Nature of Hops, Coordinates, and Detailed Balance for Nonadiabatic Simulations in the Condensed Phase.

Photoinduced processes play a crucial role in a multitude of important molecular phenomena. Accurately modeling these processes in an environment other than a vacuum requires a detailed description of the electronic states involved as well as how energy flows are coupled to the surroundings. Nonadiabatic effects must also be included in order to describe the exchange of energy between electronic and nuclear degrees of freedom correctly. In this work, we revisit the ring-opening reaction 1,3-cylohexadiene (CHD) in a solvent environment. Using our newly developed Interface for Non-Adiabatic Quantum mechanics/molecular mechanics in Solvent (INAQS) we trace the evolution of the reaction via hybrid quantum mechanics/molecular mechanics (QM/MM) surface hopping with a focus on the solvent's participation in the nonadiabatic relaxation process and the long-time approach to equilibrium. We explicitly include the MM solvent contribution to the nonadiabatic coupling vector─enabling an accurate approach to equilibrium at long times─and find that in highly multidimensional systems gradients can have little or nothing to do with the nonadiabatic couplings.

On the Fluorescence Properties and Nonradiative Transitions in Medium-Sized All-Trans Polyenes.

The nonadiabatic photodynamics of all-trans linear polyenes with N = 4-8 conjugated double bonds is studied from an electronic structure perspective. Excitation energies and stationary points for the 1Bu and 2Ag singlet states have been computed by using the state-average complete active space (SA-CASSCF) method and its second-order perturbation theory variant (MS-CASPT2). The dependence of the two low-lying excited states on the "chain length" N has been elucidated. In addition, the 1Bu-2Ag crossing seam has been mapped out in a suitable two-dimensional coordinate space and its minimum within the subspace has been determined. This minimum is found to increase substantially and monotonously in energy with increasing N. This increase is discussed and interpreted in relation to the fluorescence properties of these systems. In particular, it allows to understand the crossover from S1(2Ag) fluorescence for smaller N to S2(1Bu) (or dual) fluorescence for larger N.

INAQS, a Generic Interface for Nonadiabatic QM/MM Dynamics: Design, Implementation, and Validation for GROMACS/Q-CHEM simulations.

The accurate description of large molecular systems in complex environments remains an ongoing challenge for the field of computational chemistry. This problem is even more pronounced for photoinduced processes, as multiple excited electronic states and their corresponding nonadiabatic couplings must be taken into account. Multiscale approaches such as hybrid quantum mechanics/molecular mechanics (QM/MM) offer a balanced compromise between accuracy and computational burden. Here, we introduce an open-source software package (INAQS) for nonadiabatic QM/MM simulations that bridges the sampling capabilities of the GROMACS MD package and the excited-state infrastructure of the Q-CHEM electronic structure software. The interface is simple and can be adapted easily to other MD codes. The code supports a variety of different trajectory-based molecular dynamics, ranging from Born-Oppenheimer to surface hopping dynamics. To illustrate the power of this combination, we simulate electronic absorption spectra, free-energy surfaces along a reaction coordinate, and the excited-state dynamics of 1,3-cyclohexadiene in solution.

Methods to Calculate Electronic Excited-State Dynamics for Molecules on Large Metal Clusters with Many States: Ensuring Fast Overlap Calculations and a Robust Choice of Phase.

We present an efficient set of methods for propagating excited-state dynamics involving a large number of configuration interaction singles (CIS) or Tamm-Dancoff approximation (TDA) single-reference excited states. Specifically, (i) following Head-Gordon et al., we implement an exact evaluation of the overlap of singly-excited CIS/TDA electronic states at different nuclear geometries using a biorthogonal basis and (ii) we employ a unified protocol for choosing the correct phase for each adiabat at each geometry. For many-electron systems, the combination of these techniques significantly reduces the computational cost of integrating the electronic Schrodinger equation and imposes minimal overhead on top of the underlying electronic structure calculation. As a demonstration, we calculate the electronic excited-state dynamics for a hydrogen molecule scattering off a silver metal cluster, focusing on high-lying excited states, where many electrons can be excited collectively and crossings are plentiful. Interestingly, we find that the high-lying, plasmon-like collective excitation spectrum changes with nuclear dynamics, highlighting the need to simulate non-adiabatic nuclear dynamics and plasmonic excitations simultaneously. In the future, the combination of methods presented here should help theorists build a mechanistic understanding of plasmon-assisted charge transfer and excitation energy relaxation processes near a nanoparticle or metal surface.

