32.1 Introduction

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 to compute the integrals. Density fitting is available for all local methods up to LCCSD(T), as well as for analytical LMP2 gradients. Only iterative triples methods like LCCSDT-1b can currently not be done with density fitting.

The errors introduced by DF are negligible, and the use of the DF methods is highly recommended. Linear scaling can be obtained in DF-LMP2 using the LOCFIT option (see Ref. 11); in DF-LCCSD(T), the most important parts also scale linearly, but some transformation steps scale quadratically.

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).

Local explicitly correlated methods (DF-LMP2-R12 and DF-LMP2-F12 are described in section 29.

Before using these methods, it is strongly recommended to read the literature in order to understand the basic concepts and approximations. A recent review [1] and Ref. [2] may be suitable for an introduction.

References:

Review:
$[1]$ H.-J. Werner and K. Pflüger, On the selection of domains and orbital pairs in local correlation treatments, Ann. Rev. Comp. Chem., in press. (preprint available under http://www.theochem.uni-stuttgart.de/ werner/local/preprints/)

General local Coupled Cluster:
$[2]$ C. Hampel and H.-J. Werner, Local Treatment of electron correlation in coupled cluster (CCSD) theory, J. Chem. Phys. 104, 6286 (1996).
$[3]$ M. Schütz and H.-J. Werner, Local perturbative triples correction (T) with linear cost scaling, Chem. Phys. Letters 318, 370 (2000).
$[4]$ M. Schütz, Low-order scaling local electron correlation methods. III. Linear scaling local perturbative triples correction (T), J. Chem. Phys. 113, 9986 (2000).
$[5]$ M. Schütz and H.-J. Werner, Low-order scaling local electron correlation methods. IV. Linear scaling local coupled-cluster (LCCSD), J. Chem. Phys. 114, 661 (2001).
$[6]$ M. Schütz, Low-order scaling local electron correlation methods. V. Connected Triples beyond (T): Linear scaling local CCSDT-1b, J. Chem. Phys. 116, 8772 (2002).
$[7]$ M. Schütz, A new, fast, semi-direct implementation of Linear Scaling Local Coupled Cluster Theory, Phys. Chem. Chem. Phys. 4, 3941 (2002).

Multipole treatment of distant pairs:
$[8]$ G. Hetzer, P. Pulay, H.-J. Werner, Multipole approximation of distant pair energies in local MP2 calculations, Chem. Phys. Lett. 290, 143 (1998).

Linear scaling local MP2:
$[9]$ M. Schütz, G. Hetzer and H.-J. Werner, Low-order scaling local electron correlation methods. I. Linear scaling local MP2, J. Chem. Phys. 111, 5691 (1999).
$[10]$ G. Hetzer, M. Schütz, H. Stoll, and H.-J. Werner, Low-order scaling local electron correlation methods II: Splitting the Coulomb operator in linear scaling local MP2, J. Chem. Phys. 113, 9443 (2000).

Density fitted local methods:
$[11]$ H.-J. Werner, F. R. Manby, and P. J. Knowles, Fast linear scaling second-order Møller-Plesset perturbation theory (MP2) using local and density fitting approximations, J. Chem. Phys. 118, 8149 (2003). $[12]$ M. Schütz and F.R. Manby, Linear scaling local coupled cluster theory with density fitting. Part I: 4- external integrals, Phys. Chem. Chem. Phys. 5, 3349 (2003).
$[13]$ Polly, H.-J. Werner, F. R. Manby, and Peter J. Knowles, Fast Hartree-Fock theory using local density fitting approximations, Mol. Phys. 102, 2311 (2004).
$[14]$ H.-J. Werner and M. Schütz, Low-order scaling coupled cluster methods (LCCSD(T)) with local density fitting approximations, in preparation.

LMP2 Gradients and geometry optimization:
$[15]$ A. El Azhary, G. Rauhut, P. Pulay and H.-J. Werner, Analytical energy gradients for local second-order Møller-Plesset perturbation theory, J. Chem. Phys. 108, 5185 (1998).
$[16]$ G. Rauhut and H.-J. Werner, Analytical Energy Gradients for Local Coupled-Cluster Methods, Phys. Chem. Chem. Phys. 3, 4853 (2001).
$[17]$ M. Schütz, H.-J. Werner, R. Lindh and F.R. Manby, Analytical energy gradients for local second-order Møller-Plesset perturbation theory using density fitting approximations, J. Chem. Phys. 121, 737 (2004).

LMP2 vibrational frequencies:
$[18]$ G. Rauhut, A. El Azhary, F. Eckert, U. Schumann and H.-J. Werner, Impact of Local Approximations on MP2 Vibrational Frequencies, Spectrochimica Acta 55, 651 (1999).
$[19]$ G. Rauhut and H.-J. Werner The vibrational spectra of furoxan and dichlorofuroxan: a comparative theoretical study using density functional theory and Local Electron Correlation Methods, Phys. Chem. Chem. Phys. 5, 2001 (2003).
$[20]$ T. Hrenar, G. Rauhut and H.-J. Werner, Impact of local and density fitting approximations on harmonic vibrational frequencies, J. Phys. Chem. A., 110, 2060 (2006).

Intermolecular interactions and the BSSE problem:
$[21]$ M. Schütz, G. Rauhut and H.-J. Werner, Local Treatment of Electron Correlation in Molecular Clusters: Structures and Stabilities of (H$_2$O)$_n$, $n=2-4$, J. Phys. Chem. 102, 5997 (1998). See also [2] and references therein.
$[22]$ N. Runeberg, M. Schütz and H.-J. Werner, The aurophilic attraction as interpreted by local correlation methods, J. Chem. Phys. 110, 7210 (1999).
$[23]$ L. Magnko, M. Schweizer, G. Rauhut, M. Schütz, H. Stoll, and H.-J. Werner, A Comparison of the metallophilic attraction in (X-M-PH$_3$)$_2$ (M=Cu, Ag, Au; X=H, Cl), Phys. Chem. Chem. Phys. 4, 1006 (2002).