A coherent discrete variable representation method on a sphere

Yu, Hua -Gen

doi:10.1063/1.4996891

A coherent discrete variable representation method on a sphere

Journal Article · Tue Sep 05 00:00:00 EDT 2017 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4996891· OSTI ID:1377058

Yu, Hua -Gen ^[1]

Brookhaven National Lab. (BNL), Upton, NY (United States)

Here, the coherent discrete variable representation (ZDVR) has been extended for construct- ing a multidimensional potential-optimized DVR basis on a sphere. In order to deal with the non-constant Jacobian in spherical angles, two direct product primitive basis methods are proposed so that the original ZDVR technique can be properly implemented. The method has been demonstrated by computing the lowest states of a two dimensional (2D) vibrational model. Results show that the extended ZDVR method gives accurate eigenval- ues and exponential convergence with increasing ZDVR basis size.

View Accepted Manuscript (DOE)

Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: SC0012704

OSTI ID:: 1377058

Alternate ID(s):: OSTI ID: 1378421

Report Number(s):: BNL--114205-2017-JA; KC0301020

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 9 Vol. 147; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (30)

Discrete-Variable Representations and their Utilization Light, John C.; Carrington, Jr., Tucker Advances in Chemical Physics https://doi.org/10.1002/9780470141731.ch4	book	January 2000
Some useful discrete variable representations for problems in time-dependent and time-independent quantum mechanics Muckerman, James T. Chemical Physics Letters, Vol. 173, Issue 2-3 https://doi.org/10.1016/0009-2614(90)80078-r	journal	October 1990
Potential optimized discrete variable representation Echave, Julián; Clary, David C. Chemical Physics Letters, Vol. 190, Issue 3-4 https://doi.org/10.1016/0009-2614(92)85330-d	journal	March 1992
Analytical treatment of Coriolis coupling for three-body systems Poirier, Bill Chemical Physics, Vol. 308, Issue 3 https://doi.org/10.1016/j.chemphys.2004.03.022	journal	January 2005
On direct product based discrete variable representations for angular coordinates and the treatment of singular terms in the kinetic energy operator Schiffel, Gerd; Manthe, Uwe Chemical Physics, Vol. 374, Issue 1-3 https://doi.org/10.1016/j.chemphys.2010.07.006	journal	August 2010
Exact and constrained kinetic energy operators for polyatomic molecules: The polyspherical approach Gatti, Fabien; Iung, Christophe Physics Reports, Vol. 484, Issue 1-2 https://doi.org/10.1016/j.physrep.2009.05.003	journal	November 2009
An efficient grid calculation of vibrational states for H3∗ with geometric phase in hyperspherical coordinates Yu, Hua-Gen Chemical Physics Letters, Vol. 281, Issue 4-6 https://doi.org/10.1016/s0009-2614(97)01253-0	journal	December 1997
Non-Hermitian Quantum Mechanics Moiseyev, Nimrod https://doi.org/10.1017/CBO9780511976186	book	May 2011
The fourth age of quantum chemistry: molecules in motion Császár, Attila G.; Fábri, Csaba; Szidarovszky, Tamás Phys. Chem. Chem. Phys., Vol. 14, Issue 3 https://doi.org/10.1039/c1cp21830a	journal	January 2012
A general framework for discrete variable representation basis sets Littlejohn, Robert G.; Cargo, Matthew; Carrington, Tucker The Journal of Chemical Physics, Vol. 116, Issue 20 https://doi.org/10.1063/1.1473811	journal	May 2002
An exact variational method to calculate vibrational energies of five atom molecules beyond the normal mode approach Yu, Hua-Gen The Journal of Chemical Physics, Vol. 117, Issue 5 https://doi.org/10.1063/1.1488575	journal	August 2002
Calculation of Matrix Elements for One‐Dimensional Quantum‐Mechanical Problems Dickinson, A. S.; Certain, P. R. The Journal of Chemical Physics, Vol. 49, Issue 9 https://doi.org/10.1063/1.1670738	journal	November 1968
Calculation of Matrix Elements for One‐Dimensional Quantum‐Mechanical Problems and the Application to Anharmonic Oscillators Harris, David O.; Engerholm, Gail G.; Gwinn, William D. The Journal of Chemical Physics, Vol. 43, Issue 5 https://doi.org/10.1063/1.1696963	journal	September 1965
A multidimensional discrete variable representation basis obtained by simultaneous diagonalization Dawes, Richard; Carrington, Tucker The Journal of Chemical Physics, Vol. 121, Issue 2 https://doi.org/10.1063/1.1758941	journal	July 2004
