The development of the QM/MM interface and its application for the on-the-fly QM/MM nonadiabatic dynamics in JADE package: Theory, implementation, and applications

Understanding the nonadiabatic dynamics of complex systems is a challenging task in computational photochemistry. Herein, we present an efficient and user-friendly quantum mechanics/molecular mechanics (QM/MM) interface to run on-the-fly nonadiabatic dynamics. Currently, this interface consists of an independent set of codes designed for general-purpose use. Herein, we demonstrate the ability and feasibility of the QM/MM interface by integrating it with our long-term developed JADE package. Tailored to handle nonadiabatic processes in various complex systems, especially condensed phases and protein environments, we delve into the theories, implementations, and applications of on-the-fly QM/MM nonadiabatic dynamics. The QM/MM approach is established within the framework of the additive QM/MM scheme, employing electrostatic embedding, link-atom inclusion, and charge-redistribution schemes to treat the QM/MM boundary. Trajectory surface-hopping dynamics are facilitated using the fewest switches algorithm, encompassing classical and quantum treatments for nuclear and electronic motions, respectively. Finally, we report simulations of nonadiabatic dynamics for two typical systems: azomethane in water and the retinal chromophore PSB3 in a protein environment. Our results not only illustrate the power of the QM/MM program but also reveal the important roles of environmental factors in nonadiabatic processes.

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.

Non-Hermitian molecular dynamics simulations of exciton-polaritons in lossy cavities

The observation that materials can change their properties when placed inside or near an optical resonator has sparked a fervid interest in understanding the effects of strong light-matter coupling on molecular dynamics, and several approaches have been proposed to extend the methods of computational chemistry into this regime. Whereas the majority of these approaches have focused on modeling a single molecule coupled to a single cavity mode, changes to chemistry have so far only been observed experimentally when very many molecules are coupled collectively to multiple modes with short lifetimes. While atomistic simulations of many molecules coupled to multiple cavity modes have been performed with semi-classical molecular dynamics, an explicit description of cavity losses has so far been restricted to simulations in which only a very few molecular degrees of freedom were considered. Here, we have implemented an effective non-Hermitian Hamiltonian to explicitly treat cavity losses in large-scale semi-classical molecular dynamics simulations of organic polaritons and used it to perform both mean-field and surface hopping simulations of polariton relaxation, propagation, and energy transfer.

Tuning the Coherent Propagation of Organic Exciton-Polaritons through the Cavity Q-factor

Transport of excitons in organic materials can be enhanced through polariton formation when the interaction strength between these excitons and the confined light modes of an optical resonator exceeds their decay rates. While the polariton lifetime is determined by the Q(uality)-factor of the optical resonator, the polariton group velocity is not. Instead, the latter is solely determined by the polariton dispersion. Yet, experiments suggest that the Q-factor also controls the polariton propagation velocity. To understand this observation, the authors perform molecular dynamics simulations of Rhodamine chromophores strongly coupled to Fabry-Pérot cavities with various Q-factors. The results suggest that propagation in the aforementioned experiments is initially dominated by ballistic motion of upper polariton states at their group velocities, which leads to a rapid expansion of the wavepacket. Cavity decay in combination with non-adiabatic population transfer into dark states, rapidly depletes these bright states, causing the wavepacket to contract. However, because population transfer is reversible, propagation continues, but as a diffusion process, at lower velocity. By controlling the lifetime of bright states, the Q-factor determines the duration of the ballistic phase and the diffusion coefficient in the diffusive regime. Thus, polariton propagation in organic microcavities can be effectively tuned through the Q-factor.

