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Affiliation(s)
- James Brown
- Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA
| | - James D. Whitfield
- Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA
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Woywod C, Roy S, Maiti KS, Ruud K. An efficient pseudo-spectral method for the description of atomic electronic wave functions – Application to the hydrogen atom in a uniform magnetic field. Chem Phys 2018; 515:299-314. [DOI: 10.1016/j.chemphys.2018.09.025] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Affiliation(s)
- Jonathan L. Jerke
- Department of Physics, Texas Southern University, Houston, Texas 77004, USA
| | - Young Lee
- Department of Physics, Texas Southern University, Houston, Texas 77004, USA
| | - C. J. Tymczak
- Department of Physics, Texas Southern University, Houston, Texas 77004, USA
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Pipek J, Nagy S. An economic prediction of refinement coefficients in wavelet-based adaptive methods for electron structure calculations. J Comput Chem 2013; 34:460-5. [PMID: 23115109 DOI: 10.1002/jcc.23154] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2012] [Revised: 09/13/2012] [Accepted: 09/17/2012] [Indexed: 11/09/2022]
Abstract
The wave function of a many electron system contains inhomogeneously distributed spatial details, which allows to reduce the number of fine detail wavelets in multiresolution analysis approximations. Finding a method for decimating the unnecessary basis functions plays an essential role in avoiding an exponential increase of computational demand in wavelet-based calculations. We describe an effective prediction algorithm for the next resolution level wavelet coefficients, based on the approximate wave function expanded up to a given level. The prediction results in a reasonable approximation of the wave function and allows to sort out the unnecessary wavelets with a great reliability.
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Affiliation(s)
- János Pipek
- Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, H-1521 Budapest, Hungary.
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Bischoff FA, Harrison RJ, Valeev EF. Computing many-body wave functions with guaranteed precision: The first-order Møller-Plesset wave function for the ground state of helium atom. J Chem Phys 2012; 137:104103. [DOI: 10.1063/1.4747538] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Affiliation(s)
| | - Robert J. Harrison
- Joint Institute for Computational Sciences, University of Tennessee and Oak Ridge National Laboratory, PO Box 2008, Oak Ridge, Tennessee 37831-6173, USA
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
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Abstract
Three-dimensional discrete tensor wavelets are applied to calculate wave functions of excess electrons solvated in polar liquids. Starting from the Hartree–Fock approximation for the electron wave functions and from the linear response to the solute charge for the solvent, we have derived the approximate free energy functional for the excess electrons. The orthogonal Coifman basis set is used to minimize the free energy functional and to approximate the electron wave functions. The scheme is applied to the calculation of the properties of the solvated electron and the singlet bipolaron formation. The obtained results indicate that the proposed algorithm is fast and rather efficient for calculating the electronic structure of the solvated molecular solutes.
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Affiliation(s)
- G. N. CHUEV
- Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Pushchino, Moscow Region, 142290, Russia
| | - M. V. FEDOROV
- Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Pushchino, Moscow Region, 142290, Russia
- Theory and Computation Group, Centre for Synthesis and Chemical Biology, Conway Institute of Biomolecular and Biomedical Research, Department of Chemistry, University College Dublin, Belfield, Dublin 4, Ireland
| | - H. J. LUO
- Fachbereich Physik, Universität Kassel, Heinrich-Plett-Str. 40, D-34132 Kassel, Germany
| | - D. KOLB
- Fachbereich Physik, Universität Kassel, Heinrich-Plett-Str. 40, D-34132 Kassel, Germany
| | - E. G. TIMOSHENKO
- Theory and Computation Group, Centre for Synthesis and Chemical Biology, Conway Institute of Biomolecular and Biomedical Research, Department of Chemistry, University College Dublin, Belfield, Dublin 4, Ireland
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Chinnamsetty SR, Espig M, Khoromskij BN, Hackbusch W, Flad HJ. Tensor product approximation with optimal rank in quantum chemistry. J Chem Phys 2007; 127:084110. [PMID: 17764232 DOI: 10.1063/1.2761871] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Tensor product decompositions with optimal separation rank provide an interesting alternative to traditional Gaussian-type basis functions in electronic structure calculations. We discuss various applications for a new compression algorithm, based on the Newton method, which provides for a given tensor the optimal tensor product or so-called best separable approximation for fixed Kronecker rank. In combination with a stable quadrature scheme for the Coulomb interaction, tensor product formats enable an efficient evaluation of Coulomb integrals. This is demonstrated by means of best separable approximations for the electron density and Hartree potential of small molecules, where individual components of the tensor product can be efficiently represented in a wavelet basis. We present a fairly detailed numerical analysis, which provides the basis for further improvements of this novel approach. Our results suggest a broad range of applications within density fitting schemes, which have been recently successfully applied in quantum chemistry.
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Affiliation(s)
- Sambasiva Rao Chinnamsetty
- Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstrasse 22-26, D-04103 Leipzig, Germany
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Abstract
A recent method for solving the time-dependent Schrodinger equation has been developed using expansions in compact-support wavelet bases in both space and time [H. Wang et al., J. Chem. Phys. 121, 7647 (2004)]. This method represents an exact quantum mixed time-frequency approach, with special initial temporal wavelets used to solve the initial value problem. The present work is a first extension of the method to multiple spatial dimensions applied to a simple two-dimensional (2D) coupled anharmonic oscillator problem. A wavelet-discretized version of norm preservation for time-independent Hamiltonians discovered in the earlier one-dimensional investigation is verified to hold as well in 2D and, by implication, in higher numbers of spatial dimensions. The wavelet bases are not restricted to rectangular domains, a fact which is exploited here in a 2D adaptive version of the algorithm.