A coherent discrete variable representation method for multidimensional systems in physics Yu, Hua-Gen The Journal of Chemical Physics, Vol. 122, Issue 16 https://doi.org/10.1063/1.1884116	journal	April 2005
Optimal grids for generalized finite basis and discrete variable representations: Definition and method of calculation Szalay, Viktor The Journal of Chemical Physics, Vol. 125, Issue 15 https://doi.org/10.1063/1.2358979	journal	October 2006
Layered discrete variable representations and their application within the multiconfigurational time-dependent Hartree approach Manthe, Uwe The Journal of Chemical Physics, Vol. 130, Issue 5 https://doi.org/10.1063/1.3069655	journal	February 2009
Multilayer multiconfiguration time-dependent Hartree method: Implementation and applications to a Henon–Heiles Hamiltonian and to pyrazine Vendrell, Oriol; Meyer, Hans-Dieter The Journal of Chemical Physics, Vol. 134, Issue 4 https://doi.org/10.1063/1.3535541	journal	January 2011
Rovibrational bound states of neon trimer: Quantum dynamical calculation of all eigenstate energy levels and wavefunctions Yang, Benhui; Chen, Wenwu; Poirier, Bill The Journal of Chemical Physics, Vol. 135, Issue 9 https://doi.org/10.1063/1.3630922	journal	September 2011
Generalized discrete variable approximation in quantum mechanics Light, J. C.; Hamilton, I. P.; Lill, J. V. The Journal of Chemical Physics, Vol. 82, Issue 3 https://doi.org/10.1063/1.448462	journal	February 1985
Solution of the Hartree–Fock equations by a pseudospectral method: Application to diatomic molecules Friesner, Richard A. The Journal of Chemical Physics, Vol. 85, Issue 3 https://doi.org/10.1063/1.451237	journal	August 1986
The discrete variable representation of a triatomic Hamiltonian in bond length–bond angle coordinates Wei, Hua; Carrington, Tucker The Journal of Chemical Physics, Vol. 97, Issue 5 https://doi.org/10.1063/1.463044	journal	September 1992
Variational properties of the discrete variable representation: Discrete variable representation via effective operators Szalay, Viktor; Ádám, Péter The Journal of Chemical Physics, Vol. 137, Issue 6 https://doi.org/10.1063/1.4740486	journal	August 2012
Phase space optimization of quantum representations: Direct-product basis sets Poirier, Bill; Light, J. C. The Journal of Chemical Physics, Vol. 111, Issue 11 https://doi.org/10.1063/1.479747	journal	September 1999
Perspective: Computing (ro-)vibrational spectra of molecules with more than four atoms Carrington, Tucker The Journal of Chemical Physics, Vol. 146, Issue 12 https://doi.org/10.1063/1.4979117	journal	March 2017
Quantum approaches to polyatomic reaction dynamics Nyman, Gunnar; Yu, Hua-Gen International Reviews in Physical Chemistry, Vol. 32, Issue 1 https://doi.org/10.1080/0144235x.2012.735863	journal	March 2013
On the overlap integral of associated Legendre polynomials Wong, B. R. Journal of Physics A: Mathematical and General, Vol. 31, Issue 3 https://doi.org/10.1088/0305-4470/31/3/019	journal	January 1998
Lebedev discrete variable representation Haxton, Daniel J. Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 40, Issue 23 https://doi.org/10.1088/0953-4075/40/23/004	journal	November 2007
Excitation, relaxation, and quantum diffusion of CO on copper Tremblay, Jean Christophe; Füchsel, Gernot; Saalfrank, Peter Physical Review B, Vol. 86, Issue 4 https://doi.org/10.1103/physrevb.86.045438	journal	July 2012
Recent Advances in Quantum Dynamics of Bimolecular Reactions Zhang, Dong H.; Guo, Hua Annual Review of Physical Chemistry, Vol. 67, Issue 1 https://doi.org/10.1146/annurev-physchem-040215-112016	journal	May 2016

Similar Records

Multidimensional time-dependent discrete variable representations in multiconfiguration Hartree calculations

Journal Article · Mon Aug 08 00:00:00 EDT 2005 · Journal of Chemical Physics · OSTI ID:20723016

Discrete variable representation method applied to the determination of J = 0 vibrational bound states of NO{sub 2}

Journal Article · Tue Sep 05 00:00:00 EDT 1995 · International Journal of Quantum Chemistry · OSTI ID:501883

A discrete variable representation for electron-hydrogen atom scattering

Thesis/Dissertation · Mon Aug 01 00:00:00 EDT 1994 · OSTI ID:10196995

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

A coherent discrete variable representation method on a sphere

Citation Formats

References (30)

Similar Records

Related Subjects