Kinetic Energy Partition Method for Competing Modes

• Published in: Journal of the Chinese Chemical Society (Taipei) 2014-11, Vol.61 (11), p.1205-1210
• Main Authors: Mineo, Hirobumi, Chao, Sheng D.
• Format: Article
• Language: English
• Subjects: Basis set expansion; Energy; Kinetics; Quantum eigenvalue problems; Schroedinger equation
• ISSN: 0009-4536; 2192-6549
• DOI: 10.1002/jccs.201400008

We present a new basis set expansion method for quantum dynamics systems with two competing modes where the interaction potentials are equally dominant. The new idea introduced here is a kinetic energy partition scheme instead of the usual division of the potential energy. The partition results in two kinetic energy terms with their effective masses. By distributing each partial kinetic energy to the respective potential, the full Hamiltonian can be expressed as the sum of the two competing modes. The solution procedure is illustrated by using a system consisting of a particle under the action of two harmonic potentials with different equilibrium distances and force constants. Next we apply this method to obtain the potential energy curves for the prototype hydrogen molecule ion. This new expansion converges very fast to the exact solutions for both eigenvalues and eigenfunctions. The H2+ ground and first excited state potential energies curves calculated by the LCAO‐MO method and the KEP method are plotted, together with the Gaussian09 program package calculation using the HF/6‐311++G(d,p) basis set for the ground state and CIS/6‐311++G(d,p) basis set for the first excited state.