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Affiliation(s)
- Douglas K Sparks
- Department of Chemistry, Rice Quantum Institute and Laboratory for Nanophotonics, Rice University, Houston, Texas 77005, USA
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Fedorov MV, Chuev GN, Kuznetsov YA, Timoshenko EG. Wavelet treatment of the intrachain correlation functions of homopolymers in dilute solutions. Phys Rev E Stat Nonlin Soft Matter Phys 2004; 70:051803. [PMID: 15600642 DOI: 10.1103/physreve.70.051803] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2004] [Revised: 09/21/2004] [Indexed: 05/24/2023]
Abstract
Discrete wavelets are applied to the parametrization of the intrachain two-point correlation functions of homopolymers in dilute solutions obtained from Monte Carlo simulations. Several orthogonal and biorthogonal basis sets have been investigated for use in the truncated wavelet approximation. The quality of the approximation has been assessed by calculation of the scaling exponents obtained from the des Cloizeaux ansatz for the correlation functions of homopolymers with different connectivities in a good solvent. The resulting exponents are in better agreement with those from recent renormalization group calculations as compared to the data without the wavelet denoising. We also discuss how the wavelet treatment improves the quality of data for correlation functions from simulations of homopolymers at varied solvent conditions and of heteropolymers.
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Affiliation(s)
- M V Fedorov
- Theory and Computation Group, Centre for Synthesis and Chemical Biology, Conway Institute of Biomolecular and Biomedical Research, Department of Chemistry, University College Dublin, Belfield, Dublin 4, Ireland.
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Abstract
A new algorithm is developed to solve integral equations for simple liquids. The algorithm is based on the discrete wavelet transform of radial distribution functions. The Coifman 2 basis set is employed for the wavelet treatment. To solve integral equations we have applied the combined scheme in which the coarse part of the solution is calculated by wavelets, while the fine part by the direct iterations. Tests on the PY and HNC approximations have indicated that the proposed procedure is more effective than the conventional method based on the hybrid algorithm. Possibilities for application of the method to molecular liquids and mixed quantum-classical systems are discussed.
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Affiliation(s)
- G N Chuev
- Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Pushchino, Moscow Region 142290, Russia.
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Chuev GN, Fedorov MV. Wavelet algorithm for solving integral equations of molecular liquids. A test for the reference interaction site model. J Comput Chem 2004; 25:1369-77. [PMID: 15185331 DOI: 10.1002/jcc.20068] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
A new efficient method is developed for solving integral equations based on the reference interaction site model (RISM) of molecular liquids. The method proposes the expansion of site-site correlation functions into the wavelet series and further calculations of the approximating coefficients. To solve the integral equations we have applied the hybrid scheme in which the coarse part of the solution is calculated by wavelets with the use of the Newton-Raphson procedure, while the fine part is evaluated by the direct iterations. The Coifman 2 basis set is employed for the wavelet treatment of the coarse solution. This wavelet basis set provides compact and accurate approximation of site-site correlation functions so that the number of basis functions and the amplitude of the fine part of solution decrease sufficiently with respect to those obtained by the conventional scheme. The efficiency of the method is tested by calculations of SPC/E model of water. The results indicated that the total CPU time to obtain solution by the proposed procedure reduces to 20% of that required for the conventional hybrid method.
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Affiliation(s)
- Gennady N Chuev
- Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Pushchino, Moscow Region, 142290, Russia.
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Wang H, Acevedo R, Mollé H, Mackey JL, Kinsey JL, Johnson BR. Multiscale quantum propagation using compact-support wavelets in space and time. J Chem Phys 2004; 121:7647-57. [PMID: 15485224 DOI: 10.1063/1.1793952] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
Orthogonal compact-support Daubechies wavelets are employed as bases for both space and time variables in the solution of the time-dependent Schrodinger equation. Initial value conditions are enforced using special early-time wavelets analogous to edge wavelets used in boundary-value problems. It is shown that the quantum equations may be solved directly and accurately in the discrete wavelet representation, an important finding for the eventual goal of highly adaptive multiresolution Schrodinger equation solvers. While the temporal part of the basis is not sharp in either time or frequency, the Chebyshev method used for pure time-domain propagations is adapted to use in the mixed domain and is able to take advantage of Hamiltonian matrix sparseness. The orthogonal separation into different time scales is determined theoretically to persist throughout the evolution and is demonstrated numerically in a partially adaptive treatment of scattering from an asymmetric Eckart barrier.
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Affiliation(s)
- Haixiang Wang
- Department of Chemistry, Rice Quantum Institute and Laboratory for Nanophotonics, Rice University, MS 600, Houston, TX 77005-1892, USA
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Chuev GN, Fedorov MV. Wavelet treatment of radial distribution functions of solutes. Phys Rev E Stat Nonlin Soft Matter Phys 2003; 68:027702. [PMID: 14525159 DOI: 10.1103/physreve.68.027702] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2003] [Indexed: 05/24/2023]
Abstract
Discrete wavelets are applied to parametrize the radial distribution functions of hydrated ions and hydrophobic solutes. The data on radial distribution functions are derived from the integral equation theory and neutron scattering experiment. The Coifman and the discrete Meyer basis sets are used for the wavelet approximation. The quality of the approximation is verified by calculations of the solvation energy, the coordination number, and the change in chemical potential of solutes.
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Affiliation(s)
- G N Chuev
- Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Puschino, Moscow Region 142290, Russia
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