Algebraic discrete variable representation approach applied to Lennard-Jones and H₂ potentials

Abstract

An algebraic method based on a discrete variable representation (DVR) scheme is applied to describe 1D potentials. The approach is based on the algebraic realisation of the coordinate and momentum in the framework of a complete basis associated with the 1D Morse potential. The diagonalisation of the matrix representations of the coordinate and momentum in this scheme provides discrete bases that establish the DVR approach, allowing the matrix representation of the Hamiltonian to be expressed in a simple form in terms of diagonal matrices through the use of the transformation coefficients. The advantage of this approach is that it may be suitable for any potential using only algebraic means at an affordable computational cost. Application to obtain the solutions associated with the Lennard-Jones potential and the ab initio potential of the H₂ molecule is presented. Reliable, accurate vibrational energies as well as wave functions are obtained in both cases.

GRAPHICAL ABSTRACT

Keywords:

• Algebraic approach
• morse potential
• discrete variable representation
• Lennard-Jones potential
• adiabatic H₂ potential

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is partially supported by DGAPA-UNAM, Mexico, under project IN-212020.