Analytic Calculation of the Berry Curvature and Diagonal Born-Oppenheimer Correction for Molecular Systems in Uniform Magnetic Fields

Abstract

The diagonal nonadiabatic term arising from the Born--Oppenheimer wave-function ansatz contains contributions from a vector and scalar potential. The former is provably zero when the wave function can be taken to be real valued, and the latter, known as the diagonal Born--Oppenheimer correction (DBOC), is typically small in magnitude. Therefore, unless high accuracy is sought, the diagonal nonadiabatic term is usually neglected when calculating molecular properties. In the presence of a magnetic field, the wave function is generally complex, and the geometric vector potential gives rise to a screening force that is qualitatively important for molecular dynamics. This screening force is written in terms of the Berry curvature and is added to the bare Lorentz force acting on the nuclei in the presence of the field. In this work, we derive analytic expressions for the Berry curvature and DBOC using both first and second quantization formalisms for the case of generalized and restricted Hartree--Fock theories in a uniform magnetic field. The Berry curvature and DBOC are calculated as a function of the magnetic field strength and the bond distance for the ground-state singlets of H${}_2$, LiH, BH, and CH${}^{+}$. We also examine the stability and time-reversal symmetry of the underlying self-consistent field solutions. The character of the DBOC and Berry curvature is found to depend upon the magnetic field and varies between molecules. We also identify instances of broken time-reversal symmetry for the dissociation curves of BH and CH${}^{+}$.

29 Pages, 14 Figures, 34 individual figures (figure panels)

References in corpus (3)

• Ab-Initio Molecular Dynamics with Screened Lorentz Forces. Part I. Calculation and Atomic Charge Interpretation of Berry Curvature
• Ab-Initio Molecular Dynamics with Screened Lorentz Forces. Part II. Efficient Propagators and Rovibrational Spectra in Strong Magnetic Fields
• Electron corrected Lorentz forces in solids and molecules in magnetic field

Cited by in corpus (5)

• Total Angular Momentum Conservation in Ab Initio Born-Oppenheimer Molecular Dynamics
• 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