Configuration Interaction between Covalent and Ionic States in the Quantal and Semiclassical Limits with Application to Coherent and Hopping Charge Migration

On the exact continuous mapping of fermions

We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to map a general many-fermion Hamiltonian and then consider two specific models that encode the fundamental physics of many fermionic systems, the Anderson impurity and Hubbard models. We use these models to demonstrate how efficient mappings of these Hamiltonians can be constructed using a judicious choice of index ordering of the fermions. This development provides an alternative exact route to calculate the static and dynamical properties of fermionic systems and sets the stage to exploit the quantum-classical and semiclassical hierarchies to systematically derive methods offering a range of accuracies, thus enabling the study of problems where the fermionic degrees of freedom are coupled to complex anharmonic nuclear motion and spins which lie beyond the reach of most currently available methods.

Theoretical description of charge migration with a single Slater-determinant and beyond

Triggered by the interest to study charge migration in large molecular systems, a simple methodology has recently been proposed based on straightforward density functional theory calculations. This approach describes the time evolution of the initially created hole density in terms of the time evolution of the ionized highest occupied molecular orbital (HOMO). Here we demonstrate that this time-dependent analog of Koopmans' theorem is not valid, and instead of the time evolution of the HOMO, the time evolution of the orbitals that remain occupied in the cation determines the evolution of the initially created hole in the framework of time-dependent single-determinant theories. Numerical examples underline that for a proper description of charge migration processes, an explicit treatment of the electron correlation is indispensable. Moreover, they also demonstrate that the attempts to describe charge migration based on Kohn-Sham density functional theory using conventional exchange-correlation functionals are doomed to fail due to the well-known self-interaction error.

Semiclassical representations of electronic structure and dynamics

We use a new formulation of the semiclassical coherent state propagator to derive and evaluate several different approximate representations of electron dynamics. For each representation we examine: (1) its ability to treat quantum effects and electron correlation, (2) its expected scaling with system size, and (3) the types of systems for which it can be used. We also apply two of the methods to a pair of model problems, namely the minimal basis electron dynamics in H2 and the magnetization dynamics in a cluster model of the Kagome lattice, in order to verify the feasibility of these approaches for realistic systems. Based on all these criteria, we find that the representation that takes the electron spins as the classical variables is particularly promising for the quantitative and qualitative description of large systems.