Optimal diabatic states based on solvation parameters

Alguire, Ethan; Subotnik, Joseph E.

doi:10.1063/1.4766463

Cited by 14 publications

(23 citation statements)

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“…Equation 12 expresses the coupling through the adiabatic energies E i and E j , transition dipole moments M i and M j of the complex, and transition moments μ A and μ B of individual chromophores. The vectors μ A and μ B are computed for molecules A and B using atomic coordinates that are the same as those in the complex AB.…”

Section: ■ Methodsmentioning

confidence: 99%

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Estimation of Electronic Coupling for Singlet Excitation Energy Transfer

Voityuk

2014

J. Phys. Chem. C

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Electronic coupling is a key parameter that controls the efficiency of excitation energy transfer (EET) and exciton delocalization. A new approach to estimate electronic coupling is introduced. Within a two-state model, the EET coupling V of two chromophores is expressed via the vertical excitation energies (E i and E j ), transition dipole moments (M i and M j ) of the system and transition moments (μ A and μ B ) of the individual chromophores:}. These quantities are directly available from quantum mechanical calculations. As the estimated coupling accounts for both short-range and long-range interactions, this approach allows for the treatment of systems with short intermolecular distances, in particular, π-stacked chromophores. For a system of two identical chromophores, the coupling is given bywhere F i and F j are the corresponding oscillator strengths and cos θ is determined by the relative position of the chromophores in the dimer. Thus, the coupling can be derived from purely experimental data. The developed approach is used to calculate the EET coupling and exciton delocalization in two π-stacks of pyrimidine nucleobases 5′-TT-3′ and 5′-CT-3′ showing quite different EET properties. ■ INTRODUCTIONTheoretical and computational methods have been successfully applied to study excitation energy transfer (EET) in various molecular systems. Recent developments in this field were considered in detail in several reviews. 1−4 The efficiency of EET between two chromophores A and B, A*−B → A−B*, is controlled by electronic coupling of two diabatic states φ A and φ B . In the reference states, the exciton is localized on the corresponding molecules. Commonly, φ A and φ B are defined as excited states of the separated chromophores. The electronic coupling of the reference excited states is a key parameter that controls delocalization of excited states and the probability of energy transfer between the chromophores. 1−4The coupling of singlet excited states V includes both a shortrange term, which depends on the orbital overlap between the excited states, and a long-range Coulomb contribution. The Coulomb coupling of two molecules A and B can be estimated as the interaction of their transition dipole moments μ A and μ Bwhere R AB is the intermolecular distance. This widely used dipole−dipole scheme suggested by Forster 60 year ago 5 provides good estimates when the spatial extension of the transition densities in the molecules is much smaller than the distance R AB . More accurate values can be computed using transition atomic charges 6In eq 2, i runs over all atoms of the molecule A, and j runs over all atoms of B; q i and q j are transition charges derived from quantum mechanical (QM) calculations of excited states φ A and φ B of the individual molecules. At large distances between the chromophores, V dd ≈ V tc . Both eq 1 and eq 2 account only for the long-range interaction of the excited states, whereas the orbital and exchange terms are neglected. The performance of the transition charge (TC) model was discussed...

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Section: ■ Methodsmentioning

confidence: 99%

“…[9][10][11][12]17,18 We define the diabatic states φ A and φ B to be the states where the exciton is localized on chromophores A and B, respectively. Such states can be approximately represented by excited states of individual molecules.…”

Section: ■ Methodsmentioning

confidence: 99%

Estimation of Electronic Coupling for Singlet Excitation Energy Transfer

Voityuk

2014

J. Phys. Chem. C

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“…13 When the objective function (2.1) is invariant to a class of transformations of the Hamiltonian, these transformations can be used to self-consistently represent the effective Hamiltonian in a diabatic basis. Diabatic state representations 7,14-16 can be extremely useful for the development of models of non-adiabatic processes, [17][18][19] solvent interactions, 15,20,21 or to understand and communicate the results of calculation in chemically intuitive language. 22 The term "diabatic" is used more often than it is defined, so I offer a brief review.…”

Section: Sa-casscf Ensembles and Their Invariancesmentioning

confidence: 99%

“…In this way, the concept of states that are "diabatic with respect to nuclear displacements" can also be generalized to concept of states that are "diabatic with respect to environmental interactions." 15,21 It is often the case that the interaction of interest is coupling to the nuclear displacements. An electronic representation that is adiabatic with respect to interaction via the nuclear displacements has been referred to as "strictly diabatic."…”

