Potential energy curves profiles

Figure 3. Computed potential energy curves for the diabatic and adiabatic state in the [HsN-H-NH ] system in the gas phase using 6-31G(d) basis set. The HF and MOVE energy profiles are overlapping.

Figure 7 Qualitative depiction of the energy profile along the reaction co-ordinate for the Sn2 reaction Cl ICII3CI >CICn3 I Cl, which involves nucleophilic substitution of the chloride of methylchloride by a chloride ion. The potential energy curves drop as the two reactants approach until a loose complex is formed. Then the energy rises rapidly to the transition state, which has two equal C-Cl interatomic distances (zero on the abscissa). The energy profile looks quite different in the gas and solution phases. Compared to the reactants (or products), the loose complex and the TS are poorly solvated, so the energies for these are much higher in solution than in a vacuum.

Quantum mechanical calculations in the gas phase and DMSO solution at different temperatures can highlight the hazards of standard 0 K gas-phase calculations.259 For the Wittig reaction, a small barrier in the potential energy curve is transformed into a significant entropic barrier in the free energy profile, and the formally neutral oxaphosphetane intermediate is displaced in favour of the zwitterionic betaine in the presence of DMSO. 

The effects of the solvent and finite temperature (entropy) on the Wittig reaction have been studied by using DFT in combination with molecular dynamics and a continuum solvation model.62 The free energy profile has been found to have a significant entropic barrier to the addition step of the reaction where only a small barrier was present in the potential energy curve. 

Everett and Powl (1976) applied both the 9-3 and the 10-4 expressions in their theoretical treatment of potential energy profiles for the adsorption of small molecules in slit-like and cylindrical micropores. As one would expect, the two corresponding potential energy curves were of a similar shape, but the differences between them became greater as the pore size was reduced. Strictly, the replacement of the summation by integration is dependent on the distance between the molecule and the surface plane, becoming more accurate as the distance is increased (Steele, 1974). 

Figure 6-6. Reaction path profile (potential energy curve) for the elementary process of NO synthesis O + N2 — NO + N, showing adiabatic and non-adiabatic reaction channels.

Figure 5. Adiabatic potential energy curves for H+MuH (dotted) [51, unpublished], see [21] for H+H2. Valley bottom and ridge profile are shown as continuous lines.

Before analysis of the interactions of the nucleic acid bases with the clay minerals in the presence of water and cation one needs to understand the individual interactions of NAs with isolated water and with a cation. Such theoretical study was performed for 1 -methylcytosine (MeC) [139]. The study revealed influence of water and cation in the proton transfer for this compound. This leads to the formation of imino-oxo (MeC ) tautomer. Topology of the proton transfer potential surface and thermodynamics of stepwise hydration of MeCNa+ and MeC Na+ complexes is further discussed. The one dimensional potential energy profile for this process followed by the proton transfer with the formation of hydrated MeC Na+ is presented in Fig. 21.2. One-dimensional potential energy profile for amino-imino proton transfer in monohydrated N1-methylcytosine (this represents the situation when tautomerization is promoted by a single water molecule without the influence of Na+ cation) and for the case of pure intramolecular proton transfer (tautomerization is not assisted by any internal interactions) is also included. The most important features of this profile do not depend on the presence or absence of Na+ cation. All the potential energy curves have local minima corresponding to MeC and MeC. However, the significant difference is observed in the relative position of local minima and transition state, which results in a different thermodynamic and kinetic behavior for all presented cases (see Fig. 21.2). 

Fig. 7. Potential energy curves (panel a) and theoretical and experimental spectral profiles (panels b, c) for the Rydberg emission spectra of Ds. As revealed by panel a, the initial, upper electronic state is characterized by a near-equilateral triangular shape and the transition directly probes the curve crossing (conical intersection) in the ground state occurring for R = ry/3l2 (see the arrow). The experimental and theoretical spectra are from Refs. 117 and 120, respectively.

The use of FOISTs, even for this more complicated system, leads to requisite alterations in the spatial profiles, so that they peak at the internuclear distances required to facilitate Frank-Condon transitions to the appropriate portion of the excited state potential energy curves, enhancing photodissociation ont of the desired channel. 

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