α-CASSCF: An Efficient, Empirical Correction for SA-CASSCF To Closely Approximate MS-CASPT2 Potential Energy Surfaces

Conical Intersection Accessibility Dictates Brightness in Red Fluorescent Proteins

Red fluorescent protein (RFP) variants are highly sought after for in vivo imaging since longer wavelengths improve depth and contrast in fluorescence imaging. However, the lower energy emission wavelength usually correlates with a lower fluorescent quantum yield compared to their green emitting counterparts. To guide the rational design of bright variants, we have theoretically assessed two variants (mScarlet and mRouge) which are reported to have very different brightness. Using an α-CASSCF QM/MM framework (chromophore and all protein residues within 6 Å of it in the QM region, for a total of more than 450 QM atoms), we identify key points on the ground and first excited state potential energy surfaces. The brighter variant mScarlet has a rigid scaffold, and the chromophore stays largely planar on the ground state. The dimmer variant mRouge shows more flexibility and can accommodate a pretwisted chromophore conformation which provides easier access to conical intersections. The main difference between the variants lies in the intersection seam regions, which appear largely inaccessible in mScarlet but partially accessible in mRouge. This observation is mainly related with changes in the cavity charge distribution, the hydrogen-bonding network involving the chromophore and a key ARG/THR mutation (which changes both charge and steric hindrance).

Generalized Semiclassical Ehrenfest Method: A Route to Wave Function-Free Photochemistry and Nonadiabatic Dynamics with Only Potential Energies and Gradients

We reconsider recent methods by which direct dynamics calculations of electronically nonadiabatic processes can be carried out while requiring only adiabatic potential energies and their gradients. We show that these methods can be understood in terms of a new generalization of the well-known semiclassical Ehrenfest method. This is convenient because it eliminates the need to evaluate electronic wave functions and their matrix elements along the mixed quantum-classical trajectories. The new approximations and procedures enabling this advance are the curvature-driven approximation to the time-derivative coupling, the generalized semiclassical Ehrenfest method, and a new gradient correction scheme called the time-derivative matrix (TDM) scheme. When spin-orbit coupling is present, one can carry out dynamics calculations in the fully adiabatic basis using potential energies and gradients calculated without spin-orbit coupling plus the spin-orbit coupling matrix elements. Even when spin-orbit coupling is neglected, the method is useful because it allows calculations by electronic structure methods for which nonadiabatic coupling vectors are unavailable. In order to place the new considerations in context, the article starts out with a review of background material on trajectory surface hopping, the semiclassical Ehrenfest scheme, and methods for incorporating decoherence. We consider both internal conversion and intersystem crossing. We also review several examples from our group of successful applications of the curvature-driven approximation.

Potential energy interpolation with target-customized weighting coordinates: application to excited-state dynamics of photoactive yellow protein chromophore in water

Interpolation of potential energy surfaces (PESs) can provide a practical route to performing molecular dynamics simulations with a reliability matching a high-level quantum chemical calculation. An obstacle to its widespread use is perhaps the lack of general and optimal interpolation settings that can be applied in a black-box manner for any given molecular system. How to set up the weights for interpolation is one such task, and we still need to diversify the approaches in order to treat various systems. Here, we develop a new interpolation weighting scheme, which allows us to choose the weighting coordinates in a system-specific manner, by amplifying the contribution from specific internal coordinates. The new weighting scheme with an appropriate selection of coordinates is proved to be effective in reducing the interpolation error along the reaction pathway. As a demonstration, we consider the photoactive yellow protein chromophore system, as it constitutes itself as an interesting target that bears long-standing questions related to excited-state dynamics inside protein environments. We build its two-state diabatic interpolated PES with the new weighting scheme. We indeed see the utility of our scheme by conducting nonadiabatic molecular dynamics simulations with the required semi-global PES based on a limited number of data points.

