Infinite-order diagrammatic summation approach to the explicitly correlated congruent transformed Hamiltonian

Michael G. Bayne, John Drogo, Arindam Chakraborty

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We present the development of a real-space and projected congruent transformation method for treating electron correlation in chemical systems. This method uses an explicitly correlated function for performing congruent transformation on the electronic Hamiltonian. As a result of this transformation, the electronic Hamiltonian is transformed into a sum of two-, three-, four-, five-, and six-particle operators. Efficient computational implementation of these many-particle operators continues to be challenging for application of the congruent transformation approach for many-electron systems. In this work, we present a projected congruent transformed Hamiltonian (PCTH) approach to avoid computation of integrals involving operators that couple more than two particles. The projected congruent transformation becomes identical to the real-space congruent transformation in the limit of infinite basis size. However, for practical calculations, the projection is always performed on a finite-dimensional space. We show that after representing the contributing expressions of the PCTH in terms of diagrams, it is possible to identify a subset of diagrams that can be summed up to infinite order. This technique, denoted as partial infinite-order summation (PIOS), partly alleviates the limitation from the finite-basis representation of the PCTH method. The PCTH and PCTH-PIOS methods were applied to an isoelectronic series of 10-electron systems (Ne,HF,H2O,NH3,CH4) and results were compared with configuration interaction (CISD) calculations. The results indicate that the PCTH-PIOS method can treat electron-electron correlations while avoiding explicit construction and diagonalization of the Hamiltonian matrix.

Original languageEnglish (US)
Article number032515
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number3
StatePublished - Mar 21 2014

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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