Conformations, structural transitions and visible near-infrared absorption spectra of four-, five- and six-coordinated Cu(II) aqua complexes.

We have performed Car-Parrinello molecular dynamics simulations at ambient conditions for four-, five- and six-coordinated Cu(II) aqua complexes. The molecular geometry has been investigated in terms of Cu-O, Cu-H bond lengths and O-Cu-O bond angles and compared with earlier experimental measurement results and theoretical calculations. We find that the average Cu-O and Cu-H bond lengths increase with increasing coordination number. We have also observed relatively faster structural transition in the case of five-coordinated complex between trigonal bipyramidal and square pyramidal geometry. This result deviates from the findings of the earlier report (A. Pasquarello et al., Science, 2001, 291, 856) on copper(II) in aqueous solution and we attribute these differences to the neglect of solvent environment in our calculations. The averaged absorption spectra for the copper(II) aqua complexes have been computed using spin-restricted density functional linear response formalism taking 100 snap shots from a trajectory of 0.48 ps. We find that the calculated spectra are significantly different, showing clear features that distinguish each coordination model. Comparison with the experimentally reported absorption spectra is made wherever it is possible and the results obtained favor the distorted fivefold-coordination arrangement for the molecular structure of the Cu(II) ion in aqueous solution.

Density functional restricted-unrestricted approach for nonlinear properties: application to electron paramagnetic resonance parameters of square planar copper complexes.

The density functional restricted-unrestricted approach for treatments of spin polarization effects in molecular properties using spin restricted Kohn-Sham theory has been extended from linear to nonlinear properties. It is shown that the spin polarization contribution to a nonlinear property has the form of a quadratic response function that includes the zero-order Kohn-Sham operator, in analogy to the lower order case where the spin polarization correction to an expectation value has the form of a linear response function. The developed approach is used to formulate new schemes for computation of electronic g-tensors and hyperfine coupling constants, which include spin polarization effects within the framework of spin restricted Kohn-Sham theory. The proposed computational schemes are in the present work employed to study the spin polarization effects on electron paramagnetic resonance spin Hamiltonian parameters of square planar copper complexes. The obtained results indicate that spin polarization gives rise to sizable contributions to the hyperfine coupling tensor of copper in all investigated complexes, while the electronic g-tensors of these complexes are only marginally affected by spin polarization and other factors, such as choice of exchange-correlation functional or molecular structures, will have more pronounced impact on the accuracy of the results.

Degenerate Perturbation Theory for Electronic g Tensors: Leading-Order Relativistic Effects.

A new approach for the evaluation of the leading-order relativistic corrections to the electronic g tensors of molecules with a doublet ground state is presented. The methodology is based on degenerate perturbation theory and includes all relevant contributions to the g tensor shift up to order O(α(4)) originating from the one-electron part of the Breit-Pauli Hamiltonian-that is, it allows for the treatment of scalar relativistic, spin-orbit, and mixed corrections to the spin and orbital Zeeman effects. This approach has been implemented in the framework of spin-restricted density functional theory and is in the present paper, as a first illustration of the theory, applied to study relativistic effects on electronic g tensors of dihalogen anion radicals X2(-) (X = F, Cl, Br, I). The results indicate that the spin-orbit interaction is responsible for the large parallel component of the g tensor shift of Br2(-) and I2(-), and furthermore that both the leading-order scalar relativistic and spin-orbit corrections are of minor importance for the perpendicular component of the g tensor in these molecules since they effectively cancel each other. In addition to investigating the g tensors of dihalogen anion radicals, we also critically examine the importance of various relativistic corrections to the electronic g tensor of linear molecules with Σ-type ground states and present a two-state model suitable for an approximate estimation of the g tensor in such molecules.