Orbital angular momentum dynamics

The dynamical variables Ll that correspond to the three components of the orbital angular momentum pseudovector are related to the dynamical variables q and p corresponding to position and momentum by... 

In connection with the Jahn-Teller effect the role of A may be well defined. It has been shown that if a dynamic Jahn-Teller effect is operative, very substantial quenching of orbital angular momentum may take place — the Ham effect. In the case of T ground terms, if the dynamic Jahn-Teller frequencies bear the right relationship to spin-orbit coupling and temperature, A may be reduced to values well below 0.5.113119... 

Frank s research career began at a time when Solid State Physics was a new topic in Physics. He contributed very much to what became an all-embracing topic in both basic physics and in its numerous applications in chemistry as well as physics in areas now frequently described as Condensed Matter . He pointed out how random strains can force a dynamic Jahn-Teller system to reflect distorted static behaviour in certain cases particularly in EPR spectra. This involved considerations of the orbital angular momentum of the magnetic ions present in these systems and he showed how the Ham Effect , as it became known, could explain why the electronic angular momentum could be quenched in many systems. 

Molecular structure and shape are related to orbital angular momentum and chemical change is shown to be dictated by the quantum potential. The empirical parameters used in computer simulations such as molecular mechanics and dynamics are shown to derive in a fundamental way from the relationship between covalence and the golden ratio. 

The dynamics of the reactions of alkali atoms with hydrogen halides are constrained by angular momentum conservation to convert almost all the initial orbital angular momentum into rotational angular momentum of the alkali halide product, as mentioned in Sect. 2.2. This is confirmed by electric deflection analyses of the alkali halide products from the reactions K, Rb and Cs + HBr [280—282]. Time-of-flight measurements of the product translational energy distributions for the reactions [278]... 

Each channel is defined by a unique set of quantum numbers for the target degrees of freedom. There are five such labels for each channel. They are (1) J — the total angular momentum and (2) M, its projection on an axis fixed in space. In addition there are labels (3) n for the vibrational motion of the molecule, (4) j for the molecular rotational degree of freedom, and (5) l for the atom-molecule orbital angular momentum. The equations for one set of (J,M) are uncoupled from equations for other values of (J,M). The equations for a function labeled by one value of (n,j,Z) are coupled to values of all the other functions labeled by (the same or) different values of (n,j, ). The number of coupled equations we have to solve therefore depends on the number of molecular vibration-rotation states we have to treat in the scattering dynamics at each collision energy. 

Since the scope of this article is purely theoretical, we just outline below the state of the experimental situation. The ideal experiment in Chemical Dynamics would be that in which starting with reactants in definite intramolecular quantum-states and running towards each other in a definite way (relative velocity and orbital angular momentum) the distribution of the products over the various intramolecular quantum-states and the state of the relative motion (direction and velocity) would be measured. Such an experiment would show whether there is a preferential molecular orientation at the heart of the collision, what the lifetime of the intermediate complex is, how the excess energy is distributed over the various degrees of freedom of... 

The above description of the excited states in terms of excitation amplitudes is frame and basis set dependent. A more convenient description is in terms of state multipoles. It can be generalised to excited states of different orbital angular momentum and provides more physical insight into the dynamics of the excitation process and the subsequent nature of the excited ensemble. The angular distribution and polarisation of the emitted photons are closely related to the multipole parameters (Blum, 1981). The representation in terms of state multipoles exploits the inherent symmetry of the excited state, leads to simple transformations under coordinate rotations, and allows for easy separation of the dynamical and geometric factors associated with the radiation decay. 

Molecular dynamics simulations have shown that for isolated reactants rotational excitation contributes to the enhanced reactivity (cf. Fig. 5, Ref. 97). In the kinematic limit, initial reagent rotational excitation is needed for a finite orbital angular momentum of the relative motion of the products. This is intuitively clear for the H2 -f I2 —t 2 HI reaction, where there is a large change in the reduced mass. The rather slow separation of the heavy iodine atoms means that rotational excitation of HI is needed if the two product molecules are to separate. This is provided by the initial rotational excitation of the reactants. The extensive HI rotation is evident in Fig. 9 which depicts the bond distances of this four-center reaction on a fs time scale. 

Another important effect due to the spin-orbit coupling comes into play whether the upper ionic core is specifically involved or not. This is because the excitation dynamics is very sensitive not only to the ionization potential or binding energy of the active electron but also to m, the projection of the orbital angular momentum along the polarization axis. Since spin-orbit terms are not... 

D) -f- HCl correlates with the products HCl(X Il) -I- Cl by means of the stable singlet molecule HOCl. Consequently, the dynamics of the reaction are dominated by the insertion of the oxygen atom into the HCl bond giving a vibrationally excited HOCl complex which decomposes giving a non-statistical OH(d = 0) rotational distribution [442]. The distribution is very similar to that from the reaction 0 ( D) + H2, but there is no selective population of the lower X doublet component of the OH in 0( D) + HCl. The lack of selectivity for this planar reaction can arise from the larger initial orbital angular momentum for 0 ( D) -t- HCl or the occurrence of non-adiabatic transitions. 

The question as to whether or not orbital angular momentum is a good quantum number in electronic states of molecules, as well as in atomic states, is one that is extraordinarily important in molecular theory. A good quantum number means physically that the dynamical variable is a good constant of the electronic motion. In quantum mechanics a sufficient condition for the conservation of a dynamical variable is that the operator for the variable commutes with the Hamiltonian operator. 

If, on the other hand, a dynamically independent spin is introduced, the appropriate orbital angular momentum operator is... 

These Ba reactions fall into a class of kinematically constrained reactions H + H L HH + L, where H and L denote heavy and light atoms, respectively [116,117], One consequence is that initial orbital angular momentum is channelled into rotational angular momentum of the diatomic product. With the assumption of constant product recoil energy, which can be used to interpret the dynamics of a number of Ba(lS) reactions [118], the formation of low and high v product vibrational levels is associated with large and small impact parameters, respectively. Thus, the variation of the spin-orbit effect with product vibrational level for the Ba( D) reactions provides information on the dependence of the reaction dynamics on incident impact parameter. 

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