On-the-Fly Nonadiabatic Dynamics Simulations of Single-Walled Carbon Nanotubes with Covalent Defects.

Single-walled carbon nanotubes (SWCNTs) with covalent surface defects have been explored recently due to their promise for use in single-photon telecommunication emission and in spintronic applications. The all-atom dynamic evolution of electrostatically bound excitons (the primary electronic excitations) in these systems has only been loosely explored from a theoretical perspective due to the size limitations of these large systems (>500 atoms). In this work, we present computational modeling of nonradiative relaxation in a variety of SWCNT chiralities with single-defect functionalizations. Our excited-state dynamics modeling uses a trajectory surface hopping algorithm accounting for excitonic effects with a configuration interaction approach. We find a strong chirality and defect-composition dependence on the population relaxation (varying over 50-500 fs) between the primary nanotube band gap excitation E11 and the defect-associated, single-photon-emitting E11* state. These simulations give direct insight into the relaxation between the band-edge states and the localized excitonic state, in competition with dynamic trapping/detrapping processes observed in experiment. Engineering fast population decay into the quasi-two-level subsystem with weak coupling to higher-energy states increases the effectiveness and controllability of these quantum light emitters.

Polariton enhanced free charge carrier generation in donor-acceptor cavity systems by a second-hybridization mechanism.

Cavity quantum electrodynamics has been studied as a potential approach to modify free charge carrier generation in donor-acceptor heterojunctions because of the delocalization and controllable energy level properties of hybridized light-matter states known as polaritons. However, in many experimental systems, cavity coupling decreases charge separation. Here, we theoretically study the quantum dynamics of a coherent and dissipative donor-acceptor cavity system, to investigate the dynamical mechanism and further discover the conditions under which polaritons may enhance free charge carrier generation. We use open quantum system methods based on single-pulse pumping to find that polaritons have the potential to connect excitonic states and charge separated states, further enhancing free charge generation on an ultrafast timescale of several hundred femtoseconds. The mechanism involves polaritons with optimal energy levels that allow the exciton to overcome the high Coulomb barrier induced by electron-hole attraction. Moreover, we propose that a second-hybridization between a polariton state and dark states with similar energy enables the formation of the hybrid charge separated states that are optically active. These two mechanisms lead to a maximum of 50% enhancement of free charge carrier generation on a short timescale. However, our simulation reveals that on the longer timescale of picoseconds, internal conversion and cavity loss dominate and suppress free charge carrier generation, reproducing the experimental results. Thus, our work shows that polaritons can affect the charge separation mechanism and promote free charge carrier generation efficiency, but predominantly on a short timescale after photoexcitation.

Coupling between Emissive Defects on Carbon Nanotubes: Modeling Insights.

Covalent functionalization of single-walled carbon nanotubes (SWCNTs) with organic molecules results in red-shifted emissive states associated with sp3-defects in the tube lattice, which facilitate their improved optical functionality, including single-photon emission. The energy of the defect-based electronic excitations (excitons) depends on the molecular adducts, the configuration of the defect, and concentration of defects. Here we model the interactions between two sp3-defects placed at various distances in the (6,5) SWCNT using time-dependent density functional theory. Calculations reveal that these interactions conform to the effective model of J-aggregates for well-spaced defects (>2 nm), leading to a red-shifted and optically allowed (bright) lowest energy exciton. H-aggregate behavior is not observed for any defect orientations, which is beneficial for emission. The splitting between the lowest energy bright and optically forbidden (dark) excitons and the pristine excitonic band are controlled by the single-defect configurations and their axial separation. These findings enable a synthetic design strategy for SWCNTs with tunable near-infrared emission.

Predicting phosphorescence energies and inferring wavefunction localization with machine learning.

