Optimized virtual orbitals for correlated calculations: an alternative approach

Abstract

We propose an alternative formulation for creating the optimized virtual orbital space (OVOS). Our technique exploits and extends the method developed by Adamowicz and co-workers [L. Adamowicz, R.J. Bartlett. J. chem. Phys., 86, 6314 (1987); L. Adamowicz, R.J. Bartlett, A.J. Sadlej. J. chem. Phys., 88, 5749 (1988).]. The aim of the OVOS technique is to reduce the original SCF basis of the virtual molecular orbitals and to reduce the computer time in the coupled cluster (CC) and related highly sophisticated correlated methods. OVOS is created by using an invariant unitary rotation of the virtual orbitals subspace. New optimization functionals are proposed and implemented. The first type are ‘energy’ functionals. Their optimization leads to the minimal difference between the CCSD, CCD, or the second-order perturbation energy, MP2, in the original orbital basis and the OVOS basis, respectively. Alternatively, linearized ‘overlap’ functionals optimize the overlap between the correlated wave function in the full and the OVOS space, respectively. The original exponential parametrization was replaced by the efficient algorithm for the virtual orbital subspace rotation based on the Lagrangian multipliers technique which ensures orthogonality within rotated virtual orbitals. The method is illustrated by calculations of correlation energies and/or reaction energies, spectroscopic constants or dipole moments of HF, HCN, HNC, CO and F2 molecules and dissociation energies of pentane to propene and ethane. The ‘overlap’ functional is shown to be more efficient than the ‘energy’ one, particularly in representing triple excitations using OVOS. The basis set dependence of the efficiency of the OVOS technique was also studied.