On rotational-vibrational spectrum of diatomic beryllium molecule

The eigenvalue problem for second-order ordinary differential equation (SOODE) in a finite interval with the boundary conditions of the first, second and third kind is formulated. A computational scheme of the finite element method (FEM) is presented that allows the solution of the eigenvalue problem for a SOODE with the known potential function using the programs ODPEVP and KANTBP 4M that implement FEM in the Fortran and Maple, respectively. Numerical analysis of the solution using the KANTBP 4M program is performed for the SOODE exactly solvable eigenvalue problem. The discrete energy eigenvalues and eigenfunctions are analyzed for vibrational-rotational states of the diatomic beryllium molecule solving the eigenvalue problem for the SOODE numerically with the table-valued potential function approximated by interpolation Lagrange and Hermite polynomials and its asymptotic expansion for large values of the independent variable specified as Fortran function. The efficacy of the programs is demonstrated by the calculations of twelve eigenenergies of vibrational bound states with the required accuracy, in comparison with those known from literature, and the vibrational-rotational spectrum of the diatomic beryllium molecule. © COPYRIGHT SPIE. Downloading of the abstract is permitted for personal use only.

Gusev A.A. 1 , Chuluunbaatar O. 1, 2 , Vinitsky S.I. 1, 3 , Derbov V.L. 4 , Góźdź A. 5 , Krassovitskiy P.M. 1, 6 , Filikhin I.7 , Mitin A.V.8, 9, 10 , Hai L.L. 11 , Lua T.T.11
  • 1 Joint Institute for Nuclear Research, Dubna, Russian Federation
  • 2 Institute of Mathematics, National University of Mongolia, Ulaanbaatar, Mongolia
  • 3 RUDN University, Moscow, Russia, 6 Miklukho-Maklaya st, Moscow, 117198, Russian Federation
  • 4 N.G. Chernyshevsky Saratov National Research State University, Saratov, Russian Federation
  • 5 Institute of Physics, University of M. Curie-Sk Lodowska, Lublin, Poland
  • 6 Institute of Nuclear Physics, Almaty, Kazakhstan
  • 7 Department of Mathematics and Physics, North Carolina Central University, Durham, NC 27707, United States
  • 8 Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, Russian Federation
  • 9 Chemistry Department, Lomonosov Moscow State University, Moscow, Russian Federation
  • 10 Joint Institute for High Temperatures of RAS, Moscow, Russian Federation
  • 11 Ho Chi Minh City University of Education, Ho Chi Minh city, Viet Nam
Beryllium; Boundary conditions; FORTRAN (programming language); Molecular modeling; Molecules; Ordinary differential equations; Polynomials; Asymptotic expansion; Computational schemes; Eigenvalue problem; Hermite polynomials; Independent variables; Rotational spectra; Second-order ordinary differential equations; Vibrational-rotational state; Eigenvalues and eigenfunctions
Date of creation
Date of change
Short link

Other records