Conductance Calculations for Real Systems on the Nanoscale

Abstract

Electron transport across molecular junctions is a rapidly growing topic at the borderline between physics and chemistry. We review calculations which were done in the Landauer transport formalism for monovalent systems, ranging from clusters to fullerenes. A realistic description of molecular conductance can be achieved by a density functional based approach to the calculation of the electronic transport properties.

Conductance Properties of Stilbenoid Molecules

“…Modern electronic transport calculations for molecular wires started to flourish in the early 1990s, triggered by work of the Ratner20 and Datta21 groups. In our computational approach22 we combine a density‐functional‐based tight‐binding (DF‐TB) formalism23 with numerical Green function techniques to investigate electronic transport within the Landauer theory. The basic quantity to be calculated in the following is the two‐terminal conductance g =( e 2 / π ${{\hbar}}$ ) T ( E F ), which is proportional to the transmission probability T ( E F ) at the equilibrium Fermi energy E F in the linear response regime and at zero temperature.…”

“…The function G ( E ), as given by Equation (2), is the Green function of the scattering region including self‐energy interactions Σ L , R with the left (L) and right (R) electrodes:22 G ( E )=( E S − H − Σ L − Σ R ) −1 …”

“…A recent review and further details of the methodology are given in ref. 22. Σ L,R =( V + L,R ‐ E S + L,R ) g L,R ( E )( V L,R ‐ E S L,R ) …”

Conductance Properties of Stilbenoid Molecules

“…Modern electronic transport calculations for molecular wires started to flourish in the early 1990s, triggered by work of the Ratner20 and Datta21 groups. In our computational approach22 we combine a density‐functional‐based tight‐binding (DF‐TB) formalism23 with numerical Green function techniques to investigate electronic transport within the Landauer theory. The basic quantity to be calculated in the following is the two‐terminal conductance g =( e 2 / π ${{\hbar}}$ ) T ( E F ), which is proportional to the transmission probability T ( E F ) at the equilibrium Fermi energy E F in the linear response regime and at zero temperature.…”

“…The function G ( E ), as given by Equation (2), is the Green function of the scattering region including self‐energy interactions Σ L , R with the left (L) and right (R) electrodes:22 G ( E )=( E S − H − Σ L − Σ R ) −1 …”

“…A recent review and further details of the methodology are given in ref. 22. Σ L,R =( V + L,R ‐ E S + L,R ) g L,R ( E )( V L,R ‐ E S L,R ) …”

Reverse Exponential Decay of Electrical Transmission in Nanosized Graphite Sheets

“…Electrical transmission through molecular junctions consisting of single molecules is an important issue in the development of molecular electronics in nanotechnology. Landauer's formalism , using a Green's function method is of great use in calculating the conductance of molecular wires at the single molecule level, e.g., benzen-1,4-dithiol, − fullerene C 60 , − and tape-porphyrin oligomers . Sophisticated algorithms based on the formalism combined with density functional theory (DFT) , were recently proposed. − In the fundamental understanding of electrical transmission in molecular wires, issues of adsorption of molecules on electrodes, heteroatomic effects, and correlation between molecular length L and conductance are important.…”

Theory of vibrationally inelastic electron transport through molecular bridges

“…The experimental demonstration of the possibility to connect two electrodes by a single molecule and to measure a current through such a molecular junction [1][2][3] has stimulated increasing theoretical efforts to elucidate the basic mechanisms of electron transport in such systems (see, for example, [4][5][6][7][8] and references therein). Most of the theoretical work in recent years has been devoted to the determination of the electronic structure of molecular junctions, employing a variety of methods that include extended Hückel approaches [9][10][11][12][13][14], ab initio quantum-chemistry methods [15][16][17], and density functional theory [18][19][20][21][22][23].…”

Conductance Properties of Stilbenoid Molecules

“…Modern electronic transport calculations for molecular wires started to flourish in the early 1990s, triggered by work of the Ratner20 and Datta21 groups. In our computational approach22 we combine a density‐functional‐based tight‐binding (DF‐TB) formalism23 with numerical Green function techniques to investigate electronic transport within the Landauer theory. The basic quantity to be calculated in the following is the two‐terminal conductance g =( e 2 / π ${{\hbar}}$ ) T ( E F ), which is proportional to the transmission probability T ( E F ) at the equilibrium Fermi energy E F in the linear response regime and at zero temperature.…”

