Analyzing the electric response of molecular conductors using “electron deformation” orbitals and occupied‐virtual electron transfer

Abstract

The concept of "electron deformation orbitals" (EDOs) is used to investigate the electric response of conducting metals and oligophenyl chains. These orbitals and their eigenvalues are obtained by diagonalization of the deformation density matrix (difference between the density matrices of the perturbed and unperturbed systems) and can be constructed as linear combinations of the unperturbed molecular orbitals within "frozen geometry" conditions. This form of the EDOs allows calculating the part of the electron deformation density associated to an effective electron transfer from occupied to virtual orbitals (valence to conduction band electron transfer in the band model of conductivity). It is found that the "electron deformation" orbitals pair off, displaying the same eigenvalue but opposite sign. Each pair represents an amount of accumulation/depletion of electron charge at different molecular regions. In the oligophenyl systems investigated only one pair contributes effectively to the charge flow between molecular ends, resulting from the promotion of electrons from occupied orbitals to close in energy virtual orbitals of appropriate symmetry and overlapping. Analysis of this pair along explains the differences in conductance of olygophenyl chains based on phenyl units.

Study of electron transport in polybenzenoid chains covalently attached to gold atoms through unsaturated methylene linkers

“…(7) of Ref. [29]. This quantity may be simply obtained from the diagonal elements of the electron deformation density matrix (induced by the external voltage), d ii l , when constructed in the basis of unperturbed MOs.…”

“…(3) runs over all the unoccupied MOs. Alternatively, N occ→vir may be obtained from the coefficients of the virtual orbitals in the EDOs [29]. These EDOs are obtained by diagonalization of the electron deformation density matrix (difference between the perturbed and unperturbed density matrices) and represent accumulation and depletion of electron density.…”

“…In Ref. [29], we showed that replacing a segment of gold atoms in a metallic wire by a C1 chain of equivalent length provokes almost no changes in its electric response (analysed in terms of EDOs). Similar oligophenyl chains with direct contact to a gold atom or linked to the electrode through a saturated carbon atom were shown to display the characteristic exponential decay of the conductance with the chain length.…”

“…Here, we have applied a recently developed method of analysis of the molecular electric response in terms of EDOs [29]. In this method, the electron deformation density induced by the electric potential is transformed into the basis of unperturbed MOs (occupied + virtual) and later diagonalized to get a set of EDOs constructed as linear combination of them.…”

“…In a very recent work, we also proposed a simple computational tool to calculate the amount of electrons promoted from occupied orbitals to unoccupied ones by the external electric potential and qualitatively relate it with the molecular electric conductance [29]. In addition, this electron promotion may be obtained from the eigenvectors and eigenvalues of the deformation density matrix.…”