Section: Sa-casscf Ensembles and Their Invariancesmentioning

confidence: 99%

Canonical-ensemble state-averaged complete active space self-consistent field (SA-CASSCF) strategy for problems with more diabatic than adiabatic states: Charge-bond resonance in monomethine cyanines

Olsen

2015

The Journal of Chemical Physics

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This paper reviews basic results from a theory of the a priori classical probabilities (weights) in state-averaged complete active space self-consistent field (SA-CASSCF) models. It addresses how the classical probabilities limit the invariance of the self-consistency condition to transformations of the complete active space configuration interaction (CAS-CI) problem. Such transformations are of interest for choosing representations of the SA-CASSCF solution that are diabatic with respect to some interaction. I achieve the known result that a SA-CASSCF can be self-consistently transformed only within degenerate subspaces of the CAS-CI ensemble density matrix. For uniformly distributed ("microcanonical") SA-CASSCF ensembles, self-consistency is invariant to any unitary CAS-CI transformation that acts locally on the ensemble support. Most SA-CASSCF applications in current literature are microcanonical. A problem with microcanonical SA-CASSCF models for problems with "more diabatic than adiabatic" states is described. The problem is that not all diabatic energies and couplings are self-consistently resolvable. A canonical-ensemble SA-CASSCF strategy is proposed to solve the problem. For canonical-ensemble SA-CASSCF, the equilibrated ensemble is a Boltzmann density matrix parametrized by its own CAS-CI Hamiltonian and a Lagrange multiplier acting as an inverse "temperature," unrelated to the physical temperature. Like the convergence criterion for microcanonical-ensemble SA-CASSCF, the equilibration condition for canonical-ensemble SA-CASSCF is invariant to transformations that act locally on the ensemble CAS-CI density matrix. The advantage of a canonical-ensemble description is that more adiabatic states can be included in the support of the ensemble without running into convergence problems. The constraint on the dimensionality of the problem is relieved by the introduction of an energy constraint. The method is illustrated with a complete active space valence-bond (CASVB) analysis of the charge/bond resonance electronic structure of a monomethine cyanine: Michler's hydrol blue. The diabatic CASVB representation is shown to vary weakly for "temperatures" corresponding to visible photon energies. Canonical-ensemble SA-CASSCF enables the resolution of energies and couplings for all covalent and ionic CASVB structures contributing to the SA-CASSCF ensemble. The CASVB solution describes resonance of charge- and bond-localized electronic structures interacting via bridge resonance superexchange. The resonance couplings can be separated into channels associated with either covalent charge delocalization or chemical bonding interactions, with the latter significantly stronger than the former.

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“…Obviously, S 1 and S 3 are not usefully mixed at this geometry; the energy gap between them is significant. 61 For a more physical example, we turn to p-benzoquinone.…”

Section: A Validation By Finite Difference: Lih Boys-diabatic Derivamentioning

confidence: 99%

Derivative couplings and analytic gradients for diabatic states, with an implementation for Boys-localized configuration-interaction singles

Fatehi

Alguire

Subotnik

2013

The Journal of Chemical Physics

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We demonstrate that Boys-localized diabatic states do indeed exhibit small derivative couplings, as is required of quasidiabatic states. In doing so, we present a general formalism for calculating derivative couplings and analytic gradients for diabatic states. We then develop additional equations specific to the case of Boys-localized configuration-interaction singles (CIS)--in particular, the analytic gradient of the CIS dipole matrix--and we validate our implementation against finite-difference results. In a forthcoming paper, we will publish additional algorithmic and computational details and apply our method to the Closs energy-transfer systems as a further test of the validity of Boys-localized diabatic states.

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Optimal diabatic states based on solvation parameters

Cited by 14 publications

References 55 publications

Estimation of Electronic Coupling for Singlet Excitation Energy Transfer

Estimation of Electronic Coupling for Singlet Excitation Energy Transfer

Canonical-ensemble state-averaged complete active space self-consistent field (SA-CASSCF) strategy for problems with more diabatic than adiabatic states: Charge-bond resonance in monomethine cyanines

Derivative couplings and analytic gradients for diabatic states, with an implementation for Boys-localized configuration-interaction singles

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