Hamiltonian atom-diatom molecular

Miller, Handy, and Adams have recently shown how one can construct a classical Hamiltonian for a general molecular system based on the reaction path and a harmonic approximation to the potential surface about it. The coordinates of this model are the reaction coordinate and the normal mode coordinates for vibrations transverse to the reaction path these are essentially a polyatomic version of the natural collision coordinates introduced by Marcus and by Hofacker for A + BC AB 4- C reactions. One of the important practical aspects of this model is that all of the quantities necessary to define it are obtainable from a relatively modest number of db initio quantum chemistry calculations, essentially independent of the number of atoms in the system. This thus makes possible an ab initio theoretical description of the dynamics of reactions more complicated than atom-diatom reactions. 

This Hamiltonian is natural for describing inelastic scattering of a diatom from the surface, and is also suitable for describing the process of dissociative adsorption. However, this set of molecular coordinates is not very suitable when the diatomic distance r is very large because the wavefunction is highly peaked around 0 = 90°. One alternative is to simply use the atomic coordinates which is obviously ideal for describing the dif-... 

In 1992 Dmitriev, Khait, Kozlov, Labzowsky, Mitrushenkov, Shtoff and Titov [151] used shape consistent relativistic effective core potentials (RECP) to compute the spin-dependent parity violating contribution to the effective spin-rotation Hamiltonian of the diatomic molecules PbF and HgF. Their procedure involved five steps (see also [32]) i) an atomic Dirac-Hartree-Fock calculation for the metal cation in order to obtain the valence orbitals of Pb and Hg, ii) a construction of the shape consistent RECP, which is divided in a electron spin-independent part (ARECP) and an effective spin-orbit potential (ESOP), iii) a molecular SCF calculation with the ARECP in the minimal basis set consisting of the valence pseudoorbitals of the metal atom as well as the core and valence orbitals of the fluorine atom in order to obtain the lowest and the lowest H molecular state, iv) a diagonalisation of the total molecular Hamiltonian, which... 

We can treat a molecule by applying perturbation theory to the corresponding united atom, taking the perturbation H as the difference between the molecular and united-atom Hamiltonians H = H, - Hua- Using perturbation theory, one finds that the purely electronic energy of a diatomic molecule has the following form at small values of the intemuclear distance R [W. A. Bingel, / Chem. Phy, 30, 1250... 

Now consider small values of R. One can treat a diatomic molecule by applying perturbation theory to the united atom (UA) formed by merging the two atoms of the molecule. The perturbation is the difference between the molecular and the united-atom Hamiltonians H = One finds that the molecular purely electronic en-... 

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