Gas phase energies

For the gas phase, energy transfers both as a result of a thermal driving force and as a by-product of vaporization. Thus,... 

Equation (4-6) is especially useful in that the total energy of a hybrid QM and MM system is separated into two independent terms - the gas-phase energy and... 

Table 11-6. Vertical excitation energy shifts in eV for uracil and thymine in aqueous phase compared to gas phase, using various levels of theory. The ordering of the states is according to the gas phase energies...

So far we have not touched on the fact that the important topic of solvation energy is not yet taken into account. The extent to which solvation influences gas-phase energy values can be considerable. As an example, gas-phase data for fundamental enolisation reactions are included in Table 1. Related aqueous solution phase data can be derived from equilibrium constants 31). The gas-phase heats of enolisation for acetone and propionaldehyde are 19.5 and 13 keal/mol, respectively. The corresponding free energies of enolisation in solution are 9.9 and 5.4 kcal/mol. (Whether the difference between gas and solution derives from enthalpy or entropy effects is irrelevant at this stage.) Despite this, our experience with gas-phase enthalpies calculated by the methods described in this chapter leads us to believe that even the current approach is most valuable for evaluation of reactivity. 

Fig. 13. Reaction profile for DMSO exchange on solvated Li+ enthalpy B3LYP(CPCM)/6-311+G including thermodynamic contributions at B3LYP/LANL2DZp gas-phase energy values B3LYP/6-311+G including AZPE at B3LYP/LANL2DZp, in parentheses T.S. = transition state (92).

Care must however be taken with the method. The final value is a sum of many, often small, contributions. Errors in these values can quickly lead to qualitatively incorrect results. The gas phase energy is furthermore the difference of two large numbers, and the ab initio calculations must therefore be of sufficient accuracy. The importance of zero-point energy and other thermodynamic properties must also be checked. 

Figure 2. I2 in acetonitrile. Nonequilibrium free energy surface. Contours in kcal mol"1, with the gas phase energy of the separated / and I species as a reference. The line cutting across the contours represents the ESP.

First of all, quantum calculations allow one to predict basicity scales in agreement with experiment provided that the calculations are performed on the preferred conformation of the isolated molecule. If this is not done, a given term within a consistent series may jump from one rank to another as a function of the conformation used for the calculations. The determinant role of preferred conformation on any property (barrier to internal rotation and inversion, dipole moment, first adiabatic ionization potential, acidity and basicity in the gas phase, energy of complexation to BF3, etc.) was clearly demonstrated. We further show the importance of the role of preferred conformation in explaining some of the anomalies in Drago s systematics. 

Parameterized models proposed by Cramer, Truhlar and their coworkers are based on semi-empirical wavefunctions. The resulting solvation energies can then be added to gas-phase energies obtained at any level of calculation. 

Figure 4.23. plot for — and —C bond cleavage reactions calculated from DFT. Final state ( fs ) and transition state (/iTS) energies are relative to initial state gas-phase energies. Adapted from Ref. [78]. 

Although theoretical studies indicate very small gas-phase energy differences between the syn and anti conformers of the 3-carbaldehydes of furan, thiophene and pyrrole with a slight preference for the syn conformer (65a, R = H), in chloroform solution the furan- and thiophene-3-carbaldehydes adopt the anti conformers (65b, R = H) to the extent of 100 and 80%, respectively (82T3245). However, N-substituted 3-(trifluoroacetyl)pyrroles (65, R = CF3) exist in solution as mixtures of rotational isomers (80JCR(S)42). 

C dl The gas phase energy of the given resonance structure where the fragments are at infinite seperation. 

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