Symmetry-adapted formulation of the G-particle-hole hypervirial equation method

Highly accurate 2-body reduced density matrices of atoms and molecules have been directly determined without calculation of their wave functions with the use of the G-particle-hole hypervirial (GHV) equation method (Alcoba et?al. in Int. J. Quantum Chem. 109:3178, 2009). Very recently, the computational efficiency of the GHV method has been significantly enhanced through the use of sum factorization and matrix-matrix multiplication (Alcoba et?al. in Int. J. Quantum Chem 111:937, 2011). In this paper, a detailed analysis of the matrix contractions involved in GHV calculations is carried out. The analysis leads to a convenient strategy for exploiting point group symmetry, by which the computational efficiency of the GHV method is further improved. Implementation of the symmetry-adapted formulation of the method is reported. Computer timings and hardware requirements are illustrated for several representative chemical systems. Finally, the method is applied to the well-known challenging calculation of the torsional potential in ethylene.