Phosphorescence is commonly utilized for applications including light-emitting diodes and photovoltaics. Machine learning (ML) approaches trained on ab initio datasets of singlet-triplet energy gaps may expedite the discovery of phosphorescent compounds with the desired emission energies. However, we show that standard ML approaches for modeling potential energy surfaces inaccurately predict singlet-triplet energy gaps due to the failure to account for spatial localities of spin transitions. To solve this, we introduce localization layers in a neural network model that weight atomic contributions to the energy gap, thereby allowing the model to isolate the most determinative chemical environments. Trained on the singlet-triplet energy gaps of organic molecules, we apply our method to an out-of-sample test set of large phosphorescent compounds and demonstrate the substantial improvement that localization layers have on predicting their phosphorescence energies. Remarkably, the inferred localization weights have a strong relationship with the ab initio spin density of the singlet-triplet transition, and thus infer localities of the molecule that determine the spin transition, despite the fact that no direct electronic information was provided during training. The use of localization layers is expected to improve the modeling of many localized, non-extensive phenomena and could be implemented in any atom-centered neural network model.

Machine learning transition temperatures from 2D structure.

A priori knowledge of physicochemical properties such as melting and boiling could expedite materials discovery. However, theoretical modeling from first principles poses a challenge for efficient virtual screening of potential candidates. As an alternative, the tools of data science are becoming increasingly important for exploring chemical datasets and predicting material properties. Herein, we extend a molecular representation, or set of descriptors, first developed for quantitative structure-property relationship modeling by Yalkowsky and coworkers known as the Unified Physicochemical Property Estimation Relationships (UPPER). This molecular representation has group-constitutive and geometrical descriptors that map to enthalpy and entropy; two thermodynamic quantities that drive thermal phase transitions. We extend the UPPER representation to include additional information about sp2-bonded fragments. Additionally, instead of using the UPPER descriptors in a series of thermodynamically-inspired calculations, as per Yalkowsky, we use the descriptors to construct a vector representation for use with machine learning techniques. The concise and easy-to-compute representation, combined with a gradient-boosting decision tree model, provides an appealing framework for predicting experimental transition temperatures in a diverse chemical space. An application to energetic materials shows that the method is predictive, despite a relatively modest energetics reference dataset. We also report competitive results on diverse public datasets of melting points (i.e., OCHEM, Enamine, Bradley, and Bergström) comprised of over 47k structures. Open source software is available at https://github.com/USArmyResearchLab/ARL-UPPER.

NEXMD Software Package for Nonadiabatic Excited State Molecular Dynamics Simulations.

We present a versatile new code released for open community use, the nonadiabatic excited state molecular dynamics (NEXMD) package. This software aims to simulate nonadiabatic excited state molecular dynamics using several semiempirical Hamiltonian models. To model such dynamics of a molecular system, the NEXMD uses the fewest-switches surface hopping algorithm, where the probability of transition from one state to another depends on the strength of the derivative nonadiabatic coupling. In addition, there are a number of algorithmic improvements such as empirical decoherence corrections and tracking trivial crossings of electronic states. While the primary intent behind the NEXMD was to simulate nonadiabatic molecular dynamics, the code can also perform geometry optimizations, adiabatic excited state dynamics, and single-point calculations all in vacuum or in a simulated solvent. In this report, first, we lay out the basic theoretical framework underlying the code. Then we present the code's structure and workflow. To demonstrate the functionality of NEXMD in detail, we analyze the photoexcited dynamics of a polyphenylene ethynylene dendrimer (PPE, C30H18) in vacuum and in a continuum solvent. Furthermore, the PPE molecule example serves to highlight the utility of the getexcited.py helper script to form a streamlined workflow. This script, provided with the package, can both set up NEXMD calculations and analyze the results, including, but not limited to, collecting populations, generating an average optical spectrum, and restarting unfinished calculations.

Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials.

Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.

Numerical tests of coherence-corrected surface hopping methods using a donor-bridge-acceptor model system.

