Local correlation methods

Runeberg, N., Schiitz, M. and Werner, H.-J. (1999) The aurophilic attraction as interpreted by local correlation methods. Journal of Chemical Physics, 110, 7210-7215. 

Saebe, S., Tong, W. and Pulay, P. Efficient elimination of basis set superposition errors by the local correlation method Accurate ab initio studies of the water dimer, J. Chem. Phys., 98, 2170-2175. 

MW Local correlation methods Melting/boiling points... 

S. Ssebo, W. Tong, and P. Pulay, /. Chem. Phys., 98, 2170 (1993). Efficient Elimination of Basis Set Superposition Errors by the Local Correlation Method Accurate Ab Initio Studies... 

A difficulty with this local approach to dynamical correlation is that, in Moller-Plesset theory, for example, the zero-order Fock operator is no longer diagonal in the space of the Slater determinants, making the application of such theories slightly more complicated than theories based on canonical orbitals. Currently, the development of local correlation methods is an active area of research [57-63]. The diatomics-inmolecules (DIM) method and the triatomics-in-molecules (TRIM) method, for instance, recover typically 95% and 99.7%, respectively, of the full MP2 correlation energy [63]. By means of a linear scaling local variant of the CCSDT method,... 

The history and the present state of the treatment of electron correlation is reviewed. For very small atoms or molecules calculations of higher than spectroscopic accuracy are possible. A detailed account for many-electron methods in terms of one-electron basis sets is given with particular attention to the scaling of computer requirements with the size of the molecule. The problems related to the correlation cusp, especially the slow convergence of a basis expansion, as well as their solutions are discussed. The unphysical scaling with the particle number may be overcome by localized-correlation methods. Finally density functional methods as an alternative to traditional ab-initio methods are reviewed. 

Saebo, S., Tong, W. and Pulay, P. Efficient elimination of basis set superposition errors by the local correlation method Accurate ab initio studies of the water dimer,/. Chem. Phys., 98, 2170-2175. Gianinetti, E., Raimondi, M. and Tomaghi, E. (1996) Modification of the Roothaan equations to exclude BSSE from molecular interaction calculations, Int. J. Quantum Chem., 60, 157-166. Eamulari, A., Raimondi, M., Sironi, M. and Gianinetti, E. (1998) Hartree-Focklimit properties of water dimer in absence of BSSE, Chem. Phys., 232, 275-287. 

Keywords Coupled-cluster theory Local correlation methods Cluster-inmolecule formalism Linear scaling algorithms Single-reference coupled-cluster methods CCSD approach CCSD(T) approach Completely renormalized coupled-cluster approaches CR-CC(2,3) approach Large molecular systems Bond breaking Normal alkanes Water clusters... 

The second part contains detailed discussions and performance analyses of parallel algorithms for a number of important and widely used quantum chemistry procedures and methods. The book presents schemes for the parallel computation of two-electron integrals, details the Hartree-Fock procedure, considers the parallel computation of second-order Moller-Plesset energies, and examines the difficulties of parallelizing local correlation methods. 

Local correlation methods represent an importantnew class of correlated electronic structure methods that aim at computing molecular properties with the same accuracy as their conventional counterparts but at a significantly lower computational cost. We discuss the challenges of parallelizing local correlation methods in the context of local second-order Moller-Plesset perturbation theory, illustrating a parallel implementation and presenting benchmarks as well. 

Another way to speed up convergence is to use localized SCF MOs (Section 15.9) instead of canonical SCF MOs in the CSFs. Cl calculations on 1,3-butadiene using this localized correlation method showed speedups by factors of 20 to 40, since fewer CSFs needed to be included [S. Saeb0 and P. Pulay, Chem. Phys. Lett., 113,13 (1985)]. 

Low-order scaling local correlation methods II Splitting the Coulomb operator in linear scaling local second-order Moller-Plesset perturbation theory ... 

