A general diagrammatic algorithm for contraction and subsequent simplification of second-quantized expressions

• Published in: The Journal of chemical physics Vol. 121; no. 8; pp. 3374 - 3383
• Main Authors: Bochevarov, Arteum D., Sherrill, C. David
• Format: Journal Article
• Language: English
• Published: United States 22.08.2004
• Subjects: Algorithms; Models, Theoretical
• ISSN: 0021-9606; 1089-7690; 1520-9032; 1089-7690
• DOI: 10.1063/1.1774977

We present a general computer algorithm to contract an arbitrary number of second-quantized expressions and simplify the obtained analytical result. The functions that perform these operations are a part of the program Nostromo which facilitates the handling and analysis of the complicated mathematical formulas which are often encountered in modern quantum-chemical models. In contrast to existing codes of this kind, Nostromo is based solely on the Goldstone-diagrammatic representation of algebraic expressions in Fock space and has capabilities to work with operators as well as scalars. Each Goldstone diagram is internally represented by a line of text which is easy to interpret and transform. The calculation of matrix elements does not exploit Wick’s theorem in a direct way, but uses diagrammatic techniques to produce only nonzero terms. The identification of equivalent expressions and their subsequent factorization in the final result is performed easily by analyzing the topological structure of the diagrammatic expressions.