Surface hopping (SH) is a popular mixed quantum-classical method for modeling nonadiabatic excited state processes in molecules and condensed phase materials. The method is simple, efficient, and easy to implement, but the use of classical and independent nuclear trajectories introduces an overcoherence in the electronic density matrix which, if ignored, often leads to spurious results, such as overestimated reaction rates. Several methods have been proposed to incorporate decoherence into SH simulations, but a lack of insightful benchmarks makes their relative accuracy unknown. Herein, we run numerical simulations of common coherence-corrected SH methods including Truhlar's decay-of-mixing (DOM) and Subotnik's augmented SH using a Donor-bridge-Acceptor (DbA) model system. Numerical simulations are carried out in the superexchange regime, where charge transfer proceeds from a donor to an acceptor as a result of donor-bridge and bridge-acceptor couplings. The computed donor-to-acceptor reaction rates are compared to the reference Marcus theory results. For the DbA model under consideration, augmented SH recovers Marcus theory with quantitative accuracy, whereas DOM is only qualitatively accurate depending on whether predefined parameters in the decoherence rate are chosen wisely. We propose a general method for parameterizing the decoherence rate in the DOM method, which improves the method's reaction rates and presumably increases its transferability. Overall, the decoherence method of choice must be chosen with great care and this work provides insight using an exactly solvable model.

NEXMD Modeling of Photoisomerization Dynamics of 4-Styrylquinoline.

Isomerization of molecular systems is ubiquitous in chemistry and biology, and is also important for many applications. Atomistic simulations can help determine the tunable parameters influencing this process. In this paper, we use the Nonadiabatic EXcited state Molecular Dynamics (NEXMD) software to study the photoisomerization of a representative molecule, 4-styrylquinoline (SQ). trans-SQ transforms into dihydrobenzophenanthridine (DHBP) upon irradiation with laser light, with the cis conformer acting as an intermediate. We study how varying three different external stimuli (i.e., apolar versus polar solvent, low versus high photoexcitation energy, and vacuum versus a constant temperature thermostat) affects the trans-to- cis photoisomerization of SQ. Our results show that polarization effects due to implicit solvation and the thermostat play a crucial role in the isomerization process, whereas photoexcitation energy plays a lesser role on the outcome and efficiency. We also show that NEXMD captures the correct energy profile between the ground and first singlet excited state, showing that there are two distinct reaction pathways to the final stable product that vary by the number of photons absorbed, in agreement with experiment. Ultimately, NEXMD proves to be an effective tool for investigating excited state single molecule dynamics subject to various environments and initial conditions.

Transferable Dynamic Molecular Charge Assignment Using Deep Neural Networks.

The ability to accurately and efficiently compute quantum-mechanical partial atomistic charges has many practical applications, such as calculations of IR spectra, analysis of chemical bonding, and classical force field parametrization. Machine learning (ML) techniques provide a possible avenue for the efficient prediction of atomic partial charges. Modern ML advances in the prediction of molecular energies [i.e., the hierarchical interacting particle neural network (HIP-NN)] has provided the necessary model framework and architecture to predict transferable, extensible, and conformationally dynamic atomic partial charges based on reference density functional theory (DFT) simulations. Utilizing HIP-NN, we show that ML charge prediction can be highly accurate over a wide range of molecules (both small and large) across a variety of charge partitioning schemes such as the Hirshfeld, CM5, MSK, and NBO methods. To demonstrate transferability and size extensibility, we compare ML results with reference DFT calculations on the COMP6 benchmark, achieving errors of 0.004e- (elementary charge). This is remarkable since this benchmark contains two proteins that are multiple times larger than the largest molecules in the training set. An application of our atomic charge predictions on nonequilibrium geometries is the generation of IR spectra for organic molecules from dynamical trajectories on a variety of organic molecules, which show good agreement with calculated IR spectra with reference method. Critically, HIP-NN charge predictions are many orders of magnitude faster than direct DFT calculations. These combined results provide further evidence that ML (specifically HIP-NN) provides a pathway to greatly increase the range of feasible simulations while retaining quantum-level accuracy.

Discovering a Transferable Charge Assignment Model Using Machine Learning.

Partial atomic charge assignment is of immense practical value to force field parametrization, molecular docking, and cheminformatics. Machine learning has emerged as a powerful tool for modeling chemistry at unprecedented computational speeds given accurate reference data. However, certain tasks, such as charge assignment, do not have a unique solution. Herein, we use a machine learning algorithm to discover a new charge assignment model by learning to replicate molecular dipole moments across a large, diverse set of nonequilibrium conformations of molecules containing C, H, N, and O atoms. The new model, called Affordable Charge Assignment (ACA), is computationally inexpensive and predicts dipoles of out-of-sample molecules accurately. Furthermore, dipole-inferred ACA charges are transferable to dipole and even quadrupole moments of much larger molecules than those used for training. We apply ACA to dynamical trajectories of biomolecules and produce their infrared spectra. Additionally, we find that ACA assigns similar charges to Charge Model 5 but with greatly reduced computational cost.

