The trust-region self-consistent field method: towards a black-box optimization in Hartree-Fock and Kohn-Sham theories

The trust-region self-consistent field (TRSCF) method is presented for optimizing the total energy E(SCF) of Hartree-Fock theory and Kohn-Sham density-functional theory. In the TRSCF method, both the Fock/Kohn-Sham matrix diagonalization step to obtain a new density matrix and the step to determine the optimal density matrix in the subspace of the density matrices of the preceding diagonalization steps have been improved. The improvements follow from the recognition that local models to E(SCF) may be introduced by carrying out a Taylor expansion of the energy about the current density matrix. At the point of expansion, the local models have the same gradient as E(SCF) but only an approximate Hessian. The local models are therefore valid only in a restricted region-the trust region-and steps can only be taken with confidence within this region. By restricting the steps of the TRSCF model to be inside the trust region, a monotonic and significant reduction of the total energy is ensured in each iteration of the TRSCF method. Examples are given where the TRSCF method converges monotonically and smoothly, but where the standard DIIS method diverges.     

Modulation ellipsometry and its application to the study of the electrode-electrolyte interface

A methodology has been developed for following rapidly small changes of the ellipsometric parameters Δ₀ and ψ₀ and of the reflectivity necessary for the unique determination of $\text{n}\text{?}\text{= n ?}\text{i}\text{k}$ and thickness of a surface film. Intensity changes at given settings of the polarizer and analyzer are quantitatively related to these parameters. Examples are given of the application of this technique to the electrochemical interface of Pt and Au electrodes.     

Methylene excitation energies,transition probabilities,and frequency dependent polarizabilities

The electronic structure of the low-lying valence states of the polyatomic free radical methylene (CH₂) is investigated at two different geometries using multiconfigurational self-consistent field (MC SCF) and multiconfigurational random phase approximation (MC TDHF MC RPA) techniques. Oscillator strengths and polarizabilities of CH₂ are also examined with the MC TDHF MC RPA.     

Excited state properties from the equations of motion method. Application of the MCTDHF-MCRPA to the dipole moments and oscillator strengths of the A 1Π, a′3Π, a′3Σ+ and d3Δ low-lying valence states of CO

By examining the exact operator O_λ⁺ which is the solution of the equations of motion-Green's function method, we rederive expressions for non-reference (usually excited) state properties. Hence, additional useful information such as state expectation values, oscillator strengths, and frequency dependent and independent polarizabilities may be easily obtained from an equation of motion-Green's function calculation. With the multiconfigurational random phase approximation (MCRPA), which is equivalent to the multiconfigurational time dependent Hartree-Fock (MCTDHF), excitation energies, oscillator strengths, and excitation operators from the ground states are obtained for the low-lying valence (under 10 eV above the ground state) states of CO at the experimental ground state equilibrium geometry. We apply these techniques to obtain the excited state dipole moments for and oscillator strengths between the A ¹Π, a ³Π, a′ ³Σ⁺, and d ³Δ states of CO and compare our results to other calculations and experiments.