Solving the vibrational Schrödinger equation on an arbitrary multidimensional potential energy surface by the finite element method

Xu, Dong; Stare, Jernej; Cooksy, Andrew L.

doi:10.1016/j.cpc.2009.06.010

Cited by 11 publications

(4 citation statements)

References 79 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using these surfaces, we then employed our own software, FENMvib [5], to extract the wavefunctions and energies of the vibrational states corresponding to excitation of the isomerization coordinate. Support of this project has led us to extend the capabilities of FEMvib to automatically interpolate and extrapolate the grid-based potential energy surface by means of distributed approximating functionals [6].…”

Section: Results Summary 21 Computational Quantum Mechanicsmentioning

confidence: 99%

An Integrated Experimental and Computational Study of Relocalization in pi-Conjugated Combustion Intermediates

Cooksy¹

2010

Self Cite

View full text Add to dashboard Cite

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggesstions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports,

show abstract

Section: Results Summary 21 Computational Quantum Mechanicsmentioning

confidence: 99%

An Integrated Experimental and Computational Study of Relocalization in pi-Conjugated Combustion Intermediates

Cooksy¹

2010

Self Cite

View full text Add to dashboard Cite

show abstract

“…In developing a general FEM approach for anharmonic and coupled bound vibrations, Xu et al 43 have repeated this calculation, needing only 100ϫ 100 square grids to obtain the converged results shown in the second column of Table IV. A wavelet calculation was performed in a direct product basis of scaling functions in R and x, each with its own scale factor. For a particular set of parameters, Sato and Iwata solved the eigenproblem using the finite element method ͑FEM͒ with square grids up to 557 on a side to calculate the first 17 eigenvalues.…”

Section: Two-dimensional Model Of Hydrogen Atom Transfermentioning

confidence: 99%

“…There is good overall agreement, except that our transitions are all ϳ0.03% higher than those of Yamashita and Kato. The need for such general methods that apply, e.g., to any orthogonal or nonorthogonal coordinates and to any PES, has been recently discussed at length by Xu et al 43 and led in their case to a FEM approach. It can be seen from Table V that the wavelet and DVR calculations fully agree except for some small differences in higher transitions that were regarded as too unimportant to pursue further.…”

Section: ͑31͒mentioning

confidence: 99%

Matrix-free application of Hamiltonian operators in Coifman wavelet bases

Acevedo

Lombardini

Johnson

2010

The Journal of Chemical Physics

View full text Add to dashboard Cite

A means of evaluating the action of Hamiltonian operators on functions expanded in orthogonal compact support wavelet bases is developed, avoiding the direct construction and storage of operator matrices that complicate extension to coupled multidimensional quantum applications. Application of a potential energy operator is accomplished by simple multiplication of the two sets of expansion coefficients without any convolution. The errors of this coefficient product approximation are quantified and lead to use of particular generalized coiflet bases, derived here, that maximize the number of moment conditions satisfied by the scaling function. This is at the expense of the number of vanishing moments of the wavelet function (approximation order), which appears to be a disadvantage but is shown surmountable. In particular, application of the kinetic energy operator, which is accomplished through the use of one-dimensional (1D) [or at most two-dimensional (2D)] differentiation filters, then degrades in accuracy if the standard choice is made. However, it is determined that use of high-order finite-difference filters yields strongly reduced absolute errors. Eigensolvers that ordinarily use only matrix-vector multiplications, such as the Lanczos algorithm, can then be used with this more efficient procedure. Applications are made to anharmonic vibrational problems: a 1D Morse oscillator, a 2D model of proton transfer, and three-dimensional vibrations of nitrosyl chloride on a global potential energy surface.

show abstract

“…Some numerical methodologies have been used to solve differential equations of mathematical physics including 1/ N expansion,1, 2 finite element,3, 4 homotopy analysis,5, 6 multipole,7 Runge–Kutta techniques,8, 9 and so forth. Although these techniques are completely reliable, they have their own complexity and cumbersomeness.…”

Section: Introductionmentioning

confidence: 99%

Approximate analytical versus numerical solutions of Schrödinger equation under molecular Hua potential

Hassanabadi

Yazarloo

Zarrinkamar

et al. 2012

Int J of Quantum Chemistry

View full text Add to dashboard Cite

show abstract

Solving the vibrational Schrödinger equation on an arbitrary multidimensional potential energy surface by the finite element method

Cited by 11 publications

References 79 publications

An Integrated Experimental and Computational Study of Relocalization in pi-Conjugated Combustion Intermediates

An Integrated Experimental and Computational Study of Relocalization in pi-Conjugated Combustion Intermediates

Matrix-free application of Hamiltonian operators in Coifman wavelet bases

Approximate analytical versus numerical solutions of Schrödinger equation under molecular Hua potential

Contact Info

Product

Resources

About