Using *ScalIT* for Performing Accurate Rovibrational Spectroscopy Calculations for Triatomic Molecules: A Practical Guide

Affiliation(s)

Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas, USA.

Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas, USA.

Abstract

This paper presents a practical guide for use of the* ScalIT* software package to perform highly accurate bound rovibrational spectroscopy calculations for triatomic molecules. At its core, *ScalIT* serves as a massively scalable iterative sparse matrix solver, while assisting modules serve to create rovibrational Hamiltonian matrices, and analyze computed energy levels (eigenvalues) and wavefunctions (eigenvectors). Some of the methods incorporated into the package include: phase space optimized discrete variable representation, preconditioned inexact spectral transform, and optimal separable basis preconditioning. *ScalIT* has previously been implemented successfully for a wide range of chemical applications, allowing even the most state-of-the-art calculations to be computed with relative ease, across a large number of computational cores, in a short amount of time.

This paper presents a practical guide for use of the

Keywords

Rovibrational Spectroscopy, Iterative Matrix Solver, Lanczos, Quasiminimal Residual, Molecular Bound States, HO2

Rovibrational Spectroscopy, Iterative Matrix Solver, Lanczos, Quasiminimal Residual, Molecular Bound States, HO2

Cite this paper

Petty, C. and Poirier, B. (2014) Using*ScalIT* for Performing Accurate Rovibrational Spectroscopy Calculations for Triatomic Molecules: A Practical Guide. *Applied Mathematics*, **5**, 2756-2763. doi: 10.4236/am.2014.517263.

Petty, C. and Poirier, B. (2014) Using

References

[1] Chen, W. and Poirier, B. (2010) Quantum Dynamical Calculation of All Rovibrational States of HO2 for Total Angular Momentum J = 0 – 10. Journal of Theoretical and Computational Chemistry, 9, 435-469.

http://dx.doi.org/10.1142/S0219633610005815

[2] Poirier, B. (1998) Quantum Reactive Scattering for Three Body Systems via Optimized Preconditioning, as Applied to the O+HCl Reaction. The Journal of Chemical Physics, 108, 5216-5224.

http://dx.doi.org/10.1063/1.475958

[3] Chen, W. and Poirier, B. (2006) Parallel Implementation of Efficient Preconditioned Linear Solver for Grid-Based Applications in Chemical Physics. I: Block Jacobi Diagonalization. Journal of Computational Physics, 219, 185-197.

http://dx.doi.org/10.1016/j.jcp.2006.04.012

[4] Chen, W. and Poirier, B. (2006) Parallel Implementation of Efficient Preconditioned Linear Solver for Grid-Based Applications in Chemical Physics. II: QMR Linear Solver. Journal of Computational Physics, 219, 198-209.

http://dx.doi.org/10.1016/j.jcp.2006.03.03

[5] Chen, W. and Poirier, B. (2010) Parallel Implementation of an Efficient Preconditioned Linear Solver for Grid-Based Applications in Chemical Physics. III: Improved Parallel Scalability for Sparse Matrix Vector Products. Journal of Parallel and Distributed Computing, 70, 779-782.

http://dx.doi.org/10.1016/j.jpdc.2010.03.008

[6] Chen, W. and Poirier, B. (2010) Quantum Dynamics on Massively Parallel Computers: Efficient Numerical Implementation for Preconditioned Linear Solvers and Eigensolvers. Journal of Theoretical and Computational Chemistry, 9, 825-846.

http://dx.doi.org/10.1142/S021963361000602X

[7] Yang, B., Chen, W. and Poirier, B. (2011) Rovibrational Bound States of Neon Trimer: Quantum Dynamical Calculation of All Eigenstate Energy Levels and Wavefunctions. The Journal of Chemical Physics, 135, Article ID: 094306.

http://dx.doi.org/10.1063/1.3630922

[8] Poirier, B. and Light, J.C. (1999) Phase Space Optimization of Quantum Representations: Direct-Product Basis Sets. The Journal of Chemical Physics, 111, 4869-4885.

http://dx.doi.org/10.1063/1.479747

[9] Poirier, B. and Light, J.C. (2001) Phase Space Optimization of Quantum Representations: Three-Body Systems and the Bound States of HCO. The Journal of Chemical Physics, 114, 6562-6571.

http://dx.doi.org/10.1063/1.1354181

[10] Poirier, B. (2001) Phase Space Optimization of Quantum Representations: Non-Cartesian Coordinate Spaces. Foundations of Physics, 31, 1581-1610.

http://dx.doi.org/10.1023/A:1012642832253

[11] Bian, W. and Poirier, B. (2003) Accurate and Highly Efficient Calculation of the O(1D)HCl Vibrational Bound States Using a Combination of Methods. Journal of Theoretical and Computational Chemistry, 2, 583-597.

http://dx.doi.org/10.1142/S0219633603000768

[12] Huang, S.W. and Carrington Jr., T. (2000) A New Iterative Method for Calculating Energy Levels and Wave Functions. The Journal of Chemical Physics, 112, 8765-8771.

http://dx.doi.org/10.1063/1.481492

[13] Poirier, B. and Carrington Jr., T. (2001) Accelerating the Calculation of Energy Levels and Wave Functions Using an Efficient Preconditioner with the Inexact Spectral Transform Method. The Journal of Chemical Physics, 114, 9254-9264.

http://dx.doi.org/10.1063/1.1367396

[14] Poirier, B. and Carrington Jr., T. (2002) A Preconditioned Inexact Spectral Transform Method for Calculating Resonance Energies and Widths, as Applied to HCO. The Journal of Chemical Physics, 116, 1215-1227.

