Ab initio energies

G2/CBS models, essentially all die correlation energy of the bond being broken must be recovered. This in mm necessitates large basis sets and sophisticated correlation methods. This is also the reason why ab initio energies are not converted into heats of formation, as is normally done for semi-empirical methods (eq. (3.89)), since the resulting values are poor unless a very high level of theory is employed. 

Figure 3. Ab initio energy for deformation of methyl cation out-of-plane deformation of third hydrogen from HCH plane (165).

Table IX presents both the theoretical ab initio energies of the components of reaction (102) and the experimental values which allow evaluation of the error introduced by neglecting the correlation energy.

Let us consider the ab initio task first. At each data point, we require the ab initio energy, gradient and second derivatives. Up to now, PESs have been constructed for about a dozen reactions involving four atoms, two involving five atoms and two involving six atoms. Roughly speaking, several... 

Table 2. Ab Initio Energies and Structures for Stationary Points on the Clj +...

Sakane, S. Liu, W. B. Doren, D. J. Shock, E. L. Wood, R. H., Prediction of the Gibbs energies and an improved equation of state for water at extreme conditions from ab initio energies with classical simulations, Geochim. Cosmochim. Acta 2001, 65, 4067 1075... 

Energy changes are for the isodesmic reaction shown in Scheme 13.33 h Calculated from the ab initio energies of R-[16]-OH and R-[17].33... 

Structure Ab Initio energy (Hartree Units) Relative Energy (kcal/mol) Distance N5-H2 (A)... 

Table 4. Ab initio energy profile during the proton transfer starting from the reduced tetrahydrofolate. ...

A method involving the use of atom equivalents for relating ab initio energies to heats of formation has also been suggested (Ibrahim et a/., 1985 and 1987). In this approach, atom equivalents were determined based on the environment in which they reside consequently, this method corresponds to an intermediate method between group and bond additivity methods. 

Wiberg. K. B., Group equivalents for converting ab initio energies to enthalpies of formation, J. Comp. Chem. 5, 197 (1984). 

The parameters of the model potential (52) have been fitted (separately for Vs and V3) to ab initio energy surfaces calculated at the MP4 level and corrected for the basis set superposition error. The parameters of the additive potential Vs were fitted to 65 calculated points on the potential curve of Bes, the parameters of the 3-body potential V3 were fitted to the EalBea) potential surface with total number of calculated points equal to 108. It is important to note that in the fitting procedure we find the sum (or difference) of exchange and dispersion terms for each m-body potentials V . This sum is correct for all distances considered. But we cannot expect the same from the absolute... 

Figure 21-11 Comparison of calculated exact" ab initio energies of H2 as a function of internuclear distance, r, with the energies calculated for simple MO and simple VB methods. The dissociation energy calculated by the ab initio procedure is in close agreement with the experimental value of 102 kcal. The zero of the energy scale in this figure is the energy of widely separated hydrogen atoms.

Crespo-Hernandez CE, Arce R, Ishikawa Y, Gorb L, Leszczynski J, Close DM (2004) Ab initio energy thresholds of DNA and RNA bases in qas phase and in aqueous solution. J Phys Chem B 108 6373-6377... 

Energy profiles for alternative intramolecular cyclizations of 4-(aminoalkyl)-e>-quinones (90) (n = 1-3) have been calculated using the AMI method and ab initio energies of the transition states have been determined. In all the cases, cyclization at position 5 to form (91) occurs via a significantly lower energy transition state... 

If the ab initio energy has been corrected by adding the zero-point energy (cf. Eq. 5.94), giving the total internal energy at 0 K, this should be pointed out ab initio energy, corrected for ZPE ... 

As has been pointed out, the ZPE-corrected ab initio energy is preferred over the uncorrected for calculating relative energies. At the end of a calculation lolal (HF or correlated) is given if we wish to include ZPE and get a frequency calculation is necessary. The format in which these quantities appear at the end of a calculation depends on the program. 

Fig. 5.24 Absolute and relative ab initio energies, with and without ZPE correction. These are from HF/3-21G1 1 calculations. The calculated reaction energy for the (E) to (Z) (cis to trans) isomerization is —8.51 kJ moF1...

Fig. 5.25 The reaction energy, the energy difference of products and reactants, determines the extent of a reaction, i.e. its equilibrium constant. The activation energy (the simple ab initio energy difference shown here is not exactly the conventional Arrhenius activation energy), the energy difference of transition state and reactants, partially determines the rate constant. Unfortunately, energy is ambiguous, since chemists use the terms potential energy, enthalpy (heat energy), and free energy see Section 5.5.2.1...

The energies in hartrees are ab initio energies including ZPE. The calculations on 02 are UHF, on triplet 02. Calculations are by the author, experimental energies are from reference [39], Tables 2-13 and 2-14. 

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