Photoexcited Nonadiabatic Dynamics of Solvated Push-Pull π-Conjugated Oligomers with the NEXMD Software.

Solvation can be modeled implicitly by embedding the solute in a dielectric cavity. This approach models the induced surface charge density at the solute-solvent boundary, giving rise to extra Coulombic interactions. Herein, the Nonadiabatic EXcited-state Molecular Dynamics (NEXMD) software was used to model the photoexcited nonradiative relaxation dynamics in a set of substituted donor-acceptor oligo( p-phenylenevinylene) (PPVO) derivatives in the presence of implicit solvent. Several properties of interest including optical spectra, excited state lifetimes, exciton localization, excited state dipole moments, and structural relaxation are calculated to elucidate dependence of functionalization and solvent polarity on photoinduced nonadiabatic dynamics. Results show that solvation generally affects all these properties, where the magnitude of these effects vary from one system to another depending on donor-acceptor substituents and molecular polarizability. We conclude that implicit solvation can be directly incorporated into nonadiabatic simulations within the NEXMD framework with little computational overhead and that it qualitatively reproduces solvent-dependent effects observed in solution-based spectroscopic experiments.

Correction Scheme for Comparison of Computed and Experimental Optical Transition Energies in Functionalized Single-Walled Carbon Nanotubes.

Covalent functionalization of single-walled carbon nanotubes (SWCNTs) introduces red-shifted emission features in the near-infrared spectral range due to exciton localization around the defect site. Such chemical modifications increase their potential use as near-infrared emitters and single-photon sources in telecommunications applications. Density functional theory (DFT) studies using finite-length tube models have been used to calculate their optical transition energies. Predicted energies are typically blue-shifted compared to experiment due to methodology errors including imprecise self-interaction corrections in the density functional and finite-size basis sets. Furthermore, artificial quantum confinement in finite models cannot be corrected by a constant-energy shift since they depend on the degree of exciton localization. Herein, we present a method that corrects the emission energies predicted by time-dependent DFT. Confinement and methodology errors are separately estimated using experimental data for unmodified tubes. Corrected emission energies are in remarkable agreement with experiment, suggesting the value of this straightforward method toward predicting and interpreting the optical features of functionalized SWCNTs.

Cooperative enhancement of the nonlinear optical response in conjugated energetic materials: A TD-DFT study.

Conjugated energetic molecules (CEMs) are a class of explosives with high nitrogen content that posses both enhanced safety and energetic performance properties and are ideal for direct optical initiation. As isolated molecules, they absorb within the range of conventional lasers. Crystalline CEMs are used in practice, however, and their properties can differ due to intermolecular interaction. Herein, time-dependent density functional theory was used to investigate one-photon absorption (OPA) and two-photon absorption (TPA) of monomers and dimers obtained from experimentally determined crystal structures of CEMs. OPA scales linearly with the number of chromophore units, while TPA scales nonlinearly, where a more than 3-fold enhancement in peak intensity, per chromophore unit, is calculated. Cooperative enhancement depends on electronic delocalization spanning both chromophore units. An increase in sensitivity to nonlinear laser initiation makes these materials suitable for practical use. This is the first study predicting a cooperative enhancement of the nonlinear optical response in energetic materials composed of relatively small molecules. The proposed model quantum chemistry is validated by comparison to crystal structure geometries and the optical absorption of these materials dissolved in solution.

Communication: Proper treatment of classically forbidden electronic transitions significantly improves detailed balance in surface hopping.

Surface hopping is the most popular method for nonadiabatic molecular dynamics. Many have reported that it does not rigorously attain detailed balance at thermal equilibrium, but does so approximately. We show that convergence to the Boltzmann populations is significantly improved when the nuclear velocity is reversed after a classically forbidden hop. The proposed prescription significantly reduces the total number of classically forbidden hops encountered along a trajectory, suggesting that some randomization in nuclear velocity is needed when classically forbidden hops constitute a large fraction of attempted hops. Our results are verified computationally using two- and three-level quantum subsystems, coupled to a classical bath undergoing Langevin dynamics.

