Ethan Alguire

Analytic derivative couplings between configuration-interaction-singles states with built-in electron-translation factors for translational invariance

We present a method for analytically calculating the derivative couplings between a pair of configuration-interaction-singles (CIS) excited states obtained in an atom-centered basis. Our theory is exact and has been derived using two completely independent approaches: one inspired by the Hellmann-Feynman theorem and the other following from direct differentiation. (The former is new, while the latter is in the spirit of existing approaches in the literature.) Our expression for the derivative couplings incorporates all Pulay effects associated with the use of an atom-centered basis, and the computational cost is minimal, roughly comparable to that of a single CIS energy gradient. We have validated our method against CIS finite-difference results and have applied it to the lowest lying excited states of naphthalene; we find that naphthalene derivative couplings include Pulay contributions sufficient to have a qualitative effect. Going beyond standard problems in analytic gradient theory, we have also constructed a correction, based on perturbative electron-translation factors, for including electronic momentum and eliminating spurious components of the derivative couplings that break translational symmetry. This correction is general and can be applied to any level of electronic structure theory.

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

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.

Derivative couplings between TDDFT excited states obtained by direct differentiation in the Tamm-Dancoff approximation

Working within the Tamm-Dancoff approximation, we calculate the derivative couplings between time-dependent density-functional theory excited states by assuming that the Kohn-Sham superposition of singly excited determinants represents a true electronic wavefunction. All Pulay terms are included in our derivative coupling expression. The reasonability of our approach can be established by noting that, for closely separated electronic states in the infinite basis limit, our final expression agrees exactly with the Chernyak-Mukamel expression (with transition densities from response theory). Finally, we also validate our approach empirically by analyzing the behavior of the derivative couplings around the T1/T2 conical intersection of benzaldehyde.

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

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.

Derivative Couplings between Time-Dependent Density Functional Theory Excited States in the Random-Phase Approximation Based on Pseudo-Wavefunctions: Behavior around Conical Intersections.

In this paper, we present a formalism for derivative couplings between time-dependent density functional theory (TD-DFT) excited states within the randomphase approximation (RPA) using analytic gradient theory. Our formalism is based on a pseudo-wavefunction approach in a companion paper (DOI 10.1021/jp505767b), and can be checked against finite-difference overlaps. Our approach recovers the correct properties of derivative couplings around a conical intersection (CI), which is a crucial prerequisite for any derivative coupling expression. As an example, we study the test case of protonated formaldimine (CH2NH2(+)).

Communication: An inexpensive, variational, almost black-box, almost size-consistent correction to configuration interaction singles for valence excited states

Configuration interaction singles (CIS) describe excited electronic states only qualitatively and improvements are imperative as a means of recovering chemical accuracy. In particular, variational improvements would be ideal to account for state crossings and electronic relaxation. To accomplish such an objective, in this communication we present a new suite of algorithms, abbreviated VOO-CIS for variationally orbital optimized CIS. We show below that VOO-CIS yields a uniform improvement to CIS, rebalancing the energies of CT states versus non-CT states within the same framework. Furthermore, VOO-CIS finds energetic corrections for CT states that are even larger than those predicted by CIS(D). The computational cost of VOO-CIS depends strongly on the number of excited states requested (n), but otherwise should be proportional to the cost of CIS itself.

Calculating Derivative Couplings between Time-Dependent Hartree-Fock Excited States with Pseudo-Wavefunctions.

A pseudo-wavefunction description of time-dependent Hartree-Fock (TDHF) states is proposed and used to develop an analytic expression for derivative couplings between TDHF excited states based on the Hellmann-Feynman theorem. The resulting expression includes Pulay terms associated with using an atom-centered basis as well as a correction to ensure translational invariance. We demonstrate that our formalism recovers the well-known Chernyak-Mukamel expression near a crossing and in the limit of a complete basis, and thus our approach is consistent with time-dependent response theory. In a companion paper (DOI 10.1021/jp5057682 ), we investigate these derivative couplings near conical intersections and show that they behave correctly.

Diabatic couplings for charge recombination via Boys localization and spin-flip configuration interaction singles

We describe a straightforward technique for obtaining diabatic couplings applicable to charge transfer from or charge recombination to the electronic ground state. Our method is nearly black box, requiring minimal chemical intuition from the user, and merges two well-established approaches in electronic structure theory: first, smooth and balanced adiabatic states are generated using spin-flip-configuration interaction singles (SF-CIS) based on a triplet HF state; second, Boys localization is applied to rotate all adiabatic states into charge-localized diabatic states. The method is computationally inexpensive, scaling only with the cost of CIS, and does not require a choice of active space, which is usually required for such intrinsically multiconfigurational problems. Molecular LiF in vacuum and LiF solvated by a single water molecule are examined as model systems. We find nearly smooth diabatic potential energy surfaces and couplings and we find that the Condon approximation is obeyed approximately for this model problem.

Birefringent Stable Glass with Predominantly Isotropic Molecular Orientation

Birefringence in stable glasses produced by physical vapor deposition often implies molecular alignment similar to liquid crystals. As such, it remains unclear whether these glasses share the same energy landscape as liquid-quenched glasses that have been aged for millions of years. Here, we produce stable glasses of 9-(3,5-di(naphthalen-1-yl)phenyl)anthracene molecules that retain three-dimensional shapes and do not preferentially align in a specific direction. Using a combination of angle- and polarization-dependent photoluminescence and ellipsometry experiments, we show that these stable glasses possess a predominantly isotropic molecular orientation while being optically birefringent. The intrinsic birefringence strongly correlates with increased density, showing that molecular ordering is not required to produce stable glasses or optical birefringence, and provides important insights into the process of stable glass formation via surface-mediated equilibration. To our knowledge, such novel amorphous packing has never been reported in the past.

Ultrafast Electronic Relaxation through a Conical Intersection: Nonadiabatic Dynamics Disentangled through an Oscillator Strength-Based Diabatization Framework

We employ surface hopping trajectories to model the short-time dynamics of gas-phase and partially solvated 4-(N,N-dimethylamino)benzonitrile (DMABN), a dual fluorescent molecule that is known to undergo a nonadiabatic transition through a conical intersection. To compare theory vs time-resolved fluorescence measurements, we calculate the mixed quantum-classical density matrix and the ensemble averaged transition dipole moment. We introduce a diabatization scheme based on the oscillator strength to convert the TDDFT adiabatic states into diabatic states of La and Lb character. Somewhat surprisingly, we find that the rate of relaxation reported by emission to the ground state is almost 50% slower than the adiabatic population relaxation. Although our calculated adiabatic rates are largely consistent with previous theoretical calculations and no obvious effects of decoherence are seen, the diabatization procedure introduced here enables an explicit picture of dynamics in the branching plane, raising tantalizing questions about geometric phase effects in systems with dozens of atoms.