Multi-scale molecular dynamics simulations of enhanced energy transfer in organic molecules under strong coupling

Exciton transport can be enhanced in the strong coupling regime where excitons hybridize with confined light modes to form polaritons. Because polaritons have group velocity, their propagation should be ballistic and long-ranged. However, experiments indicate that organic polaritons propagate in a diffusive manner and more slowly than their group velocity. Here, we resolve this controversy by means of molecular dynamics simulations of Rhodamine molecules in a Fabry-Pérot cavity. Our results suggest that polariton propagation is limited by the cavity lifetime and appears diffusive due to reversible population transfers between polaritonic states that propagate ballistically at their group velocity, and dark states that are stationary. Furthermore, because long-lived dark states transiently trap the excitation, propagation is observed on timescales beyond the intrinsic polariton lifetime. These insights not only help to better understand and interpret experimental observations, but also pave the way towards rational design of molecule-cavity systems for coherent exciton transport.

Future Potential of Quantum Computing and Simulations in Biological Science

The review article presents the recent progress in quantum computing and simulation within the field of biological sciences. The article is designed mainly into two portions: quantum computing and quantum simulation. In the first part, significant aspects of quantum computing was illustrated, such as quantum hardware, quantum RAM and big data, modern quantum processors, qubit, superposition effect in quantum computation, quantum interference, quantum entanglement, and quantum logic gates. Simultaneously, in the second part, vital features of the quantum simulation was illustrated, such as the quantum simulator, algorithms used in quantum simulations, and the use of quantum simulation in biological science. Finally, the review provides exceptional views to future researchers about different aspects of quantum simulation in biological science.

The Photocycle of Bacteriophytochrome Is Initiated by Counterclockwise Chromophore Isomerization

Photoactivation of bacteriophytochrome involves a cis-trans photoisomerization of a biliverdin chromophore, but neither the precise sequence of events nor the direction of the isomerization is known. Here, we used nonadiabatic molecular dynamics simulations on the photosensory protein dimer to resolve the isomerization mechanism in atomic detail. In our simulations the photoisomerization of the D ring occurs in the counterclockwise direction. On a subpicosecond time scale, the photoexcited chromophore adopts a short-lived intermediate with a highly twisted configuration stabilized by an extended hydrogen-bonding network. Within tens of picoseconds, these hydrogen bonds break, allowing the chromophore to adopt a more planar configuration, which we assign to the early Lumi-R state. The isomerization process is completed via helix inversion of the biliverdin chromophore to form the late Lumi-R state. The mechanistic insights into the photoisomerization process are essential to understand how bacteriophytochrome has evolved to mediate photoactivation and to engineer this protein for new applications.

Prediction of Fluorophore Brightness in Designed Mini Fluorescence Activating Proteins

The de novo computational design of proteins with predefined three-dimensional structure is becoming much more routine due to advancements both in force fields and algorithms. However, creating designs with functions beyond folding is more challenging. In that regard, the recent design of small beta barrel proteins that activate the fluorescence of an exogenous small molecule chromophore (DFHBI) is noteworthy. These proteins, termed mini fluorescence activating proteins (mFAPs), have been shown to increase the brightness of the chromophore more than 100-fold upon binding to the designed ligand pocket. The design process created a large library of variants with different brightness levels but gave no rational explanation for why one variant was brighter than another. Here, we use quantum mechanics and molecular dynamics simulations to investigate how molecular flexibility in the ground and excited states influences brightness. We show that the ability of the protein to resist dihedral angle rotation of the chromophore is critical for predicting brightness. Our simulations suggest that the mFAP/DFHBI complex has a rough energy landscape, requiring extensive ground-state sampling to achieve converged predictions of excited-state kinetics. While computationally demanding, this roughness suggests that mFAP protein function can be enhanced by reshaping the energy landscape toward conformations that better resist DFHBI bond rotation.

The ΔSCF method for non-adiabatic dynamics of systems in the liquid phase

Computational studies of ultrafast photoinduced processes give valuable insights into the photochemical mechanisms of a broad range of compounds. In order to accurately reproduce, interpret, and predict experimental results, which are typically obtained in a condensed phase, it is indispensable to include the condensed phase environment in the computational model. However, most studies are still performed in vacuum due to the high computational cost of state-of-the-art non-adiabatic molecular dynamics (NAMD) simulations. The quantum mechanical/molecular mechanical (QM/MM) solvation method has been a popular model to perform photodynamics in the liquid phase. Nevertheless, the currently used QM/MM embedding techniques cannot sufficiently capture all solute-solvent interactions. In this Perspective, we will discuss the efficient ΔSCF electronic structure method and its applications with respect to the NAMD of solvated compounds, with a particular focus on explicit quantum mechanical solvation. As more research is required for this method to reach its full potential, some challenges and possible directions for future research are presented as well.

