"Non UBC"@en .
"DSpace"@en .
"Valeev, Edward"@en .
"2014-08-06T23:17:12Z"@en .
"2013-05-01"@en .
"One of the grand challenges of quantum chemistry is computing observables (energies, scattering cross\u00E2\u0080\u0093sections, response properties) and their confidence intervals with high precision. This requires fast methods, characterized by a low\u00E2\u0080\u0093order scaling of the computational cost with the system size and error. Despite significant advances in the area, we are still very far from this goal. This talk will address some of our recent work on fast methods, with the word fast referring to the scaling with precision (i.e. the discretization error) and with the system size. Specifically, I will discuss our efforts to compute two\u00E2\u0080\u0093particle wave functions in hierarchical (multiresolution) discontinuous spectral\u00E2\u0080\u0093element representations. [1, 2] Each volume element of the six\u00E2\u0080\u0093dimensional wave function is supported by an orthonormal basis set of tensor products of polynomials. To alleviate the severe (exponential) cost of finite\u00E2\u0080\u0093element representation in many dimensions, which makes precise representation and computation of correlated wave functions intractable, we use low\u00E2\u0080\u0093rank tensor approximations, namely the singular value decomposition SVD, and reformulate all operations necessary to solve the Schr \u00CC\u0088odinger equation in low\u00E2\u0080\u0093rank form. [3] The low-rank approximations alone are not sufficient; hence we use explicitly\u00E2\u0080\u0093correlated terms in the wave function to regularize the electron\u00E2\u0080\u0093electron Coulomb singularities of the Hamiltonian. Our approach does not assume any geometric symmetry, hence the method is tractable for molecules. [2] The method was used to compute the first\u00E2\u0080\u0093order M\u00C3\u00B8ller-Plesset wave function and the second-order energy of the helium atom with precision guaranteed by construction (our most precise value for the MP2 energy is \u00E2\u0088\u009237.379 mEh). We will further highlight the strengths and weaknesses of the adaptive discretization strategy.\n[1] F. A. Bischoff, R. J. Harrison, and E. F. Valeev, J. Chem. Phys. 137, 104103 (2012). [2] F.A.BischoffandE.F.Valeev,inpreparation.\n[3] F. A. Bischoff and E. F. Valeev, J. Chem. Phys. 134, 104104 (2011)."@en .
"https://circle.library.ubc.ca/rest/handle/2429/49340?expand=metadata"@en .
"34 minutes"@en .
"video/mp4"@en .
""@en .
"Author affiliation: Virginia Tech"@en .
"10.14288/1.0043397"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivs 2.5 Canada"@en .
"http://creativecommons.org/licenses/by-nc-nd/2.5/ca/"@en .
"Faculty"@en .
"BIRS Workshop Lecture Videos (Banff, Alta)"@en .
"Mathematics"@en .
"Quantum theory"@en .
"Partial differential equations"@en .
"Mathematical physics"@en .
"Multiresolution spectral\u00E2\u0080\u0093element representations of electronic wave functions"@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/49340"@en .