Special Issue "Computational Spectroscopy"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (31 January 2019).

Special Issue Editor

Professor Sergei Manzhos
Website
Guest Editor
Department of Mechanical Engineering, National University of Singapore
Interests: Quantum dynamics including method development to compute anharmonic vibrational spectra and multivariate potential energy surfaces; Theoretical modeling of processes in photoelectrochemical solar cells, specifically focusing on computational dyes design and non-adiabatic processes and effects due to nuclear dynamics; Computational modeling of metal-ion batteries with the focus on electrode materials for post-Li (Na, Mg) batteries and organic batteries; Large scale ab initio materials simulations based on orbital-free density functional theory and density functional tight binding, including method development in these; Modeling of molecule-surface interactions
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Special Issue Information

Dear Colleagues,

Spectroscopies, probing electronic or vibrational transitions, are workhorse material characterization techniques. Optical absorption and luminescence measurements are ubiquitously used to characterize, e.g., materials used in solar cells, organic electronics, etc. Vibrational spectra are ubiquitously used to assign species, e.g., in catalytic reactions and of course in the atmosphere and outer space. Computed spectra are of great help to assign species, that is to say, when they are accurate.

In spite of significant differences between vibrational and electronic spectroscopy, there are also similarities and possibilities of cross-fertilization. Computed vibrational and electronic spectra follow from or approximate solutions to, respectively, vibrational and electronic Schrödinger equations. The commonly used approximations are still relatively inaccurate or costly; for example, species assignment in aggregate states and at interfaces still largely relies on the harmonic approximation to vibrational spectra.

In this Special Issue, we attempt to bring together works that aim to solve vibrational, electronic, or related versions of the Schrödinger equation (such as the Kohn-Sham equation) or equations used in other applications with ideas portable to computation of vibrational or electronic spectra.  We would like to juxtapose ideas that can be used in these two applications. We welcome papers addressing the issues of coupling of degrees of freedom, basis size and completeness, selection of quadrature and collocation grids, use of rectangular matrices, approximations to calculations of excitations, etc.

Prof. Dr. Sergei Manzhos
Guest Editor

Manuscript Submission Information

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Keywords

  • Vibrational spectroscopy
  • Electronic spectroscopy
  • UV-VIS spectroscopy
  • Anharmonicity
  • Coupling
  • Basis set
  • Collocation
  • Excitation
  • Schrödinger equation
  • Differential equation keyword

Published Papers (2 papers)

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Research

Open AccessArticle
Inverse Multiquadratic Functions as the Basis for the Rectangular Collocation Method to Solve the Vibrational Schrödinger Equation
Mathematics 2018, 6(11), 253; https://doi.org/10.3390/math6110253 - 15 Nov 2018
Cited by 2
Abstract
We explore the use of inverse multiquadratic (IMQ) functions as basis functions when solving the vibrational Schrödinger equation with the rectangular collocation method. The quality of the vibrational spectrum of formaldehyde (in six dimensions) is compared to that obtained using Gaussian basis functions [...] Read more.
We explore the use of inverse multiquadratic (IMQ) functions as basis functions when solving the vibrational Schrödinger equation with the rectangular collocation method. The quality of the vibrational spectrum of formaldehyde (in six dimensions) is compared to that obtained using Gaussian basis functions when using different numbers of width-optimized IMQ functions. The effects of the ratio of the number of collocation points to the number of basis functions and of the choice of the IMQ exponent are studied. We show that the IMQ basis can be used with parameters where the IMQ function is not integrable. We find that the quality of the spectrum with IMQ basis functions is somewhat lower that that with a Gaussian basis when the basis size is large, and for a range of IMQ exponents. The IMQ functions are; however, advantageous when a small number of functions is used or with a small number of collocation points (e.g., when using square collocation). Full article
(This article belongs to the Special Issue Computational Spectroscopy)
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Open AccessFeature PaperArticle
Iterative Methods for Computing Vibrational Spectra
Mathematics 2018, 6(1), 13; https://doi.org/10.3390/math6010013 - 16 Jan 2018
Cited by 1
Abstract
I review some computational methods for calculating vibrational spectra. They all use iterative eigensolvers to compute eigenvalues of a Hamiltonian matrix by evaluating matrix-vector products (MVPs). A direct-product basis can be used for molecules with five or fewer atoms. This is done by [...] Read more.
I review some computational methods for calculating vibrational spectra. They all use iterative eigensolvers to compute eigenvalues of a Hamiltonian matrix by evaluating matrix-vector products (MVPs). A direct-product basis can be used for molecules with five or fewer atoms. This is done by exploiting the structure of the basis and the structure of a direct product quadrature grid. I outline three methods that can be used for molecules with more than five atoms. The first uses contracted basis functions and an intermediate (F) matrix. The second uses Smolyak quadrature and a pruned basis. The third uses a tensor rank reduction scheme. Full article
(This article belongs to the Special Issue Computational Spectroscopy)
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