Quantum and semiclassical dynamical studies of nonadiabatic processes in solution: achievements and perspectives

We concisely review the main methodological approaches to model nonadiabatic dynamics in isotropic solutions and their applications. Three general classes of models are identified as the most used to include solvent effects in the simulations. The first model describes the solvent as a set of harmonic collective modes coupled to the solute degrees of freedom, and the second as a continuum, while the third explicitly includes solvent molecules in the calculations. The issues related to the use of these models in semiclassical and quantum dynamical simulations are discussed, as well as the main limitations and perspectives of each approach.

Geometric and electronic structure probed along the isomerisation coordinate of a photoactive yellow protein chromophore

Understanding the connection between the motion of the nuclei in a molecule and the rearrangement of its electrons lies at the heart of chemistry. While many experimental methods have been developed to probe either the electronic or the nuclear structure on the timescale of atomic motion, very few have been able to capture both these changes in concert. Here, we use time-resolved photoelectron imaging to probe the isomerisation coordinate on the excited state of an isolated model chromophore anion of the photoactive yellow protein. By probing both the electronic structure changes as well as nuclear dynamics, we are able to uniquely measure isomerisation about a specific bond. Our results demonstrate that the photoelectron signal dispersed in time, energy and angle combined with calculations can track the evolution of both electronic and geometric structure along the adiabatic state, which in turn defines that chemical transformation.

Resolving concerted nuclear and electronic motion in real-time is a primary goal in chemistry. The authors monitor nuclear and valence electronic dynamics in the excited state single-bond isomerisation of a chromophore of photoactive yellow protein, using time-resolved photoelectron imaging and electronic structure calculations.

Aggregation-Dependent Photoreactive Hemicyanine Assembly as a Photobactericide

Organic materials that show substantial reactivity under visible light have received considerable attention due to their wide applications in chemical and biological systems. Hemicyanine pigments possess a strong intramolecular donor-acceptor structure and thereby display intense absorption in the visible spectral region. However, most excitons are consumed via the twisted intramolecular charge-transfer (TICT) process, making hemicyanines generally inert to light. Herein, we describe the development of an amphiphilic hemicyanine dye whose aggregation could be easily regulated using salt or counterions. More importantly, its intrinsic photoreactivity was successfully induced by steric restriction and cofacial arrangement within the H-aggregate, thus creating an effective photobactericide. This strategy could be extended to the development of photocatalysts for photosynthesis and a photosensitizer for photodynamic therapy.

Hydrogen-Bonding Interaction Regulates Photoisomerization of a Single-Bond-Rotation Locked Photoactive Yellow Protein Chromophore in Protein

We have employed the QM(CASPT2//CASSCF)/MM method to explore the excited-state isomerization and decay mechanism of a single-bond-rotation locked photoactive yellow protein (PYP) chromophore in wild-type and mutant proteins. The S₁ state is a spectroscopically bright state in the Franck-Condon region. In this state, there exist two excited-state isomerization pathways separately related to the clockwise and anticlockwise rotations of the C=C bond. The clockwise path is favorable because of a small barrier of 2 kcal/mol and uses a novel bicycle-pedal unidirectional photoisomerization mechanism in which the involved two dihedral angles rotate asynchronously because of the reinforced hydrogen-bonding interaction between the chromophore and Cys69. Near the twisted S₁ minimum, the chromophore hops to the S₀ state via the S₁/S₀ conical intersection. Finally, the R52A mutation has small effects on the excited-state properties and photoisomerization of the locked PYP chromophore. The present work provides new insights for understanding the photochemistry of PYP chromophores in protein surroundings.

