [28] and SDD
[29] and methods for treating electron correlation (QCISD, B3PW91, BLYP, B1LYP, MPW1PW91, LSDA, HF) [30±34] were also used. For each molecule, the potential energy surface for various possible states was explored at the B3LYP/6-31111G(f,p), with properties reported for the ground state at its equilibrium geometry. Bonding and electronic properties were explored using the AIM techniques pioneered by Bader and co-workers [10]. This is based around the de®nition of an interatomic surface, the `zero-¯ux surface' in the gradient of the electron density of a molecule, and hence atomic basins, V. Atomic properties reported here are q, the electronic charge, E, the atomic energy, m , the dipole moment, and Q, the root mean square of the eigenvalues of the atomic quadrupole matrix. m is a measure of how the centroid of an atom's electron density is shifted away from the nucleus, while Q measures the asphericity of the atom's density distribution. For comparison, atomic charges from the NBO [5] and Mulliken [35] schemes are also reported. Covalent bond orders as calculated by Angyan et al. [36] from the atomic overlap matrix are also reported. Bonding properties derived from the electron density, r , and its gradient are reported. Properties calculated at such points include r , the total electron density, which has been related to bond order [17], 7 2r c the second derivative or Laplacian of the density, which measures the extent to which density is concentrated or depleted (more negative 7 2r indicates greater concentration of charge). e , the bond
J.A. Platts / Journal of Molecular Structure (Theochem) 545 (2001) 111±118
113
Fig. 1. QCISD/6-31111G(f,p) distribution of 2 7 2r in NiH2: solid lines indicate charge concentration, dashed lines indicate charge depletion.
ellipticity is often taken as a measure of p-bond character [17], while the energy density, E, has been proposed as an alternative to 7 2r in determining covalent/ionic character [37]. Atomic and CP properties were calculated using the AIMPAC suite of programs [38] in particular the programs extreme and proaimv. The electron localization function (ELF) as developed by Becke and Edgecombe [39,40] was evaluated using Popelier's morphy package [41].
2. Results and discussion 2.1. Comparison of basis sets and model chemistries It has recently been shown [42] that the correct electronic ground state of nickel dihydride ( 1A1 with C2v symmetry) is obtained with hybrid DFT methods such as B3-LYP or B3-PW91, and a triple-j valence basis set with polarization and diffuse basis functions. As this molecule is well characterised with many common theoretical methods, we will use it to compare local and atomic electron density properties calculated using various theoretical models. Table 1
reports selected geometrical and density properties for 1 A1 NiH2 calculated using 13 different methods. QCISD(full)/6-31111G(f,p) optimisations proved beyond the available computational resources, so calculations are at the B3LYP/6-31111G(f,p) geometry, since Ref. [42] indicates this is appropriate. The QCISD results suggest a large degree of covalent character in the Ni±H bond, since r c is rather larger than that found in `typical' closed-shell interactions such as hydrogen bonding (H3N´ ´´HF r c 0:039) or purely ionic bonds (LiF rc 0:075). Indeed, the Ni± H bond seems closer to covalent X±H bonds such as those in PH3 rc 0:165 on this basis. Plots of 27 2r and ELF from B3LYP calculations are shown in Fig. 1, and unlike all the properties reported in Table 1 appear to show largely ionic character in the Ni±H bond. 27 2r show distinct regions of charge concentrations centred on each atom, with no apparent charge build-up in the interatomic region, which might be expected for covalent bonds. Similarly, there is no evidence either in Fig. 1 or in topological analysis (not reported) for bonding maxima in ELF, which are associated with covalent bonding. Both scalar ®elds show what appear to be maxima associated with Ni d-orbitals and approximately
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J.A. Platts / Journal of Molecular Structure (Theochem) 545 (2001) 111±118
Table 2 NiH2 1A1 B3LYP properties with various basis sets (all properties in atomic units unless otherwise stated) Basis
6-31111G(f,p)
6-31G(f)
6-311G
6-31111G(3f,3p)
SDD
LANL2DZ
Ê) rN±H (A H±N±H (8) rc 7 2r c q(H) AIM E(H) m (H) q(Ni) AIM E(Ni) m (Ni) Bond order
1.426 84.5 0.152 0.059 20.149 20.602 0.189 0.298 21508.231 0.194 1.090
1.442 103.1 0.143 0.094 20.233 20.636 0.228 0.466 21507.921 0.038 1.036
1.435 97.8 0.144 0.075 20.189 20.618 0.239 0.380 21508.122 0.050 1.045
1.427 84.9 0.152 0.068 20.153 20.603 0.190 0.307 21508.230 0.181 1.092
1.432 87.9 0.139 0.142 20.145 20.926 0.195 0.290 2170.221 0.197 1.084
1.442 86.4 0.130 0.172 20.164 20.947 0.195 0.328 2168.523 0.167 1.067
spherical charge concentrations on the hydrides. On this basis it seems that such maps are not appropriate for allocating ionic/covalent character of metal± ligand bonds. It is apparent from Table 1 that all gradientcorrected functionals considered result in remarkably similar density properties, with r c varying by only a few percent between the functionals used. A slight change is noted for the pure DFT functional BLYP, as opposed to the hybrid functionals used, but this is only minor compared with the differences discussed below. In general therefore, we assert that any of the gradient-corrected functionals employed here are capable of reproducing the essential features of NiH2, as compared to QCISD results. As noted above, all properties consistently point to a high degree of covalent character in the Ni±H bond, as re¯ected by the charge accumulation in the interatomic region and the small values of atomic charge (much less than the formal Ni 21 and H 12 values). This picture of the Ni±H bond is lent further support by the covalent bond order, which is very close to 1.0 for all the non-local functionals considered. By contrast, both the local spin density approximation (LSDA) and Hartree±Fock (HF) show substantial failures in at least some properties. LSDA does not describe NiH2 at all well: the H±Ni±H angle is around half that found previously, and each atom is approximately neutral. In fact, LSDA predicts NiH2 to have a cyclic structure, with a third bond CP between H's and an associated ring CP, a clear failure when compared to other methods. It is noteworthy that there is no minimum on the LSDA energy surface analogous to
those found for all other methods. The HF/631111G(f,p) results are also wrong, though in a different way from the LSDA. Here, the ionic component of the bond is greatly overestimated, with relatively low charge build-up in the bond and larger atomic charges. This lack of covalency is also evident in the large H±Ni±H angle, since there is now much greater repulsion between the negatively charged H atoms. The effects of basis set variation, keeping the B3LYP functional ®xed, are recorded in Table 2. The results are broadly similar across the various basis sets, and are consistent with the picture of covalency discussed above. The only major discrepancy in Table 2, is found for the 6-31G(f) basis, which overestimates the charge separation by around 50%. The similar sized 6-311G basis, which has no f-functions, is much closer to the larger basis results, indicating that polarization functions are less important than a proper description of the d-orbitals involved in bonding. This is supported by the fact that inclusion of three separate sets of polarization functions makes little difference to the 6-31111G(f,p) results. Calculations using two different effective core potentials (ECPs) result in longer bonds with less charge accumulation than those with all-electron bases sets, but (perhaps fortuitously) atomic charges and dipoles are very similar to all-electron calculations. 2.2. Trends in ®rst-row TM dihydrides On the basis of the results discussed above, we selected the B3LYP/6-31111G(f,p) method to
ScH2
a
Calculated from MH2 ! M 1 2H.
