Origin of rotation and inversion barriers

In addition to- predicting a total energy, quantum mechanics enables one to calculate the average values of its kinetic and potential energy contributions, the latter consisting of the nuclear-electron attractive potential energy (V, ), 

The electron-nuclear interaction energy is the only attractive interaction in a molecular system and it is the decrease in the potential energy resulting from this interaction that is responsible for the formation of a bound molecular state from the separated atoms. Because of the virial theorem and in the absence of external forces acting on the nuclei, the total energy E equals i V (eqn (6.64)) where V = is the total potential energy. 

Following similar arguments, one would expect Case II, where the decrease in energy results from a decrease in the repulsive contributions to AE, to be characteristic of processes dominated by increases in internuclear separations of bonded atoms or, equivalently, for the reverse process, an energy increase resulting from an increase in repulsive interactions because of dominant decreases in internuclear separations. Considered from the point of view of AE 0, Case I is exemplified by barriers to internal rotation and Case II by barriers to inversion. Payne and Allen (1977) have discussed various combinations of energy components in the classification of barriers as repulsive or attractive dominant. 

The atomic contributions to the energy changes are given in Table 6.6. The changes in the energies of the individual atoms are small, a reflection of the 

Contour maps of the electronic charge density for the staggered and eclipsed conformers of ethane (a) and for the bent and linear conformers of water (b). The outermost contour ha.s the value 0.001 au. The remaining contours increase in value according to the scale given in the Appendix (Table A2). The bond paths, the interatomic surfaces, and the bond critical 

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