Chemical control of excited-state reactivity of the anionic green fluorescent protein chromophore

Controlling excited-state reactivity is a long-standing challenge in photochemistry, as a desired pathway may be inaccessible or compete with other unwanted channels. An important example is internal conversion of the anionic green fluorescent protein (GFP) chromophore where non-selective progress along two competing torsional modes (P: phenolate and I: imidazolinone) impairs and enables Z-to-E photoisomerization, respectively. Developing strategies to promote photoisomerization could drive new areas of applications of GFP-like proteins. Motivated by the charge-transfer dichotomy of the torsional modes, we explore chemical substitution on the P-ring of the chromophore as a way to control excited-state pathways and improve photoisomerization. As demonstrated by methoxylation, selective P-twisting appears difficult to achieve because the electron-donating potential effects of the substituents are counteracted by inertial effects that directly retard the motion. Conversely, these effects act in concert to promote I-twisting when introducing electron-withdrawing groups. Specifically, 2,3,5-trifluorination leads to both pathway selectivity and a more direct approach to the I-twisted intersection which, in turn, doubles the photoisomerization quantum yield. Our results suggest P-ring engineering as an effective approach to boost photoisomerization of the anionic GFP chromophore.

Rehybridization dynamics into the pericyclic minimum of an electrocyclic reaction imaged in real-time

Electrocyclic reactions are characterized by the concerted formation and cleavage of both σ and π bonds through a cyclic structure. This structure is known as a pericyclic transition state for thermal reactions and a pericyclic minimum in the excited state for photochemical reactions. However, the structure of the pericyclic geometry has yet to be observed experimentally. We use a combination of ultrafast electron diffraction and excited state wavepacket simulations to image structural dynamics through the pericyclic minimum of a photochemical electrocyclic ring-opening reaction in the molecule α-terpinene. The structural motion into the pericyclic minimum is dominated by rehybridization of two carbon atoms, which is required for the transformation from two to three conjugated π bonds. The σ bond dissociation largely happens after internal conversion from the pericyclic minimum to the electronic ground state. These findings may be transferrable to electrocyclic reactions in general.

Steric and Electronic Origins of Fluorescence in GFP and GFP-like Proteins

Fluorescent proteins have become routine tools for biological imaging. However, their nanosecond lifetimes on the excited state present computational hurdles to a full understanding of these photoactive proteins. In this work, we simulate approximately 0.5 nanoseconds of ab initio molecular dynamics to elucidate steric and electronic features responsible for fluorescent protein behavior. Using green fluorescent protein (GFP) and Dronpa2─widely used fluorescent proteins with contrasting functionality─as case studies, we leverage previous findings in the gas phase and solution to explore the deactivation mechanisms available to these proteins. Starting with ground-state analyses, we identify steric (the distribution of empty pockets near the chromophore) and electronic (electric fields exerted on chromophore moieties) factors that offer potential avenues for rational design. Picosecond timescale simulations on the excited state reveal that the chromophore can access twisted structures in Dronpa2, while the chromophore is largely confined to planarity in GFP. We couple ab initio multiple spawning (AIMS) and enhanced sampling simulations to discover and characterize conical intersection seams that facilitate internal conversion, which is a rare event in both systems. Our AIMS simulations correctly capture the relative fluorescence profiles of GFP and Dronpa2 within the first few picoseconds, and we attribute the diminished fluorescence intensity of Dronpa2, relative to GFP, to flexible chromophore intermediates on the excited state. Furthermore, we predict that twisted chromophore intermediates produce red-shifted intensities in the Dronpa2 fluorescence spectrum. If confirmed experimentally, this spectroscopic signature would provide valuable insights when screening and developing novel fluorescent proteins.

Chiral photochemistry of achiral molecules

Chirality is a molecular property governed by the topography of the potential energy surface (PES). Thermally achiral molecules interconvert rapidly when the interconversion barrier between the two enantiomers is comparable to or lower than the thermal energy, in contrast to thermally stable chiral configurations. In principle, a change in the PES topography on the excited electronic state may diminish interconversion, leading to electronically prochiral molecules that can be converted from achiral to chiral by electronic excitation. Here we report that this is the case for two prototypical examples – cis-stilbene and cis-stiff stilbene. Both systems exhibit unidirectional photoisomerization for each enantiomer as a result of their electronic prochirality. We simulate an experiment to demonstrate this effect in cis-stilbene based on its interaction with circularly polarized light. Our results highlight the drastic change in chiral behavior upon electronic excitation, opening up the possibility for asymmetric photochemistry from an effectively nonchiral starting point.