2 State A1 Ê) rM±H (A 1.819 H±M±H (8) 119.0 Energy 2761.765 rc 0.073 7 2r c 0.109 e 0.348 Ec 20.019 q(H)AIM 20.655 E(H) 20.658 m (H) 0.067 Q(H) 1.443 q(H)NBO 20.598 q(H)Mull 20.285 q(M)AIM 1.310 E(M) 2760.449 m (M) 0.251 Q(M) 1.714 Q(M)NBO 1.195 q(M)Mull 0.570 Bond order 0.772 Bond energy a (kJ mol 21) 184.3
Name A1
1.761 124.6 2850.557 0.092 0.044 0.017 20.037 20.575 20.659 0.003 1.181 20.506 20.261 1.151 2849.238 0.545 3.446 1.012 0.522 0.810 272.1
3
TiH2 B2
1.709 120.8 2945.099 0.094 0.104 0.211 20.036 20.533 20.654 0.007 1.126 20.477 20.224 1.067 2943.790 0.401 2.127 0.953 0.448 0.886 265.2
4
VH2 B2
1.650 111.7 21045.598 0.105 0.076 0.004 20.045 20.440 20.645 0.092 0.977 20.373 20.201 0.880 21044.308 0.213 2.747 0.746 0.402 0.941 222.6
5
CrH2
Table 3 Properties of ®rst-row TM dihydrides (atomic units unless otherwise stated)
Sg
1.691 180.0 21152.152 0.094 0.125 0.0 20.034 20.550 20.644 0.027 1.218 20.600 20.198 1.099 21150.863 0.0 2.040 1.199 0.397 0.797 235.7
6
MnH2
Sg
1.652 180.0 21264.842 0.102 0.110 0.0 20.040 20.522 20.650 0.020 1.126 20.580 20.193 1.043 21263.542 0.0 2.384 1.159 0.386 0.810 245.7
5
FeH2 A2
1.580 141.4 21383.891 0.112 0.137 0.180 20.049 20.406 20.633 0.106 0.960 20.457 20.175 0.811 21382.624 0.086 1.472 0.913 0.350 0.959 261.0
4
CoH2 A1
1.426 84.5 21509.434 0.152 0.059 0.003 20.086 20.149 20.602 0.189 0.593 20.117 20.046 0.298 21508.231 0.194 3.214 0.235 0.092 1.090 236.0
1
NiH2
Dg
1.559 180.0 21509.427 0.115 0.168 0.0 20.050 20.422 20.637 0.109 1.721 20.533 20.153 0.843 21508.152 0.0 2.191 1.065 0.306 0.898 225.9
3
B2
1.525 121.5 21641.628 0.117 0.108 0.038 20.058 20.226 20.590 0.138 0.743 20.271 20.135 0.451 21640.447 0.044 1.961 0.542 0.269 0.951 198.1
2
CuH2
Sg
1.542 180.0 21780.521 0.116 0.140 0.0 20.055 20.386 20.624 0.073 0.939 20.517 20.156 0.772 21779.274 0.0 1.993 1.034 0.311 0.887 214.4
1
ZnH2
J.A. Platts / Journal of Molecular Structure (Theochem) 545 (2001) 111±118 115
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J.A. Platts / Journal of Molecular Structure (Theochem) 545 (2001) 111±118
study all the ®rst-row TM dihydrides. Most of these have had their ground states and geometry reported previously [20,42±45], although there is some disagreement about the correct ground state of CoH2 [46]. Full results, including geometry, energy, bond and atomic properties, for all ten TM dihydrides are reported in Table 3. In most cases, the ground state is found to be `high-spin': the only exception to this being NiH2 for which the 1A1 state is more stable than the high spin 3Dg state [42]. NiH2 is also an exception from the broad trend of decreasing M±H distance along the row expected on the basis of covalent radii (a much smaller deviation is seen for MnH2). It appears that the low-spin ground state of NiH2 results in anomalous behaviour when compared to the other dihydrides Ð this is evident in several other properties discussed below. For the purposes of comparison, we also include results for the highspin 3Dg state of NiH2. All molecules considered are best represented by the conventional metal dihydride structure, rather than the alternative dihydrogen±metal complex. This could be inferred from the geometry of the molecules, but is unequivocally con®rmed by the lack of bond CP between Hs in all 10 molecules. In fact, only the `failed' LSDA calculation on NiH2 results in such a CP. Two open-shell molecules, MnH2 and FeH2, are found to be linear (as is ZnH2, a conventional VSEPR structure). It is perhaps signi®cant that two of these linear molecules are among the highest-spin molecules considered, although the other quintet molecule reported, CrH2, is bent. As noted above, there are just two M±H bonds per molecule in each case, with no evidence for any H´ ´ ´H bonding whatsoever. Properties evaluated at the M±H bond CPs are broadly similar and in the range discussed for NiH2 above, suggesting at least some covalent character. In particular, the energy density at the CP, Ec, is negative throughout the sequence, which can be taken as a sign of covalency. As with bond length, r c tends to increase and Ec becomes more negative along the row, though NiH2 is again an exception, which may be indicative of increased bond strength along the row. Bond ellipticities are rather large in some cases, although these cannot be associated with p-bonding, and are probably due simply to the rather low-density values in the bonds. Turning now to atomic properties, each molecule
