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Generation and Coherent Control of Pulsed Quantum Frequency Combs

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Self-consistent, constrained linear-combination-of-atomic-potentials approach to quantum mechanics.

Brett I Dunlap¹, Igor V Schweigert

¹Code 6189, Theoretical Chemistry Section, US Naval Research Laboratory, Washington, DC 20375-5342, USA. dumontr@mcmaster.ca

The Journal of Chemical Physics

|February 2, 2011

Summary

This study introduces variational perturbation theory for precise Kohn-Sham (KS) potential calculations in density-functional theory. The method offers stationary potentials and energies without iterative steps, simplifying accurate derivative computations.

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Area of Science:

Computational Chemistry
Quantum Chemistry
Density-Functional Theory

Background:

The Kohn-Sham (KS) potential is crucial in density-functional theory (DFT) for determining electronic orbitals.
Accurate calculation of the KS potential and its derivatives is essential for reliable electronic structure predictions.

Purpose of the Study:

To develop and validate a novel variational perturbation theory for approximating the KS potential.
To provide a method for precise calculation of KS potential derivatives without iterative procedures.

Main Methods:

Development of variational perturbation theory through second order.
Application of linear-combination of atomic potentials (LCAP) approximation for stationary KS potentials.
Calculation of energy and KS potential derivatives using finite differences of self-consistent field (SCF) calculations.

Main Results:

Variational perturbation theory yields stationary KS potentials and even-order perturbed energies.
The method avoids computationally intensive iterative steps required by coupled-perturbed methods.
Precision of derivatives is independent of the fidelity of the LCAP KS potential approximation.
Fourth derivatives of energy and first/second derivatives of KS potentials were computed for standard molecules.

Conclusions:

The developed variational perturbation theory offers an efficient and accurate approach for KS potential and derivative calculations in DFT.
Constrained and unconstrained calculations showed no significant differences, simplifying the application of the method.