SOS-MP2 method

The scaled-opposite-spin MP2 (SOS-MP2) method omits the E l contribution entirely and takes E = 1.3 os [Y. Jung et al., /. Chem. Phys., 121, 9793 (2004) J. Comput. Chem., 28, 1953 (2007)]. The SOS-MP2 method gives results slightly less accurate than the SCS-MP2 method, but is faster and can be applied to larger molecules than SCS-MP2. Of course, the use of empirical parameters makes the SCS-MP2 and SOS-MP2 methods no longer strictly ab initio methods. 

The HF method tends to overestimate the barriers, making unstable molecules seem stabler than they really are. Geometries are discussed further in Section 5.5.1. Approximate versions of the MP2 method that speed up the process with little loss of accuracy are available in some program suites LMP2, localized MP2, and RI-MP2, resolution of identity MP2. LMP2 starts with a Slater determinant which has been altered so that its MOs are localized, corresponding to our ideas of bonds and lone pairs (Section 5.2.3.1), and permits only excitations into spatially nearby virtual orbitals [93]. RI-MP2 approximates four-center integrals (Section 5.3.2) by three-center ones [94]. 

The accuracy of ab initio geometries is astonishing, in view of the approximations present the 3-21G( ) basis set is small and the 6-31G is only moderately large, and so these probably cannot approximate closely the true wavefunction the HF method does not account properly for electron correlation, and the MP2 method is only the simplest approach to handling electron correlation the Hamiltonian in both the HF and the MP2 methods used here neglects relativity and spin-orbit coupling. Yet with all these approximations the largest error (Table 5.7) in bond... 

Jung et al. [81] reported a variant of this approach that used the multiplicative factor of zero for the SS component and 1.3 for the OS component. This calculation, SOS-MP2 (scaled opposite-spin MP2), can be performed with only an 0(n4) operation cost when combined with Almlof s Laplace transform technique [82], The SOS approximation can be applied to CIS(D) [69], A similar simplification was often adopted in the GW method under the name COHSEX approximation [32] also partly from an operation cost consideration. 

The Hartree-Fock (HF) method seriously underestimates the DDE for all of the examples in Table 3.1. This results from the inherent lesser electron correlation in the radicals than in the parent species, and electron correlation is completely neglected in the HF method. Inclusion of some electron correlation, as in the MP2 method, dramatically improves the estimated BDEs. In a stndy of the BDE of the C-H bond in 19 small molecules, Radom found that the mean absolute deviation (MAD) at the MP2/6-311+G(2df,p)//MP2/6-31G(d) level is 3.6 kcal mor. This error is generally larger than that associated with the experimental method, and so DPEs obtained using MP2 may be problematic. 

The MP2 method has been found to accurately describe the energetics of water clusters, providing that sufficiently flexible atomic basis sets are employed [5,11,20, 67,68]. However, whUe MP2 calculations are feasible for clusters containing up to 30 or so water molecules, the steep 0 N )) computational scaling of conventional MP2 calculations with system size precludes their use in carrying out Monte Carlo or molecular dynamics simulations of water clusters containing six or more monomers. 

A number of approaches have been proposed for the computation of NMR properties in the framework of DF approaches [86-91]. Here we will make explicit reference to the GIAO model, which appears particularly effective [92,93]. It has been recently pointed out that the MP2 method predicts chemical shifts which are closer to experiment than those obtained using DF approaches, including the B3LYP model [93]. It is so natural to include, as a stringent test, the computation of chemical shieldings. In particular, we have selected some examples in order to investigate the different possible hybridizations of carbon atoms. We have next added the ozone molecule, which is a particularly difficult test for NMR properties [90,92], The results are collected in table XIII. 

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