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Abstract
This article reviews the developments made primarily by the author in mathematical theories and algorithms for systematic many-body descriptions of correlated electrons and anharmonic lattice vibrations in polymers and molecular crystals. It also documents underlying size-extensive electron-correlation methods and their computerized implementations as well as a few pivotal applications.
Acknowledgements
Dr Mitsuo Tasumi and Dr Samuel B. Trickey are thanked for a critical reading of the manuscript prior to publication. The author is indebted to many collaborators of the work described in this article, whose names can be found in the bibliography. This work is supported by the US Department of Energy (DE-FG02-04ER15621), the US National Science Foundation (CHE-0844448), and the American Chemical Society Petroleum Research Fund (48440-AC6). S.H. is a Camille Dreyfus Teacher-Scholar.
Notes
Notes
1. Scaling of force constants, even when performed carefully, was often criticized by some as too empirical or arbitrary. However, it was embraced by others, especially, spectroscopists who were less concerned about computational methods but more interested in correct band assignments and spectral interpretation. It is a testament to Pulay's insight into the real needs of experimentalists.
2. With a HF reference, MBPT and MP give the same correlation energies order-by-order. They are distinguished from each other by the fact that MBPT is diagrammatically defined and each term in the energy expression is size-extensive. MP energy expressions, on the other hand, are not manifestly size-extensive and have non-size-extensive terms that vanish through mutual cancellation.