LMP2 method

There is also a local MP2 (LMP2) method. LMP2 calculations require less CPU time than MP2 calculations. LMP2 is also less susceptible to basis set superposition error. The price of these improvements is that about 98% of the MP2 energy correction is recovered by LMP2. 

Recently, Friesner et al.124 proposed a method referred to as J2 theory to predict accurate thermochemical data. This approach is based on the generalized valence bond-localized Moller-Plesset method (GVB-LMP2) and includes parameters that depend on the number of electron pairs and whether the pairs are a or 7t types. Thus, the parameterization in the J2 method is molecule dependent. The GVB-LMP2 method scales as n3 as opposed to n6 or n7 for the MP4, QCISD, or CCSD methods, so J2 is much faster than G2. The J2 method... 

The LMP2 method has been combined with the pseudospectral (PS) method (Section 15.5) to further reduce computation times [R. B. Murphy et al.,/. Chem. Phys., 103,1481 (1995)]. 

An alternative choice is to take the unperturbed MCSCF wave function as the generalized valence-bond (GVB) wave function (Section 15.25). When combined with a PS-LMP2 treatment, this gives the PS-GVB-LMP2 method [R. B. Murphy, W. T. Pollard, and R. A. Friesner,/. Chem. Phys., 106,5073 (1997)]. 

A method to speed up MP2 calculations on large molecules is the local MP2 (LMP2) method of Saebp and Pulay [S. Saebd and P. Pulay, Annu. Rev. Phys. Chem., 44, 213 (1993)]. Here, instead of using canonical SCE MOs in the Hartree-Fock reference determinant d>o. one transforms to localized MOs (Section 15.8). Also, instead of using the virtual orbitals found in the SCF calculation as the orbitals a and b in (16.13) to which electrons are excited, one uses atomic orbitals that are orthogonal to the localized occupied MOs. Also, in (16.13), one includes only unoccupied orbitals a and b that are in the neighborhood of the localized MOs i and j. 

The DF-MP2 method has been combined with the LMP2 method to give the DF-LMP2 method [H. J. Werner et al J. Chem. Phys., 118, 8149 (2003)]. The DF-LMP2 method is so efficient, that for large molecules, the preceding Hartree-Fock part of the calculation takes a lot longer than the MP2 part of the calculation. 

In Sections 5.3 and 5.4 we consider Laplace-transform MP2 (LTMP2) and local MP2 (LMP2) methods extensions to periodic systems, implemented in computer codes GAUSSIAN03 [107] and CRYSCOR [117], respectively. These two extensions are similar to their molecular counterparts in the preliminary calculation of delocalized canonical orbitals (Bloch functions for periodic systems) and further construction of localized crystalline orbitals (Wannier functions for periodic systems). However the correlation effects for periodic systems may be taken into account in another way when the SCF calculations are made in Wannier-functions basis. Such an approach was named the incremental scheme [5,49,110] and is considered in the next section. 

The possibihty to ehminate the WFs tails may have a significant impact on the efficiency of LMP2 methods. For these methods the most expensive step is the evaluation and transformation of four-index two-electron integrals, where the computational cost is governed by the spatial extent of the AO support of the individual WFs. The details of the evaluation of these integrals can be found in [109]. 

Table 2 contains the initial timing results for GVB-LMP2 applied up to 29 GVB pairs and 338 basis functions. Although the GVB-LMP2 method is more demanding than LMP2, calculations of this size are not practical with comparable methods such as QCISD,... 

The LMP2 and GVB-LMP2 methods can also be u.sed to study thermochemistry. As in all ab initio correlation methods which are applicable to molecules of reasonable size, it is not possible to converge the basis set and electron correlation sufficiently to achieve chemical accuracy without the use of... 

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