Analytic Gradients for Density Fitting MP2 Using Natural Auxiliary Functions.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• The natural auxiliary function (NAF) approximation reduces auxiliary basis set size in density fitting for quantum chemical calculations.
• NAF has demonstrated efficiency in accelerating correlation models like MP2 and coupled-cluster methods.

Purpose of the Study:

• To introduce the theory of analytic derivatives for correlation methods using the NAF approximation, specifically for MP2.
• To develop and propose a detailed algorithm for gradient calculation within the NAF framework using Lagrange multipliers.

Main Methods:

• Implementation of the NAF approximation for analytic derivative calculations.
• Application of the method of Lagrange multipliers for gradient computation.
• Benchmark calculations on small and medium-sized molecular systems.

Main Results:

• The NAF approximation yields sufficiently accurate gradients for MP2 calculations.
• Optimized geometric parameters obtained with NAF are comparable to traditional methods.
• A moderate time reduction of 15-20% was observed for both small and medium-sized molecules.

Conclusions:

• The NAF approximation is a viable and efficient approach for calculating analytic derivatives in MP2 theory.
• This method achieves a good balance between computational speedup and accuracy for molecular geometry optimization.