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Published March 28, 2009 | Published + Erratum
Journal Article Open

Quadratic canonical transformation theory and higher order density matrices


Canonical transformation (CT) theory provides a rigorously size-extensive description of dynamic correlation in multireference systems, with an accuracy superior to and cost scaling lower than complete active space second order perturbation theory. Here we expand our previous theory by investigating (i) a commutator approximation that is applied at quadratic, as opposed to linear, order in the effective Hamiltonian, and (ii) incorporation of the three-body reduced density matrix in the operator and density matrix decompositions. The quadratic commutator approximation improves CT's accuracy when used with a single-determinant reference, repairing the previous formal disadvantage of the single-reference linear CT theory relative to singles and doubles coupled cluster theory. Calculations on the BH and HF binding curves confirm this improvement. In multireference systems, the three-body reduced density matrix increases the overall accuracy of the CT theory. Tests on the H2OH2O and N2N2 binding curves yield results highly competitive with expensive state-of-the-art multireference methods, such as the multireference Davidson-corrected configuration interaction (MRCI+Q), averaged coupled pair functional, and averaged quadratic coupled cluster theories.

Additional Information

© 2009 American Institute of Physics. Received 15 December 2008; accepted 3 February 2009; published online 23 March 2009. This work was supported by Cornell University, the National Science Foundation under CAREER Program No. CHE-0645380, and the Department of Energy Office of Science under Award No. DE-FG02-07ER46432. E.N. would like to acknowledge the support of the National Science Foundation Graduate Research Fellowship Program.


Our recent article1 was published without its supplementary material, which consists of the operator algebra program and the full list of terms involved in each of the commutator and residual functions. This Erratum provides the missing material.2 The individual terms for each function are included as separate text files. The operator algebra program, along with the scripts necessary to generate the functions' terms, can be found in the tar file. This file may be decompressed using the GNU tar archiving utility via the following command: tar -xzvf sqa_v0.2.tar.gz. The operator algebra program is written entirely in the PYTHON programming language, documentation for which is available at www.python.org.

Attached Files

Published - 1_2E3086932.pdf

Erratum - 1_2E3125004.pdf


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