Abstract
We present a parallelized contracted basis-iterative calculation of vibrational energy levels of CH\(_5^+\) (a 12D calculation). We use Radau polyspherical coordinates and basis functions that are products of eigenfunctions of bend and stretch Hamiltonians. The basis functions have amplitude in all of the 120 equivalent minima. Many low-lying levels are well converged. A new parallelization scheme is presented.
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References
Marx, D., Parrinello, M.: Structural quantum effects and three-center two-electron bonding in CH\(_5^+\). Nature (London) 375, 216 (1995)
White, E.T., Tang, J., Oka, T.: CH\(_5^+\): The Infrared Spectrum Observed. Science 284, 135 (1999)
Huang, X., McCoy, A.B., Bowman, J.M., Johnson, L.M., Savage, C., Dong, F., Nesbitt, D.J.: Quantum Deconstruction of the Infrared Spectrum of CH5\(_5^+\). Science 311, 60 (2006)
Wang, X.-G., Carrington Jr., T.: Vibrational energy levels of CH\(_5^+\). J. Chem. Phys. 129, 234102 (2008)
East, A.L.L., Kolbuszewski, M., Bunker, P.R.: Ab Initio Calculation of the Rotational Spectrum of CH\(_5^+\) and CD\(_5^+\). J. Phys. Chem. A 101, 6746 (1997)
Jin, Z., Braams, B.J., Bowman, J.M.: An ab Initio Based Global Potential Energy Surface Describing CH\(_5^+\) \(\longrightarrow\) CH\(_3^+\) + H2. J. Phys. Chem. A 110, 1569 (2006)
Bramley, M.J., Carrington Jr., T.: A general discrete variable method to calculate vibrational energy levels of three- and four-atom molecules. J. Chem. Phys. 99, 8519 (1993)
Wang, X.-G., Carrington Jr., T.: New ideas for using contracted basis functions with a Lanczos eigensolver for computing vibrational spectra of molecules with four or more atoms. J. Chem. Phys. 117, 6923–6934 (2002)
Wang, X.-G., Carrington Jr., T.: A contracted basis-Lanczos calculation of the vibrational levels of methane: solving the Schroedinger equation in nine dimensions. J. Chem. Phys. 119, 101–117 (2003)
Paige, C.C.: Computational variants of the Lanczos method for the eigenvalue problem. J. Inst. Math. Appl. 10, 373–381 (1972)
Cullum, J.K., Willoughby, R.A.: Lanczos algorithms for large symmetric eigenvalue computations. Theory, vol. 1. Birkhauser, Boston (1985)
The size of the even basis with l max = m max = 18 is about 215 million. For this basis, 20 quadrature points are used for the θ coordinates and 40 for the φ coordinates
Wang, X.-G., Carrington Jr., T.: A finite basis representation Lanczos calculation of the bend energy levels of methane. J. Chem. Phys. 118, 6946 (2003)
Bramley, M.J., Carrington Jr., T.: Calculation of triatomic vibrational eigenstates: Product or contracted basis sets, Lanczos or conventional eigensolvers? What is the most efficient combination? J. Chem. Phys. 101, 8494 (1994)
Bunker, P.R., Jensen, P.: Molecular Symmetry and Spectroscopy. NRC Research Press, Ottawa (1998)
Wang, X.-G., Carrington Jr., T.: A symmetry-adapted Lanczos method for calculating energy levels with different symmetries from a single set of iterations. J. Chem. Phys. 114, 1473 (2001)
Clarke, L.J., Štich, I., Payne, M.C.: Large-scale ab initio total energy calculations on parallel computers. Comp. Phys. Comm. 72, 14 (1992)
Haynes, P., Côté, M.: Parallel fast Fourier transforms for electronic structure calculations. Comp. Phys. Comm. 130, 130 (2000)
Wei, H., Carrington Jr., T.: The discrete variable representation for a triatomic Hamiltonian in bond length-bond angle coordinates. J. Chem. Phys. 97, 3029 (1992)
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Wang, XG., Carrington, T. (2010). A Parallel Algorithm for Computing the Spectrum of CH\(_5^+\) . In: Mewhort, D.J.K., Cann, N.M., Slater, G.W., Naughton, T.J. (eds) High Performance Computing Systems and Applications. HPCS 2009. Lecture Notes in Computer Science, vol 5976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12659-8_9
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DOI: https://doi.org/10.1007/978-3-642-12659-8_9
Publisher Name: Springer, Berlin, Heidelberg
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