General technique for analytical derivatives of post-projected Hartree-Fock

The maximum occupancy condition for the localized property-optimized orbitals

It is shown analytically that the Chemist's Localized Property-optimized Orbitals (CLPOs), which are the localized orbitals obtainable from the results of ab initio calculations by the open-source program JANPA (http://janpa.sourceforge.net/) according to the recently proposed optimal property partitioning condition, form the Lewis structure with nearly maximum possible total electron occupancy. The conditions required for this additional optimality to hold are discussed. In particular, when a single-determinant wavefunction is used to describe the molecular system without a noticeable electron delocalization, CLPOs derived from this wavefunction approximately optimize the same target quantity as the Natural Bond Orbitals (NBOs), establishing in this way the link between the two sets of localized orbitals. The performance of CLPO and NBO methods is compared by using a dataset containing 7101 small molecules, and the relevant methodological features of both methods are discussed.

Extending spin-symmetry projected coupled-cluster to large model spaces using an iterative null-space projection technique

Recently, we introduced an orbital-invariant approximate coupled-cluster (CC) method in the spin-projection manifold. The multi-determinantal property of spin-projection means that the parametrization in the spin-extended CC (ECC) ansatz is nonorthogonal and overcomplete. Therefore, the linear dependencies must be removed by an orthogonalization procedure to obtain meaningful solutions. Multi-reference methods often achieve this by diagonalizing a metric of the equation system, but this is not feasible with ECC because of the enormous size of the metric, a consequence of the incomplete active space of the spin-projected Hartree-Fock reference. As a result, the applicability of ECC has been limited to small benchmark systems, for which the ansatz was shown to be superior to the configuration interaction and linearized approximations. In this article, we provide a solution to this problem that completely avoids the metric diagonalization by iteratively projecting out its null-space from the working equations. As the additional computational cost required for this iterative projection is only marginal, it greatly expands the application range of ECC. We demonstrate the potential of approximate ECC by studying the complete basis set limit of F₂ and transition metal complexes such as NiO, Mn₂ , and [Cu₂ O₂ ]²⁺ , which have all been hindered by the prohibitively large metric size. We also identify the potential inadequacy of the molecular orbitals given by spin-projected Hartree-Fock in some cases, and propose possible solutions. © 2018 Wiley Periodicals, Inc.

Orbital-invariant spin-extended approximate coupled-cluster for multi-reference systems

We present an approximate treatment of spin-extended coupled-cluster (ECC) based on the spin-projection of the broken-symmetry coupled-cluster (CC) ansatz. ECC completely eliminates the spin-contamination of unrestricted CC and is therefore expected to provide better descriptions of dynamical and static correlation effects, but introduces two distinct problems. The first issue is the emergence of non-terminating amplitude equations, which are caused by the de-excitation effects inherent in symmetry projection operators. In this study, we take a minimalist approach and truncate the Taylor series of the exponential ansatz at a certain order such that the approximation safely recovers the traditional CC without spin-projection. The second issue is that the nonlinear equations of ECC become underdetermined, although consistent, yielding an infinitude of solutions. This problem arises because of the redundancies in the excitation manifold, as is common in other multi-reference approaches. We remove the linear dependencies in ECC by employing an orthogonal projection manifold. We also propose an efficient solver for our method, in which the components are usually sparse but not diagonal-dominant. It is shown that our approach is rigorously orbital-invariant and provides more accurate results than its configuration interaction and linearized CC analogues for chemical systems.