TY - JOUR

T1 - Infinite-order diagrammatic summation approach to the explicitly correlated congruent transformed Hamiltonian

AU - Bayne, Michael G.

AU - Drogo, John

AU - Chakraborty, Arindam

PY - 2014/3/21

Y1 - 2014/3/21

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevA.89.032515

DO - 10.1103/PhysRevA.89.032515

M3 - Article

AN - SCOPUS:84898061028

VL - 89

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 3

M1 - 032515

ER -