Rototranslational Sum Rules for Nuclear Dynamics via Traveling Pseudopotentials

Area of Science:

• Condensed matter physics
• Quantum chemistry

Background:

• Established principles of rototranslational symmetry are crucial in physics.
• Linear-response theory and its applications in solids and molecules are widely used.
• Atomic pseudopotentials are essential for efficient electronic structure calculations.

Purpose of the Study:

• To establish exact sum rules relating interatomic force constants and electromagnetic susceptibility.
• To generalize symmetry principles to the nonadiabatic regime.
• To address and resolve numerical inconsistencies in pseudopotential treatments.

Main Methods:

• Derivation of exact sum rules.
• Analysis of frequency-dependent electromagnetic susceptibility.
• Development of velocity-dependent pseudopotentials.
• Restoration of Galilean covariance in the Schrödinger equation.

Main Results:

• Established exact sum rules linking interatomic forces and susceptibility.
• Identified and resolved violations of sum rules due to pseudopotential treatment.
• Introduced a velocity-dependent pseudopotential adaptation.
• Restored Galilean covariance and the identity between mechanical and electromagnetic perturbations.

Conclusions:

• The developed methods fix inconsistencies in linear-response theory.
• Restored the validity of the Larmor theorem.
• Reconciled inertial and electrical definitions of the Drude weight in metals.