Fingerprinting the Excited-State Dynamics in Methyl Ester and Methyl Ether Anions of Deprotonated para-Coumaric Acid

Chromophores based on the para-hydroxycinnamate moiety are widespread in the natural world, including as the photoswitching unit in photoactive yellow protein and as a sunscreen in the leaves of plants. Here, photodetachment action spectroscopy combined with frequency- and angle-resolved photoelectron imaging is used to fingerprint the excited-state dynamics over the first three bright action-absorption bands in the methyl ester anions (pCEs^-) of deprotonated para-coumaric acid at a temperature of ∼300 K. The excited states associated with the action-absorption bands are classified as resonances because they are situated in the detachment continuum and are open to autodetachment. The frequency-resolved photoelectron spectrum for pCEs^- indicates that all photon energies over the S₁(ππ*) band lead to similar vibrational autodetachment dynamics. The S₂(nπ*) band is Herzberg-Teller active and has comparable brightness to the higher lying 2¹(ππ*) band. The frequency-resolved photoelectron spectrum over the S₂(nπ*) band indicates more efficient internal conversion to the S₁(ππ*) state for photon energies resonant with the Franck-Condon modes (∼80%) compared with the Herzberg-Teller modes (∼60%). The third action-absorption band, which corresponds to excitation of the 2¹(ππ*) state, shows complex and photon energy-dependent dynamics, with 20-40% of photoexcited population internally converting to the S₁(ππ*) state. There is also evidence for a mode-specific competition between prompt autodetachment and internal conversion on the red edge of the 2¹(ππ*) band. There is no evidence for recovery of the ground electronic state and statistical electron ejection (thermionic emission) following photoexcitation over any of the three action-absorption bands. The photoelectron spectra for the deprotonated methyl ether derivative (pCEt^-) at photon energies over the S₁(ππ*) and S₂(nπ*) bands indicate diametrically opposed dynamics compared with pCEs^-, namely, intense thermionic emission due to efficient recovery of the ground electronic state.

Photoactive Yellow Protein Chromophore Photoisomerizes around a Single Bond if the Double Bond Is Locked

Photoactivation in the Photoactive Yellow Protein, a bacterial blue-light photoreceptor, proceeds via photoisomerization of the double C═C bond in the covalently attached chromophore. Quantum chemistry calculations, however, have suggested that in addition to double-bond photoisomerization, the isolated chromophore and many of its analogues can isomerize around a single C-C bond as well. Whereas double-bond photoisomerization has been observed with X-ray crystallography, experimental evidence of single-bond photoisomerization is currently lacking. Therefore, we have synthesized a chromophore analogue, in which the formal double bond is covalently locked in a cyclopentenone ring, and carried out transient absorption spectroscopy experiments in combination with nonadiabatic molecular dynamics simulations to reveal that the locked chromophore isomerizes around the single bond upon photoactivation. Our work thus provides experimental evidence of single-bond photoisomerization in a photoactive yellow protein chromophore analogue and suggests that photoisomerization is not restricted to the double bonds in conjugated systems. This insight may be useful for designing light-driven molecular switches or motors.

Four resonance structures elucidate double-bond isomerisation of a biological chromophore

Four resonance structures determining the electronic structure of the chromophore’s ground and first excited states. Changing the relative energies of the structures by hydrogen-bonding interactions tunes all chromophore’s photochemical properties.

Ultrafast valence to non-valence excited state dynamics in a common anionic chromophore

Non-valence states in neutral molecules (Rydberg states) have well-established roles and importance in photochemistry, however, considerably less is known about the role of non-valence states in photo-induced processes in anions. Here, femtosecond time-resolved photoelectron imaging is used to show that photoexcitation of the S₁(ππ*) state of the methyl ester of deprotonated para-coumaric acid – a model chromophore for photoactive yellow protein (PYP) – leads to a bifurcation of the excited state wavepacket. One part remains on the S₁(ππ*) state forming a twisted intermediate, whilst a second part leads to the formation of a non-valence (dipole-bound) state. Both populations eventually decay independently by vibrational autodetachment. Valence-to-non-valence internal conversion has hitherto not been observed in the intramolecular photophysics of an isolated anion, raising questions into how common such processes might be, given that many anionic chromophores have bright valence states near the detachment threshold.