The authors report non-adiabatic first principles molecular dynamics to show how an achiral molecule can be converted to a chiral one upon photoexcitation. These results demonstrate the possibility of asymmetric photochemistry starting from achiral reactants.

State-averaged CASSCF with polarizable continuum model for studying photoreactions in solvents: Energies, analytical nuclear gradients, and non-adiabatic couplings

This paper presents state-averaged complete active space self-consistent field in polarizable continuum model (PCM) for studies of photoreactions in solvents. The wavefunctions of the solute and the PCM surface charges of the solvent are optimized simultaneously such that the state-averaged free energy is variationally minimized. The method supports both fixed weights and dynamic weights where the weights are automatically adjusted based on the energy gaps. The corresponding analytical nuclear gradients and non-adiabatic couplings are also derived. Furthermore, we show how the new method can be entirely formulated in terms of seven basic operations, which allows the implementation to benefit from existing high-performance libraries on graphical processing units. Results demonstrating the accuracy and performance of the implementation are presented and discussed. We also apply the new method to the study of minimal conical intersection search and photoreaction energy pathways in solvents. Effects from the polarity of the solvents and different formulas of dynamic weights are compared and discussed.

Conformer-specific photochemistry imaged in real space and time

[Figure: see text].

Resolving the ultrafast dynamics of the anionic green fluorescent protein chromophore in water

The chromophore of the green fluorescent protein (GFP) is critical for probing environmental influences on fluorescent protein behavior. Using the aqueous system as a bridge between the unconfined vacuum system and a constricting protein scaffold, we investigate the steric and electronic effects of the environment on the photodynamical behavior of the chromophore. Specifically, we apply ab initio multiple spawning to simulate five picoseconds of nonadiabatic dynamics after photoexcitation, resolving the excited-state pathways responsible for internal conversion in the aqueous chromophore. We identify an ultrafast pathway that proceeds through a short-lived (sub-picosecond) imidazolinone-twisted (I-twisted) species and a slower (several picoseconds) channel that proceeds through a long-lived phenolate-twisted (P-twisted) intermediate. The molecule navigates the non-equilibrium energy landscape via an aborted hula-twist-like motion toward the one-bond-flip dominated conical intersection seams, as opposed to following the pure one-bond-flip paths proposed by the excited-state equilibrium picture. We interpret our simulations in the context of time-resolved fluorescence experiments, which use short- and long-time components to describe the fluorescence decay of the aqueous GFP chromophore. Our results suggest that the longer time component is caused by an energetically uphill approach to the P-twisted intersection seam rather than an excited-state barrier to reach the twisted intramolecular charge-transfer species. Irrespective of the location of the nonadiabatic population events, the twisted intersection seams are inefficient at facilitating isomerization in aqueous solution. The disordered and homogeneous nature of the aqueous solvent environment facilitates non-selective stabilization with respect to I- and P-twisted species, offering an important foundation for understanding the consequences of selective stabilization in heterogeneous and rigid protein environments.

Modeling Spin-Crossover Dynamics

In this article, we review nonadiabatic molecular dynamics (NAMD) methods for modeling spin-crossover transitions. First, we discuss different representations of electronic states employed in the grid-based and direct NAMD simulations. The nature of interstate couplings in different representations is highlighted, with the main focus on nonadiabatic and spin-orbit couplings. Second, we describe three NAMD methods that have been used to simulate spin-crossover dynamics, including trajectory surface hopping, ab initio multiple spawning, and multiconfiguration time-dependent Hartree. Some aspects of employing different electronic structure methods to obtain information about potential energy surfaces and interstate couplings for NAMD simulations are also discussed. Third, representative applications of NAMD to spin crossovers in molecular systems of different sizes and complexities are highlighted. Finally, we pose several fundamental questions related to spin-dependent processes. These questions should be possible to address with future methodological developments in NAMD.

