Chemical structures from the analysis of domain-averaged Fermi holes: multiple metal-metal bonding in transition metal compounds

The recently proposed approach based on the analysis of domain-averaged Fermi holes was applied to the study of the nature of metal-metal bonding in transition metal complexes and clusters. The main emphasis was put on the scrutiny of the systems assumed to contain direct multiple metal-metal bonds. The studied systems involve: (1) systems of the type M(2)X(6) (M = Mo, W, X = CH(3)) anticipated to contain metal-metal triple bonds; (2) the molecule of W(2)Cl(8) ((4-)) as the representative of the systems with quadruple metal-metal bonding; (3) diatomic molecules Mo(2) and V(2) considered as the potential candidates for higher than quadruple metal-metal bonding. Although the resulting picture of bonding has been usually shown to agree with the original expectations based on early simple MO models, some examples were also found in which the conclusions of the reported analysis display dramatic sensitivity to the quality of the wave function used for the generation of the Fermi holes. In addition to this we also report some examples where the original theoretical predictions of multiplicity of metal-metal bonds have to be corrected.     

A versatile electronic hole in one-electron oxidized NiIIbis-salicylidene phenylenediamine complexes

The nickel complexes 1(+)-3(+) exhibit a delocalized radical character, the extent of which depends on the electronic properties of the phenolate para-substituent.     

A reinterpretation of the nature of the Fermi hole

A reinterpretation of the Boyd-Coulson [R. J. Boyd and C. A. Coulson, J. Phys. B 7, 1805 (1974)] definition of the Fermi hole is presented. Through this reinterpretation, which makes no reference to the hypothetical Hartree level, we are able to show the essentially identical character of the Boyd-Coulson definition with the one based on a conditional probability analysis. The basis-set dependence of the Fermi hole is emphasized and the effect of canonical, localized and delocalized Kohn-Sham and Hartree-Fock basis sets is examined for selected atoms and molecules.     

A new look at the ylidic bond in phosphorus ylides and related compounds: energy decomposition analysis combined with a domain-averaged fermi hole analysis

Geometries and bond dissociation energies of the ylide compounds H2CPH3, H2CPMe3, H2CPF3, (BH2)2CPH3, H2CNH3, H2CAsH3, H2SiPH3, and (BH2)2SiPH3 have been calculated using ab initio (MP2, CBS-QB3) and DFT (B3LYP, BP86) methods. The nature of the ylidic bond R2E1-E2X3 was investigated with an energy decomposition analysis and with the domain-averaged Fermi hole (DAFH) analysis. The results of the latter method indicate that the peculiar features of the ylidic bond can be understood in terms of donor-acceptor interactions between closed-shell R2E1 and E2X3 fragments. The DAFH analysis clearly shows that there are two bonding contributions to the ylidic bond. The strength of the donor and acceptor contributions to the attractive orbital interactions can be estimated from the energy decomposition analysis (EDA) calculations, which give also the contributions of the electrostatic attraction and the Pauli repulsion of the chemical bonding. The EDA and DAFH results clearly show that the orbital interactions take place through the singlet ground state of the R2E1 fragment where the donor orbital of E1 yields pi-type back-donation while the E2X3 lone-pair orbital yields sigma-type bonding. Both bonds are polarized toward E2X3 when E2 = P, while the sigma-type bonding remains more polarized at E2X3 when E2 = N, As. This shows that the phosphorus ylides exhibit a particular bonding situation which is clearly different from that of the nitrogen and arsenic homologues. With ylides built around a P-C linkage, the pi-acceptor strength of phosphorus and the sigma-acceptor strength at carbon contribute to a double bond which is enhanced by electrostatic contributions. The strength of the sigma and pi components and the electrostatic attraction are then fine-tuned by the substituents at C and P, which yields a peculiar type of carbon-phosphorus bonding. The EDA data reveal that the relative strength of the ylidic bond may be determined not only by the R2E1 --> E2X3 pi back-donation, but also by the electrostatic contribution to the bonding. The calculations of the R2E1-E2X3 bond dissociation energy using ab initio methods predict that the order of the bond strength is H2C-PMe3 > H2C-PF3 > H2C-PH3 > (BH2)2C-PH3 > H2C-AsH3 > H2C-NH3 approximately H2Si-PH3 approximately (BH2)2Si-PH3. The DFT methods predict a similar trend, but they underestimate the bond strength of (BH2)2CPH3.     

Localized orbitals and the Fermi hole

The relationship between localized orbitals and the Fermi hole is demonstrated with contour maps of the Fermi hole in the water molecule. These contour maps indicate the presence of regions in which the Fermi hole is relatively stable, regions in which the shape of the Fermi hole changes rapidly, and regions in which the Fermi hole follows the probe electron smoothly. If a single orbital dominates any region of space, the Fermi hole resembles that orbital for any position of the probe electron in the dominated region.     

