Methods zero point correction

Many semiempirical methods compute energies as heats of formation. The researcher should not add zero-point corrections to these energies because the thermodynamic corrections are implicit in the parameterization. 

Theoretically transient three-membered rings containing hypervalent silicon as a structural motif (Fig. 1) have been studied at the SCF and DFT level and the relevant bond lengths are shown in Table 1 (substituents at C and E are not included in Table 1). Characterization of the transition state as early or late can be assumed from the difference between C-E and E-Si bond lengths. From Table 2 the method dependence of the barrier to selected 1,2-silyl-shifts can be taken. Generally, inclusion of electron correlation substantially diminishes the barrier while zero-point correction has only a minor effect. Barriers to silyl migration are in general much smaller than those to related... 

The classical and vibrational adiabatic (zero-point corrected) reaction barriers obtained by various DFT methods for the reaction CH4 + 30 - CH3 + OH are listed in Table 6. Results obtained by conventional correlated ab initio methods as well as the experimental value are included for comparison purposes. The DFT calculations employed the 6-31G(d,p) basis set and the (50,194) grid, with fully optimized geometries. The PMP4 and POL-CI calculations [72] were carried out with larger, triple-zeta-quality basis sets. 

Finally, the activation energies (without zero point corrections) calculated for the 1,5-hydrogen shift in cycloheptatriene by MROPT2, CASSCF, and B3LYP are 38.7, 60.2, and 40.6 kcal/mol, respectively, and a zero point correction would lower these energies by about 4 kcal/mol. Clearly, the CASSCF method without dynamic correlation is suspect just as in the Cope rearrangement (see Chapter 7, Section 4.1). 

Table 2. Silica-water reaction zero-point corrected activation energies for the forward direction. Note the marked dependence on the size of the system and the method/basis-set.

Table 3.4. Results for the Transition states of elementary processes of H2CO, calculated with different methods geometrical parameters in A (for distances r) and degrees (for angles a) the activation baniere A Eg and its zero point corrected value A Eq in kcal/moL...

The second, third, and fourth corrections to [MPd/b-Jl lG(d,p)] are analogous to A (- -). The zero point energy has been discussed in detail (scale factor 0.8929 see Scott and Radom, 1996), leaving only HLC, called the higher level correction, a purely empirical correction added to make up for the practical necessity of basis set and Cl truncation. In effect, thermodynamic variables are calculated by methods described immediately below and HLC is adjusted to give the best fit to a selected group of experimental results presumed to be reliable. 

Frequencies computed with methods other than Hartree-Fock are also scaled to similarly eliminate known systematic errors in calculated frequencies. The followng table lists the recommended scale factors for frequencies and for zero-point energies and for use in computing thermal energy corrections (the latter two items are discussed later in this chapter), for several important calculation types ... 

CBS-4 is the less expensive of these two methods. It begins with a FlF/3-21G(d) geometry optimization the zero-point energy is computed at the same level. It then uses a large basis set SCF calculation as a base energy, and an MP2/6-31+Gt calculation with a CBS extrapolation to correct the energy through second order. A... 

Compute the frequencies at each optimized geometry using the same method to obtain the zero point energy corrections. 

One of the simplest chemical reactions involving a barrier, H2 + H —> [H—H—H] —> II + H2, has been investigated in some detail in a number of publications. The theoretical description of this hydrogen abstraction sequence turns out to be quite involved for post-Hartree-Fock methods and is anything but a trivial task for density functional theory approaches. Table 13-7 shows results reported by Johnson et al., 1994, and Csonka and Johnson, 1998, for computed classical barrier heights (without consideration of zero-point vibrational corrections or tunneling effects) obtained with various methods. The CCSD(T) result of 9.9 kcal/mol is probably very accurate and serves as a reference (the experimental barrier, which of course includes zero-point energy contributions, amounts to 9.7 kcal/mol). 

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