Q-Force: Quantum Mechanically Augmented Molecular Force Fields.

The quality of molecular dynamics simulations strongly depends on the accuracy of the underlying force fields (FFs) that determine all intra- and intermolecular interactions of the system. Commonly, transferable FF parameters are determined based on a representative set of small molecules. However, such an approach sacrifices accuracy in favor of generality. In this work, an open-source and automated toolkit named Q-Force is presented, which augments these transferable FFs with molecule-specific bonded parameters and atomic charges that are derived from quantum mechanical (QM) calculations. The molecular fragmentation procedure allows treatment of large molecules (>200 atoms) with a low computational cost. The generated Q-Force FFs can be used at the same computational cost as transferable FFs, but with improved accuracy: We demonstrate this for the vibrational properties on a set of small molecules and for the potential energy surface on a complex molecule (186 atoms) with photovoltaic applications. Overall, the accuracy, user-friendliness, and minimal computational overhead of the Q-Force protocol make it widely applicable for atomistic molecular dynamics simulations.

Influence of the Environment on Shaping the Absorption of Monomeric Infrared Fluorescent Proteins.

Infrared fluorescent proteins (iRFPs) are potential candidates for deep-tissue in vivo imaging. Here, we provide molecular-level insights into the role of the protein environment in the structural stability of the chromophore within the protein binding pocket through the flexible hydrogen-bonding network using molecular dynamics simulation. Furthermore, we present systematic excited-state analysis to characterize the nature of the first two excited states and the role of the environment in shaping the nature of the chromophore's excited states within the hybrid quantum mechanics/molecular mechanics framework. Our results reveal that the environment red-shifts the absorption of the chromophore by about 0.32 eV compared to the isolated counterpart, and besides the structural stability, the protein environment does not alter the nature of the excited state of the chromophore significantly. Our study contributes to the fundamental understanding of the excited-state processes of iRFPs in a complex environment and provides a design principle for developing iRFPs with desired spectral properties.

Deciphering the Chemical Basis of Fluorescence of a Selenium-Labeled Uracil Probe when Bound at the Bacterial Ribosomal A-Site.

We unveil in this work the main factors that govern the turn-on/off fluorescence of a Se-modified uracil probe at the ribosomal RNA A-site. Whereas the constraint into an "in-plane" conformation of the two rings of the fluorophore is the main driver for the observed turn-on fluorescence emission in the presence of the antibiotic paromomycin, the electrostatics of the environment plays a minor role during the emission process. Our computational strategy clearly indicates that, in the absence of paromomycin, the probe prefers conformations that show a dark S1 electronic state with participation of nπ* electronic transition contributions between the selenium atom and the π-system of the uracil moiety.

PySurf: A Framework for Database Accelerated Direct Dynamics.

The greatest restriction to the theoretical study of the dynamics of photoinduced processes is computationally expensive electronic structure calculations. Machine learning algorithms have the potential to reduce the number of these computations significantly. Here, PySurf is introduced as an innovative code framework, which is specifically designed for rapid prototyping and development tasks for data science applications in computational chemistry. It comes with powerful Plugin and Workflow engines, which allows intuitive customization for individual tasks. Data is automatically stored through the database framework, which enables additional interpolation of properties in previously evaluated regions of the conformational space. To illustrate the potential of the framework, a code for nonadiabatic surface hopping simulations based on the Landau-Zener algorithm is presented here. Deriving gradients from the interpolated potential energy surfaces allows for full-dimensional nonadiabatic surface hopping simulations using only adiabatic energies (energy only). Simulations of a pyrazine model and ab initio-based calculations of the SO2 molecule show that energy-only calculations with PySurf are able to correctly predict the nonadiabatic dynamics of these prototype systems. The results reveal the degree of sophistication, which can be achieved by the database accelerated energy-only surface hopping simulations being competitive to commonly used semiclassical approaches.

Competing ultrafast photoinduced electron transfer and intersystem crossing of [Re(CO) 3 (Dmp)(His124)(Trp122)] + in Pseudomonas aeruginosa azurin: a nonadiabatic dynamics study.