Two-Photon Absorption in Conjugated Energetic Molecules.

Time-dependent density functional theory (TD-DFT) was used to investigate the relationship between molecular structure and the one- and two-photon absorption (OPA and TPA, respectively) properties of novel and recently synthesized conjugated energetic molecules (CEMs). The molecular structures of CEMs can be strategically altered to influence the heat of formation and oxygen balance, two factors that can contribute to the sensitivity and strength of an explosive material. OPA and TPA are sensitive to changes in molecular structure as well, influencing the optical range of excitation. We found calculated vertical excitation energies to be in good agreement with experiment for most molecules. Peak TPA intensities were found to be significant and on the order of 10(2) GM. Natural transition orbitals for essential electronic states defining TPA peaks of relatively large intensity were used to examine the character of relevant transitions. Modification of molecular substituents, such as additional oxygen or other functional groups, produces significant changes in electronic structure, OPA, and TPA and improves oxygen balance. The results show that certain molecules are apt to undergo nonlinear absorption, opening the possibility for controlled, direct optical initiation of CEMs through photochemical pathways.

Communication: Global flux surface hopping in Liouville space.

Recent years have witnessed substantial progress in the surface hopping (SH) formulation of non-adiabatic molecular dynamics. A generalization of the traditional fewest switches SH (FSSH), global flux SH (GFSH) utilizes the gross population flow between states to derive SH probabilities. The Liouville space formulation of FSSH puts state populations and coherences on equal footing, by shifting the hopping dynamics from Hilbert to Liouville space. Both ideas have shown superior results relative to the standard FSSH in Hilbert space, which has been the most popular approach over the past two and a half decades. By merging the two ideas, we develop GFSH in Liouville space. The new method is nearly as straightforward as the standard FSSH, and carries comparable computational expense. Tested with a representative super-exchange model, it gives the best performance among all existing techniques in the FSSH series. The obtained numerical results match almost perfectly the exact quantum mechanical solutions. Moreover, the results are nearly invariant under the choice of a basis state representation for SH, in contrast to the earlier techniques which exhibit notable basis set dependence. Unique to the developed approach, this property is particularly encouraging, because exact quantum dynamics is representation independent. GFSH in Liouville space significantly improves accuracy and applicability of SH for a broad range of chemical and physical processes.

Mixed quantum-classical equilibrium in global flux surface hopping.

Global flux surface hopping (GFSH) generalizes fewest switches surface hopping (FSSH)­one of the most popular approaches to nonadiabatic molecular dynamics­for processes exhibiting superexchange. We show that GFSH satisfies detailed balance and leads to thermodynamic equilibrium with accuracy similar to FSSH. This feature is particularly important when studying electron-vibrational relaxation and phonon-assisted transport. By studying the dynamics in a three-level quantum system coupled to a classical atom in contact with a classical bath, we demonstrate that both FSSH and GFSH achieve the Boltzmann state populations. Thermal equilibrium is attained significantly faster with GFSH, since it accurately represents the superexchange process. GFSH converges closer to the Boltzmann averages than FSSH and exhibits significantly smaller statistical errors.

Fewest Switches Surface Hopping in Liouville Space.

The novel approach to nonadiabatic quantum dynamics greatly increases the accuracy of the most popular semiclassical technique while maintaining its simplicity and efficiency. Unlike the standard Tully surface hopping in Hilbert space, which deals with population flow, the new strategy in Liouville space puts population and coherence on equal footing. Dual avoided crossing and energy transfer models show that the accuracy is improved in both diabatic and adiabatic representations and that Liouville space simulation converges faster with the number of trajectories than Hilbert space simulation. The constructed master equation accurately captures superexchange, tunneling, and quantum interference. These effects are essential for charge, phonon and energy transport and scattering, exciton fission and fusion, quantum optics and computing, and many other areas of physics and chemistry.