shows a pattern of positive metal and negative hydride to a greater or lesser degree. The early TMs (Sc±Mn) have relatively large charge separation, re¯ecting their lower electronegativity, while the late metals Ni and Cu show almost no charge separation whatsoever. This trend is re¯ected in AIM, NBO, and Mulliken charges, but as noted previously [47] AIM and NBO values are very similar, with Mulliken charges much smaller. Dipolar polarisation of the hydrogens are small in the early TM dihydrides, re¯ecting their largely hydridic nature, but as the covalent nature of the M±H bond increases the H's density is polarised more toward the metal. Conversely, quadrupolar polarisations fall across the row as density is transferred into the internuclear region. Covalent bond orders are rather high, rising from 0.77 for ScH2 to 1.09 for NiH2, indicating that even the most `ionic' molecule in Table 3, ScH2, has a large covalent bonding character. Thus it seems the dihydrides considered here are best described as covalent molecules, albeit with signi®cant polar or ionic character in the earlier TMs. Finally, it is interesting to note the differences between the ground 1A1 and ®rst excited 3Dg states of NiH2, both of which are reported in Table 3. The triplet state is linear and shows much greater ionicity than the bent ground state, and indeed appears to be rather more ionic than the trends in properties across the row suggest. Properties such as atomic charges and multipoles in the 3Dg state are much larger than might be expected on this basis. Also, atomic energies clearly indicate that the singlet state is lower in energy due to increased stabilisation of the Ni atom, and at the expense of stabilisation of the hydrides. The above trends are only approximate, and in each case NiH2 stands out from the others. Much more rigorous trends, which incorporate NiH2, are found between several bond and atomic properties and the covalent bond order. The most accurate of these correlations are summarised in Table 4. The ®ts to bond order follow expected patterns: a shorter metal± hydride bond means greater covalency, as does increased electron density and more negative energy density at the CP. The extent of charge separation across the M±H bond shows a close inverse correlation with bond order (q(H) and q(M) give identical statistics since q(M) 2 £ q(H)). An unexpected correlation is found with the quadrupolar polarisation
J.A. Platts / Journal of Molecular Structure (Theochem) 545 (2001) 111±118 Table 4 Correlations between covalent bond order and density properties Property
R2
sd
rM±H rc Ec q(H) Q(H)
0.740 0.814 0.820 0.821 0.850
0.053 0.045 0.044 0.044 0.040
of the hydride, Q(H), which has previously been used to describe metal±ligand p-bonding [48]. A plot of bond order vs. Q(H) (Fig. 2) shows that covalency is associated with reduced quadrupolar polarisation, i.e. with more spherical H atoms. p-bonding cannot be a factor here, since H has no p-electrons to donate or low-lying p-orbitals to ®ll: instead, this seems to be due to the more negative hydrides accommodating their extra density by distorting themselves away from sphericality. Indeed, q(H) and Q(H) are closely correlated (R 2 0.97), such that these two properties are essentially describing the same effect. Table 3 also contains M±H bond energies, as calculated from atomisation energies, i.e. one-half the energy of dissociation into M 1 2H in their atomic ground states. Bond energies calculated in this manner are in the typical range for covalent bonds, i.e. 200± 300 kJ mol 21. However, no trend whatsoever is
117
apparent in these `atomisation' bond energies Ð the highest value is found for TiH2, which appears to be a rather weak bond using the criteria discussed above. Similarly, NiH2 is clearly the most strongly bound of the ten molecules considered, but only has a middling bond energy of 236 kJ mol 21. Attempts to correlate bond energy with other properties failed utterly Ð plots of bond energy against various properties gave essentially random scatter, and single and multiple linear regressions could not yield any statistically signi®cant relationship. This may be due to the electronic reorganisation of the metal on going from the (formally) M 21 in MH2 to the neutral ground state M, or to ionic contributions to the total bond energy not re¯ected in the properties considered here. 3. Conclusions We have shown that, for the model compound NiH2, local and integrated electron density properties at the QCISD level can be reproduced by any gradient-corrected density functional used with a triple-j valence basis set or bigger. All these methods reproduce the expected dihydride structure with a large degree of covalency in the N±H bonds. By contrast, the LDA functional results in a Ni±dihydrogen complex with a characteristic H±H bond critical
Fig. 2. Plot of Bond Order vs Q(H).
