Density fitting

BL Sibanda, TL Blundell, JM Thornton. Conformation of (I-hairpms m protein stractures A systematic classification with applications to modelling by homology, electron density fitting and protein engineering. J Mol Biol 206 759-777, 1989. 

The density fitting functions may or may not be the same as those used in expanding the orbitals. The fitting constants a are chosen so that the Coulomb energy arising from the difference between the exact and fitted densities is minimized, subject to the constraint of charge conservation. The J integrals then become... 

Piquemal, J., Cisneros, G. A., Reinhardt, P., Gresh, N., Darden, T. Towards a force field based on density fitting. J. Chem. Phys. 2006, 124,104101-104113. 

Transferred electron density fragments obtained by AFDF method can provide excellent approximations. One such approach, formulated in terms of transferability of fragment density matrices within the AFDF framework is a tool that has been suggested as an approach to macromolecular quantum chemistry [114, 115, 130, 142-146] and to a new density fitting algorithm in the crystallographic structure refinement process [161]. 

Do so, we use the formalism of the variational density fitting method [55, 56] where the Coulomb self-interaction energy of the error is minimized ... 

As electric fields and potential of molecules can be generated upon distributed p, the second order energies schemes of the SIBFA approach can be directly fueled by the density fitted coefficients. To conclude, an important asset of the GEM approach is the possibility of generating a general framework to perform Periodic Boundary Conditions (PBC) simulations. Indeed, such process can be used for second generation APMM such as SIBFA since PBC methodology has been shown to be a key issue in polarizable molecular dynamics with the efficient PBC implementation [60] of the multipole based AMOEBA force field [61]. 

Cisneros GA, Piquemal J-P, Darden TA (2005) Intermolecular electrostatic energies using density fitting. J ChemPhys 123 044109... 

Gallant, R. T. and A. St-Amant. 1996. Linear scaling for the charge density fitting procedure of the linear combination of Gaussian-type orbitals density functional method. Chem. Phys. Lett. 256, 569. 

H. J. Werner, F. R. Manby, and P. J. Knowles, Fast linear scaling second order Mpller Plesset perturbation theory (MP2) using local and density fitting approximations. J. Chem. Phys. 118, 8149 8160 (2003). 

Nissink, J.W.M., Verdonk, M.L., Kroon, J., Mietzner, T., and Klebe, G. Superposition of molecules electron density fitting using fourier transforms. /. Comb. Chem. 1997, 38, 638-645. 

Accessing software for electron density fitting and structure validation... 

Manby, F.R. Density fitting in second-order linear-r12 Moller-Plesset perturbation theory. J. Chem. Phys. 2003, 119, 4607-13. 

R. T. Gallant and A. St-Amant, Chem. Phys. Lett., 256 569 (1996). Linear Scaling for the Charge Density Fitting Procedure of the Linear Combination of Gaussian-Type Orbitals Density Functional Method. 

A superior method for the calculation of excited-state PE surfaces is CC2, which is a simplified and computationally efficient variant of coupled-cluster theory with single and double excitations [22], CC2 can be considered as the equivalent of MP2 for excited electronic states. Efficient implementations of CC2 with density fitting [23] and analytic gradients [24] allow reaction path calculations for rather large systems. Being a singlereference method, CC2 fails in the vicinity of conical intersections of excited states with the electronic ground state. 

A. HeBelmann, G. Jansen, M. Schtitz, Density-functional theory-symmetry-adapted intermolecular perturbation theory with density fitting A new efficient method to study intermolecular interaction energies. J. Chem. Phys. 122, 014103 (2005)... 

R. Podeszwa, R. Bukowski, K. Szalewicz, Density-fitting method in symmetry-adapted perturbation theory based on Kohn-Sham description of monomers. J. Chem. Theory Comput. 2, 400-412 (2006)... 

Thus, if it is assumed that the local virial theorem is valid for the model electron densities fitted to the experimental structure factors, the kinetic, g(r), and potential, v(r), energy densities may be mapped, as well as the energy characteristics of the (3,-1) bond critical points evaluated [38]. 

The evaluation of the expressions (1-67), (1-87), and (1-94) can be simplified by using the density fitting technique225,227. In this approach the product is expanded in terms of auxiliary atomic orbitals k. In such a case the orbital expressions corresponding to Eqs. (1-67), (1-87), and (1-94) greatly simplify. For the dispersion energy Eq. (1-94) takes the form ... 

Except for occasional discussions of the basis set dependence of the results, the numerical implementation issues such as grid integration techniques, electron-density fitting, frozen-cores, pseudopotentials, and linear-scaling techniques, are omitted. 

Tel. 713-798-6565, fax 713-797-6718, e-mail faq dino.qci.bioch.bcm.tmc.edu Molecular graphics and crystallographic applications. Evans Sutherland. CHAIN is a newer, supported program for electron density fitting and molecular graphics that runs on Evans Sutherland (PS300s and ESVs) and Silicon Graphics. 

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