Photoactive biomolecules rely on chromophores whose photochemistry depends on the environment. Here, the excited state dynamics of a model for the anionic biochromophore in photoactive yellow protein is investigated by time-resolved photoelectron spectroscopy showing involvement of a non-valence state, and lack of E-Z isomerisation in the gas phase.

Protonation of the Biliverdin IXα Chromophore in the Red and Far-Red Photoactive States of a Bacteriophytochrome

The tetrapyrrole chromophore biliverdin IXα (BV) in the bacteriophytochrome from Deinococcus radiodurans (DrBphP) is usually assumed to be fully protonated, but this assumption has not been systematically validated by experiments or extensive computations. Here, we use force field molecular dynamics simulations and quantum mechanics/molecular mechanics calculations with density functional theory and XMCQDPT2 methods to investigate the effect of the five most probable protonation forms of BV on structural stability, binding pocket interactions, and absorption spectra in the two photochromic states of DrBphP. While agreement with X-ray structural data and measured UV/vis spectra suggest that in both states the protonated form of the chromophore dominates, we also find that a minor population with a deprotonated D-ring could contribute to the red-shifted tail in the absorption spectra.

Stepwise photosensitized thymine dimerization mediated by an exciton intermediate

ABSTRACT

Cyclobutane thymine dimerization is the most prominent DNA photoinduced damage. While the ultrafast mechanism that proceeds in the singlet manifold is nowadays well established, the triplet-state pathway is not completely understood. Here we report the underlying mechanism of the photosensitized dimerization process in the triplet state. Quantum chemical calculations, combined with wavefunction analysis, and nonadiabatic molecular dynamics simulations demonstrate that this is a stepwise reaction, traversing a long-lived triplet biradical intermediate, which is characterized as a Frenkel exciton with very small charge-transfer character. The low yield of the reaction is regulated by two factors: (i) a relatively large energy barrier that needs to be overcome to form the exciton intermediate, and (ii) a bifurcation of the ground-state potential-energy surface that mostly leads back to the Franck-Condon region because dimerization requires a very restricted combination of coordinates and velocities at the event of non-radiative decay to the ground state.

GRAPHICAL ABSTRACT

Combined UMC- DFT prediction of electron-hole coupling in unit cells of pentacene crystals

Pentacene is an organic semiconductor that draws special attention from the scientific community due to the high mobility of its charge carriers. As electron-hole interactions are important aspects in the regard of such property, a computationally inexpensive method to predict the coupling between these quasi-particles is highly desired. In this work, we propose a hybrid methodology of combining Uncoupled Monte Carlo Simulations (UMC) and Density functional Theory (DFT) methodologies to obtain a good compromise between computational feasibility and accuracy. As a first step in considering a Pentacene crystal, we describe its unit cell: the Pentacene Dimer. Because many conformations can be encountered for the dimer and considering the complexity of the system, we make use of UMC in order to find the most probable structures and relative orientations for the Pentacene-Pentacene complex. Following, we carry out electronic structure calculations in the scope of DFT with the goal of describing the electron-hole coupling on the most probable configurations obtained by UMC. The comparison of our results with previously reported data on the literature suggests that the methodology is well suited for describing transfer integrals of organic semiconductors. The observed accuracy together with the smaller computational cost required by our approach allows us to conclude that such methodology might be an important tool towards the description of systems with higher complexity.