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J.A. Platts / Journal of Molecular Structure (Theochem) 545 (2001) 111±118
point, while HF methods greatly overestimate ionicity. Using the B3LYP/6-31111G(f,p) model, we have examined trends across the ®rst-row TM dihydride series. A general trend of increasing covalency across the row is evident in most properties considered, including the electron density and energy density at the M±H bond critical point and atomic charges, energies, and multipole moments. This is con®rmed by direct calculation of covalent bond order using Angyan et al.'s de®nition. However, we can ®nd no relation between such properties and the atomisation bond energy, which appears to be dominated by electronic rearrangement of the metal. Acknowledgements The author is grateful to Dr S.T. Howard for helpful comments and discussion, and to EPSRC for a generous grant of time on their Columbus facility. References [1] G. Frenking, N. FroÈlich, Chem. Rev. 100 (2000) 717. [2] T. Ziegler, Chem. Rev. 91 (1991) 651. [3] L. Szasz, Pseudopotential Theory of Atoms and Molecules, Wiley, New York, 1986. [4] S.Q. Niu, M.B. Hall, Chem. Rev. 100 (2000) 353. [5] A.E. Reed, L.A. Curtiss, F. Weinhold, Chem. Rev. 88 (1988) 899. [6] M.J.S. Dewar, Bull. Chim. Soc. Fr. 18 (1951) C79. [7] J. Chatt, L.A. Duncanson, J. Amer. Chem. Soc. (1953) 2929. [8] S. Dapprich, G. Frenking, J. Phys. Chem. (99) (1995) 9352. [9] K. Morokuma, Acc. Chem. Res. 10 (1997) 294. [10] R.F.W. Bader, Atoms in Molecules, a Quantum Theory, Oxford University Press, Oxford, 1990. [11] R.F.W. Bader, Chem Rev. 91 (1991) 893. [12] R.J. Gillespie, I. Bytheway, T.-H. Tang, R.F.W. Bader, Inorg. Chem. 35 (1996) 3954. [13] Y.A. Abramov, L. Brammer, W.T. Klooster, R.M. Bullock, Inorg. Chem. 37 (1998) 6317. [14] T.S. Hwang, Y. Wang, J. Phys. Chem. A. 102 (1998) 3726. [15] G.T. Smith, P.R. Mallinson, C.S. Frampton, L.J. Farrugia, R.D. Peacock, J.A.K. Howard, J. Amer. Chem. Soc. 119 (1997) 5028. [16] R.F.W. Bader, Acc. Chem. Res. 8 (1975) 34. [17] R.F.W. Bader, H. Essen, J. Chem. Phys. 80 (1994) 1943. [18] F. Maseras, A. Lledos, E. Clot, O. Eisenstein, Chem. Rev. 100 (2000) 601. [19] F.A. Cotton, G. Wilkinson, P.L. Gaus, Basic Inorganic Chemistry, Wiley, New York, 1986, p. 281. [20] P.E.M. Siegbahn, M.R.A. Blomberg, C.W. Bauschlicher, J. Chem. Phys. 81 (1984) 1373.
[21] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery, Jr., R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, A.G. Baboul, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. Head-Gordon, E.S. Replogle,, J.A. Pople, gaussian 98, Revision A.9 Gaussian, Inc., Pittsburgh PA, 1998. [22] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [23] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [24] M.J.S. Dewar, C.H. Reynolds, J. Comput. Chem. 2 (1981) 140. [25] P.J. Hay, J. Chem. Phys. 66 (1977) 4377. [26] R. Ditch®eld, W.J. Hehre, J.A. Pople, J. Chem. Phys 54 (1971) 724. [27] M.J. Frisch, J.A. Pople, J.S. Binkley, J. Chem. Phys 80 (1984) 3265. [28] P.J. Hay, W.R. Wadt, J. Chem. Phys. 82 (1985) 299. [29] P. Fuentealba, H. Preuss, H. Stoll, L.V. Szentpaly, Chem. Phys. Lett. 89 (1989) 418. [30] J.P. Perdew, K. Burke, Y. Wang, Phys. Rev. B 54 (1996) 16533. [31] A.D. Becke, Phys. Rev. A 38 (1998) 3098. [32] A.D. Becke, J. Chem. Phys. 104 (1996) 1040. [33] C. Adamo, V. Barone, J. Chem. Phys. 108 (1998) 664. [34] S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58 (1980) 1200. [35] R.S. Mulliken, J. Chem. Phys. 23 (1995) 1833. [36] J.G. Angyan, M. Loos, I. Mayer, J. Phys. Chem. (98) (1994) 5244. [37] D. Cremer, E. Kraka, Angew. Chem., Int. Ed. Engl. 23 (1984) 96. [38] F.W. Biegler-KoÈnig, R.F.W. Bader, T.-H. Tang, J. Comput. Chem. 3 (1982) 317 (these programs can be obtained on request from Prof. Bader Ð [email protected], or from http://www.chemistry.mcmaster.ca/aimpac/). [39] A.D. Becke, K.E. Edgecombe, J. Chem. Phys. 92 (1990) 5397. [40] A. Savin, R. Nesper, S. Wengert, T.F. Fassler, Angew. Chem., Int. Ed. Engl. 36 (1997) 1809. [41] morphy98, a program written by P.L.A. Popelier with a contribution from R.G.A. Bone, UMIST, Manchester, England, EU 1998. See www.ch.umist.ac.uk/morphy/ for more information. [42] J.R. Barron, A.R. Kelley, R. Liu, J. Chem. Phys. 108 (1998) 1. [43] B. Ma, C.L. Collins, H.F. Schaefer, J. Amer. Chem. Soc. 118 (1996) 870. [44] H. Martini, C.M. Marian, M. Peric, Mol. Phys. 95 (1998) 27. [45] T.S. Fujii, S. Iwata, Chem. Phys. Lett. 251 (1996) 150. [46] R.J. Vanzee, S. Li, Y.M. Hamrick, W. Weltner, J. Chem. Phys. 97 (1992) 8123. [47] J.A. Platts, Phys. Chem. Chem. Phys. 2 (2000) 973. [48] C. Bo, J.P. Sarasa, J.M. Poblet, J. Phys. Chem. 97 (1993) 6362.
www.elsevier.nl/locate/theochem
Theoretical electron densities in transition metal dihydrides James A. Platts* Department of Chemistry, Cardiff University, P.O. Box 912, Cardiff CF10 3TB, UK Received 9 December 2000; revised 30 January 2001; accepted 31 January 2001
Abstract Analysis of the DFT calculated electron density distributions of the ®rst-row transition metal (TM) dihydrides are reported. Nickel dihydride was used to assess the effects of basis set and exchange-correlation functional on calculated density properties, leading to the conclusions that diffuse basis functions and gradient-corrected functionals accurately describe the essential features of NiH2. These calculations indicate a remarkably high degree of covalent character in the Ni±H bond, as measured by most density properties, although the Laplacian of the density and the electron localization function (ELF) apparently show `closed-shell' interaction. Subsequent B3LYP/6-31111G(f,p) studies of the ground states of the 10 ®rst-row TM dihydrides were performed, and similarities and trends across this series examined. The M±H bond becomes less polar and more covalent across the row, as expected on the basis of electronegativity. We go on to show that several simply calculated electron density properties, notably those at the M±H bond critical point, also recover this trend. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Electron density; Atoms in molecules; Transition metal; Hydride; Density functional
1. Introduction The nature of bonding in transition metal (TM) compounds is of great current interest: see Ref. [1] for an excellent recent review. The use of density functional theory (DFT) [2] and effective core or pseudopotential methods [3] has expanded the scope of computational studies of TM compounds to cover a great many systems of genuine chemical interest [4]. Numerous models of bonding in such compounds have been proposed, including orbital overlap methods such as the Natural Bond Orbital (NBO) scheme [5], donor±acceptor models including Dewar±Chatt± Duncanson [6,7] and Charge Decomposition Analysis
* Tel.: 144-2920-874950; fax: 144-2920-874030. E-mail address: [email protected] (J.A. Platts).
