Note on the method of molecular orbitals

Coulson, C. A.; Rushbrooke, G. S.

doi:10.1017/s0305004100017163

Cited by 594 publications

(280 citation statements)

References 4 publications

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“…The largest eigenvalue simply reflects the connectivity of the reaction graph, and the symmetrical spacing about zero indicates that the graph contains no odd-membered rings. 65 When both ADD and DAA are included, the molecular symmetry group expands to 1024 operations, which link versions in sets of 256. The group has 88 classes: four of size 1, six of size 2, sixty of size 4, four of size 16, six of size 32, and eight of size 64.…”

Section: ■ Theoretical Predictions For the Water Octamermentioning

confidence: 99%

“…The symmetrical splitting about zero again indicates that the corresponding reaction graph contains no odd-membered rings. 65 For the D 2d isomer, adding either the generator for ADD or DAA to the rigid molecule group produces a molecular symmetry group of order 128 with 20 classes: two of size 1, one of size 2, nine of size 4, five of size 8, and three of size 16. Versions are linked in sets of 16 by these operations, and the reaction graph has a connectivity of four.…”

Section: ■ Theoretical Predictions For the Water Octamermentioning

confidence: 99%

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Investigation of Terahertz Vibration–Rotation Tunneling Spectra for the Water Octamer

et al. 2013

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We report a combined theoretical and experimental study of the water octamer-h16. The calculations used the ring-polymer instanton method to compute tunnelling paths and splittings in full dimensionality. The experiments measured extensive high resolution spectra near 1.4 THz, for which isotope dilution experiments and group theoretical analysis support assignment to the octamer. Transitions appear as singlets, consistent with the instanton paths, which involve the breakage of two hydrogen-bonds and thus give tunneling splittings below experimental resolution.

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Section: ■ Theoretical Predictions For the Water Octamermentioning

confidence: 99%

Section: ■ Theoretical Predictions For the Water Octamermentioning

confidence: 99%

Investigation of Terahertz Vibration–Rotation Tunneling Spectra for the Water Octamer

et al. 2013

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“…If the HOMO and LUMO residues have the same sign, we are in the situation shown in Figure 3 To simplify the analysis even further, we now turn to the Coulson-Rushbrooke (CR) pairing theorem 46 for alternating hydrocarbons, i.e., molecules which can be viewed as bipartite. The pairing theorem relies on a particle-hole symmetry and states that the molecular energies come in pairs as ε HOMO−n = ε LUMO+n for n = 0, 1, 2, .…”

Section: Resultsmentioning

confidence: 99%

Interference enhanced thermoelectricity in quinoid type structures

Strange

Seldenthuis

Verzijl

et al. 2015

The Journal of Chemical Physics

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Quantum interference (QI) effects in molecular junctions may be used to obtain large thermoelectric responses. We study the electrical conductance G and the thermoelectric response of a series of molecules featuring a quinoid core using density functional theory, as well as a semi-empirical interacting model Hamiltonian describing the π-system of the molecule which we treat in the GW approximation. Molecules with a quinoid type structure are shown to have two distinct destructive QI features close to the frontier orbital energies. These manifest themselves as two dips in the transmission, that remain separated, even when either electron donating or withdrawing side groups are added. We find that the position of the dips in the transmission and the frontier molecular levels can be chemically controlled by varying the electron donating or withdrawing character of the side groups as well as the conjugation length inside the molecule. This feature results in a very high thermoelectric power factor S 2 G and figure of merit ZT, where S is the Seebeck coefficient, making quinoid type molecules potential candidates for efficient thermoelectric devices. C 2015 AIP Publishing LLC. [http://dx

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“…It can be seen from Eqs. (47) and (48) and (50) and (51), that the whole energy-dependence of the structural polynomials can be expressed as…”

Section: B Expansion Of the Reduced Structural Polynomialsmentioning

confidence: 99%

A new approach to the method of source-sink potentials for molecular conduction

Pickup

Fowler

Borg

et al. 2015

The Journal of Chemical Physics

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Articles you may be interested in PHYSICS 143, 194105 (2015) A new approach to the method of source-sink potentials for molecular conduction We re-derive the tight-binding source-sink potential (SSP) equations for ballistic conduction through conjugated molecular structures in a form that avoids singularities. This enables derivation of new results for families of molecular devices in terms of eigenvectors and eigenvalues of the adjacency matrix of the molecular graph. In particular, we define the transmission of electrons through individual molecular orbitals (MO) and through MO shells. We make explicit the behaviour of the total current and individual MO and shell currents at molecular eigenvalues. A rich variety of behaviour is found. A SSP device has specific insulation or conduction at an eigenvalue of the molecular graph (a root of the characteristic polynomial) according to the multiplicities of that value in the spectra of four defined device polynomials. Conduction near eigenvalues is dominated by the transmission curves of nearby shells. A shell may be inert or active. An inert shell does not conduct at any energy, not even at its own eigenvalue. Conduction may occur at the eigenvalue of an inert shell, but is then carried entirely by other shells. If a shell is active, it carries all conduction at its own eigenvalue. For bipartite molecular graphs (alternant molecules), orbital conduction properties are governed by a pairing theorem. Inertness of shells for families such as chains and rings is predicted by selection rules based on node counting and degeneracy. C 2015 AIP Publishing LLC. [http://dx

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Note on the method of molecular orbitals

Cited by 594 publications

References 4 publications

Investigation of Terahertz Vibration–Rotation Tunneling Spectra for the Water Octamer

Investigation of Terahertz Vibration–Rotation Tunneling Spectra for the Water Octamer

Interference enhanced thermoelectricity in quinoid type structures

A new approach to the method of source-sink potentials for molecular conduction

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