Perturbation methods for computing

Lu, N. Kofke, D. A. Woolf, T. B., Staging is more important than perturbation method for computation of enthalpy and entropy changes in complex systems, J. Phys. Chem. B 2003,107, 5598-5611... 

Kofke, D.A., Cummings, P.T., Precision and accuracy of staged free-energy perturbation methods for computing the chemical potential by molecular simulation, Fluid Phase... 

Lu, N.D., Woolf, T.B., Overlap perturbation methods for computing alchemical free energy changes variants, generalizations and evaluations, Mol. Phys. 2004, 102, 173-181... 

Accuracy of Staged Eree Energy Perturbation Methods for Computing the Chemical Potential by Molecular Simulation. 

An alternative approximation scheme, also proposed by Bom and Oppenheimer [5-7], employed the straightforward perturbation method. To tell the difference between these two different BO approximation, we call the latter the crude BOA (CBOA). A main purpose of this chapter is to study the original BO approximation, which is often referred to as the crude BO approximation and to develop this approximation into a practical method for computing potential energy suifaces of molecules. 

In Chapter IX, Liang et al. present an approach, termed as the crude Bom-Oppenheimer approximation, which is based on the Born-Oppen-heimer approximation but employs the straightforward perturbation method. Within their chapter they develop this approximation to become a practical method for computing potential energy surfaces. They show that to carry out different orders of perturbation, the ability to calculate the matrix elements of the derivatives of the Coulomb interaction with respect to nuclear coordinates is essential. For this purpose, they study a diatomic molecule, and by doing that demonstrate the basic skill to compute the relevant matrix elements for the Gaussian basis sets. Finally, they apply this approach to the H2 molecule and show that the calculated equilibrium position and foree constant fit reasonable well those obtained by other approaches. 

Major DT, Gao J (2007) An integrated path integral and free-energy perturbation-umbrella sampling method for computing kinetic isotope effects of chemical reactions in solution and in enzymes. J Chem Theory Comput 3 949—960... 

Zakrzewski, V.G., von Niessen, W. Vectorizable algorithm for Green-function and many-body perturbation methods. J. Comput. Chem. 1993,14,13-8. 

As shown in Table 2.4, when local buoyancy effects are weak (i.e. Ug/Ub 1), the air flow over an urban area is generally a perturbation of the oncoming flow. Then from semi-analytic models using perturbation methods faster computational schemes have been devised, e.g. for lee-wave prediction scheme 3DVOM over mountains (Vosper and Mobbs, 1996 [639]), and are being developed in a general way to allow for... 

There are two approaches often used for computing interaction energies supermolecular and perturbation methods (for reviews see Chalasihski and Gutowski, 1988 Chalasihski and Szczqsniak, 1994). In the supermolecular method the interaction energy of a pair of molecules is the difference between the energy of the pair and the energy ofthe individual molecules... 

Over the past decade or so, the capabilities of ab initio quantum theory have advanced remarkably due to improvements in computer speeds. It is now possible to compute structures by ab initio methods for relatively large molecules at the Hartree-Fock level using reasonably sophisticated basis sets [12], With the inclusion of electron correlation by Cl or perturbation methods [13], computed ab initio bond distances are now becoming competitive in quality with experimental rg values. However, since experimental r values have been largely unavailable for organic molecules of even modest size, it has not been possible to... 

Sharan S K. 2007. A finite element perturbation method for the prediction of rockburst. Computers Structures S5(n-IS) 1 304-1 309. 

Integrated Path Integral-Free Energy Perturbation/ Umbrella Sampling (PI-FEP/UM) Method for Computing KIEs... 

Both time-independent and time-dependent approaches are viable to perform such computations. Within the time-independent approach, the most widely used method for computing the rovibrational contributions to NMR properties is by means of second-order perturbation theory. To first order, the vibrationally averaged value of a property Q is expressed as... 

Lam and Goussis elaborated a detailed theory based on the application of computational perturbation methods for the investigation of reaction mechanisms. This family of methods is called computational singular perturbation theory and is often... 

The perturbation method starts with a Taylor series expansion of the solution, the external loading, and the stochastic stiffness matrix in terms of the random variables introduced by the discretization of the random parameter field. The unknown coefficients in the expansion of the solution are obtained by equating terms of equal order in the expansion. From this, approximations of the first two statistical moments can be obtained. The perturbation method is computationally more efficient than direct Monte Carlo simulation. However, higher-order approximations will increase the computational effort dramatically, and therefore accurate results are obtained for small coefficients of variation only. 

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