Vibrational energies of diatomic molecules using the finite-element method

Prabhu, DK (1995) Vibrational energies of diatomic molecules using the finite-element method. Technical Report. National Aerospace Laboratories, Bangalore, India.

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    The quantum mechanical problem of the energy states of a diatomic molecule containing Ne electrons is stated in the spatial basis. The time-independent Schrodinger equation for the system is simplified by transformation of coordinates and separation of variables is used to obtain13; the Schrodinger equations of the center-of-mass and relative (internal) motion. The Born-Oppenheimer approximation is then used in separating the internal motion into electronic and nuclear (vibrational-rotational) motions. Purely Vibrational motion is then considered and the corresponding one-dimensional time-independent Schrodinger equation is solved numerically for13; the energies by means of the finite-element method. One-dimensional elements based on Lagrange polynomials of various orders are used in the detailed study. The solution methodology includes determination of eigenvalues for which spectrum slicing is employed along with a simple bisection algorithm for root finding. The method has been used for three test cases - (1) a one-dimensional harmonic oscillator, (2) a one-dimensional anharmonic (Morse) oscillator, and (3) the ground electronic state of molecular hydrogen (H2) for various empirical internuclear potentials (Morse, Lippincott, and Hulburt-Hirschfelder) and RKR potential. The computed results are compared with the analytical solutions (where available) and experimental data.

    Item Type: Proj.Doc/Technical Report (Technical Report)
    Uncontrolled Keywords: Quantum mechanics;Diatomic molecules;Vibrational energies; Finite elements
    Subjects: ENGINEERING > Fluid Mechanics and Thermodynamics
    Division/Department: Computational and Theoretical Fluid Dynamics Division
    Depositing User: Mr. Ravikumar R
    Date Deposited: 06 Oct 2006
    Last Modified: 24 May 2010 09:51

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