MP2 level of theory

We ran an SCRF single point energy calculation for gauche dichloroethane conformers in cyclohexane (e=2.0), using the Onsager model at the Hartree-Fock and MP2 levels of theory (flfl=3.65) and using the IPCM model at the B3LYP level. The 6-31+G(d) basis set was used for all jobs. We also ran gas phase calculations for both conformations at the same model chemistries, and an IPCM calculation for the trans conformation (SCRF=Dipole calculations are not necessary for the trans conformation since it has no dipole moment). 

Table 11.2 H2O geometry as a function of basis set at the MP2 level of theory...

An analogous sulfur transfer reaction has been proposed for the thermal decomposition of neutral thiirane to give ethylene and elemental sulfur, on the basis of ah initio calculations at the G3(MP2) level of theory [135]. 

The oxygen atoms of the homo cyclic oxides occupy axial positions in solid S7O and SsO. In fact, recent ab initio MO calculations at the G3X(MP2) level of theory have demonstrated that these isomers are, by 7 and 9 kj mol respectively, more stable than the alternative structures with the oxygen atoms in equatorial positions [89]. In the case of SsO, however, the energy difference is only 1 kJ mol and the conformation with the oxygen atom in the equatorial position is more stable. This result agrees with the observation that SsO exists as two isomeric forms in the solid state depending on the crystallization conditions (see above). 

The different struetures and transitions states of interest in the neutral and negative ion reaetions are represented in Fig. 2. A first approach was done at the SCF level, using the split-valence 4-3IG basis set. In order to provide a better estimation of the energy differences implied in this reaction schemes, extensive calculations have been performed at the MP2 level of theory using the 6-311++G basis set which contains the diffuse orbitals necessary to quantitatively describe the negative ions. 

Paizs, B., Suhai, S., 1998, Comparative Study of BSSE Correction Methods at DFT and MP2 Levels of Theory, J. Comput. Chem., 19, 575. 

With the aid of a normal coordinate analysis involving different isotopomers a linear structure of the Pd-Si-0 molecule is deduced. The results of ab initio MP2 calculations (Tab. 4) confirm the experimentally obtained IR spectra and their interpretation. The Pd-C bond in PdCO is similar to the Pd-Si bond in PdSiO which means, that the donor bond is strengthened by x acceptor components. This conclusion is in line with the high value of the Pd-Si force constant (exp. f(PdSi) = 2.69, f(SiO) = 8.92 mdyn/A) as well as with the energy of PdSiO (Pd + SiO —> PdSiO + 182 kJ/mol for comparison Pd + CO —> PdCO + 162 kJ/mol, MP2 level of theory). 

Ab initio calculations were carried out at the HF, B3LYP, and MP2 levels of theory employing different basis sets (6-31G, 6-31+G, 6-311+G ) by using the Gaussian98 program (6). Compounds examined are listed in Chart 1. All structures were fully optimized and were verified by means of their Hessian... 

Since a systematic study of this point is still missing, we investigated the performances of different computational approaches through geometry optimizations of the H2Si(Cp)2ZrCH3+ species with different pure and hybrid DFT functionals, and at the HF and MP2 level of theory. The main geometrical parameters are reported in Table 1. 

Ab initio calculations at the MP2 level of theory of a collection of substituted 1,3-dioxanes, 1,3-oxathianes, and 1,3-dithianes have been employed to study both the position of the conformational equilibria and the validity of the Perlin effect <2005T7349>. The 7h,c coupling constant proved to be a valuable tool in conformational analysis both twist conformers, in addition to the chair and alternative chair forms, could be readily identified simply by comparing experimental Vh,c coupling constants to the corresponding calculated values in the particular forms. In addition, the Perlin and reversed-Perlin effects of the C2-H fragments, c in 1,3-dioxanes,... 

The optimized geometries and total energies of the conformers of 4//-1,3-dioxin 44 <1997JCC1392> and the 2-substituted derivatives 45 <2000JMT(503)145> were ab rW/rh-calculated at the MP2 level of theory employing various basis sets. 

At the MP2 level of theory, the half-chair conformer of 4//-l,3-dithiin 55 is 2.0kcalmoP more stable than the boat conformer (Equation 4) <1998JCC1064> and has a calculated twist angle of 33.2° the relative stability of the halfchair conformer was attributed to absent lone-pair-lone-pair repulsions and a decrease of torsional strain owing to an... 

Table 3 Interaction energies, BSSE corrected, (kJ mol ), and intermolecular distances (pm) for three geometries of TTTA dimers (Figure 1) for different basis sets (MP2 level of theory) cfAo, aa. and cfoo are the equilibrium atomic distances between monomers E d, Eaa, and are the interaction energies for the particular dimer geometries and AEf = A - AEq <2002MI432>...

FIGURE 1. Geometries of l-chloro-2-methylpropenylmagnesium chloride 161 optimized at the RHF, B3LYP and MP2 levels of theory with the 6-31(+)G and 6-311(+)G basis sets. The energies of these geometries were calculated by the CCSD(T) method with the corresponding basis set... 

For the very small systems in Table 7.1, it is possible to approach the exact solution of the Schrodinger equation, but, as a rule, convergence of the correlation energy is depressingly slow. Mathematically, this derives from the poor ability of products of one-electron basis functions, which is what Slater determinants are, to describe the cusps in two-electron densities that characterize electronic structure. For the MP2 level of theory, Schwartz (1962)... 

In addition to the moments of the charge distribution, molecular polarizabilities have also seen a fair degree of study comparing DFT to conventional MO methods. While data on molecular polarizabilities are less widely available, the consensus appears to be that for this property DFT methods, pure or hybrid, fail to do as well as the MP2 level of theory, with conventional functionals typically showing errors only slightly smaller than those predicted by HF (usually about 1 a.u.), while the MP2 level has errors only 25 percent as large. In certain instances, ACM functionals have been more competitive with MP2, but still not quite as good. 

When geometries optimized at the MP2/6-31G(d,p) were employed, the mean unsigned errors at the ROHF, UHF, PUHF, and MP2 levels of theory were 35.8, 45.6, 24.8, and... 

In general, then, DFT methods provide the best combination of accuracy and efficiency so long as overdelocalization effects do not poison their performance. The MP2 level of theory also provides a reasonably efficient way of carrying out h.f.s. calculations at a correlated level of theory. More highly correlated levels of MO theory are generally more accurate, but can be prohibitively expensive in large systems. 

Koch, Liu and Schleyer223 explored the C3H7+ potential energy surface at the MP2 and MP4//MP2 level of theory using a TZ + P basis [6-31 lG(d,p)]. Their results are summarized in Figure 22 (structures 28-33). The global minimum of the C3H7+ surface is occupied by the 2-propyl cation (28) that possesses C2 symmetry rather than C2v symmetry as is com-... 

From Reference 52 at MP2/6-31G //MP2/6-31G, unless stated otherwise. Not a minimum at die HF and the MP2 levels of theory. cFor benzene. 

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