(CDA) [8], and Morokuma's Energy Decomposition Analysis (EDA) [9]. Bader's Atoms in Molecules (AIM) theory [9,10] is increasingly popular in elucidating bonding and structure in organic molecules [11], and more recently has been applied to a number of problems in TM bonding [12±15]. AIM uses the electron density and its gradient vector ®eld to partition real space into discrete atomic basins: speci®c trajectories of 7r can be used to rigorously identify bonds and interatomic surfaces [10]. With this de®nition of distinct atoms in place, atomic properties such as populations, energies, and multipoles can be obtained by integrating the appropriate property density over the atom. A particular advantage of this approach is that such atoms individually obey the virial theorem [16], meaning that the total atomic energy can be determined from the atomic kinetic energy. Bonding properties are conveniently
0166-1280/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0166-128 0(01)00392-X
112
J.A. Platts / Journal of Molecular Structure (Theochem) 545 (2001) 111±118
Table 1 NiH2 1A1 properties with various theoretical models (all properties in atomic units unless otherwise stated, all calculated using the 631111G(f,p) basis set) Method Ê) rN±H (A H±N±H (8) a rc 7 2r c q(H) AIM E(H) m (H) q(Ni) AIM E(Ni) m (Ni) Bond order a
a
QCISD
B3LYP
B3PW91
BLYP
B1LYP
MPW1PW91
LSDA
HF
± ±
1.426 84.5 0.152 0.059 20.149 20.602 0.189 0.298 21508.231 0.194 1.090
1.419 81.4 0.153 0.057 20.141 20.596 0.190 0.282 21508.192 0.247 1.083
1.434 81.6 0.147 0.071 20.119 20.597 0.182 0.239 21508.304 0.132 1.092
1.428 86.2 0.151 0.058 20.164 20.605 0.188 0.327 21508.174 0.189 1.090
1.419 82.4 0.154 0.054 20.151 20.598 0.192 0.302 21508.293 0.254 1.084
1.430 45.7 0.145 0.177 20.030 20.559 0.205 0.060 21506.254 0.249 0.867
1.546 114.5 0.119 0.145 20.478 20.652 0.092 0.955 21506.458 0.089 0.896
0.147 0.096 20.153 20.617 0.167 0.306 21506.706 0.135 ±
Calculated at the B3LYP geometry.
summarised by electron density properties at the (3, 21) or `bond' critical point, the minimum on the line of maximal electron density joining two bonded nuclei [17]. In this study, we will apply the AIM methodology to a series of TM dihydrides, with the aim of exploring the bonding and observing trends across the 1st row of TM's. TM hydrides have long been used as model ligands in computational studies [18], their small size lending themselves to accurate calculations. Dihydrides are of particular interest, since they are the simplest example of a s-bond coordinating directly to a metal centre [19], and also can be considered as (simplistic) models of H2 adsorbed on metal surfaces [20]. The hydride ligand has no possibility of acting as either a p-donor or acceptor, thereby simplifying considerations of its bonding. Through a detailed AIM study of the ®rst-row TM dihydrides, we hope to discover properties that allow characterisation of bonding modes, which should prove useful in subsequent studies of more complex ligands. 1.1. Computational details All calculations were carried using the gaussian98 package [21] on EPSRC's Columbus central facility. The bulk of the calculations were at the B3LYP/631111G(f,p) level [22±25], but for NiH2 several other basis sets, namely 6-31G(f), [26] 6-311G, 6311 1 G(f), 6-31111G(3f,3p) [27], and the effective core potential basis sets LANL2DZ [28] and SDD
[29] and methods for treating electron correlation (QCISD, B3PW91, BLYP, B1LYP, MPW1PW91, LSDA, HF) [30±34] were also used. For each molecule, the potential energy surface for various possible states was explored at the B3LYP/6-31111G(f,p), with properties reported for the ground state at its equilibrium geometry. Bonding and electronic properties were explored using the AIM techniques pioneered by Bader and co-workers [10]. This is based around the de®nition of an interatomic surface, the `zero-¯ux surface' in the gradient of the electron density of a molecule, and hence atomic basins, V. Atomic properties reported here are q, the electronic charge, E, the atomic energy, m , the dipole moment, and Q, the root mean square of the eigenvalues of the atomic quadrupole matrix. m is a measure of how the centroid of an atom's electron density is shifted away from the nucleus, while Q measures the asphericity of the atom's density distribution. For comparison, atomic charges from the NBO [5] and Mulliken [35] schemes are also reported. Covalent bond orders as calculated by Angyan et al. [36] from the atomic overlap matrix are also reported. Bonding properties derived from the electron density, r , and its gradient are reported. Properties calculated at such points include r , the total electron density, which has been related to bond order [17], 7 2r c the second derivative or Laplacian of the density, which measures the extent to which density is concentrated or depleted (more negative 7 2r indicates greater concentration of charge). e , the bond
J.A. Platts / Journal of Molecular Structure (Theochem) 545 (2001) 111±118
113
Fig. 1. QCISD/6-31111G(f,p) distribution of 2 7 2r in NiH2: solid lines indicate charge concentration, dashed lines indicate charge depletion.
ellipticity is often taken as a measure of p-bond character [17], while the energy density, E, has been proposed as an alternative to 7 2r in determining covalent/ionic character [37]. Atomic and CP properties were calculated using the AIMPAC suite of programs [38] in particular the programs extreme and proaimv. The electron localization function (ELF) as developed by Becke and Edgecombe [39,40] was evaluated using Popelier's morphy package [41].
