Adiabatic approximation group

The correct way to employ the adiabatic approximation for the Hamiltonian Eq. (7) is to group the quadratic counterterm with the subsystem s (we will give below a physical justification for this grouping) ... 

Since the inner direct product of eq. (11-3) is the only one which contains the totally symmetric representation Als, only the 1B2u and 3Blu curves will mix within the harmonic approximation. In the adiabatic approximation, however, certain vibrational motions may destroy the point group symmetry and allow the 1BZu state to mix with the 3B2u and 3Elu states. 

From the conceptual point of view, there are two general approaches to the molecular structure problem the molecular orbital (MO) and the valence bond (VB) theories. Technical difficulties in the computational implementation of the VB approach have favoured the development and the popularization of MO theory in opposition to VB. In a recent review [3], some related issues are raised and clarified. However, there still persist some conceptual pitfalls and misinterpretations in specialized literature of MO and VB theories. In this paper, we attempt to contribute to a more profound understanding of the VB and MO methods and concepts. We briefly present the physico-chemical basis of MO and VB approaches and their intimate relationship. The VB concept of resonance is reformulated in a physically meaningful way and its point group symmetry foundations are laid. Finally it is shown that the Generalized Multistructural (GMS) wave function encompasses all variational wave functions, VB or MO based, in the same framework, providing an unified view for the theoretical quantum molecular structure problem. Throughout this paper, unless otherwise stated, we utilize the non-relativistic (spin independent) hamiltonian under the Bom-Oppenheimer adiabatic approximation. We will see that even when some of these restrictions are removed, the GMS wave function is still applicable. 

The operator /ft introduced in expression (200) corresponds to a possible optical and acoustical phonon interaction in the chain (this is because AH groups of which the chain is constructed would be treated as external, and then the entire compound governs the behavior of the A atoms embedded in the chain see also the next subsection). In the adiabatic approximation, it is expressed in the following way ... 

Pyda et al. (1998) studied in detail the heat capacity of PTT by adiabatic calorimetry, standard DSC and temperature-modulated differential scanning calorimetry (TMDSC) for this measurement. The computation of the heat capacity of solid PTT is based on an approximate group vibrational spectrum and the general Tarasov approach for the skeletal vibrations, using the well-established Advanced Thermal Analysis System (ATHAS) scheme. The experimental heat capacity at constant pressure is first converted to heat capacity at constant volume using the Nemst-Lindemann approximation... 

It is well known that the Born-Oppenheimer adiabatic approximation establishes geometrical shape of a molecule. The atoms (atomic groups) constituting a molecule are imagined to be placed in the vertices of certain three-dimensional (3D) shape as illustrated in Figure 9.1. 

Note that the potential matrix V( (R) is a diagonal matrix by definition, in contrast to W(s)(R). Again, in analogy to the common treatment in Sec. 3.1, we call (23) the group-Born Oppenheimer adiabatic approximation or briefly the group-adiabatic approximation. This approximation assumes that the states within the manifold g are much stronger coupled to each other — e.g. via the presence of a conical intersection of the potential surfaces — than to the rest of the electronic space. 

A general, approximate, short-cut design procedure for adiabatic bubble tray absorbers has not been developed, although work has been done in the field of nonisothermal and multicomponent hydrocarbon absorbers. An analytical expression which will predict the recovery of each component provided the stripping factor, ie, the group is known for each component on each tray of the column has been developed (102). This requires knowledge... 

In this review we will first describe two approaches which we have used to represent atomic and molecular systems without resorting to the B-0 approximations. Next, we will describe two numerical applications of the theory, which led to determining interesting non-adiabatic contributions. In the last section we will consider future theoretical work on a general non-adiabatic approach to an N-particle system with any isotropic interaction potential, including coulombic interaction, which is presently being developed in our group. 

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