Any order imaginary time propagation method for solving the Schrodinger equation

Abstract

The eigenvalue-function pair of the 3D Schrödinger equation can be efficiently computed by use of high order, imaginary time propagators. Due to the diffusion character of the kinetic energy operator in imaginary time, algorithms developed so far are at most fourth-order. In this work, we show that for a grid based algorithm, imaginary time propagation of any even order can be devised on the basis of multi-product splitting. The effectiveness of these algorithms, up to the 12${}^{\mathrm{th}}$ order, is demonstrated by computing all 120 eigenstates of a model C${}_{60}$ molecule to very high precisions. The algorithms are particularly useful when implemented on parallel computer architectures.

8 pages, 3 figures

References in corpus (1)

• Three real-space discretization techniques in electronic structure calculations

Cited by in corpus (15)

• Solving the Schrödinger eigenvalue problem by the imaginary time propagation technique using splitting methods with complex coefficients
• Information entropic measures of a quantum harmonic oscillator in symmetric and asymmetric confinement within an impenetrable box
• Finite-range effects in ultradilute quantum drops
• Improved one-dimensional model potentials for strong-field simulations
• Fourth order real space solver for the time-dependent Schrödinger equation with singular Coulomb potential
• Two-dimensional Bloch electrons in perpendicular magnetic fields: an exact calculation of the Hofstadter butterfly spectrum
• Towards a QMC-based density functional including finite-range effects: excitation modes of a ${}^{39}$K quantum droplet
• Density-based one-dimensional model potentials for strong-field simulations in $\text{He}$, ${\text{H}}_2^{+}$ and ${\text{H}}_2$
• Quantum confinement in 1D systems through an imaginary-time evolution method
• Trapped Bose-Bose mixtures at finite temperature: a quantum Monte Carlo approach
• Density functional theory beyond the Born-Oppenheimer approximation: accurate treatment of the ionic zero-point motion
• The Wigner Function of Ground State and One-Dimensional Numerics
• Quantum simulations of neutral water clusters and singly-charged water cluster anions
• Information analysis in free and confined harmonic oscillator
• Ab-initio Quantum Monte Carlo study of ultracold atomic mixtures