Orbital Subspaces Research Articles

Plane wave/pseudopotential implementation of excited state gradients in density functional linear response theory: A new routevia implicit differentiation

This work presents the formalism and implementation of excited state nuclear forces within density functional linear response theory using a plane wave basis set. An implicit differentiation technique is developed for computing nonadiabatic coupling between Kohn–Sham molecular orbital wave functions as well as gradients of orbital energies which are then used to calculate excited state nuclear forces. The algorithm has been implemented in a plane wave/pseudopotential code taking into account only a reduced active subspace of molecular orbitals. It is demonstrated for the H2 and N2 molecules that the analytical gradients rapidly converge to the exact forces when the active subspace of molecular orbitals approaches completeness.

Analytic evaluation of nonadiabatic coupling terms at the MR-CI level. I. Formalism.

An efficient and general method for the analytic computation of the nonandiabatic coupling vector at the multireference configuration interaction (MR-CI) level is presented. This method is based on a previously developed formalism for analytic MR-CI gradients adapted to the use for the computation of nonadiabatic coupling terms. As was the case for the analytic energy gradients, very general, separate choices of invariant orbital subspaces at the multiconfiguration self-consistent field and MR-CI levels are possible, allowing flexible selections of MR-CI wave functions. The computational cost for the calculation of the nonadiabatic coupling vector at the MR-CI level is far below the cost for the energy calculation. In this paper the formalism of the method is presented and in the following paper [Dallos et al., J. Chem. Phys. 120, 7330 (2004)] applications concerning the optimization of minima on the crossing seam are described.

The nature of electronic excitations in singly bonded C60 dimer

Studying excited states of molecules is rather demanding computationally, and available theoretical methods usually lack a transparent interpretation scheme. Interpretation of electronic spectra is especially important if two or more fragments can be identified in the system.We developed a method to characterize different excited states in dimer molecules. Localized dimer wave functions are determined in the following manner. Isolated monomer wave functions are projected into the exact subspace of dimer orbitals leading to nonorthogonal localized MOs. Orthogonal localized MOs emerge from these by Löwdin's procedure. The resulting orbitals have the characteristic feature that they are localized either on monomer “A”, or monomer “B”, but they preserve the local intramolecular symmetries within both fragments. In terms of these orbitals an all-single CI calculation is executed. Inspecting the CI eigenvectors, the excitations can easily be classified as to their localized vs charge transfer characters (A→A, B→B, A→B, and B→A). This procedure was used in studying excited states of the singly bonded covalent buckminsterfullerene dimer.

Hartree–Fock operators to improve virtual orbitals and configuration interaction energies

The definitions of Hartree–Fock operators able to provide virtual orbitals more suited for correlation and excited electronic states and for configuration interaction (CI) treatments have been reviewed. From the comparisons, a simple procedure to improve these operators has emerged and discussed. In our approach, the sign of the pair and total electronic densities is changed to make the interelectron potential attractive for excited electrons. The orbitals generated from the modified operators have been compared to canonical HF orbitals by performing large scale CI computations on ground and excited states of the NO+ molecule improving the CI energies and the dipole moments for all states and the convergence properties of CI. Similarly, using truncated orbital subspaces, the ground state MP2 correlation energy becomes closer to the basis limit for this property.

The multi-configurational adiabatic electron transfer theory and its invariance under transformations of charge density basis functions

The continuum multi-configurational dynamical theory of electron transfer (ET) reactions in a chemical solute immersed in a polar solvent is developed. The solute wave function is represented as a CI expansion. The corresponding decomposition of the solute charge density generates a set of dynamical variables, the discrete medium coordinates. A new expression for the free energy surface in terms of these coordinates is derived. The stochastic equations of motion derived earlier are shown to be invariant under unitary transformations of orbitals used to build the CI expansion provided the latter is complete over the corresponding orbital subspace, and also under general linear transformations of the bases employed in expanding the charge density. The interrelation between the present general treatment and the reduced theory applied previously in terms of the two-level ET model is investigated. Finally, the explicit expression for the screening potential of medium electrons is derived in the electronic Born-Oppenheimer approximation (fast (slow) electronic timescale for solvent (solute)). The theory leads to a self-consistent scheme for practical calculations of rate constants for ET reactions involving complex solutes. Illustrative test calculations for two-level ET systems are presented, and the importance of proper boundary conditions for realistic molecular cavities is demonstrated.

Path integral formulation of Roothaan's equations

AbstractThe generating functional Z(N) of the molecular orbital theory of N electrons has been projected into a subspace of atomic orbitals. By application of the saddle‐Point approximataions to the corresponding effective action, a set of equations of motion results. These equations are the classical Roothaan's equations of quantum chemistry.

Perturbation theory of the electron correlation effects for atomic and molecular properties VI. Complete active space (CAS) SCF and MBPT calculations of electric properties of the FH molecule

A comparative study of the applicability of the CAS SCF and different fourth-order MBPT methods for the calculation of molecular electric properties is performed. The accuracy of the CAS SCF results for the dipole moment and dipole polarizability tensor of the FH molecule is governed and limited by the size of the active orbital subspace, while the complete fourth-order MBPT results seem to suffer from the truncation of the correlation perturbation series. Relatively large fourth-order correlation corrections to the calculated properties, arising from single and triple substitutions, have been found and indicate the importance of a careful treatment of all substitutions contributing in the given order of the MBPT expansion.

A note on the dimension of an orbital subspace

This note contains a dimension formula for an orbital subspace in a symmetry class of tensors corresponding to an irreducible character λ of a subgroup G of S m . An algorithm for choosing a basis is also described.