Dynamics of the Electron

Leonard M. Sander

Yu Wang

We present a formulation of the correlated electron-ion dynamics (CEID) by using equations of motion for nonequilibrium Green's functions, which generalizes CEID to a general nonequilibrium statistical ensemble that allows for a variable total number of electrons. We make a rigorous connection between CEID and diagrammatic perturbation theory, which furthermore allows the key approximations in CEID to be quantified in diagrammatic terms, and, in principle, improved. We compare analytically the limiting behavior of CEID and the self-consistent Born approximation (SCBA) for a general dynamical nonequilibrium state. This comparison shows that CEID and SCBA coincide in the weak electron-phonon coupling limit, while they differ in the large ionic mass limit where we can readily quantify their difference. In particular, we illustrate the relation between CEID and SCBA by perturbation theory at the fourth order in the coupling strength.

Rubén Santamaría

Juan C. Dominguez, Ismael de Farias, Jorge A. Morales

We present the first step toward the quantum computing (QC) formulation of the electron nuclear dynamics (END) method within the variational quantum simulator (VQS) scheme: END/QC/VQS. END is a time-dependent, variational, on-the-flight, and non-adiabatic method to simulate chemical reactions. END represents nuclei with frozen Gaussian wave packets and electrons with a single-determinantal state in the Thouless non-unitary representation. Within the hybrid quantum/classical VQS, END/QC/VQS currently evaluates the metric matrix M and gradient vector V of the symplectic END/QC equations on the QC software development kit QISKIT, and calculates basis function integrals and time evolution on a classical computer. To adapt END to QC, we substitute the Thouless non-unitary representation with Fukutome unitary representation. We derive the first END/QC/VQS version for pure electronic dynamics in multielectron chemical models consisting of two-electron units with fixed nuclei. Therein, Fukutome unitary matrices factorize into triads of one-qubit rotational matrices, which leads to a QC encoding of one electron per qubit. We design QC circuits to evaluate M and V in one-electron diatomic molecules. In log2-log2 plots, errors and deviations of those evaluations decrease linearly with the number of shots and with slopes = −1/2. We illustrate an END/QC/VQS simulation with the pure electronic dynamics of H2+ We discuss the present results and future END/QC/QVS extensions.

H. Keith McDowell

The second-quantized, many-electron, atomic, and molecular Hamiltonian is partitioned both by the identity or labeling of the spin orbitals and by the dynamics of the spin orbitals into a system coupled to a bath. The electron bath is treated by a molecular time scale generalized Langevin equation approach designed to include one-electron dynamics in the system dynamics. The bath is formulated as an equivalent chain of spin orbitals through the introduction of equivalent-chain annihilation and creation operators. Both the dynamics and the quantum grand canonical statistical properties of the electron bath are examined. Two versions for the statistical properties of the bath are pursued. Using a weak bath assumption, a bath statistical average is defined which allows one to achieve a reduced dynamics description of the electron system which is coupled to the electron bath. In a strong bath assumption effective Hamiltonians are obtained which reproduce the dynamics of the bath and which lead to the same results as found in the weak bath assumption. The effective (but exact) Hamiltonian is found to be a one-electron Hamiltonian. A reduced dynamics equation of motion for the system population matrix is derived and found to agree with a previous version. This equation of motion is useful for studying electron transfer in the system when coupled to an electron bath.

Konstantin V. Kazakov