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Ideas of Quantum Chemistry P84

Ideas of Quantum Chemistry P84 shows how quantum mechanics is applied to chemistry to give it a theoretical foundation. The structure of the book (a TREE-form) emphasizes the logical relationships between various topics, facts and methods. It shows the reader which parts of the text are needed for understanding specific aspects of the subject matter. Interspersed throughout the text are short biographies of key scientists and their contributions to the development of the field. | 796 14. Intermolecular Motion of Electrons and Nuclei Chemical Reactions Example 1. Vibrationally adiabatic approximation Let us consider several versions of the reaction that differ by assuming various vibrational states of the reactants.44 Using eq. 14.29 for each set of the vibrational quantum numbers we obtain the vibrationally adiabatic potential Vadiab as a function of s Fig. 14.10 . The adiabatic potentials obtained are instructive. It turns out that The adiabatic potential corresponding to the vibrational ground state vOH vHH 0 0 gives lower barrier height than the classical potential V0 s 5.9 kcal mol vs 6.1 . The reason for this is the lower zero-vibration energy for the saddle point configuration than for the reactants.45 The adiabatic potential for the vibrational ground state has its maximum at s -5 a.u. not at the saddle point s 0. Excitation of the OH stretching vibration does not significantly change the energy profile in particular the barrier is lowered by only about 0.3 kcal mol. Thus the OH is definitely a spectator bond. This contrasts with what happens when the H2 molecule is excited. In such a case the barrier is lowered by as much as about 3 kcal mol. This suggests that donating mode the HH stretching vibration is a donating mode . s a.u. Fig. 14.10. The reaction H2 OH H2O H within the vibrationally adiabatic approximation . Three sets of the vibrational numbers uoh vhh 0 0 1 0 0 1 were chosen. Note that the height and position of the barrier depend on the vibrational quantum numbers assumed. An excitation of H2 considerably decreases the barrier height. The small squares on the right show the limiting values. According to T. Dunning Jr. and E. Kraka from Advances in Molecular Electronic Structure Theory ed. T Dunning Jr. JAI Press Greenwich CN 1989 courtesy of the authors. 44 We need the frequencies of the modes which are orthogonal to the reaction path. 45This stands to reason because when the Rubicon is crossed all the bonds are weakened