Spin Hamiltonians in Magnets: Theories and Computations

The effective spin Hamiltonian method has drawn considerable attention for its power to explain and predict magnetic properties in various intriguing materials. In this review, we summarize different types of interactions between spins (hereafter, spin interactions, for short) that may be used in effective spin Hamiltonians as well as the various methods of computing the interaction parameters. A detailed discussion about the merits and possible pitfalls of each technique of computing interaction parameters is provided.

Hole-hole Tamm-Dancoff-approximated density functional theory: A highly efficient electronic structure method incorporating dynamic and static correlation

The study of photochemical reaction dynamics requires accurate as well as computationally efficient electronic structure methods for the ground and excited states. While time-dependent density functional theory (TDDFT) is not able to capture static correlation, complete active space self-consistent field methods neglect much of the dynamic correlation. Hence, inexpensive methods that encompass both static and dynamic electron correlation effects are of high interest. Here, we revisit hole-hole Tamm-Dancoff approximated (hh-TDA) density functional theory for this purpose. The hh-TDA method is the hole-hole counterpart to the more established particle-particle TDA (pp-TDA) method, both of which are derived from the particle-particle random phase approximation (pp-RPA). In hh-TDA, the N-electron electronic states are obtained through double annihilations starting from a doubly anionic (N+2 electron) reference state. In this way, hh-TDA treats ground and excited states on equal footing, thus allowing for conical intersections to be correctly described. The treatment of dynamic correlation is introduced through the use of commonly employed density functional approximations to the exchange-correlation potential. We show that hh-TDA is a promising candidate to efficiently treat the photochemistry of organic and biochemical systems that involve several low-lying excited states-particularly those with both low-lying ππ^* and nπ^* states where inclusion of dynamic correlation is essential to describe the relative energetics. In contrast to the existing literature on pp-TDA and pp-RPA, we employ a functional-dependent choice for the response kernel in pp- and hh-TDA, which closely resembles the response kernels occurring in linear response and collinear spin-flip TDDFT.

Reduced scaling extended multi-state CASPT2 (XMS-CASPT2) using supporting subspaces and tensor hyper-contraction

We present a reduced scaling formulation of the extended multi-state CASPT2 (XMS-CASPT2) method, which is based on our recently developed state-specific CASPT2 (SS-CASPT2) formulation using supporting subspaces and tensor hyper-contraction. By using these two techniques, the off-diagonal elements of the effective Hamiltonian can be computed with only O(N³) operations and O(N²) memory, where N is the number of basis functions. This limits the overall computational scaling to O(N⁴) operations and O(N²) memory. Thus, excited states can now be obtained at the same reduced (relative to previous algorithms) scaling we achieved for SS-CASPT2. In addition, we also investigate how the energy denominators can be factorized with the Laplace quadrature when some of the denominators are negative, which is critical for excited state calculations. An efficient implementation of the method has been developed using graphical processing units while also exploiting spatial sparsity in tensor operations. We benchmark the accuracy of the new method by comparison to non-THC formulated XMS-CASPT2 for the excited states of various molecules. In our tests, the THC approximation introduces negligible errors (≈0.01 eV) compared to the non-THC reference method. Scaling behavior and computational timings are presented to demonstrate performance. The new method is also interfaced with quantum mechanics/molecular mechanics (QM/MM). In an example study of green fluorescent protein, we show how the XMS-CASPT2 potential energy surfaces and excitation energies are affected by increasing the size of the QM region up to 278 QM atoms with more than 2300 basis functions.

