Ab-Initio Molecular Dynamics with Screened Lorentz Forces. Part I. Calculation and Atomic Charge Interpretation of Berry Curvature

Abstract

The dynamics of a molecule in a magnetic field is significantly different form its zero-field counterpart. One important difference in the presence of a field is the Lorentz force acting on the nuclei, which can be decomposed as the sum of the bare nuclear Lorentz force and a screening force due to the electrons. This screening force is calculated from the Berry curvature and can change the dynamics qualitatively. It is therefore important to include the contributions from the Berry curvature in molecular dynamics simulations in a magnetic field. In this work, we present a scheme for calculating the Berry curvature numerically, by a finite-difference technique, addressing challenges related to the arbitrary global phase of the wave function. The Berry curvature is calculated as a function of bond distance for H${}_2$ at the restricted and unrestricted Hartree--Fock levels of theory and for CH${}^{+}$ as a function of the magnetic field strength at the restricted Hartree--Fock level of theory. The calculations are carried out using basis sets of contracted Gaussian functions equipped with London phase factors (London orbitals) to ensure gauge-origin invariance. In the paper, we also interpret the Berry curvature in terms of atomic charges and discuss its convergence in basis sets with and without London phase factors. Calculation of the Berry curvature allows for its inclusion in \textit{ab initio} molecular dynamics simulations in a magnetic field.

References in corpus (2)

• Electron corrected Lorentz forces in solids and molecules in magnetic field
• Regularized Born-Oppenheimer molecular dynamics

Cited by in corpus (14)

• Spin Polarization through A Molecular Junction Based on Nuclear Berry Curvature Effects
• Cholesky decomposition of complex two-electron integrals over GIAOs: Efficient MP2 computations for large molecules in strong magnetic fields
• Ab-Initio Molecular Dynamics with Screened Lorentz Forces. Part II. Efficient Propagators and Rovibrational Spectra in Strong Magnetic Fields
• Total Angular Momentum Conservation in Ab Initio Born-Oppenheimer Molecular Dynamics
• Analytic Calculation of the Berry Curvature and Diagonal Born-Oppenheimer Correction for Molecular Systems in Uniform Magnetic Fields
• Modeling Spin-Dependent Nonadiabatic Dynamics with Electronic Degeneracy: A Phase-Space Surface-Hopping Method
• A Phase-Space Semiclassical Approach for Modeling Nonadiabatic Nuclear Dynamics with Electronic Spin
• Rotational $g$ factors and Lorentz forces of molecules and solids from density-functional perturbation theory
• Magnetic-Translational Sum Rule and Approximate Models of the Molecular Berry Curvature
• Time-Dependent Nuclear-Electronic Orbital Hartree-Fock Theory in a Strong Uniform Magnetic Field
• On the Meaning of Berry Force For Unrestricted Systems Treated With Mean-Field Electronic Structure
• Molecular vibrations in the presence of velocity-dependent forces
• Phonon thermal Hall as a lattice Aharonov-Bohm effect
• Equation-of-motion coupled-cluster variants in combination with perturbative triples corrections in strong magnetic fields