We present a computational study of sub-picosecond nonadiabatic dynamics in a rhenium complex coupled electronically to a tryptophan (Trp) side chain of Pseudomonas aeruginosa azurin, a prototypical protein used in the study of electron transfer in proteins. To gain a comprehensive understanding of the photoinduced processes in this system, we have carried out vertical excitation calculations at the TDDFT level of theory as well as nonadiabatic dynamics simulations using the surface hopping including arbitrary couplings (SHARC) method coupled to potential energy surfaces represented with a linear vibronic coupling model. The results show that the initial photoexcitation populates both singlet metal-to-ligand charge transfer (MLCT) and singlet charge-separated (CS) states, where in the latter an electron was transferred from the Trp amino acid to the complex. Subsequently, a complex mechanism of simultaneous intersystem crossing and electron transfer leads to the sub-picosecond population of triplet MLCT and triplet CS states. These results confirm the assignment of the sub-ps time constants of previous experimental studies and constitute the first computational evidence for the ultrafast formation of the charge-separated states in Re-sensitized azurin.

Machine learning enables long time scale molecular photodynamics simulations.

Photo-induced processes are fundamental in nature but accurate simulations of their dynamics are seriously limited by the cost of the underlying quantum chemical calculations, hampering their application for long time scales. Here we introduce a method based on machine learning to overcome this bottleneck and enable accurate photodynamics on nanosecond time scales, which are otherwise out of reach with contemporary approaches. Instead of expensive quantum chemistry during molecular dynamics simulations, we use deep neural networks to learn the relationship between a molecular geometry and its high-dimensional electronic properties. As an example, the time evolution of the methylenimmonium cation for one nanosecond is used to demonstrate that machine learning algorithms can outperform standard excited-state molecular dynamics approaches in their computational efficiency while delivering the same accuracy.

Light-Induced Mechanistic Divergence in Gold(I) Catalysis: Revisiting the Reactivity of Diazonium Salts.

In a systematic study of the Au-catalyzed reaction of o-alkynylphenols with aryldiazonium salts, we find that essentially the same reaction conditions lead to a change in mechanism when a light source is applied. If the reaction is carried out at room temperature using a AuI catalyst, the diazonium salt undergoes electrophilic deauration of a vinyl AuI intermediate and provides access to substituted azobenzofurans. If the reaction mixture is irradiated with blue LED light, C-C bond formation due to N2 -extrusion from the diazonium salt is realized selectively, using the same starting materials without the need for an additional photo(redox) catalyst under aerobic conditions. We report a series of experiments demonstrating that the same vinyl AuI intermediate is capable of producing the observed products under photolytic and thermal conditions. The finding that a vinyl AuI complex can directly, without the need for an additional photo(redox) catalyst, result in C-C bond formation under photolytic conditions is contrary to the proposed mechanistic pathways suggested in the literature till date and highlights that the role of oxidation state changes in photoredox catalysis involving Au is thus far only poorly understood and may hold surprises for the future. Computational results indicate that photochemical activation can occur directly from a donor-acceptor complex formed between the vinyl AuI intermediate and the diazonium salt.

Highly efficient surface hopping dynamics using a linear vibronic coupling model.

We report an implementation of the linear vibronic coupling (LVC) model within the surface hopping dynamics approach and present utilities for parameterizing this model in a blackbox fashion. This results in an extremely efficient method to obtain qualitative and even semi-quantitative information about the photodynamical behavior of a molecule, and provides a new route toward benchmarking the results of surface hopping computations. The merits and applicability of the method are demonstrated in a number of applications. First, the method is applied to the SO2 molecule showing that it is possible to compute its absorption spectrum beyond the Condon approximation, and that all the main features and timescales of previous on-the-fly dynamics simulations of intersystem crossing are reproduced while reducing the computational effort by three orders of magnitude. The dynamics results are benchmarked against exact wavepacket propagations on the same LVC potentials and against a variation of the electronic structure level. Four additional test cases are presented to exemplify the broader applicability of the model. The photodynamics of the isomeric adenine and 2-aminopurine molecules are studied and it is shown that the LVC model correctly predicts ultrafast decay in the former and an extended excited-state lifetime in the latter. Futhermore, the method correctly predicts ultrafast intersystem crossing in the modified nucleobase 2-thiocytosine and its absence in 5-azacytosine while it fails to describe the ultrafast internal conversion to the ground state in the latter.