2. Results and discussion 2.1. Comparison of basis sets and model chemistries It has recently been shown [42] that the correct electronic ground state of nickel dihydride ( 1A1 with C2v symmetry) is obtained with hybrid DFT methods such as B3-LYP or B3-PW91, and a triple-j valence basis set with polarization and diffuse basis functions. As this molecule is well characterised with many common theoretical methods, we will use it to compare local and atomic electron density properties calculated using various theoretical models. Table 1
reports selected geometrical and density properties for 1 A1 NiH2 calculated using 13 different methods. QCISD(full)/6-31111G(f,p) optimisations proved beyond the available computational resources, so calculations are at the B3LYP/6-31111G(f,p) geometry, since Ref. [42] indicates this is appropriate. The QCISD results suggest a large degree of covalent character in the Ni±H bond, since r c is rather larger than that found in `typical' closed-shell interactions such as hydrogen bonding (H3N´ ´´HF r c 0:039) or purely ionic bonds (LiF rc 0:075). Indeed, the Ni± H bond seems closer to covalent X±H bonds such as those in PH3 rc 0:165 on this basis. Plots of 27 2r and ELF from B3LYP calculations are shown in Fig. 1, and unlike all the properties reported in Table 1 appear to show largely ionic character in the Ni±H bond. 27 2r show distinct regions of charge concentrations centred on each atom, with no apparent charge build-up in the interatomic region, which might be expected for covalent bonds. Similarly, there is no evidence either in Fig. 1 or in topological analysis (not reported) for bonding maxima in ELF, which are associated with covalent bonding. Both scalar ®elds show what appear to be maxima associated with Ni d-orbitals and approximately
114
J.A. Platts / Journal of Molecular Structure (Theochem) 545 (2001) 111±118
Table 2 NiH2 1A1 B3LYP properties with various basis sets (all properties in atomic units unless otherwise stated) Basis
6-31111G(f,p)
6-31G(f)
6-311G
6-31111G(3f,3p)
SDD
LANL2DZ
Ê) rN±H (A H±N±H (8) rc 7 2r c q(H) AIM E(H) m (H) q(Ni) AIM E(Ni) m (Ni) Bond order
1.426 84.5 0.152 0.059 20.149 20.602 0.189 0.298 21508.231 0.194 1.090
1.442 103.1 0.143 0.094 20.233 20.636 0.228 0.466 21507.921 0.038 1.036
1.435 97.8 0.144 0.075 20.189 20.618 0.239 0.380 21508.122 0.050 1.045
1.427 84.9 0.152 0.068 20.153 20.603 0.190 0.307 21508.230 0.181 1.092
1.432 87.9 0.139 0.142 20.145 20.926 0.195 0.290 2170.221 0.197 1.084
1.442 86.4 0.130 0.172 20.164 20.947 0.195 0.328 2168.523 0.167 1.067
spherical charge concentrations on the hydrides. On this basis it seems that such maps are not appropriate for allocating ionic/covalent character of metal± ligand bonds. It is apparent from Table 1 that all gradientcorrected functionals considered result in remarkably similar density properties, with r c varying by only a few percent between the functionals used. A slight change is noted for the pure DFT functional BLYP, as opposed to the hybrid functionals used, but this is only minor compared with the differences discussed below. In general therefore, we assert that any of the gradient-corrected functionals employed here are capable of reproducing the essential features of NiH2, as compared to QCISD results. As noted above, all properties consistently point to a high degree of covalent character in the Ni±H bond, as re¯ected by the charge accumulation in the interatomic region and the small values of atomic charge (much less than the formal Ni 21 and H 12 values). This picture of the Ni±H bond is lent further support by the covalent bond order, which is very close to 1.0 for all the non-local functionals considered. By contrast, both the local spin density approximation (LSDA) and Hartree±Fock (HF) show substantial failures in at least some properties. LSDA does not describe NiH2 at all well: the H±Ni±H angle is around half that found previously, and each atom is approximately neutral. In fact, LSDA predicts NiH2 to have a cyclic structure, with a third bond CP between H's and an associated ring CP, a clear failure when compared to other methods. It is noteworthy that there is no minimum on the LSDA energy surface analogous to
those found for all other methods. The HF/631111G(f,p) results are also wrong, though in a different way from the LSDA. Here, the ionic component of the bond is greatly overestimated, with relatively low charge build-up in the bond and larger atomic charges. This lack of covalency is also evident in the large H±Ni±H angle, since there is now much greater repulsion between the negatively charged H atoms. The effects of basis set variation, keeping the B3LYP functional ®xed, are recorded in Table 2. The results are broadly similar across the various basis sets, and are consistent with the picture of covalency discussed above. The only major discrepancy in Table 2, is found for the 6-31G(f) basis, which overestimates the charge separation by around 50%. The similar sized 6-311G basis, which has no f-functions, is much closer to the larger basis results, indicating that polarization functions are less important than a proper description of the d-orbitals involved in bonding. This is supported by the fact that inclusion of three separate sets of polarization functions makes little difference to the 6-31111G(f,p) results. Calculations using two different effective core potentials (ECPs) result in longer bonds with less charge accumulation than those with all-electron bases sets, but (perhaps fortuitously) atomic charges and dipoles are very similar to all-electron calculations. 2.2. Trends in ®rst-row TM dihydrides On the basis of the results discussed above, we selected the B3LYP/6-31111G(f,p) method to
ScH2
a
Calculated from MH2 ! M 1 2H.