Conical Intersections at the Nanoscale: Molecular Ideas for Materials

The ability to predict and describe nonradiative processes in molecules via the identification and characterization of conical intersections is one of the greatest recent successes of theoretical chemistry. Only recently, however, has this concept been extended to materials science, where nonradiative recombination limits the efficiencies of materials for various optoelectronic applications. In this review, we present recent advances in the theoretical study of conical intersections in semiconductor nanomaterials. After briefly introducing conical intersections, we argue that specific defects in materials can induce conical intersections between the ground and first excited electronic states, thus introducing pathways for nonradiative recombination. We present recent developments in theoretical methods, computational tools, and chemical intuition for the prediction of such defect-induced conical intersections. Through examples in various nanomaterials, we illustrate the significance of conical intersections for nanoscience. We also discuss challenges facing research in this area and opportunities for progress.

Locality of conical intersections in semiconductor nanomaterials

A predictive theory connecting atomic structure to the rate of recombination would enable the rational design of semiconductor nanomaterials for optoelectronic applications. Recently our group has demonstrated that the theoretical study of conical intersections can serve this purpose. Here we review recent work in this area, focusing on the thesis that low-energy conical intersections in nanomaterials share a common feature: locality. We define a conical intersection as local if (a) the intersecting states differ by the excitation of an electron between spatially local orbitals, and (b) the intersection is accessed when the energies of these orbitals are tuned by local distortions of the geometry. After illustrating the locality of the conical intersection responsible for recombination at dangling bond defects in silicon, we demonstrate the locality of low-energy conical intersections in cases where locality may be a surprise. First, we demonstrate the locality of low-energy self-trapped conical intersections in a pristine silicon nanocrystal, which has no defects that one would expect to serve as the center of a local intersection. Second, we demonstrate that the lowest energy intersection in a silicon system with two neighboring dangling bond defects localizes to a single defect site. We discuss the profound implications of locality for predicting the rate of recombination and suggest that the locality of intersections could be exploited in the experimental study of recombination, where spectroscopic studies of molecular models of defects could provide new insights.

Fluorescent Proteins Detect Host Structural Rearrangements via Electrostatic Mechanism

The rational design of genetically encoded fluorescent biosensors, which can detect rearrangements of target proteins via interdomain allostery, is hindered by the absence of mechanistic understanding of the underlying photophysics. Here, we focus on the modulation of fluorescence by mechanical perturbation in a popular biological probe: enhanced Green Fluorescent Protein (eGFP). Using a combination of molecular dynamics (MD) simulations and quantum chemistry, and a set of physically motivated assumptions, we construct a map of fluorescence quantum yield as a function of a 2D electric field imposed by the protein environment on the fluorophore. This map is transferable between Tsien's Class 2 GFP's, and it allows one to estimate the shifts in fluorescence intensity due to mechanical perturbations directly from MD simulations. We use it in combination with steered MD simulations to put forward a hypothesis for the mechanism of a genetically encoded voltage probe (ArcLight) whose mechanism is currently under debate.

On the importance of initial conditions for excited-state dynamics

The vast majority of ab initio excited-state simulations are performed within semiclassical, trajectory-based approaches. Apart from the underlying electronic-structure theory, the reliability of the simulations is controlled by a selection of initial conditions for the classical trajectories. We discuss appropriate choices of initial conditions for simulations of different experimental arrangements: dynamics initiated by continuum-wave (CW) laser fields or triggered by ultrashort laser pulses.

Understanding Nonradiative Recombination through Defect-Induced Conical Intersections

Defects are known to introduce pathways for the nonradiative recombination of electronic excitations in semiconductors, but implicating a specific defect as a nonradiative center remains challenging for both experiment and theory. In this Perspective, we present recent progress toward this goal involving the identification and characterization of defect-induced conical intersections (DICIs), points of degeneracy between the ground and first excited electronic states of semiconductor materials that arise from the deformation of specific defects. Analysis of DICIs does not require the assumption of weak correlation between the electron and hole nor of stationary nuclei. It is demonstrated that in some cases an energetically accessible DICI is present even when no midgap state is predicted by single-particle theories (e.g., density functional theory). We review recent theoretical and computational developments that enable the location of DICIs in semiconductor nanomaterials and present insights into the photoluminescence of silicon nanocrystals gleaned from DICIs.