Surface Hopping within an Exciton Picture. An Electrostatic Embedding Scheme.

We report the development and the implementation of an exciton approach that allows ab initio nonadiabatic dynamics simulations of electronic excitation energy transfer in multichromophoric systems. For the dynamics, a trajectory-based strategy is used within the surface hopping formulation. The approach features a consistent hybrid formulation that allows the construction of potential energy surfaces and gradients by combining quantum mechanics and molecular mechanics within an electrostatic embedding scheme. As an application, the study of a molecular dyad consisting of a covalently bound BODIPY moiety and a tetrathiophene group is presented using time-dependent density functional theory (TDDFT). The results obtained with the exciton model are compared to previously performed full TDDFT dynamics of the same system. Our results show excellent agreement with the full TDDFT results, indicating that the couplings that lead to excitation energy transfer (EET) are dominated by Coulomb interaction terms and that charge-transfer states are not necessary to properly describe the nonadiabatic dynamics of the system. The exciton model also reveals ultrafast coherent oscillations of the excitation between the two units in the dyad, which occur during the first 50 fs.

The modeling of the absorption lineshape for embedded molecules through a polarizable QM/MM approach.

We present a computational strategy to simulate the absorption lineshape of a molecule embedded in a complex environment by using a polarizable QM/MM approach. This strategy is presented in two alternative formulations, one based on a molecular dynamics simulation of the structural fluctuations of the system and the other using normal modes and harmonic frequencies calculated on optimized geometries. The comparison for the case of a chromophore within a strongly inhomogeneous and structured environment, namely the intercalation pocket of DNA, shows that the MD-based approach is able to reproduce the experimental spectral bandshape. In contrast, the static approach overestimates the vibronic coupling, resulting in a much broader band.

Solvent Effects on Electronically Excited States: QM/Continuum Versus QM/Explicit Models.

The inclusion of solvent effects in the calculation of excited states is vital to obtain reliable absorption spectra and density of states of solvated chromophores. Here we analyze the performance of three classical approaches to describe aqueous solvent in the calculation of the absorption spectra and density of states of pyridine, tropone, and tropothione. Specifically, we compare the results obtained from quantum mechanics/polarizable continuum model (QM/PCM) versus quantum mechanics/molecular mechanics (QM/MM) in its electrostatic-embedding (QM/MMee) and polarizable-embedding (QM/MMpol) fashions, against full-QM computations, in which the solvent is described at the same level of theory as the chromophore. We show that QM/PCM provides very accurate results describing the excitation energies of ππ* and nπ* transitions, the last ones dominated by strong hydrogen-bonding effects, for the three chromophores. The QM/MMee approach also performs very well for both types of electronic transitions, although the description of the ππ* ones is slightly worse than that obtained from QM/PCM. The QM/MMpol approach performs as well as QM/PCM for describing the energy of ππ* states, but it is not able to provide a satisfactory description of hydrogen-bonding effects on the nπ* states of pyridine and tropone. The relative intensity of the absorption bands is better accounted for by the explicit-solvent models than by the continuum-solvent approach.

Excited-State Gradients in Polarizable QM/MM Models: An Induced Dipole Formulation.

Charge and structural relaxation of electronically excited states in embedded systems are strongly affected by the environment. It is known that the largest part of environment effects comes from electrostatics. However, polarization can also play a role by tuning the electronic and geometrical properties of the states, finally modifying the fluorescence. Here we present the formulation of analytical excited-state gradients within a polarizable QM/MM approach and their implementation within the ONIOM framework. A time-dependent DFT level of theory is used in combination with an induced dipole formulation of the polarizable embedding. The formation and relaxation of the bright excited state of an organic dye (DAPI) intercalated in a DNA pocket is used to quantify the role played by the mutual polarization between the QM subsystem and the embedding and also to investigate the onset of overpolarization, which is a known limit of the model with potentially detrimental effects. On the one hand, the results indicate the robustness of the QM-classical interface and, on the other hand, show the non-negligible effect of polarization between DAPI and a DNA pocket in determining the fluorescence properties of the embedded dye.