Frozen local hole approximation

The frozen local hole approximation (FLHA) is an adiabatic approximation which is aimed to simplify the correlation calculations of valence and conduction bands of solids and polymers or, more generally, of the ionization potentials and electron affinities of any large system. Within this approximation correlated local hole states (CLHSs) are explicitly generated by correlating local Hartree-Fock (HF) hole states, i.e., (N-1)-particle determinants in which the electron has been removed from a local occupied orbital. The hole orbital and its occupancy are kept frozen during these correlation calculations, implying a rather stringent configuration selection. Effective Hamilton matrix elements are then evaluated with the above CLHSs; diagonalization finally yields the desired correlation corrections for the cationic hole states. We compare and analyze the results of the FLHA with the results of a full multireference configuration interaction with single and double excitations calculation for two prototype model systems, (H2)n ladders and H-(Be)n-H chains. Excellent numerical agreement between the two approaches is found. Comparing the FLHA with a full correlation treatment in the framework of quasidegenerate variational perturbation theory reveals that the leading contributions in the two approaches are identical. In the same way it could be shown that a much less demanding self-consistent field (SCF) calculation around a frozen local hole fully recovers, up to first order, all the leading single excitation contributions. Thus, both the FLHA and the above SCF approximation are well justified and provide a very promising and efficient alternative to fully correlated wave-function-based treatments of the valence and conduction bands in extended systems.     

Parallel electron correlation effect and Fermi hole structure

Based on the charge density functional theory, a simple method is proposed to calculate the parallel electron correlation coefficient, correlation charge, and exchange correlation energy. In contrast to the result in the literature, our analysis reveals that the Fermi hole has its fine structure which is different from the model suggested in the literature. © 1996 John Wiley & Sons, Inc.     

Analytic models of domain-averaged Fermi holes: a new tool for the study of the nature of chemical bonds

Simple analytical models are introduced that significantly enhance the ability to understand and rationalise the nature of bonding interactions depicted by domain-averaged Fermi hole (DAFH) analysis. The examples presented show that besides shedding new light on the role of electron-sharing in ordinary two-centre two-electron (2c-2e) chemical bonds that are well represented by the classical Lewis model, the proposed approach also provides interesting new insights into the nature of bonding interactions that go beyond the traditional Lewis paradigm. This is, for example, the case of 3c-2e multicentre bonding, but a straightforward extension of the approach also reveals for direct metal-metal bonding the existence of a completely new type of bonding interaction that involves the mutual exchange of electrons between the lone pairs on adjacent metal atoms.     

Exchange and correlation in the Thomas–Fermi approximation

We present the exchange and correlation potential calculated analytically as a function of the Hartree potential. We arrived at this expression by using the Thomas–Fermi approximation. This is an alternative way of calculating the exchange and correlation potential which can be very efficient.     

Interaction energy calculation scheme employing one-electron hamiltonian approximation for the evaluation of short-range interactions

A semiempirical scheme for the calculation of intermolecular energy is presented. A distinctive feature of the scheme is the employment of the one-electron Hamiltonian approximation in EHT parametrization for the calculation of exchange repulsion and charge transfer energies. Electrostatic, induction and dispersion components are calculated according to known approximate formulas containing point multipole moments and bond polarizabilities. The proposed scheme is applied to the calculation of binding energies and equilibrium geometries of various molecular dimers.     

A local one-electron operator for the generalized-overlap amplitudes

An approach to the N-electron behavior is presented which emphasizes the dynamics of an individual electron. The generalized overlap amplitudes (GOAS ), although formally defined by an integration over the coordinates of N ? 1 electrons, are, instead, resolved as a column vector, eigenfunction to a local one-electron differential operator. These amplitudes have no restrictions of linear independence between them, but each satisfies the one-electron boundary conditions at the nuclei and at large distances. The one-electron (or charge) density is the sum of the squares of the elements of the column. The energy density, a constant times the one-electron density, maintains this one-to-one relationship throughout modifications in total number of electrons or external potential, although the constant of proportionality, the total energy of the system, may change in the process. Indistinguishability of electrons and antisymmetry is always observed by the dynamics of each electron. A numerical example, the ground state of helium, is presented. © 1995 John Wiley & Sons, Inc.     

Thomas–Fermi approximation for the quasi‐two‐dimensional electron gas

To take into account static correlation effects in the quasi‐two‐dimensional electron gas a screened Coulombic interaction between particles is studied. The Thomas–Fermi approximation is used and the potential screening appears as a function of the Wigner–Seitz density parameter r_s and the effective width t of the system. With the self‐consistent field theory applied to the modified deformable jellium, the ground‐state energy per particle and the conditions for electron localization are obtained in terms of the interparticle distance and the screening parameter μ. A critical minimum characteristic width t_c is obtained; below t_c no long‐range order is obtained. For larger widths a stable localized state is predicted at finite densities. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 269–276, 2001