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Generalized electronic diabatic scheme: Diagonalizing the electronic Hamiltonian for artificial molecular systems. How do molecular meccanos move?
Author(s) -
Tapia O.
Publication year - 2003
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.10713
Subject(s) - diabatic , hamiltonian (control theory) , scanning tunneling microscope , quantum mechanics , electronic structure , quantum , hilbert space , superposition principle , physics , classical mechanics , chemistry , mathematics , adiabatic process , mathematical optimization
A quantum–classic model is presented and used to describe systems ranging from normal molecules up to electronic systems sensed in real space. The quantum system is a set of n ‐electrons; a positive background in real space completes the model. A generalized electronic diabatic (GED) theory is introduced. The diabatic functions diagonalize the electronic Hamiltonian for any arrangement of the positive background. Physical quantum states are represented as linear superpositions in the diabatic basis; this latter is always fixed. For systems sensed in real space, the coefficients of the linear superposition are functions of the real space configuration coordinates. Physical changes are produced by interactions with external sources/sinks of energy. An interaction couples different diabatic states; diagonalizing the electronic Hamiltonian plus the couplings leads to new coefficients describing physical states. Among other things, these couplings can be used to simulate the effects produced by scanning tunneling microscopy, atomic force, and transmission electron microscopy on substrates located in real space. The important thing is that time–evolution in electronic Hilbert space can be related to actual motion in real space. The experiment of lateral hopping of a substrate on a metallic surface induced by vibration excitation and followed with scanning tunneling microscope is discussed. A result of the present work is that motion of molecular meccanos reflects then time–evolution in electronic Hilbert space. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004