The Classical Approach Vibrational and Nonbonded Force Field Energies

4 The Classical Approach Vibrational and Nonbonded ( Force Field ) Energies 

The Born-Oppenheimer approximation uncouples electron and nuclear motion. The latter concerns massive (at least, relative to electrons) bodies, and much lower velocities while the formal velocity of an electron may approach the speed of light, a molecule in the gas phase travels at about the speed of a supersonic jet plane. While electronic energies must be calculated by quantum mechanics, nuclear motions are more easily described in a classical framework. 

For a molecule with N nuclei, there are 3N degrees of freedom, with three ascribed to rigid-body translation, three to rotation, and 3N-6 to vibration, or the change of the reciprocal positions of the nuclei. The classical potential energy of such vibrations can be written as  

The conformation of a gas-phase molecule can be derived by minimizing the strain energy Eqs. (1.1.23)—(1.1.26). A powerful simulation tool for the collective behavior of a molecular ensemble is molecular dynamics (MD) [11], In the classical approach, the total instantaneous energy of a molecular system, E(tot) is again a sum of terms as in Eqs. (1.1.23)—(1.1.26). Note that the above functional forms assume that the electronic structure is not significantly perturbed, that is, E(elec-tronic) = constant. 

The total kinetic energy of the multimolecular system is the sum of the kinetic energies of all atoms, and can be equated to the equipartition value, in the key link between molecular motion and temperature  

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