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Electron correlation from path resummations: the double-excitation star.

Alex J W Thom¹, George H Booth, Ali Alavi

¹University of Cambridge, Chemistry Department, Lensfield Road, Cambridge, UK CB2 1EW. ajwt3@cam.ac.uk

Physical Chemistry Chemical Physics : PCCP

|October 2, 2009

Summary

We developed a new method for approximate N-electron path-integral evaluation. This approach efficiently calculates energies and binding curves comparable to coupled cluster methods for various molecules.

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Area of Science:

Quantum chemistry
Computational physics
Electronic structure theory

Background:

Path-integral methods are crucial for understanding molecular systems.
Accurate evaluation of N-electron path-integrals remains computationally challenging.
Approximations are needed to make these calculations feasible.

Purpose of the Study:

To develop an efficient approximation for N-electron path-integral evaluation.
To introduce a method based on resumming a selected subset of paths.
To assess the accuracy of this method against established theories like CCSD.

Main Methods:

Resummation over a selected subset of paths in the N-electron path-integral.
Focusing on the double excitation star graph.
Calculating energy in O[N4] time after integral precomputation.

Main Results:

The double excitation star graph energy is efficiently calculable.
The method achieves binding curve quality similar to Coupled Cluster Singles Doubles (CCSD) theory.
Successful application to N2, water dimer, Ne2, and Ar2 dimers.

Conclusions:

The proposed path-integral resummation offers an efficient and accurate alternative for electronic structure calculations.
This method provides a viable approach for systems where traditional methods are computationally prohibitive.
The technique shows promise for studying molecular systems, including those with strong dispersion interactions.