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17.1 Introduction

The purpose of local correlation methods is to reduce the scaling of the computational effort as function of the molecular size and to make it possible to perform accurate calculations for larger molecules. In MOLPRO, local correlation methods are based on the Ansatz by Pulay (Chem. Phys. Lett. 100, 151 (1983)). The occupied valence orbitals are localized by one of the standard localization methods (by default Pipek-Mezey localization is used) and the virtual orbital space is represented by projected atomic orbitals (PAOs). Using Molpro 2012, also orbital specific virtuals (OSVs) can be used as an alternative (see JCP, DOI http://dx.doi.org/10.1063/1.3696963) in DF-LMP2, DF-LCCSD, and DF-LCCSD(T) calculations. The orbital pairs are classified according to distance criteria. By default only strong pairs, in which the two orbitals are close together and which account for most of the correlation energy are treated at the highest computational level (e.g., local coupled cluster, LCCSD), while weak pairs are treated at the local MP2 (LMP2) level. Very distant pairs can be neglected. For each of the correlated pairs, a different subspace (domain) of virtual orbitals is automatically chosen, and the excitations are restricted into these domains. The basic features of the LCCSD method are described in J. Chem. Phys. 104, 6286 (1996). A detailed description of the current DF-LCCSD(T) implementation can be found in J. Chem. Phys. 135, 144116 (2011).

A very important recent improvement of the local correlation methods is the inclusion of explicitly correlated terms. These not only istrongly reduce the basis set errors, but also errors due to the domain approximations. See J. Chem. Phys. 135, 144117 (2011) for this method and extensive benchmark results. It is strongly recommended to use these explicitly correlated methods.

The local correlation program of MOLPRO can currently perform closed-shell LMP2, LMP3, LMP4(SDTQ), LCISD, LQCISD(T), and LCCSD(T) calculations. For large molecules, all methods scale linearly with molecular size, provided very distant pairs are neglected, and the integral-direct algorithms are used.

Much higher efficiency is achieved by using density fitting (DF) approximations (see section 16) to compute the integrals. Density fitting is available for all local methods up to LCCSD(T), as well as for analytical LMP2 gradients. The errors introduced by DF are negligible, and the use of the DF methods is highly recommended.

Energy gradients are available for LMP2, DF-LMP2, DF-SCS-LMP2, and LQCISD (in the latter case only for LOCAL=1, i.e. the local calculation is simulated using the canonical program, and savings only result from the reduced number of pairs).

Naturally, the local approximation can introduce some errors, and therefore the user has to be more careful than with standard black box methods. This problem is very much reduced, however, in the explicitly correlated methods. On the other hand, the low-order scaling makes it possible to treat much larger systems at high levels of theory than it was possible so far. Before using these methods, it is strongly recommended to read the literature in order to understand the basic concepts and approximations.

References:

$[1]$ C. Hampel and H.-J. Werner, Local Treatment of electron correlation in coupled cluster (CCSD) theory, J. Chem. Phys. 104, 6286 (1996).
$[2]$ H.-J. Werner and M. Schütz, An efficient local coupled-cluster method for accurate thermochemistry of large systems, J. Chem. Phys. 135, 144116 (2011).
$[3]$ T. B. Adler and H.-J. Werner, An explicitly correlated local coupled-cluster method for calculations of large molecules close to the basis set limit, J. Chem. Phys. 135, 144117 (2011).

Further references can be found therein.



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