Ab initio studies of electron transfer. 2. Pathway analysis for homologous organic spacers

Liang, Chi-Ming; Newton, Marshall D.

doi:10.1021/j100115a023

Cited by 175 publications

(152 citation statements)

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“…This convention is suitable for the DBA complexes addressed below, although in other cases, the "bonding" relationship may be ambiguous. 58 In the limit of symmetry-equivalent D and A sites, eq 7 becomes the familiar expression, applicable to the TS for thermal electron exchange or the equilibrium geometry for optical excitation in a Robin/Day Class III system. 59 In the latter delocalized situation, there is no net ET (∆µ 12 a(2) ) 0), but in the diabatic (partially localized) representation, r DA d(2) * 0 (eq 8), and the optical excitation may be viewed as a superposition of exactly compensating ET transitions.…”

Section: The Generalized Mulliken Hush (Gmh) Modelmentioning

confidence: 99%

Reduced Electronic Spaces for Modeling Donor/Acceptor Interactions

et al. 2010

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Diabatic states for donor (D) and acceptor (A) interactions in electron transfer (ET) processes are formulated and evaluated, along with coupling elements (H DA ) and effective D/A separation distances (r DA ), for reduced electronic spaces of variable size, using the generalized Mulliken Hush model (GMH), applicable to an arbitrary state space and nuclear configuration, and encompassing Robin-Day class III and as well as class II situations. Once the electronic state space is selected (a set of n g 2 adiabatic states approximated by an orbital space based on an effective 1-electron (1-e) Hamiltonian), the charge-localized GMH diabatic states are obtained as the eigenstates of the dipole moment operator, with rotations to yield locally adiabatic states for sites with multiple states. The 1-e states and energies are expressed in terms of Kohn-Sham orbitals and orbital energies. Addressing questions as to whether the estimate of H DA "improves" as one increases n, and in what sense the GMH approach "converges" with n, we carry out calculations for three mixed-valence binuclear Ru complexes, from which we conclude that the 2-state (2-st) model gives the most appropriate estimate of the effectiVe coupling, similar (to within a rms deviation of e15%) to coupling elements obtained by superexchange correction of H DA values based on larger spaces (n ) 3-6), and thus yielding a quasi-invariant value for H DA over the range explored in the calculations (n ) 2-6). An analysis of the coupling and associated D and A states shows that the 2-st coupling involves crucial mixing with intervening bridge states (D and A "tails"), while increasingly larger state spaces for the same system yield increasingly more localized D and A states (and weaker coupling), with H DA tending to approach the limit of "bare" or "through space" coupling. These results help to reconcile seemingly contradictory assertions in the recent literature regarding the proper role of multistate frameworks in the formulation of coupling for both intra-and intermolecular ET systems.The present results are compared in detail with other reported results.

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Section: The Generalized Mulliken Hush (Gmh) Modelmentioning

confidence: 99%

Reduced Electronic Spaces for Modeling Donor/Acceptor Interactions

et al. 2010

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“…Moreover, the newly-derived expression for the effective resonance parameter of indirect interaction of external groups via the above-specified bridge exhibits alternation of sign with an increasing number of elementary fragments. The latter result implies an extension of the parity rule 44,46 to the case of AH-containing bridges. 3.…”

Section: Consideration Of Specific Examplesmentioning

confidence: 81%

“…21−37 In general, the ET properties of a certain system are representable by Hamiltonian matrix elements between wave functions of the relevant many-electron states (the so-called ET matrix elements). 4,40−42 In many cases, however, these elements may be replaced by their oneelectron analogues 43,44 that are alternatively called effective resonance parameters (especially if the Hückel type model is applied). These parameters refer to basis orbitals of external subsystems (D and A) instead of wave functions of many-electron states and embrace both direct (through-space) and indirect (bridge-assisted) interactions of these orbitals.…”

Section: The Principal Formula For the Effec-tive Alternant-hydrocarbmentioning

confidence: 99%

“…Thus, we actually obtain an extension of the perurbation-theory-based McConnell formula 66 widely used when studying the ET reactions 38,[44][45][46]48,67 and of the so-called parity rule 44,46,67 to the case of chain-like bridges consisting of N even AHs playing the role of fragments. An additional discussion of the parity rule and of its extension is undertaken in the next section.…”

Section: Expressions For Inverse Adjacency Matrices Of Various Types mentioning

confidence: 99%

“…Let us dwell now on the above-mentioned parity rule 44,46,67,68 and on its extensions following from Eqs. 26, 27 and 30.…”

Section: Consideration Of Specific Examplesmentioning

confidence: 99%

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Electron Transfer Properties of Alternant Hydrocarbons in Terms of Inverse Adjacency Matrices of Molecular Graphs

Gineitytė¹

2014

Croat. Chem. Acta

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Abstract. The study addresses electron transfer (ET) properties of systems of the type D-AH-A, where D and A are external electron-donating and accepting subsystems, respectively, and AH is an alternant hydrocarbon playing the role of the bridge. The main attention is paid to the dependence of the ET properties upon the sites of the AH, the external subsystems are attached to. As is usual in one-electron models of ET properties, the latter are considered to be proportional to off-diagonal Hamiltonian matrix elements (resonance parameters) representing effective interactions of orbitals of external groups D and A via the bridge. The block-diagonalization procedure for the common Hückel type Hamiltonian matrix of AHs is applied to derive explicit algebraic expressions for the above-specified decisive parameters. As a result, a relation is established between these parameters and elements of the inverse adjacency matrix (IAM) of the graph of the given AH referring to sites (vertices) under consideration. The common constitution of IAMs of all AHs then yields a simple and general selection rule for the effective parameters concerned. Moreover, the unified IAM of AHs is shown to be expressible in terms of entire submatrices (blocks) of the initial AM. This allows the ET properties of composite AHs to be analyzed in terms of increments of separate fragments (subgraphs) and of their interaction. The results of the study are illustrated by consideration of specific examples including the simplest benzenoids.

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Electron transfer integral between two zero-overlap states

Li¹,

Tian²,

He³

et al. 1996

J. Comput. Chem.

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In the research of electron transfer (ET) reactions, the theoretical calculation of the ET matrix element VBA is of special importance. Some examples in which the two electron‐localized states have a zero overlap were found. Thus, a new procedure for VBA calculation was developed and applied to the investigation of the donor‐acceptor 90° oriented ET reactions. This procedure, which is a supplement necessary to the recently developed approach suitable for a nonorthogonal case, was derived in detail. To check the rationality of the zero value of VBA in the reaction O2O−2 → O−2O2, the angle dependence of SBA and VBA between two electron‐localized states was calculated. © 1996 by John Wiley & Sons, Inc.

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Ab initio studies of electron transfer. 2. Pathway analysis for homologous organic spacers

Cited by 175 publications

References 2 publications

Reduced Electronic Spaces for Modeling Donor/Acceptor Interactions

Reduced Electronic Spaces for Modeling Donor/Acceptor Interactions

Electron Transfer Properties of Alternant Hydrocarbons in Terms of Inverse Adjacency Matrices of Molecular Graphs

Electron transfer integral between two zero-overlap states

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