Double many-body expansion DMBE

This procedure has been employed in the construction of the diabatic potential matrix for the l A and 2 A electronic states of H3 with conical intersection by Abrol and Kuppermann," in which the diabatization angle 7 (a function of internal nuclear coordinates) was calculated by solving the three-dimensional Poisson equation (with an optimal set of boundary conditions) for the entire U domain of nuclear configuration space bearing important significance for reactive scattering. The procedure was also employed by Mota and Varandas in their construction of the double many-body expansion (DMBE) diabatic potential matrix for the l A and 2 A states of the HN2 system, with a newly proposed diabatization scheme where the diabatization angle is represented by some specific functions. Earlier construction of the DK (Dobbyn and Knowles)... 

DMBE The double many-body expansion (DMBE) is a function in which, like MBE, the various 2-, 3-,. .., //-atom terms are combined to represent the potential for an //-atom system. It is based on partitioning the energy into an extended-Hartree-Fock-type term (EHF) and a dynamical correlation (DC) energy (resulting from the DC of the electrons) both of these terms are represented by MBEs. For example, the DMBE potential for a four-atom system has the form... 

Data from the PES obtained by the double many-bodied expansion (DMBE) method for the linear transition state H-H-H [5]... 

The second example is the hydrogen atom tunneling in the triatomic molecule HO2 for zero total angular momentum (/ = 0). In this case an analytical DMBE (double many-body expansion) potential function is available [126]. Since the quantum mechanically exact calculation can be carried out, the numerical results based on the present semi-classical theory are compared with the exact results. The exact numerical calculations are carried out in the hyperspherical elliptic coordinates (p, f, r]) [127,128], which are convenient for describing a light atom transfer between two heavy atoms. The coordinate p is called hyperradius, which represents the mass scaled radius of the hypersphere and is defined as... 

BEBO = bond-energy-bond-order CID = collision-induced dissociation DC = dynamical correlation DIM = diatom-ics-in-molecules DMBE = double many-body expansion EHF = extended Hartree-Fock FFT = fast Fourier transform IVR = intramolecular energy distribution LEPS = London-Eyring-Polanyi-Sato MBE = many-body expansion MEP = minimum energy path PES = potential energy surface TST = transition-state theory. 

---