Formulas and Numerical Tables for Overlap Integrals

Mulliken, Robert S.; Rieke, Carol A.; Orloff, D.; Orloff, H.

doi:10.1063/1.1747150

Cited by 961 publications

(208 citation statements)

References 13 publications

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“…When the orbitals are normalized such that the diagonal elements of the overlap matrix are 1, then the off-diagonal elements between the neighboring sites are typically ∼ 0.3. 33 Our analysis shows that the overlap matrix does not play an important role, and the results that we present below turn out to be insensitive to such deviation from orthonormality. Therefore, we will take S to be the unit matrix (e.g, S ii = 1, S ij = 0 for i = j) in the remainder of the analysis.…”

Section: Tight-binding Modelmentioning

confidence: 52%

Charge Transport Across Insulating Self-Assembled Monolayers: Non-equilibrium Approaches and Modeling To Relate Current and Molecular Structure

et al. 2014

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This paper examines charge transport by tunneling across a series of electrically (insulating molecules with the structure HS(CH 2 ) 4 CONH(CH 2 ) 2 R) in the form of selfassembled monolayers (SAMs), supported on silver. The molecules examined were studied experimentally by Yoon et al. (Angew. Chem. Int. Ed., 51, 4658−4661, 2012), using junctions of the structure AgS(CH 2 ) 4 CONH(CH 2 ) 2 R//Ga 2 O 3 /EGaIn. The tail group R had approximately the same length for all molecules, but a range of different structures. Changing the R entity over a range of different structures (aliphatic to aromatic) does not influence the conductance significantly. To rationalize this surprising result, we investigate transport through these SAMs theoretically, using both full quantum methods and a generic, independent-electron tight-binding toy model. We find that the frontier orbitals HOMO, HOMO-1, HOMO-2 and HOMO-3, have similar structures for all of the different R-groups, and that the HOMO, which is largely responsible for the transport in these molecules, is always strongly localized on the thiol group. The relative insensitivity of the current density to the structure of the R group is due not only to these similar frontier orbitals but also to a combination of energy levels (ε) and tunneling amplitudes (t), which lead to similar conductance for different tail groups, i.e. the large difference between ε's in conjugated and saturated groups is compensated by tunneling amplitudes inside the tail group. In addition, the coupling of the tail group to the alkane chain is much weaker for conjugated groups than for saturated ones. Conductance change in these molecules is not influenced by the broadening of the molecular levels connected to the left and right electrodes, since in all these molecules the effective coupling to the silver substrate is the same, whereas the other effective couplings are determined by the weak connection to the oxide Ga 2 O 3 layer. All these factors combine to produce currents largely insensitive to the R group.An estimation of the attenuation constant, β, of the simplified Simmons equation obtained using these methods is β = 1.1 per CH 2 group, in good agreement with observed results. Our analysis sketches the potential landscapes across which tunneling occurs, and suggests that it will be difficult to change rates of tunneling by simple changes 2 in molecular structure. This work indicates that significant control over SAMs largely composed of nominally insulating groups may be possible when tail groups are used that are significantly larger than those used in the experiments of Yoon et al. 13

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Section: Tight-binding Modelmentioning

confidence: 52%

Charge Transport Across Insulating Self-Assembled Monolayers: Non-equilibrium Approaches and Modeling To Relate Current and Molecular Structure

et al. 2014

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“…This is introduced so that the constant ∆ 1 sets an energy scale that is physically relevant. The functional dependence on R and φ can be justified from orbital overlap integrals [28] together with a valence bond theory description of four-electron three-orbital systems (see page 68 of Ref. 21).…”

Section: B Effective Hamiltonianmentioning

confidence: 99%

Effect of quantum nuclear motion on hydrogen bonding

McKenzie

Bekker

Athokpam

et al. 2014

The Journal of Chemical Physics

160

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This work considers how the properties of hydrogen bonded complexes, X-H· · · Y, are modified by the quantum motion of the shared proton. Using a simple two-diabatic state model Hamiltonian, the analysis of the symmetric case, where the donor (X) and acceptor (Y) have the same proton affinity, is carried out. For quantitative comparisons, a parametrization specific to the O-H· · · O complexes is used. The vibrational energy levels of the one-dimensional ground state adiabatic potential of the model are used to make quantitative comparisons with a vast body of condensed phase data, spanning a donor-acceptor separation (R) range of about 2.4 − 3.0Å, i.e., from strong to weak hydrogen bonds. The position of the proton (which determines the X-H bond length) and its longitudinal vibrational frequency, along with the isotope effects in both are described quantitatively. An analysis of the secondary geometric isotope effect, using a simple extension of the two-state model, yields an improved agreement of the predicted variation with R of frequency isotope effects. The role of bending modes is also considered: their quantum effects compete with those of the stretching mode for weak to moderate Hbond strengths. In spite of the economy in the parametrization of the model used, it offers key insights into the defining features of H-bonds, and semi-quantitatively captures several trends.

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“…The overlap integral, S ij , between two atoms' 2pπ orbitals, i and j, is given by the Mulliken formulas, 26 S ij (r, θ i , θ j , φ) = cos θ i cos θ j cos φ S 2pπ,2pπ (r)…”

Section: Off-diagonal Disordermentioning

confidence: 99%

Monte Carlo simulations of charge transport in organic systems with true off-diagonal disorder

Jakobsson

Linares

Stafström

2012

The Journal of Chemical Physics

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In this work, a novel method to model off-diagonal disorder in organic materials has been developed. The off-diagonal disorder is taken directly from the geometry of the system, which includes both a distance and an orientational dependence on the constituent molecules, and does not rely on a parametric random distribution. The geometry of the system is generated by running molecular dynamics simulations on phenylene-vinylene oligomers packed into boxes. The effect of the kind of randomness generated in this way is then investigated by means of Monte Carlo simulations of the charge transport in these boxes and a comparison is made to the commonly used model of offdiagonal disorder, where only the distance dependence is accounted for. It is shown that this new refined way of treating the disorder has a significant impact on the charge transport, while still being compliant with previously published and confirmed results.

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Formulas and Numerical Tables for Overlap Integrals

Cited by 961 publications

References 13 publications

Charge Transport Across Insulating Self-Assembled Monolayers: Non-equilibrium Approaches and Modeling To Relate Current and Molecular Structure

Charge Transport Across Insulating Self-Assembled Monolayers: Non-equilibrium Approaches and Modeling To Relate Current and Molecular Structure

Effect of quantum nuclear motion on hydrogen bonding

Monte Carlo simulations of charge transport in organic systems with true off-diagonal disorder

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