Normal-ordered second-quantized Hamiltonian for molecular vibrations.

Area of Science:

• Quantum chemistry
• Computational physics
• Molecular dynamics

Background:

• Quantum dynamics simulations require accurate Hamiltonians.
• Representing potential energy surfaces in various coordinate systems is crucial.
• Vibrational Self-Consistent Field (XVSCF) and related methods are essential for molecular vibrations.

Purpose of the Study:

• To derive a normal-ordered second-quantized Hamiltonian for quantum dynamics.
• To connect Hamiltonian excitation amplitudes to XVSCF and self-consistent phonon methods.
• To establish a framework for efficient derivation of vibrational perturbation theory equations.

Main Methods:

• Derivation of a Hamiltonian in a normal-ordered second-quantized form.
• Taylor series expansion of potential energy surfaces in arbitrary orthogonal coordinates.
• Identification of Hamiltonian amplitudes with XVSCF/self-consistent phonon parameters.

Main Results:

• The constant, first-, and second-order excitation amplitudes correspond to ground-state energy, gradients, and frequencies.
• Demonstrated size-extensive properties of these amplitudes (V(1-n/2) dependence).
• Provided a pathway for rapid derivation of XVSCF and vibrational many-body perturbation equations.

Conclusions:

• The derived Hamiltonian offers a unified approach to vibrational structure calculations.
• This formalism simplifies the derivation of advanced vibrational methods.
• The results facilitate efficient and accurate quantum dynamics simulations.