Optimization of orbital-specific virtuals in local Møller-Plesset perturbation theory

Abstract

We present an orbital-optimized version of our orbital-specific-virtuals second-order Møller-Plesset perturbation theory (OSV-MP2). The OSV model is a local correlation ansatz with a small basis of virtual functions for each occupied orbital. It is related to the Pulay-Saebø approach, in which domains of virtual orbitals are drawn from a single set of projected atomic orbitals; but here the virtual functions associated with a particular occupied orbital are specifically tailored to the correlation effects in which that orbital participates. In this study, the shapes of the OSVs are optimized simultaneously with the OSV-MP2 amplitudes by minimizing the Hylleraas functional or approximations to it. It is found that optimized OSVs are considerably more accurate than the OSVs obtained through singular value decomposition of diagonal blocks of MP2 amplitudes, as used in our earlier work. Orbital-optimized OSV-MP2 recovers smooth potential energy surfaces regardless of the number of virtuals. Full optimization is still computationally demanding, but orbital optimization in a diagonal or Kapuy-type MP2 approximation provides an attractive scheme for determining accurate OSVs.

The orbital-specific-virtual local coupled cluster singles and doubles method

“…Other theoretical improvements offered by the OSV method include the recovery of smooth potential energy surfaces (without the need for unphysical smoothing schemes [35][36][37] ) even for modest numbers of OSVs, particularly when fully optimized OSVs are used. 34 It should be noted, however, that there are also disadvantages relative to PAOs, such as higher memory requirements and less straightforward generalization to openshell cases.…”

“…We recently described a tensor factorization that lies between the PAO and PNO methods, the orbitalspecific virtual (OSV) method. 1,34 The OSV factorization associates a set of virtual orbitals with each occupied orbital ("orbital specific") rather than to each orbital pair ij as in the PNO method. This leads to simplifications relative to the PNO method, in particular in the integral transformation.…”

Efficient and accurate treatment of weak pairs in local CCSD(T) calculations

“…Local MOs spanning the occupied space (LMOs) are usually obtained by applying a localization procedure such as Pipek-Mezey 10 or Boys 11 to the occupied canonical orbitals obtained from the preceding Hartree-Fock calculation. For the virtual space, e.g., projected atomic orbitals (PAOs), [12][13][14][15][16][17] orbital specific virtuals (OSVs), 6,[18][19][20][21] or pair natural orbitals (PNOs) [22][23][24][25][26][27][28][29] can be used, either exclusively, or also in combination.…”

The orbital-specific virtual local triples correction: OSV-L(T)

“…46 In either case, the resulting unitary (orthogonal) transformation matrices Q i transform from canonical virtuals (4) becomes smaller than a certain threshold l OSV . This criterion will be used throughout the current work.…”