http://dx.doi.org/10.1063/1.1428752

[15] Poirier, B. and Miller, W.H. (1997) Optimized Preconditioners for Green Function Evaluation in Quantum Reactive Scattering Calculations. Chemical Physics Letters, 265, 77-83.

http://dx.doi.org/10.1016/S0009-2614(96)01408-X

[16] Poirier, B. (1997) Optimal Separable Bases and Series Expansions. Physical Review A, 56, 120-130.

http://dx.doi.org/10.1103/PhysRevA.56.120

[17] Poirier, B. (2000) Efficient Preconditioning Scheme for Block Partitioned Matrices with Structured Sparsity. Numerical Linear Algebra with Applications, 7, 715-726.

http://dx.doi.org/10.1002/1099-1506(200010/12)7:7/8<715::AID-NLA220>3.0.CO;2-R

[18] Wyatt, R.E. (1995) Matrix Spectroscopy: Computation of Interior Eigenstates of Large Matrices Using Layered Iteration. Physical Review E, 51, 3643-3658.

http://dx.doi.org/10.1103/PhysRevE.51.3643

[19] Yang, B. and Poirier, B. (2012) Quantum Dynamical Calculation of Rovibrational Bound States of Ne2Ar. Journal of Physics B, 45, Article ID: 135102.

http://dx.doi.org/10.1088/0953-4075/45/13/135102

[20] Yang, B. and Poirier, B. (2012) Rovibrational Bound States of the Ar2Ne Complex. Journal of Theoretical and Computational Chemistry, 12, Article ID: 1250107.

http://dx.doi.org/10.1142/S0219633612501076

[21] Lung, C. and Leforestier, C. (1989) Accurate Determination of Potential Energy Surface for CD3H. The Journal of Chemical Physics, 90, 3198-3203.

http://dx.doi.org/10.1063/1.455871

[22] Bentley, J., Brunet, J., Wyatt, R.E., Friesner, R. and Leforestier, C. (1989) Quantum Mechanical Study of the Ã^{l}A” →X^{l} Σ^{+} SEP Spectrum for HCN. Chemical Physics Letters, 161, 393-400.

http://dx.doi.org/10.1016/0009-2614(89)85104-8

[23] Bramley, M. and Carrington Jr., T. (1993) A General Dicrete Variable Method to Calculate Vibrational Energy Levels of Three and Four Atom Molecules. The Journal of Chemical Physics, 99, 8519-8541.

http://dx.doi.org/10.1063/1.465576

[24] Bramley, M. and Carrington Jr., T. (1994) Calculation of Triatomic Vibrational Eigenstates: Product or Contracted Basis Sets, Lanczos or Conventional Eigensolvers? What is the Most Efficient Combination? The Journal of Chemical Physics, 101, 8494-8507.

http://dx.doi.org/10.1063/1.468110

[25] Wang, X. and Carrington Jr., T. (2001) A Symmetry-Adapted Lanczos Method for Calculating Energy Levels with Different Symmetries from a Single Set of Iterations. The Journal of Chemical Physics, 114, 1473-1477.

http://dx.doi.org/10.1063/1.1331357

[26] Geus, R. and R?llin, S. (2001) Towards a Fast Parallel Sparse Symmetric Matrix-Vector Multiplication. Parallel Computing, 27, 883-896.

http://dx.doi.org/10.1016/S0167-8191(01)00073-4

[27] http://www.mcs.anl.gov/petsc/

[28] Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T. (1989) Numerical Recipes. Cambridge University Press, Cambridge.

[29] Colbert, D.T. and Miller, W.H. (1992) A Novel Discrete Variable Representation for Quantum Mechanical Reactive Scattering via the S-Kohn Method. The Journal of Chemical Physics, 96, 1982-1991.

http://dx.doi.org/10.1063/1.462100

[30] Petty, C. and Poirier, B. (2013) Quantum Dynamical Calculation of Bound Rovibrational States of HO2 up to Largest Possible Total Angular Momentum, J ≤ 130. The Journal of Chemical Physics A, 117, 7280-7297.

http://dx.doi.org/10.1021/jp401154m

[31] Zhang. H. and Smith, S. (2001) Calculation of Product State Distributions from Resonance Decay via Lanczos Subspace Filter Diagonalization: Application to HO2. The Journal of Chemical Physics, 115, 5751-5758.

http://dx.doi.org/10.1063/1.1400785

[32] Zhang, H. and Smith, S. (2003) Calculation of Bound and Resonance States of HO2 for Nonzero Total Angular Momentum. The Journal of Chemical Physics, 118, 10042-10050.

http://dx.doi.org/10.1063/1.1572132

[33] Zhang, H. and Smith, S. (2004) Converged Quantum Calculations of HO2 Bound States and Resonances for J = 6 and 10. The Journal of Chemical Physics, 120, 9583-9593.

http://dx.doi.org/10.1063/1.1711811

[34] Zhang, H. and Smith, S. (2005) Unimolecular Rovibrational Bound and Resonance States for Large Angular Momentum: J = 20 Calculations for HO2. The Journal of Chemical Physics, 123, Article ID: 014308.

http://dx.doi.org/10.1063/1.1949609

[35] Zhang, H. and Smith, S. (2006) HO2 Ro-Vibrational Bound State Calculations for Large Angular Momentum: J = 30; 40 and 50. The Journal of Chemical Physics, 110, 3246-3253.

http://dx.doi.org/10.1021/jp0582336