Systematic calculation of molecular vibrational spectra through a complete Morse expansion

Bordoni, Andrea; Manini, Nicola

doi:10.1002/qua.21189

Cited by 20 publications

(65 citation statements)

References 47 publications

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“…There are many proposals to study the collective behavior of a system of diatomic molecules via the algebraic model of a potential interaction between the two ions . Morse potential has been a good proposal, since in recent articles it has been resolved exactly, and therefore, the vibrational thermodynamic functions of the gas have been obtained . It is considered that the expression of one‐dimensional Hamiltonian for the MP (SU(2)) is,

H = - \frac{ℏ^{2}}{2 μ} \frac{d^{2}}{d x^{2}} + D {true(1 - \exp true[- \frac{true(x - x_{e} true)}{d} true] true)}^{2},

with D the depth of well, d the width, x e the displacement from the equilibrium position, and μ the reduced mass of the oscillating system.…”

Section: A Comparison Of Some Thermodynamic Properties Between Gmp Anmentioning

confidence: 99%

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Thermodynamic properties of diatomic molecule systems under SO(2,1)‐anharmonic Eckart potential

Valencia-Ortega

Arias-Hernandez

2018

Int J of Quantum Chemistry

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Due to one of the most representative contributions to the energy in diatomic molecules being the vibrational, we consider the generalized Morse potential (GMP) as a typical interaction for one‐dimensional microscopic systems, which describes local anharmonic effects. From the Eckart potential (EP) model, it is possible to find a connection with the GMP model, as well as obtaining the analytical expression for the energy spectrum because it is based on SOtrue(2,1true) algebras. This gives the macroscopic properties such as vibrational mean energy U, specific heat C, Helmholtz free energy F, and entropy S for a heteronuclear diatomic system, as well as with the exact partition function and its approximation for the high temperature region. Finally, a comparison is made between the graphs of some thermodynamic functions obtained with the GMP and the Morse potential (MP) for H Cl molecules.

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H = - \frac{ℏ^{2}}{2 μ} \frac{d^{2}}{d x^{2}} + D {true(1 - \exp true[- \frac{true(x - x_{e} true)}{d} true] true)}^{2},

with D the depth of well, d the width, x e the displacement from the equilibrium position, and μ the reduced mass of the oscillating system.…”

Section: A Comparison Of Some Thermodynamic Properties Between Gmp Anmentioning

confidence: 99%

“…[10,18] Morse potential has been a good proposal, [24] since in recent articles it has been resolved exactly, and therefore, the vibrational thermodynamic functions of the gas have been obtained. [25,26] It is considered that the expression of one-dimensional Hamiltonian for the MP (SU(2)) is,…”

Section: A C Om Pa R I Son Of Som E T He Rm Od Yn a M I C P R Ope Rmentioning

confidence: 99%

Thermodynamic properties of diatomic molecule systems under SO(2,1)‐anharmonic Eckart potential

Valencia-Ortega

Arias-Hernandez

2018

Int J of Quantum Chemistry

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“…with χ κ (ξ ) being a basis function and C ν,κ being unknown coefficients to be calculated from Eq. (21). In this work we use the Hermite basis set with where H κ (λξ ) is the orthogonal Hermite polynomial of degree κ and λ is an arbitrary parameter.…”

Section: Numerical Examplementioning

confidence: 99%

“…They were calculated by solving numerically Eq. (21) with N = 30 and λ = 3. Comparison of the found pseudoenergies with the vibrational energies of molecular hydrogen calculated by others [20,21] shows that the relative error is less than 0.5% for the two low-lying states.…”

Section: Numerical Examplementioning

confidence: 99%

Pseudostate description of diatomic-molecule scattering from a hard-wall potential

Lugovskoy¹,

Bray²

2013

Phys. Rev. A

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A collinear scattering of a structured particle from a hard wall is studied with consideration of vibrational transitions initiated by the collision. It is shown that this problem can be solved analytically in the framework of the source-function method. With the use of the continuum discretization technique we are able to take into account both discrete and continuum states. No approximations of the interatomic potential is required. We illustrate our approach for the case of a hydrogen molecule bound by the realistic Morse potential.

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“…In concrete, we describe the stretching modes with a formalism based on the Morse oscillator, 9 with some similarity to the algebraic approaches of ref 10. The main advantage of a potential expansion in terms of Morse coordinates is that one can use a quantum mechanical basis on which the matrix representation of the Hamiltonian operator is sparse and can be computed analytically using algebraic techniques based on generalized step operators.…”

Section: Introductionmentioning

confidence: 99%

Algebraic-Matrix Calculation of Vibrational Levels of Triatomic Molecules

2009

Self Cite

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We introduce an accurate and efficient algebraic technique for the computation of the vibrational spectra of triatomic molecules, of both linear and bent equilibrium geometry. The full three-dimensional potential energy surface (PES), which can be based on entirely ab initio data, is parametrized as a product Morse-cosine expansion, expressed in bond angle internal coordinates, and includes explicit interactions among the local modes. We describe the stretching degrees of freedom in the framework of a Morse-type expansion on a suitable algebraic basis, which provides exact analytical expressions for the elements of a sparse Hamiltonian matrix. Likewise, we use a cosine power expansion on a spherical harmonics basis for the bending degree of freedom. The resulting matrix representation in the product space is very sparse, and vibrational levels and eigenfunctions can be obtained by efficient diagonalization techniques. We apply this method to carbonyl sulfide, hydrogen cyanide, water, and nitrogen dioxide. When we base our calculations on high-quality PESs tuned to the experimental data, the computed spectra are in very good agreement with the observed band origins.

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Systematic calculation of molecular vibrational spectra through a complete Morse expansion

Cited by 20 publications

References 47 publications

Thermodynamic properties of diatomic molecule systems under SO(2,1)‐anharmonic Eckart potential

Thermodynamic properties of diatomic molecule systems under SO(2,1)‐anharmonic Eckart potential

Pseudostate description of diatomic-molecule scattering from a hard-wall potential

Algebraic-Matrix Calculation of Vibrational Levels of Triatomic Molecules

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