2 State A1 Ê) rM±H (A 1.819 H±M±H (8) 119.0 Energy 2761.765 rc 0.073 7 2r c 0.109 e 0.348 Ec 20.019 q(H)AIM 20.655 E(H) 20.658 m (H) 0.067 Q(H) 1.443 q(H)NBO 20.598 q(H)Mull 20.285 q(M)AIM 1.310 E(M) 2760.449 m (M) 0.251 Q(M) 1.714 Q(M)NBO 1.195 q(M)Mull 0.570 Bond order 0.772 Bond energy a (kJ mol 21) 184.3
Name A1
1.761 124.6 2850.557 0.092 0.044 0.017 20.037 20.575 20.659 0.003 1.181 20.506 20.261 1.151 2849.238 0.545 3.446 1.012 0.522 0.810 272.1
3
TiH2 B2
1.709 120.8 2945.099 0.094 0.104 0.211 20.036 20.533 20.654 0.007 1.126 20.477 20.224 1.067 2943.790 0.401 2.127 0.953 0.448 0.886 265.2
4
VH2 B2
1.650 111.7 21045.598 0.105 0.076 0.004 20.045 20.440 20.645 0.092 0.977 20.373 20.201 0.880 21044.308 0.213 2.747 0.746 0.402 0.941 222.6
5
CrH2
Table 3 Properties of ®rst-row TM dihydrides (atomic units unless otherwise stated)
Sg
1.691 180.0 21152.152 0.094 0.125 0.0 20.034 20.550 20.644 0.027 1.218 20.600 20.198 1.099 21150.863 0.0 2.040 1.199 0.397 0.797 235.7
6
MnH2
Sg
1.652 180.0 21264.842 0.102 0.110 0.0 20.040 20.522 20.650 0.020 1.126 20.580 20.193 1.043 21263.542 0.0 2.384 1.159 0.386 0.810 245.7
5
FeH2 A2
1.580 141.4 21383.891 0.112 0.137 0.180 20.049 20.406 20.633 0.106 0.960 20.457 20.175 0.811 21382.624 0.086 1.472 0.913 0.350 0.959 261.0
4
CoH2 A1
1.426 84.5 21509.434 0.152 0.059 0.003 20.086 20.149 20.602 0.189 0.593 20.117 20.046 0.298 21508.231 0.194 3.214 0.235 0.092 1.090 236.0
1
NiH2
Dg
1.559 180.0 21509.427 0.115 0.168 0.0 20.050 20.422 20.637 0.109 1.721 20.533 20.153 0.843 21508.152 0.0 2.191 1.065 0.306 0.898 225.9
3
B2
1.525 121.5 21641.628 0.117 0.108 0.038 20.058 20.226 20.590 0.138 0.743 20.271 20.135 0.451 21640.447 0.044 1.961 0.542 0.269 0.951 198.1
2
CuH2
Sg
1.542 180.0 21780.521 0.116 0.140 0.0 20.055 20.386 20.624 0.073 0.939 20.517 20.156 0.772 21779.274 0.0 1.993 1.034 0.311 0.887 214.4
1
ZnH2
J.A. Platts / Journal of Molecular Structure (Theochem) 545 (2001) 111±118 115
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J.A. Platts / Journal of Molecular Structure (Theochem) 545 (2001) 111±118
study all the ®rst-row TM dihydrides. Most of these have had their ground states and geometry reported previously [20,42±45], although there is some disagreement about the correct ground state of CoH2 [46]. Full results, including geometry, energy, bond and atomic properties, for all ten TM dihydrides are reported in Table 3. In most cases, the ground state is found to be `high-spin': the only exception to this being NiH2 for which the 1A1 state is more stable than the high spin 3Dg state [42]. NiH2 is also an exception from the broad trend of decreasing M±H distance along the row expected on the basis of covalent radii (a much smaller deviation is seen for MnH2). It appears that the low-spin ground state of NiH2 results in anomalous behaviour when compared to the other dihydrides Ð this is evident in several other properties discussed below. For the purposes of comparison, we also include results for the highspin 3Dg state of NiH2. All molecules considered are best represented by the conventional metal dihydride structure, rather than the alternative dihydrogen±metal complex. This could be inferred from the geometry of the molecules, but is unequivocally con®rmed by the lack of bond CP between Hs in all 10 molecules. In fact, only the `failed' LSDA calculation on NiH2 results in such a CP. Two open-shell molecules, MnH2 and FeH2, are found to be linear (as is ZnH2, a conventional VSEPR structure). It is perhaps signi®cant that two of these linear molecules are among the highest-spin molecules considered, although the other quintet molecule reported, CrH2, is bent. As noted above, there are just two M±H bonds per molecule in each case, with no evidence for any H´ ´ ´H bonding whatsoever. Properties evaluated at the M±H bond CPs are broadly similar and in the range discussed for NiH2 above, suggesting at least some covalent character. In particular, the energy density at the CP, Ec, is negative throughout the sequence, which can be taken as a sign of covalency. As with bond length, r c tends to increase and Ec becomes more negative along the row, though NiH2 is again an exception, which may be indicative of increased bond strength along the row. Bond ellipticities are rather large in some cases, although these cannot be associated with p-bonding, and are probably due simply to the rather low-density values in the bonds. Turning now to atomic properties, each molecule
shows a pattern of positive metal and negative hydride to a greater or lesser degree. The early TMs (Sc±Mn) have relatively large charge separation, re¯ecting their lower electronegativity, while the late metals Ni and Cu show almost no charge separation whatsoever. This trend is re¯ected in AIM, NBO, and Mulliken charges, but as noted previously [47] AIM and NBO values are very similar, with Mulliken charges much smaller. Dipolar polarisation of the hydrogens are small in the early TM dihydrides, re¯ecting their largely hydridic nature, but as the covalent nature of the M±H bond increases the H's density is polarised more toward the metal. Conversely, quadrupolar polarisations fall across the row as density is transferred into the internuclear region. Covalent bond orders are rather high, rising from 0.77 for ScH2 to 1.09 for NiH2, indicating that even the most `ionic' molecule in Table 3, ScH2, has a large covalent bonding character. Thus it seems the dihydrides considered here are best described as covalent molecules, albeit with signi®cant polar or ionic character in the earlier TMs. Finally, it is interesting to note the differences between the ground 1A1 and ®rst excited 3Dg states of NiH2, both of which are reported in Table 3. The triplet state is linear and shows much greater ionicity than the bent ground state, and indeed appears to be rather more ionic than the trends in properties across