Optimal diabatic bases via thermodynamic bounds

Yeganeh, Sina; Voorhis, Troy Van

doi:10.1063/1.3626566

Cited by 4 publications

(5 citation statements)

References 24 publications

(27 reference statements)

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“…Using eq , one finds the correct limiting cases: strong mixing of the gas-phase adiabats in the case of high temperature and weak mixing in the case of small Pekar factor (i.e., weak solvent). Moreover, all indications are that the ER -ϵ algorithm should produce diabatic states where both the derivative and diabatic couplings are consistently small, in the spirit of an optimal diabatic basis considered by Michael Herman , and Yeganeh and van Voorhis …”

Section: Discussion and Open Questionsmentioning

confidence: 99%

“…Moreover, all indications are that the ER-ϵ algorithm should produce diabatic states where both the derivative and diabatic couplings are consistently small, in the spirit of an optimal diabatic basis considered by Michael Herman 87,88 and Yeganeh and van Voorhis. 89 Nevertheless, the ER-ϵ approach is not a panacea. While ERϵ is certainly more robust than ER alone, the method does not eliminate all necessary overmixing.…”

Section: A Dense Manifold Of Diabatic Statesmentioning

confidence: 99%

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The Requisite Electronic Structure Theory To Describe Photoexcited Nonadiabatic Dynamics: Nonadiabatic Derivative Couplings and Diabatic Electronic Couplings

Subotnik

Alguire

et al. 2015

Acc. Chem. Res.

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Electronically photoexcited dynamics are complicated because there are so many different relaxation pathways: fluorescence, phosphorescence, radiationless decay, electon transfer, etc. In practice, to model photoexcited systems is a very difficult enterprise, requiring accurate and very efficient tools in both electronic structure theory and nonadiabatic chemical dynamics. Moreover, these theoretical tools are not traditional tools. On the one hand, the electronic structure tools involve couplings between electonic states (rather than typical single state energies and gradients). On the other hand, the dynamics tools involve propagating nuclei on multiple potential energy surfaces (rather than the usual ground state dynamics). In this Account, we review recent developments in electronic structure theory as directly applicable for modeling photoexcited systems. In particular, we focus on how one may evaluate the couplings between two different electronic states. These couplings come in two flavors. If we order states energetically, the resulting adiabatic states are coupled via derivative couplings. Derivative couplings capture how electronic wave functions change as a function of nuclear geometry and can usually be calculated with straightforward tools from analytic gradient theory. One nuance arises, however, in the context of time-dependent density functional theory (TD-DFT): how do we evaluate derivative couplings between TD-DFT excited states (which are tricky, because no wave function is available)? This conundrum was recently solved, and we review the solution below. We also discuss the solution to a second, pesky problem of origin dependence, whereby the derivative couplings do not (strictly) satisfy translation variance, which can lead to a lack of momentum conservation. Apart from adiabatic states, if we order states according to their electronic character, the resulting diabatic states are coupled via electronic or diabatic couplings. The couplings between diabatic states |ΞA⟩ and |ΞB⟩ are just the simple matrix elements, ⟨ΞA|H|ΞB⟩. A difficulty arises, however, because constructing exactly diabatic states is formally impossible and constructing quasi-diabatic states is not unique. To that end, we review recent advances in localized diabatization, which is one approach for generating adiabatic-to-diabatic (ATD) transformations. We also highlight outstanding questions in the arena of diabatization, especially how to generate multiple globally stable diabatic surfaces.

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Section: Discussion and Open Questionsmentioning

confidence: 99%

Section: A Dense Manifold Of Diabatic Statesmentioning

confidence: 99%

The Requisite Electronic Structure Theory To Describe Photoexcited Nonadiabatic Dynamics: Nonadiabatic Derivative Couplings and Diabatic Electronic Couplings

Subotnik

Alguire

et al. 2015

Acc. Chem. Res.

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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%

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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“…Certainly solvent can play a role in understanding diabatic states. 40 In fact, a strong motivation for this paper is the recent work of Yeganeh and Van Voorhis, 41 who incorporated temperature and system-solvent coupling parameters into a new method for evaluating diabatic states for a model spin-boson Hamiltonian. In this paper, we report a new localized diabatization method that is both sensitive to environmental conditions and which produces diabatic states for arbitrary systems, in a sense extending the approach used in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we report a new localized diabatization method that is both sensitive to environmental conditions and which produces diabatic states for arbitrary systems, in a sense extending the approach used in Ref. 41. All of this is done within the framework of conventional electronic structure calculations.…”

Section: Introductionmentioning

confidence: 99%

Optimal diabatic states based on solvation parameters

Alguire

Subotnik

2012

The Journal of Chemical Physics

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A new method for obtaining diabatic electronic states of a molecular system in a condensed environment is proposed and evaluated. This technique, which we denote as Edmiston-Ruedenberg (ER)-ε diabatization, forms diabatic states as a linear combination of adiabatic states by minimizing an approximation to the total coupling between states in a medium with temperature T and with a characteristic Pekar factor C. ER-ε diabatization represents an improvement upon previous localized diabatization methods for two reasons: first, it is sensitive to the energy separation between adiabatic states, thus accounting for fluctuations in energy and effectively preventing over-mixing. Second, it responds to the strength of system-solvent interactions via parameters for the dielectric constant and temperature of the medium, which is physically reasonable. Here, we apply the ER-ε technique to both intramolecular and intermolecular excitation energy transfer systems. We find that ER-ε diabatic states satisfy three important properties: (1) they have small derivative couplings everywhere; (2) they have small diabatic couplings at avoided crossings, and (3) they have negligible diabatic couplings everywhere else. As such, ER-ε states are good candidates for so-called "optimal diabatic states."

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Optimal diabatic bases via thermodynamic bounds

Cited by 4 publications

References 24 publications

The Requisite Electronic Structure Theory To Describe Photoexcited Nonadiabatic Dynamics: Nonadiabatic Derivative Couplings and Diabatic Electronic Couplings

The Requisite Electronic Structure Theory To Describe Photoexcited Nonadiabatic Dynamics: Nonadiabatic Derivative Couplings and Diabatic Electronic Couplings

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

Optimal diabatic states based on solvation parameters

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