MP2 methods

Correlation can be added as a perturbation from the Hartree-Fock wave function. This is called Moller-Plesset perturbation theory. In mapping the HF wave function onto a perturbation theory formulation, HF becomes a hrst-order perturbation. Thus, a minimal amount of correlation is added by using the second-order MP2 method. Third-order (MP3) and fourth-order (MP4) calculations are also common. The accuracy of an MP4 calculation is roughly equivalent to the accuracy of a CISD calculation. MP5 and higher calculations are seldom done due to the high computational cost (A time complexity or worse). 

The final application considered in this chapter is chosen to illustrate the application of a QM-MM study of an enzyme reaction that employs an ab initio Hamiltonian in the quantum region [67]. Because of the computational intensity of such calculations there are currently very few examples in the literahire of QM-MM shidies that use a quanhim mechanical technique that is more sopliisticated than a semiempirical method. MuUiolland et al. [67] recently reported a study of part of the reaction catalyzed by citrate synthase (CS) in wliich the quanhim region is treated by Hartree-Fock and MP2 methods [10,51],... 

Prior to the widespread usage of methods based on Density Functional Theory, the MP2 method was one of the least expensive ways to improve on Hartree-Fock and it was thus often the first correlation method to be applied to new problems. It can successfully model a wide variety of systems, and MP2 geometries are usually quite accurate. Thus, MP2 remains a very useful tool in a computational chemist s toolbox. We ll see several examples of its utility in the exercises. 

The very large basis set we used does not enable either the HF or MP2 method to predict an accurate structure for FOOF. CCSD does pretty well using only the 6-31G(d) basis set and produces a structure in excellent agreement with experiment with the larger basis set. 

Beginning with the final optimized structure from step 1, obtain the fii equilibrium geometry using the fuU MP2 method—requested with t MP2(Full keyword in the route section—which includes inner sh electrons. The 6-31G(d) basis set is again used. This geometry is used 1 all subsequent calculations. 

The components of the final G2 energy are listed as well as the computed value (in red). Note that the G1 energy is also given, as well as the value predicted by the G2(MP2) method, a related procedure to G2 designed to be less expensive. ... 

As an example, the G2(MP2) method involves tlie following steps ... 

There are several different CBS methods, each having its own set of prescriptions and resulting computational cost and accuracy, they are known under the acronyms CBS-4, CBS-q, CBS-Q and CBS-APNO. As an explicit example, we will take the CBS-Q model, " which is computationally similar to the G2(MP2) method. 

Optimizing the geometry at a correlated level, the MP2 method with a DZP type basis (6-31G(d,p) for example) would be a good starting points. 

Table 2 Energy differences between the lowest singlet and triplet states of the trimethylene-based 1,3-diradicals calculated by (6,6)CASSCF and (6,6) CAS-MP2 methods with the 6-3IG basis sets...

Figure 13. Comparison of the ab initio instanton trajectory by the CCSD(T)/(aug-)cc-pVDZ method with those obtained by (b) the global MP2 method and (c) analytic potential energy function.

Valdes and Sordo have studied the interaction of PH3 and NH3 with BrCl using either all-electron or effective core potential (ECP) MP2 methods, and several different basis sets [178]. They found that ECPs could give results nearly equivalent to their all-electron counterparts. PH3 was found to form... 

The calculated deprotonation energies of ethane, ethylene and acetylene by SCF Hartree-Fock (FIF) and MP2 methods follow the expected order 456, 455 (basis... 

However, the values in Tables 26-30 are directly calculated BDEs, according to equation 1. Taking only those molecules for which there are reliable experimental information (Table 26), and excluding the problematic (S 2) cases (CCH-, COOH-, NCO-, CN-, NC-, CHCH2- and N3 ) and the decomposed radical (CH3CO2 ), the average MP2 error for CH3—Y is 2.0 kcalmol-1 (21 cases) and for MP4 is 3.8 kcal mol-1 (19 cases). It thus seems that the particular choice of basis set and level of calculation used here gives the best cancellation of errors for the MP2 method. 

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