the row suggest. Properties such as atomic charges and multipoles in the 3Dg state are much larger than might be expected on this basis. Also, atomic energies clearly indicate that the singlet state is lower in energy due to increased stabilisation of the Ni atom, and at the expense of stabilisation of the hydrides. The above trends are only approximate, and in each case NiH2 stands out from the others. Much more rigorous trends, which incorporate NiH2, are found between several bond and atomic properties and the covalent bond order. The most accurate of these correlations are summarised in Table 4. The ®ts to bond order follow expected patterns: a shorter metal± hydride bond means greater covalency, as does increased electron density and more negative energy density at the CP. The extent of charge separation across the M±H bond shows a close inverse correlation with bond order (q(H) and q(M) give identical statistics since q(M) 2 £ q(H)). An unexpected correlation is found with the quadrupolar polarisation
J.A. Platts / Journal of Molecular Structure (Theochem) 545 (2001) 111±118 Table 4 Correlations between covalent bond order and density properties Property
R2
sd
rM±H rc Ec q(H) Q(H)
0.740 0.814 0.820 0.821 0.850
0.053 0.045 0.044 0.044 0.040
of the hydride, Q(H), which has previously been used to describe metal±ligand p-bonding [48]. A plot of bond order vs. Q(H) (Fig. 2) shows that covalency is associated with reduced quadrupolar polarisation, i.e. with more spherical H atoms. p-bonding cannot be a factor here, since H has no p-electrons to donate or low-lying p-orbitals to ®ll: instead, this seems to be due to the more negative hydrides accommodating their extra density by distorting themselves away from sphericality. Indeed, q(H) and Q(H) are closely correlated (R 2 0.97), such that these two properties are essentially describing the same effect. Table 3 also contains M±H bond energies, as calculated from atomisation energies, i.e. one-half the energy of dissociation into M 1 2H in their atomic ground states. Bond energies calculated in this manner are in the typical range for covalent bonds, i.e. 200± 300 kJ mol 21. However, no trend whatsoever is
117
apparent in these `atomisation' bond energies Ð the highest value is found for TiH2, which appears to be a rather weak bond using the criteria discussed above. Similarly, NiH2 is clearly the most strongly bound of the ten molecules considered, but only has a middling bond energy of 236 kJ mol 21. Attempts to correlate bond energy with other properties failed utterly Ð plots of bond energy against various properties gave essentially random scatter, and single and multiple linear regressions could not yield any statistically signi®cant relationship. This may be due to the electronic reorganisation of the metal on going from the (formally) M 21 in MH2 to the neutral ground state M, or to ionic contributions to the total bond energy not re¯ected in the properties considered here. 3. Conclusions We have shown that, for the model compound NiH2, local and integrated electron density properties at the QCISD level can be reproduced by any gradient-corrected density functional used with a triple-j valence basis set or bigger. All these methods reproduce the expected dihydride structure with a large degree of covalency in the N±H bonds. By contrast, the LDA functional results in a Ni±dihydrogen complex with a characteristic H±H bond critical
Fig. 2. Plot of Bond Order vs Q(H).
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J.A. Platts / Journal of Molecular Structure (Theochem) 545 (2001) 111±118
point, while HF methods greatly overestimate ionicity. Using the B3LYP/6-31111G(f,p) model, we have examined trends across the ®rst-row TM dihydride series. A general trend of increasing covalency across the row is evident in most properties considered, including the electron density and energy density at the M±H bond critical point and atomic charges, energies, and multipole moments. This is con®rmed by direct calculation of covalent bond order using Angyan et al.'s de®nition. However, we can ®nd no relation between such properties and the atomisation bond energy, which appears to be dominated by electronic rearrangement of the metal. Acknowledgements The author is grateful to Dr S.T. Howard for helpful comments and discussion, and to EPSRC for a generous grant of time on their Columbus facility. References [1] G. Frenking, N. FroÈlich, Chem. Rev. 100 (2000) 717. [2] T. Ziegler, Chem. Rev. 91 (1991) 651. [3] L. Szasz, Pseudopotential Theory of Atoms and Molecules, Wiley, New York, 1986. [4] S.Q. Niu, M.B. Hall, Chem. Rev. 100 (2000) 353. [5] A.E. Reed, L.A. Curtiss, F. Weinhold, Chem. Rev. 88 (1988) 899. [6] M.J.S. Dewar, Bull. Chim. Soc. Fr. 18 (1951) C79. [7] J. Chatt, L.A. Duncanson, J. Amer. Chem. Soc. (1953) 2929. [8] S. Dapprich, G. Frenking, J. Phys. Chem. (99) (1995) 9352. [9] K. Morokuma, Acc. Chem. Res. 10 (1997) 294. [10] R.F.W. Bader, Atoms in Molecules, a Quantum Theory, Oxford University Press, Oxford, 1990. [11] R.F.W. Bader, Chem Rev. 91 (1991) 893. [12] R.J. Gillespie, I. Bytheway, T.-H. Tang, R.F.W. Bader, Inorg. Chem. 35 (1996) 3954. [13] Y.A. Abramov, L. Brammer, W.T. Klooster, R.M. Bullock, Inorg. Chem. 37 (1998) 6317. [14] T.S. Hwang, Y. Wang, J. Phys. Chem. A. 102 (1998) 3726. [15] G.T. Smith, P.R. Mallinson, C.S. Frampton, L.J. Farrugia, R.D. Peacock, J.A.K. Howard, J. Amer. Chem. Soc. 119 (1997) 5028. [16] R.F.W. Bader, Acc. Chem. Res. 8 (1975) 34. [17] R.F.W. Bader, H. Essen, J. Chem. Phys. 80 (1994) 1943. [18] F. Maseras, A. Lledos, E. Clot, O. Eisenstein, Chem. Rev. 100 (2000) 601. [19] F.A. Cotton, G. Wilkinson, P.L. Gaus, Basic Inorganic Chemistry, Wiley, New York, 1986, p. 281. [20] P.E.M. Siegbahn, M.R.A. Blomberg, C.W. Bauschlicher, J. Chem. Phys. 81 (1984) 1373.
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