Analysis of vector potential approach for calculating linear and nonlinear responses of infinite periodic systems to a finite static external electric field

Abstract

The vector potential approach for calculating the polarization of an infinite periodic system induced by a uniform finite electrostatic field is described in detail. It is demonstrated that the resulting secular equation can also be obtained from one particular version of the modern theory of polarization. A key element of this computationally advantageous crystal orbital treatment is an efficient procedure for smoothing the occupied orbitals as a function of the wave vector $k$. Based on a carefully constructed model polymer Hamiltonian, we find good convergence of the self-consistent field solutions even when many $k$ points are required for accuracy, and even at fields well beyond the estimated threshold for Zener tunneling. Characteristic signals for the onset of breakdown due to Zener tunneling are established. An analytical expression for the forces is obtained and used to determine geometry relaxation due to the field. The validity and accuracy of the approach are demonstrated through comparison with results for long finite chains. Finally, some interesting implications for donor-acceptor substitution at the chain ends are discussed.