QM/MM Study of Substituent and Solvent Effects on the Excited State Dynamics of the Photoactive Yellow Protein Chromophore

Substituent and solvent effects on the excited state dynamics of the Photoactive Yellow Protein chromophore are studied using the average solvent electrostatic potential from molecular dynamics (ASEP/MD) method. Four molecular models were considered: the ester and thioester derivatives of the p-coumaric acid anion and their methylated derivatives. We found that the solvent produces dramatic modifications on the free energy profile of the S1 state: 1) Two twisted structures that are minima in the gas phase could not be located in aqueous solution. 2) Conical intersections (CIs) associated with the rotation of the single bond adjacent to the phenyl group are found for the four derivatives in water solution but only for thio derivatives in the gas phase. 3) The relative stability of minima and CIs is reverted with respect to the gas phase values, affecting the prevalent de-excitation paths. As a consequence of these changes, three competitive de-excitation channels are open in aqueous solution: the fluorescence emission from a planar minimum on S1, the trans-cis photoisomerization through a CI that involves the rotation of the vinyl double bond, and the nonradiative, nonreactive, de-excitation through the CI associated with the rotation of the single bond adjacent to the phenyl group. In the gas phase, the minima are the structures with the lower energy, while in solution these are the conical intersections. In solution, the de-excitation prevalent path seems to be the photoisomerization for oxo compounds, while thio compounds return to the initial trans ground state without emission.

Electric Field Keeps Chromophore Planar and Produces High Yield Fluorescence in Green Fluorescent Protein

The green fluorescent protein and its designed variants fluoresce efficiently. Because the isolated chromophore is not fluorescent in a practical sense, it is apparent that the protein environment plays a crucial role in its efficiency. Because of various obstacles in studying excited state dynamics of complex systems, however, the detailed mechanism of this efficiency enhancement is not yet clearly elucidated. Here, by adopting excited state nonadiabatic molecular dynamics simulations together with an interpolated quantum chemical potential model of the chromophore, we find that the strong electric field from the protein matrix contributes dominantly to the motional restriction of the chromophore. The delay in twisting motion subsequently obstructs the nonradiative decay that competes with fluorescence, leading naturally to an enhancement in light-emitting efficiency. Surprisingly, steric constraints make only a minor contribution to these aspects. Through residue specific analyses, we identify a group of key residues that control the excited state behavior. Testing a series of mutant GFPs with different brightnesses also supports the view regarding the importance of protein electrostatics. Our findings may provide a useful guide toward designing new fluorescent chemical systems in the future.

Probing the Interstate Coupling near a Conical Intersection by Optical Spectroscopy

Conical intersections are points where adiabatic potential energy surfaces cross. The interstate coupling between the potential energy surfaces plays a crucial role in many processes associated with conical intersections. Still no method exists to measure this coupling driving the chemical reactions between the potential energy surfaces involved. In this Letter, using a generic model for photoisomerization, we propose a novel experimental approach to estimate the coupling that mixes the electronic states near a conical intersection. The approach is based on analyzing the vibrational wavepacket of the reactant in the adiabatic ground and excited electronic states. The nuclear wavepacket dynamics are extracted from linear absorption and two-dimensional electronic spectroscopy. Comparing the frequencies of the coupling mode in the adiabatic ground and excited states from models with and without coupling between the potential energy surfaces suggests an experimental tool to determine the interstate coupling.

Femtosecond structural dynamics drives the trans/cis isomerization in photoactive yellow protein

A variety of organisms have evolved mechanisms to detect and respond to light, in which the response is mediated by protein structural changes after photon absorption. The initial step is often the photoisomerization of a conjugated chromophore. Isomerization occurs on ultrafast time scales and is substantially influenced by the chromophore environment. Here we identify structural changes associated with the earliest steps in the trans-to-cis isomerization of the chromophore in photoactive yellow protein. Femtosecond hard x-ray pulses emitted by the Linac Coherent Light Source were used to conduct time-resolved serial femtosecond crystallography on photoactive yellow protein microcrystals over a time range from 100 femtoseconds to 3 picoseconds to determine the structural dynamics of the photoisomerization reaction.

