Wave functions during separation

The study of the two-electron systems was greatly simplified by the fact that the total wave function could be factorized into a space part and a spin part according to Eq. III. I. ForiV = 3, 4,. . , such a separation of space and spin is no longer possible, and an explicit treatment of the spin is actually needed in considering correlation effects. This question of the connection between space and spin in an antisymmetric spin function is a rather complicated problem, which has been brought to a simple solution first during the last few years. 

The wave functions change character, of course, during the dissociation process. The asymptotic region is the simplest and we start with that. Table 16.9 shows the most important Rumer tableaux when CO and H2 are well separated from one another. 

Ihe approximation of separating electronic and nuclear motions is called the Bomr-Oppenheimer approximation and is basic to quantum chemistry. [The American physicist J. Robert Oppenheimer (1904-1967) was a graduate student of Bom in 1927. During World War II, Oppenheimer directed the Los Alamos laboratory that developed the atomic bomb.] Born and Oppenheimer s mathematical treatment indicated that the tme molecular wave function is adequately approximated as... 

The translation motion of the whole system of interacting particles can be described by the motion of its center-of-mass in respect to a body-fixed coordinate system This will be a free (inertial) motion with a constant velocity as far as the collision complex can be considered as an isolated system Such is approximately the situation during a collision in a dilute gas where, because of the large intermolecular distances, the interactions of the collision complex with the other molecules may be neglected. As is known from classical mechanics, the free center-of-mass motion can be completely separated from the internal motions, which can then be described in a coordinate system having its origin in the center-of-mass. In quantum mechanics a similar separation is possible by a product representation of the wave function... 

The Bom—Oppenheimer approximation is the assumption that because the nuclei are several thousand times more massive than the electrons, the nuclei are essentially clamped in place during the absorption so that the wave function can be separated into its respective electronic and vibrational parts. The probability of a transition occurring between two different energy levels is proportional to the square of the transition moment integral, /VIqi, shown in Equation (9.10), where u is the dipole moment operator. Expansion of this equation yields Equation (9.11), where e is the... 

Figure 6.4 illustrates for a diatomic molecule, the possible excited-state potential energy curves that permit dissociation. As mentioned previously (the Franck-Condon principle) electronic transitions occur so rapidly that the nuclei are, in effect, clamped during transition. Quantum mechanics requires that the transition occur between states which have large probability amplitudes at the same internuclear separation. The vibrational wave function of the ground state is maximum at the center of the well those of excited states have major maxima near the classical... 

In Cl theory, only the configuration expansion is variationally optimized - the orbitals are generated separately in a preceding Hartree-Fock or MCSCF calculation and are held fixed during the optimization of the configuration expansion. In contrast, the MCSCF wave function of Section 5.5... 

As mentioned earlier, the process facilities have been designed to operate in environmental conditions based on a 1-year storm condition. During the 2 years that have elapsed, several bad weather periods have been experienced during which significant wave heights of 21 ft [6.S ml have been observed. It has been established that the worst environmental conditions encountered so far do cause liquid movement in the separators but have not adversely affected (he functioning of the process and utility systems and do not cause level alarms or shutdowns. 

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