First-principles theories for anharmonic lattice vibrations.

Area of Science:

• Condensed Matter Physics
• Quantum Chemistry
• Materials Science

Background:

• Lattice vibrations in extended periodic systems are crucial for material properties.
• Accurate theoretical descriptions require accounting for anharmonic effects.
• Existing vibrational methods often lack size-extensivity, limiting their application to large systems.

Purpose of the Study:

• To develop size-extensive generalizations of vibrational methods for anharmonic lattice vibrations.
• To address nonphysical size dependence in vibrational self-consistent field (VSCF) formalisms.
• To provide accurate calculations for extended periodic systems.

Main Methods:

• Size-extensive generalizations of VSCF, vibrational Moller-Plesset perturbation (VMP), and vibrational coupled-cluster (VCC) methods.
• Utilizing a quartic force field (QFF) in delocalized normal coordinates.
• Algebraic identification and elimination of nonphysical terms in VSCF.

Main Results:

• Development of a strictly size-extensive "quartic" VSCF (qVSCF) method.
• qVSCF accounts for anharmonic effects from quartic force constants and provides lattice structure corrections.
• Second-order VMP and VCC methods based on qVSCF accurately capture anharmonic effects from cubic and quartic force constants in a size-extensive manner.
• Algebraic proof demonstrating the lack of size-extensivity in vibrational configuration-interaction methods.

Conclusions:

• The developed qVSCF, VMP, and VCC methods offer accurate and size-extensive treatments of anharmonic lattice vibrations.
• These methods are readily extendable to higher-order Taylor expansions of potential energy surfaces.
• The findings pave the way for more reliable theoretical predictions of properties for extended periodic materials.