Frozen molecule approximation, hydrogen

The well-established perturbation theory of intermolecular interaction [53 59] can be applied to hydrogen-bonded systems in combination with the frozen molecule approximation, when the interaction is either sufficiently weak [60 62], or when the interaction is treated at a more qualitative level. When the interaction becomes larger, structural relaxations become sizable. Then the more usual approach to treat the hydrogen-bonded complex or cluster as a supermolecule becomes more practical and also more appropriate. However, also in this case, the detailed analysis of the interaction energy is often done with the aid of different variants of energy partitioning techniques [63,64] which closely follow the lines of intermolecular perturbation theory. 

In the previous section, we treated rr-electron rotation within a frozen-nuclei approximation. However, the effects of nonadiabatic coupling should not be ignored when the duration of n-electron rotations becomes close to the period of molecular vibrations. Therefore, in this section, we explicitly take into account vibrational degrees of freedom and perform nuclear WP simulations in a model chiral aromatic molecule irradiated by a linearly polarized laser pulse. The potentials of the vibrational modes were determined by ab initio MO methods [12]. For reducing computational time, while maintaining properties of jt-electronic structures, we used 2,5-dichloropyrazine (DCP, Fig. 6.4) instead of 2,5-dichloro[n](3,6)pyrazinophane (DCPH), in which the ansa group is replaced by hydrogen atoms. 

Huckel (properly, Huckel) molecular orbital theory is the simplest of the semiempirical methods and it entails the most severe approximations. In Huckel theory, we take the core to be frozen so that in the Huckel treatment of ethene, only the two unbound electrons in the pz orbitals of the carbon atoms are considered. These are the electrons that will collaborate to form a n bond. The three remaining valence electrons on each carbon are already engaged in bonding to the other carbon and to two hydrogens. Most of the molecule, which consists of nuclei, nonvalence electrons on the carbons and electrons participating in the cr... 

Because of its molecular structure, each water molecule can form hydrogen bonds with four other water molecules. Each of the latter molecules can form hydrogen bonds with other water molecules. The maximum number of hydrogen bonds form when water has frozen into ice (Figure 3.8). Energy is required to break these bonds. When ice is warmed to its melting point, approximately 15%... 

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