Double many-body expansion

Topographical Aspects, Calculation, and Functional Representation via a Double Many-Body Expansion Method... 

The partitioning of the potential energy into EHF and corr contributions proves to be most useful when used in conjunction with the many-body expansion in what has been called the double many-body expansion (DM BE).17-21 The three first terms are... 

Pastrana, M.R., Quintales, LA.M., Brandao, J., and Vatandas, A.J.C. (1990) Reeahbration of a single-valued double many-body expansion potential energy surface for ground-state HO2, J. Phys. Chan. 94, 8073-8080. 

G. C. Lynch, R. Steckler, D. W. Schwenke, A. J. C. Varandas, D. G. Truhlar, and B. C. Garrett, Use of scaled external correlation, a double many-body expansion, and variational transition state theory to calibrate a potential energy surface for FH2, J. Chem. Phys. 94 7136 (1991). 

Double Many-Body Expansion Potential Energy Surface for 04( A), Dynamics of the 0( P) + 03( Ai) Reaction, and Second Virial Coefficients of Molecular Oxygen... 

Other global surfaces include works by Santoro et al. [350, 351] and Salzgeber et al. [347] (these are modified forms of the smfaces by Hirsch et al. [184]), and double many-body expansion smfaces of Varandas [455] and Reignier et al. [333]. The last do not take nonadiabatic coupling into account. 

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)... 

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. 

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]... 

Recalibration of a Single-Valued Double Many-Body Expansion Potential-Energy Surface of Ground-State HO2 and Dynamics Calculations for the O -F OH — H -F O2 Reaction J. Troe and V. G. Ushakov, /. Chem. Phys., 115,3621 (2001). Theoretical Studies of the HO-F O HO2 H-F O2 Reaction, n. Classical Trajectory Calculations on an Ab Initio Potential for Temperatures Between 300 and 5000 K. 

Most theoretical treatments of Rl and -Rl have been based on the potential energy surface developed( 2) by Varandas and Pais(VP). This surface is based on a double many-body expansion of the potential and used in a multiproperty fit including spectroscopic, dynamical and ab initio information. The surface has the merit of giving a relatively smooth global representation for the O4 system, it yields accurate thermal rate constants for the reverse reaction(i9, J-45) and other dynamical properties but displays some minima which are most likely... 

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