“…The function G ( E ), as given by Equation (2), is the Green function of the scattering region including self‐energy interactions Σ L , R with the left (L) and right (R) electrodes:22 G ( E )=( E S − H − Σ L − Σ R ) −1 …”

“…A recent review and further details of the methodology are given in ref. 22. Σ L,R =( V + L,R ‐ E S + L,R ) g L,R ( E )( V L,R ‐ E S L,R ) …”

Reverse Exponential Decay of Electrical Transmission in Nanosized Graphite Sheets

“…Electrical transmission through molecular junctions consisting of single molecules is an important issue in the development of molecular electronics in nanotechnology. Landauer's formalism , using a Green's function method is of great use in calculating the conductance of molecular wires at the single molecule level, e.g., benzen-1,4-dithiol, − fullerene C 60 , − and tape-porphyrin oligomers . Sophisticated algorithms based on the formalism combined with density functional theory (DFT) , were recently proposed. − In the fundamental understanding of electrical transmission in molecular wires, issues of adsorption of molecules on electrodes, heteroatomic effects, and correlation between molecular length L and conductance are important.…”

Theory of vibrationally inelastic electron transport through molecular bridges

“…The experimental demonstration of the possibility to connect two electrodes by a single molecule and to measure a current through such a molecular junction [1][2][3] has stimulated increasing theoretical efforts to elucidate the basic mechanisms of electron transport in such systems (see, for example, [4][5][6][7][8] and references therein). Most of the theoretical work in recent years has been devoted to the determination of the electronic structure of molecular junctions, employing a variety of methods that include extended Hückel approaches [9][10][11][12][13][14], ab initio quantum-chemistry methods [15][16][17], and density functional theory [18][19][20][21][22][23].…”

Conductance Properties of Stilbenoid Molecules

“…Modern electronic transport calculations for molecular wires started to flourish in the early 1990s, triggered by work of the Ratner20 and Datta21 groups. In our computational approach22 we combine a density‐functional‐based tight‐binding (DF‐TB) formalism23 with numerical Green function techniques to investigate electronic transport within the Landauer theory. The basic quantity to be calculated in the following is the two‐terminal conductance g =( e 2 / π ${{\hbar}}$ ) T ( E F ), which is proportional to the transmission probability T ( E F ) at the equilibrium Fermi energy E F in the linear response regime and at zero temperature.…”

“…The function G ( E ), as given by Equation (2), is the Green function of the scattering region including self‐energy interactions Σ L , R with the left (L) and right (R) electrodes:22 G ( E )=( E S − H − Σ L − Σ R ) −1 …”

“…A recent review and further details of the methodology are given in ref. 22. Σ L,R =( V + L,R ‐ E S + L,R ) g L,R ( E )( V L,R ‐ E S L,R ) …”

Reverse Exponential Decay of Electrical Transmission in Nanosized Graphite Sheets

“…Electrical transmission through molecular junctions consisting of single molecules is an important issue in the development of molecular electronics in nanotechnology. Landauer's formalism , using a Green's function method is of great use in calculating the conductance of molecular wires at the single molecule level, e.g., benzen-1,4-dithiol, − fullerene C 60 , − and tape-porphyrin oligomers . Sophisticated algorithms based on the formalism combined with density functional theory (DFT) , were recently proposed. − In the fundamental understanding of electrical transmission in molecular wires, issues of adsorption of molecules on electrodes, heteroatomic effects, and correlation between molecular length L and conductance are important.…”

Theory of vibrationally inelastic electron transport through molecular bridges

“…The experimental demonstration of the possibility to connect two electrodes by a single molecule and to measure a current through such a molecular junction [1][2][3] has stimulated increasing theoretical efforts to elucidate the basic mechanisms of electron transport in such systems (see, for example, [4][5][6][7][8] and references therein). Most of the theoretical work in recent years has been devoted to the determination of the electronic structure of molecular junctions, employing a variety of methods that include extended Hückel approaches [9][10][11][12][13][14], ab initio quantum-chemistry methods [15][16][17], and density functional theory [18][19][20][21][22][23].…”