Electron-translation factor

Some details of END using a multiconfigurational electronic wave function with a complete active space (CASMC) have been introduced in terms of an orthonormal basis and for a fixed nuclear framework [25], and were recently [26] discussed in some detail for a nonoithogonal basis with electron translation factors. 

The state mixing term, the first in the r.h.s., usually dominates, at least in the presence of avoided crossings. Its determination reduces to a simple problem of interpolation of the Hu matrix elements, according to eq.(16). The second term corresponds, for large R, to the electron translation factor (see for instance [38]). This term depends on the choice of the reference frame that is, for baricentric frames, it depends on the isotopic masses. It contains the Gn matrix, which may be determined by numerical differentiation of the quasi-diabatic wavefunctions [16] this calculation is more demanding, especially in the case of many internal coordinates. It is therefore interesting to adopt the approximation ... 

In particular for high collision energies it is advantageous to include in this atomic basis so-called electronic translation factors exp ife-r, with k = mPf./Mf. for nucleus k to produce traveling atomic orbitals. The Lagrangian can now be written as... 

In the quantal method, the explicit introduction of electron translation factors is inconvenient and it has proved more appropriate to introduce some suitable system of reaction co-ordinates (Mittleman, 1969 Thorson and Delos, 1978 Delos, 1981 Soloviev and Vinitsky, 1985) which modifies the definition of the adiabatic states so that the asymptotic conditions of the collision are automatically accounted for. Since the method is not yet standard, a description of its essential features will be presented in section 3. 

Abstract. Cross sections for electron transfer in collisions of atomic hydrogen with fully stripped carbon ions are studied for impact energies from 0.1 to 500 keV/u. A semi-classical close-coupling approach is used within the impact parameter approximation. To solve the time-dependent Schrodinger equation the electronic wave function is expanded on a two-center atomic state basis set. The projectile states are modified by translational factors to take into account the relative motion of the two centers. For the processes C6++H(1.s) —> C5+ (nlm) + H+, we present shell-selective electron transfer cross sections, based on computations performed with an expansion spanning all states ofC5+( =l-6) shells and the H(ls) state. 

The partition function of the atomic species consists of the electronic and translational contributions only, but for the diatomic molecule A2 the partition function involves the electronic, translational and rotational factors, and also the contribution of one vibrational mode. The translational partition function is given by equation (16.16) as... 

The fact that asymptotically the electron travels with one of the nuclei is generally taken into account by inclusion of translational factors given by Schneidermann and Russek ... 

The standard entropy that enters into the frequency factor of the rate coefficient contains electronic, translational, vibrational and rotational contributions ... 

The classical molecular partition function for dilute diatomic and polyatomic gases without electronic excitation contains three factors. The translational factor is the same as given by the formula in Eq. (27.4-12), since the translational motion of a molecule is the same as that of an atom ... 

This argument can be generalized to any number of subsystems and energy levels. For the case of a molecular system in a given electronic state, the factorization into translational, vibrational, and rotational contributions gives... 

Calculation of Thermodynamic Properties We note that the translational contributions to the thermodynamic properties depend on the mass or molecular weight of the molecule, the rotational contributions on the moments of inertia, the vibrational contributions on the fundamental vibrational frequencies, and the electronic contributions on the energies and statistical weight factors for the electronic states. With the aid of this information, as summarized in Tables 10.1 to 10.3 for a number of molecules, and the thermodynamic relationships summarized in Table 10.4, we can calculate a... 

The important information about the properties of smectic layers can be obtained from the relative intensities of the (OOn) Bragg peaks. The electron density profile along the layer normal is described by a spatial distribution function p(z). The function p(z) may be represented as a convolution of the molecular form factor F(z) and the molecular centre of mass distribution f(z) across the layers [43]. The function F(z) may be calculated on the basis of a certain model for layer organization [37, 48]. The distribution function f(z) is usually expanded into a Fourier series f(z) = cos(nqoz), where the coefficients = (cos(nqoz)) are the de Gennes-McMillan translational order parameters of the smectic A phase. According to the convolution theorem, the intensities of the (OOn) reflections from the smectic layers are simply proportional to the square of the translational order parameters t ... 

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