Control of Nonadiabatic Passage through a Conical Intersection by a Dynamic Resonance

Nonadiabatic processes, dominated by dynamic passage of reactive fluxes through conical intersections (CIs), are considered to be appealing means for manipulating reaction paths, particularly via initial vibrational preparation. Nevertheless, obtaining direct experimental evidence of whether specific-mode excitation affects the passage at the CI is challenging, requiring well-resolved time- or frequency-domain experiments. Here promotion of methylamine-d2 (CH3ND2) molecules to spectral-resolved rovibronic states on the excited S1 potential energy surface, coupled to sensitive D photofragment probing, allowed us to follow the N-D bond fission dynamics. The branching ratios between slow and fast D photofragments and the internal energies of the CH3ND(X̃) photofragments confirm correlated anomalies for predissociation initiated from specific rovibronic states. These anomalies reflect the existence of a dynamic resonance that strongly depends on the energy of the initially excited rovibronic states, the evolving vibrational mode on the repulsive S1 part during N-D bond elongation, and the manipulated passage through the CI that leads to CH3ND radicals excited with C-N-D bending. This resonance plays an important role in the bifurcation dynamics at the CI and can be foreseen to exist in other photoinitiated processes and to control their outcome.

Solvent effects on de-excitation channels in the p-coumaric acid methyl ester anion, an analogue of the photoactive yellow protein (PYP) chromophore

Environmental effects on the deactivation channels of the PYP chromophore in the gas phase and water solution are compared at the CASPT2//CASSCF/cc-pVDZ level.

Diabatic Population Matrix Formalism for Performing Molecular Mechanics Style Simulations with Multiple Electronic States

An accurate description of nonbonded interactions is important in investigating dynamics of molecular systems. In many situations, fixed point charge models are successfully applied to explaining various chemical phenomena. However, these models with conventional formulations will not be appropriate in elucidating the detailed dynamics during nonadiabatic events. This is mainly because the chemical properties of any molecule, especially its electronic populations, significantly change with respect to molecular distortions in the vicinity of the surface crossing. To overcome this issue in molecular simulations yet within the framework of the fixed point charge model, we define a diabatic electronic population matrix and substitute it for the conventional adiabatic partial charges. We show that this matrix can be readily utilized toward attaining more reliable descriptions of Coulombic interactions, in combination with the interpolation formalism for obtaining the intramolecular interaction potential. We demonstrate how the mixed formalism with the diabatic charges and the interpolation can be applied to molecular simulations by conducting adiabatic and nonadiabatic molecular dynamics trajectory calculations of the green fluorescent protein chromophore anion in aqueous environment.

Constructing polyatomic potential energy surfaces by interpolating diabatic Hamiltonian matrices with demonstration on green fluorescent protein chromophore

Simulating molecular dynamics directly on quantum chemically obtained potential energy surfaces is generally time consuming. The cost becomes overwhelming especially when excited state dynamics is aimed with multiple electronic states. The interpolated potential has been suggested as a remedy for the cost issue in various simulation settings ranging from fast gas phase reactions of small molecules to relatively slow condensed phase dynamics with complex surrounding. Here, we present a scheme for interpolating multiple electronic surfaces of a relatively large molecule, with an intention of applying it to studying nonadiabatic behaviors. The scheme starts with adiabatic potential information and its diabatic transformation, both of which can be readily obtained, in principle, with quantum chemical calculations. The adiabatic energies and their derivatives on each interpolation center are combined with the derivative coupling vectors to generate the corresponding diabatic Hamiltonian and its derivatives, and they are subsequently adopted in producing a globally defined diabatic Hamiltonian function. As a demonstration, we employ the scheme to build an interpolated Hamiltonian of a relatively large chromophore, para-hydroxybenzylidene imidazolinone, in reference to its all-atom analytical surface model. We show that the interpolation is indeed reliable enough to reproduce important features of the reference surface model, such as its adiabatic energies and derivative couplings. In addition, nonadiabatic surface hopping simulations with interpolation yield population transfer dynamics that is well in accord with the result generated with the reference analytic surface. With these, we conclude by suggesting that the interpolation of diabatic Hamiltonians will be applicable for studying nonadiabatic behaviors of sizeable molecules.

