Kohn-Sham Molecular Orbitals Research Articles

Structure and bonding of methyl alkali metal molecules

We have carried out a theoretical investigation of the methyl alkali metals CH3 M with M=Li, Na, K and Rb using density functional theory (DFT) at the BP86/TZ2P level. Our purpose is to determine how the structure and thermochemistry (e.g., C-M bond lengths and strengths) of these organoalkali metal compounds depend on the metal atom, and to understand the emerging trends in terms of quantitative Kohn-Sham molecular orbital (KS-MO) theory. The C-M bond becomes longer and weaker if one goes from Li to the more electropositive Rb. Also, the polarity of the C-M bond increases along this series but it preserves a strong intrinsic preference to homolytic over ionic dissociation in the gas phase. We show that a description of the bonding mechanism in terms of a polar C-M electron-pair bond between the methyl radical and alkali metal atom is just as natural as an ionic description (i.e., in terms of CH3-+M+) and that it provides a straightforward way of understanding all observed trends.

Redox Site Confinement in Highly Unsymmetric Dimanganese Complexes

A set of highly preorganized pyrazolate-bridged dimanganese complexes L(Mn)MnX have been prepared and structurally characterized. They can be described as hybrid organometallic/Werner-type systems that consist of a low-spin CpMn(I)(CO)2 subunit (Mn1) and a proximate tripodal tetradentate {N4} binding pocket accommodating a high-spin Mn(II) ion (Mn2), with Mn...Mn distances of approximately 4.3 A and different coligands bound to Mn2. Density functional theory (DFT) calculations (both the hybrid B3LYP and the pure BP86 functionals and the all-electron basis sets 6-311G and 6-311G*) confirm that the valence alpha and beta Kohn-Sham molecular orbitals (MOs) of these mixed-valent Mn(I)Mn(II) compounds have predominant Mn(3d) character and an almost perfectly localized nature: all five unpaired electrons are essentially localized at the Werner-type Mn2, whereas Mn1 possesses an effective closed-shell structure with the MOs of highest energy centered there. One-electron oxidation occurs in a clean process at approximately E(1/2) = -0.6 V (versus ferrocene/ferrocinium), giving the low-spin/high-spin Mn(II)Mn(II) species. UV/vis and IR spectroelectrochemistry as well as a detailed theoretical analysis reveal that the redox process takes place with strict site control at the organometallic subunit, while it does not significantly influence the spin and charge distribution on the Werner-type site. Positions and shifts of the nu(C[triple bond]O) absorptions are largely reproduced by the DFT calculations. These systems thus represent an exceptional example of the effect the unsymmetry of a dinucleating ligand scaffold has on the spin and charge distribution in homobimetallic complexes and might offer interesting prospects for the study of the cooperative effects of bimetallic arrays.

Generalized Christoffel?Darboux formulae and the frontier Kohn?Sham molecular orbitals

The Christoffel–Darboux formula for classical orthogonal polynomials is generalized to arbitrary sets of orthogonal functions in three dimensions, yielding an explicit link between frontier Kohn–Sham molecular orbitals and the Kohn–Sham density matrix. Methods using this result could significantly accelerate Kohn–Sham density functional theory calculations, as only a subset of the Kohn–Sham equations would need to be addressed. The result can also be seen as an explicit justification for the utility of frontier molecular orbital theory.

Electron correlation effects on the shape of the Kohn-Sham molecular orbital

Even systems in which strong electron correlation effects are present, such as the large near-degeneracy correlation in a dissociating electron pair bond exemplified by stretched H2, are represented in the Kohn–Sham (KS) model of non-interacting electrons by a determinantal wavefunction built from the KS molecular orbitals. As a contribution to the discussion on the status and meaning of the KS orbitals we investigate, for the prototype system of H2 at large bond distance, and also for a one-dimensional molecular model, how the electron correlation effects show up in the shape of the KS σg orbital. KS orbitals φHL and φFCI obtained from the correlated Heitler-London and full configuration interaction wavefunctions are compared to the orbital φLCAO, the traditional linear combination of atomic orbitals (LCAO) form of the (approximate) Hartree-Fock orbital. Electron correlation manifests itself in an essentially non-LCAO structure of the KS orbitals φHL and φFCI around the bond midpoint, which shows up particularly clearly in the Laplacian of the KS orbital. There are corresponding features in the kinetic energy density ts of the KS system (a well around the bond midpoint) and in the one-electron KS potential vs (a peak). The KS features are lacking in the Hartree-Fock orbital, in a minimal LCAO approximation as well as in the exact one.