Tensor factorizations of local second-order Møller–Plesset theory
Efficient electronic structure methods can be built around efficient tensor representations of the wavefunction. Here we first describe a general view of tensor factorization for the compact representation of electronic wavefunctions. Next, we use this language to construct a low-complexity representation of the doubles amplitudes in local second-order Møller–Plesset perturbation theory. We introduce two approximations—the direct orbital-specific virtual approximation and the full orbital-specific virtual approximation. In these approximations, each occupied orbital is associated with a small set of correlating virtual orbitals. Conceptually, the representation lies between the projected atomic orbital representation in Pulay–Saebø local correlation theories and pair natural orbital correlation theories. We have tested the orbital-specific virtual approximations on a variety of systems and properties including total energies, reaction energies, and potential energy curves. Compared to the Pulay–Saebø ansatz, we find that these approximations exhibit favorable accuracy and computational times while yielding smooth potential energy curves.
© 2011 American Institute of Physics. Received 24 August 2010; accepted 30 November 2010; published online 27 January 2011 Y.K. was supported by Ministry of Education, Culture, Sports, Science, and Technology-Japan (MEXT) Grant-in-Aid for Young Scientists (B) 21750028. He also thanks the Core Research for Evolutional Science and Technology Program, High Performance Computing for Multi-Scale and Multi-Physics Phenomena of the Japan Science and Technology Agency for the financial support for his visiting research at University of Bristol. Early work on this project was performed while F.R.M. was a visiting scholar at Cornell University. G.K.C. acknowledges support from the National Science Foundation CAREER Award CHE-0645380. The authors acknowledge Professor P. Pulay for valuable discussions.
Published - 1_2E3528935.pdf
Accepted Version - 1008.4943.pdf
Supplemental Material - suppl.pdf