MP2 Correlation Energy

Specifies the calculation of electron correlation energy using the Mpller-Plesset second order perturbation theory (MP2). This option can only be applied to Single Point calculations. 

MP2 correlation energy calculations may increase the computational time because a two-electron integral transformation from atomic orbitals (AO s) to molecular orbitals (MO s) is required. HyperChem may also need additional main memory and/or extra disk space to store the two-electron integrals of the MO s. 

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CBS model chemistries make the correction resulting from these extrapolations to the second-order (MP2) correlation energy ... 

Figure 4.6 The RMS errors in MP2 correlation energies obtained with the cc-pVnZ basis set (n = Zroax = 2, 3, 4, 5, and 6).

Table 4-4 Convergence of the (Zmax + 5) 3 extrapolated cc-pVnZ correlation-consistent basis set MP2 correlation energies (Eh) to the MP2-R12 limit see Eq. (6.2).

The Dunning cc-pVnZ basis sets can be used with our PNO extrapolations to form a potent new combination. We shall consider the SCF energy first, then the MP2 correlation energy, and finally higher-order correlation energy through CCSD(T). 

Table 7 Convergence of the scaled PNO extrapolated CBS/cc-pVnZ, correlation-consistent basis set higher-order [i.e. CCSD(T)-MP2] correlation energies (Eh) to the CCSD(T)-R12 limit.

MP2 correlation energies (Table 4.6), and the higher-order contributions to the correlation energy (Table 4.7), we can now combine these components to obtain total electronic energies. There are many plausible combinations of basis sets and extrapolation procedures that must ultimately be explored. Efficient methods should use smaller basis sets for the CCSD(T) component than for the SCF and MP2 ones. The use of intermediate basis sets for the MP4(SDQ) component should also be explored, since we found this effective for the CBS-QB3 model (Table 4.2). 

The total correlation energy, as obtained from a second-order Moller-Plesset (MP2) [71] calculation, can easily be split into parallel- and antiparallel-spin contributions. The MP2 correlation energy 2 is given by [81]... 

Equations (13) and (15) reduce to the usual MP2 correlation energy expression by substituting t — 0 and, therefore, MP2 and MP2-R12 as defined above converge to the same complete-basis-set limit, however, at vastly different rates. These... 

Figure 2. The MP2 correlation energy of ScCO. The calculation was done with the Wachters "contraction 3" s,p Sc basis with Hay s augmented 5d basis and an additional 4p" function. The 6-31C> basis set was used for C and 0. The C-0 bond length was constrained to be the MP2 optimized bond length, 2.175 bohr, of free CO.

The constant "c" is roughly proportional to the product of the atomic polarizabilities. Following this model for ScCO gives a very poor fit to the inter-molecular correlation energy. A modified term such as c/(R2 (-A2) provides a much better fit to the MP2 correlation energy. Of course, in the empirical potential a repulsive term is included which can model both the short range overlap repulsion in the SCF energy, and the inadequacy of the R term. 

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,... 

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