A disadvantage of such local correlation methods is that the approximation of neglecting interactions between distant orbitals introdnces small discontinnities into the mol-ecnle s potential-energy surface, which might interfere with geometry optimization. A compntationally efficient version of local CCSD that avoids such discontinuities has been developed [J. E. Subotnik et al., J. Chem. Phys., 125, 074116 (2006)]. 

The localized molecular orbitals (LMO) are extensively used not only for the chemical-bonding analysis in molecules but also in the local correlation methods [41] (we consider the problem of electron correlation in molecules and crystals in Chap. 5). The LMO are generated from the canonical MO occupied by electrons and found in the Hartree-Fock or DFT calculations. This generation is based on one or other localization criteria [42]. 

The essential progress in the correlation effects inclusion was achieved in the so-called local correlation methods [109,110] taking into account the short-range nature of the correlation. In these methods, the localized MOs are generated from the occupied canonical MOs using different localization criteria, see Sect. 3.3.1. For the virtual space the atomic-orbital basis is projected out of the occupied MO space. 

Only recently was the MP2 theory applied to the periodic systems based on the local correlation methods and use of Wannier functions [109,115]. 

While for the molecules the local correlation methods are already implemented in the MOLPRO code [116] the implementation of this approach to the periodic systems is the main goal of the new CRYSCOR project [117]. 

At first, aU these methods were developed for closed-shell systems only. Later research in this area was directed towards local methods for open-shell systems and excited states, local triples corrections beyond (T) (triples included in coupled cluster iterations), [138], local energy gradients for geometry optimizations of large molecules [139], combination of the local correlation method with explicitly correlated wavefunctions. It is evident from the discussion that these local 0 N) methods open the applications of coupled-cluster theory to entirely new classes of molecules, which were far ont-of-scope for such an accurate treatment before. Possible applications lie, for example, in the determination of the thermochemistry of reactions involving... 

Another potential application field are intermolecular complexes and clusters [140]. Here, the local correlation method has some conceptual advantages, insofar that it eliminates the notorious basis-set superposition error (BSSE) [141]. This allows for the BSSE-free calculation of interaction energies structures of large molecular clusters i.e. involving many monomers) without the expensive counterpoise correction that is required in conjuction with canonical methods. There are many more application areas one could think of. 

One of the most impressive applications of the local correlation methods is their extension to the periodic systems. Having in mind to discuss this extension on the MP2 level in the next section we restrict the discussion here to the consideration of local MP2 methods for molecular systems with closed shells, referring the reader to the papers discussing local CC methods [128,133,134,142,143]. 

The practical methods of post-HF calculations for solids were discussed during the workshop Local correlation methods from molecules to crystals [156]. Computational strategies were considered and new developments suggested in this area of research (the texts of invited speaker talks are published on an Internet site [156]). In particular, it was stated that the development of post-HF methods for crystals is essentially connected with the progress in the localized Wannier-function (LWF)... 

Definitions and conventions introduced are not specific of any given level of local correlation theory and can be used both in CC and MP theory. In [109] the MP2, the simplest local correlation method, was considered. 

To improve the efficiency of the local correlation methods in nonconducting crystals the technique for constructing compact (fitted) WFs in AO basis sets was suggested [157], Nevertheless, the results are general and can also be applied to other cases where the LCAO expansion of WFs is a critical issue. 

Fitted Wannier Functions for Periodic Local Correlation Methods... 

The atomic functions projected onto the orthogonal complement of the occupied space (PAOs), which represent in the framework of local correlation methods the virtual states (see Sect. 5.4.1) are also locahzed functions. Therefore, similar techniques could also be used to restrict the spatial extent of these PAOs. However, since PAOs are to be constructed by projecting out the space spanned by the fitted WFs or NO-LOs (rather than the untruncated parental WFs or NOLOs), one can anticipate that PAOs wiU automatically possess a hmited support, determined basically by the WF AO fit domains. 

---