Reaction Path Following with Sparse Interpolation

Computing the potential energy of an N-atom molecule is an expensive optimization process of 3N - 6 molecular coordinates, so following reaction pathways as a function of all 3N - 6 coordinates is unfeasible for large molecules. In this paper, we present a method that isolates d < 3N - 6 molecular coordinates and continuously follows reaction paths on d-dimensional potential energy surfaces approximated by a Smolyak's sparse grid interpolation algorithm.1 Compared to dense grids, sparse grids efficiently improve the ratio of invested storage and computing time to approximation accuracy and thus allow one to increase the number of coordinates d in molecular reaction path following simulations. Furthermore, evaluation of the interpolant is much less expensive than the evaluation of the actual energy function, so our technique offers a computationally efficient way to simulate reaction paths on ground and excited state potential energy surfaces. To demonstrate the capabilities of our method, we present simulation results for the isomerization of 2-butene with two, three, and six degrees of freedom.

A comprehensive study of isomerization and protonation reactions in the photocycle of the photoactive yellow protein

A comprehensive picture of the overall photocycle was obtained to reveal a wide range of structural signals in the photoactive yellow protein.

Control Mechanisms of Photoisomerization in Protonated Schiff Bases

We performed ab initio excited-state molecular dynamics simulations of a gas-phase photoexcited protonated Schiff base (C1-N2═C3-C4═C5-C6) to search for control mechanisms of its photoisomerization. The excited molecule twists by ∼90° around either the N2C3 bond or the C4C5 bond and relaxes to the ground electronic state through a conical intersection with either a trans or cis outcome. We show that a large initial distortion of several dihedral angles and a specific normal vibrational mode combining pyramidalization and double-bond twisting can lead to a preferential rotation of atoms around the C4C5 bond. We also show that selective pretwisting of several dihedral angles in the initial ground state thermal ensemble (by analogy to a protein pocket) can significantly increase the fraction of photoreactive (cis → trans) trajectories. We demonstrate that new ensembles with higher degrees of control over the photoisomerization reaction can be obtained by a computational directed evolution approach on the ensembles of molecules with the pretwisted geometries.

Adiabatic and nonadiabatic contributions to the energy of a system subject to a time-dependent perturbation: complete separation and physical interpretation

When a time-dependent perturbation acts on a quantum system that is initially in the nondegenerate ground state ∣0> of an unperturbed Hamiltonian H(0), the wave function acquires excited-state components ∣k> with coefficients c(k)(t) exp(-iE(k)t/ℏ), where E(k) denotes the energy of the unperturbed state ∣k>. It is well known that each coefficient c(k)(t) separates into an adiabatic term a(k)(t) that reflects the adjustment of the ground state to the perturbation--without actual transitions--and a nonadiabatic term b(k)(t) that yields the probability amplitude for a transition to the excited state. In this work, we prove that the energy at any time t also separates completely into adiabatic and nonadiabatic components, after accounting for the secular and normalization terms that appear in the solution of the time-dependent Schrödinger equation via Dirac's method of variation of constants. This result is derived explicitly through third order in the perturbation. We prove that the cross-terms between the adiabatic and nonadiabatic parts of c(k)(t) vanish, when the energy at time t is determined as an expectation value. The adiabatic term in the energy is identical to the total energy obtained from static perturbation theory, for a system exposed to the instantaneous perturbation λH'(t). The nonadiabatic term is a sum over excited states ∣k> of the transition probability multiplied by the transition energy. By evaluating the probabilities of transition to the excited eigenstates ∣k'(t)> of the instantaneous Hamiltonian H(t), we provide a physically transparent explanation of the result for E(t). To lowest order in the perturbation parameter λ, the probability of finding the system in state ∣k'(t)> is given by λ(2) ∣b(k)(t)∣(2). At third order, the transition probability depends on a second-order transition coefficient, derived in this work. We indicate expected differences between the results for transition probabilities obtained from this work and from Fermi's golden rule.