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.

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 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(+)).

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.

Exploring non-Condon effects in a covalent tetracene dimer: how important are vibrations in determining the electronic coupling for singlet fission?

Singlet fission (SF) offers opportunities for wavelength-selective processing of solar photons with an end goal of achieving higher efficiency inexpensive photovoltaic or solar-fuels-producing devices. In order to evaluate new molecular design strategies and for theoretical exploration of dynamics, it is important to put in place tools for efficient calculation of the electronic coupling between single-exciton reactant and multiexciton product states. For maximum utility, the couplings should be calculated at multiple nuclear geometries (rather than assumed constant everywhere, i.e., the Condon approximation) and we must be able to evaluate couplings for covalently linked multichromophore systems. With these requirements in mind, here we discuss the simplest methodology possible for rapid calculation of diabatic one-electron coupling matrix elements-based on Boys localization and rediagonalization of molecular orbitals. We focus on a covalent species called BT1 that juxtaposes two tetracene units in a partially cofacial geometry via a norbornyl bridge. In BT1, at the equilibrium C2v structure, the "nonhorizontal" couplings between HOMOs and LUMOs (t(HL) and t(LH)) vanish by symmetry. We then explore the impact of molecular vibrations through the calculation of t(AB) coupling gradients along 183 normal modes of motion. Rules are established for the types of motions (irreducible representations in the C2v point group) that turn on tHL and tLH values as well as for the patterns that emerge in constructive versus destructive interference of pathways to the SF product. For the best modes, calculated electronic coupling magnitudes for SF (at root-mean-squared deviation in position at 298 K), are within a factor of 2 of that seen for noncovalent tetracene dimers relevant to the molecular crystal. An overall "effective" electronic coupling is also given, based on the Stuchebrukhov formalism for non-Condon electron transfer rates.

Analysis of localized diabatic states beyond the condon approximation for excitation energy transfer processes.

In a previous paper [ Fatehi , S. ; et al. J. Chem. Phys. 2013 , 139 , 124112 ], we demonstrated a practical method by which analytic derivative couplings of Boys-localized CIS states can be obtained. In this paper, we now apply that same method to the analysis of triplet-triplet energy transfer systems studied by Closs and collaborators [ Closs , G. L. ; et al. J. Am. Chem. Soc. 1988 , 110 , 2652 ]. For the systems examined, we are able to conclude that (i) the derivative coupling in the BoysOV basis is negligible, and (ii) the diabatic coupling will likely change little over the configuration space explored at room temperature. Furthermore, we propose and evaluate an approximation that allows for the inexpensive calculation of accurate diabatic energy gradients, called the "strictly diabatic" approximation. This work highlights the effectiveness of diabatic state analytic gradient theory in realistic systems and demonstrates that localized diabatic states can serve as an acceptable approximation to strictly diabatic states.