Gaussian nuclear model

Extending this lattice to the llxllxll case (that is 1331 basis functions), Ralston and Wilson(66) reported an energy of —1.094929 hartree for the hydrogen molecular ion with a nuclear separation of 2.0 bohr an error of 7705 /xhartree. These authors considered an extension of the Gaussian Cell model, which they termed a molecular lattice basis set, since the lattice basis set is required to describe only molecular effects, being supplemented by atomic basis sets of high precision. This basis set is written... 

In principle, one could fit a linear combination of Gaussians to other nuclear models, such as the Fermi model, which depend smoothly on r, but in practice a single Gaussian has been good enough for most applications. 

The point charge model is sufficiently accurate if one is interested in valence properties of atoms and molecules, however, more realistic finite nucleus models may be used instead. In recent years a Gaussian nuclear charge distribution (Visser et al. 1987),... 

A practical advantage of the finite-nucleus model is that extremely high exponents of the one-particle basis functions are avoided. Since for quantities of chemical interest it is not very important which nuclear model is actually used, the Gaussian charge distribution is often applied, being the most convenient choice. 

Much of the initial development of Gaussian modeling and definition of dispersion paramenters was done during and after World War I in addressing the problem of poison gas dispersal. These studies involved the definition of risk factors, such as exposure and dose. The next intensive development effort came during and after World War II with the nuclear weapons program. 

Free and Lombardi (FL) models, Renner-Teller effect, triatomic molecules, 618-621 Free electrons, electron nuclear dynamics (END), time-dependent variational principle (TDVP), 333-334 Frozen Gaussian approximation direct molecular dynamics ... 

Figure 32. Vibronic periodic orbits of a coupled electronic two-state system with a single vibrational mode (Model IVa). All orbits are displayed as a function of the nuclear position x and the electronic population N, where N = Aidia (left) and N = (right), respectively. As a further illustration, the three shortest orbits have been drawn as curves in between the diabatic potentials Vi and V2 (left) as well as in between the corresponding adiabatic potentials Wi and W2 (right). The shaded Gaussians schematically indicate that orbits A and C are responsible for the short-time dynamics following impulsive excitation of V2 at (xo,po) = (3,0), while orbit B and its symmetric partner determine the short-time dynamics after excitation of Vi at (xo,po) = (3, —2.45).

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