Angular momentum preservation

The total vibrational energy is a sum of energies of 3N-6 distinct harmonic oscillators. Indeed, 3N-6 is the final number of coordinates in Equation 8. Namely, the number of 3N+3 coordinates of the initial equation has been reduced by three through the elimination of internal rotations. Furthermore, the equation of nuclear motion (mainly its potential) has to be invariant under rotations and translations of a molecule as a whole (which is equivalent to the momentum and angular momentum preservation laws). The latter requirement leads to a further reduction of the number of coordinates by six (five in the case of linear molecules for which there are only two possible rotations). 

Imagine a well isolated space ship observed in an inertial coordinate system. Its energy is preserved, its centre of mass moves along a straight line with constant velocity the total, or centre-of-mass, momentum vector is preserved), it rotates about an axis with an angular velocity total angular momentum preserved ). The same is true for a molecule or atom, but the conservation laws have to be formulated in the language of quantum mechanics. 

Thus, PBCs function to preserve mass, particle number, and, it can be shown, total energy in the simulation cell. In an MD simulation, PBCs also conserve linear momentum since linear momentum is not conserved in real contained systems, where container walls disrupt the property, this is equivalent to reducing the number of degrees of freedom by 3. However, this effect on system properties is typically negligible for systems of over 100 atoms. Obviously, PBCs do not conserve angular momentum in the simulation cell of an MD simulation, but over time the movement of atoms in and out of each wall of the cell will be such that... 

As discussed in the introduction to this chapter the final rotation of the photofragment reflects three sources overall rotation of the parent molecule, which is preserved in the electronic excitation process, internal bending or torsional motion in the electronic ground state, and final state interaction. The latter two sources have been analyzed in Sections 10.1-10.4. The influence of overall rotation will be discussed in this section. Its relative contribution increases gradually with the magnitude of the total angular momentum J and therefore it increases with the temperature of the molecular sample. As we will demonstrate below, the conversion of overall rotation of the parent molecule in the electronic ground state into... 

Thus, the method of description presented in this section permits us to preserve the clarity of the picture and, at the same time, to elucidate thoroughly the essence of the phenomena connected with the effect of a magnetic field on the intensity and polarization of the radiation of a system with a large angular momentum. This is going to be the subject of the following two sections. 

Operator equations have been employed by George and Ross (1971) to analyse symmetry in chemical reactions. In order to preserve the identity of electronic states of reactants and products, these authors worked within a quasi-adiabatic representation of electronic motions. By introducing a chain of approximations, going from separate conservation of total electronic spin to complete neglect of dynamics, they discussed the Wigner-Witmer angular momentum correlation rules, Shuler s rules for linear molecular conformations and the Woodward-Hoffmann rules. 

Van Vleck introduced the pure precession approximation for diatomic molecules. The basic idea is that if the one-electron atomic orbital angular momentum is preserved in a diatomic molecule then the A-doubling and spin-rotation constants can be predicted, for example, in a 4pa(2l,+) and a 4p7r(2n) state. This pure precession picture can easily be generalized to... 

---