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.

Sensory feedback expands dynamic complexity and aids in robustness against noise.

It has been hypothesized that sensory feedback is a critical component in determining the functionality of a central pattern generator. To test this, Yu and Thomas's recent work Yu and Thomas (Biol Cybern 115(2):135-160, 2021) built a model of a half-center oscillator coupled to a simple muscular model with sensory feedback. They showed that sensory feedback increases robustness against external noise, while simultaneously expanding the potential repertoire of functions the half-center oscillator can perform. However, they show that this comes at the cost of robustness against internal noise.

Non-adiabatic molecular dynamics by accelerated semiclassical Monte Carlo.

Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficient as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In most cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems.

Raman scattering in molecular junctions: a pseudoparticle formulation.

We present a formulation of Raman spectroscopy in molecular junctions based on a many-body state representation of the molecule. The approach goes beyond the previous effective single orbital formalism and provides a convenient way to incorporate computational methods and tools proven for equilibrium molecular spectroscopy into the realm of current carrying junctions. The presented framework is illustrated by first principle simulations of Raman response in a three-ring oligophenylene vinylene terminating in amine functional groups (OPV3) junction. The calculated shift in Stokes lines and estimate of vibrational heating by electric current agree with available experimental data. In particular, our results suggest that participation of the OPV3 cation in Raman scattering under bias may be responsible for the observed shift, and that the direction of the shift depends on renormalization of normal modes. This work is a step toward atomistic quantum ab initio modeling of the optical response of nonequilibrium electronic dynamics in molecular junctions.

Semiclassical Monte Carlo: a first principles approach to non-adiabatic molecular dynamics.

Modeling the dynamics of photophysical and (photo)chemical reactions in extended molecular systems is a new frontier for quantum chemistry. Many dynamical phenomena, such as intersystem crossing, non-radiative relaxation, and charge and energy transfer, require a non-adiabatic description which incorporate transitions between electronic states. Additionally, these dynamics are often highly sensitive to quantum coherences and interference effects. Several methods exist to simulate non-adiabatic dynamics; however, they are typically either too expensive to be applied to large molecular systems (10's-100's of atoms), or they are based on ad hoc schemes which may include severe approximations due to inconsistencies in classical and quantum mechanics. We present, in detail, an algorithm based on Monte Carlo sampling of the semiclassical time-dependent wavefunction that involves running simple surface hopping dynamics, followed by a post-processing step which adds little cost. The method requires only a few quantities from quantum chemistry calculations, can systematically be improved, and provides excellent agreement with exact quantum mechanical results. Here we show excellent agreement with exact solutions for scattering results of standard test problems. Additionally, we find that convergence of the wavefunction is controlled by complex valued phase factors, the size of the non-adiabatic coupling region, and the choice of sampling function. These results help in determining the range of applicability of the method, and provide a starting point for further improvement.

Quantum transport with two interacting conduction channels.

The transport properties of a conduction junction model characterized by two mutually coupled channels that strongly differ in their couplings to the leads are investigated. Models of this type describe molecular redox junctions (where a level that is weakly coupled to the leads controls the molecular charge, while a strongly coupled one dominates the molecular conduction), and electron counting devices in which the current in a point contact is sensitive to the charging state of a nearby quantum dot. Here we consider the case where transport in the strongly coupled channel has to be described quantum mechanically (covering the full range between sequential tunneling and co-tunneling), while conduction through the weakly coupled channel is a sequential process that could by itself be described by a simple master equation. We compare the result of a full quantum calculation based on the pseudoparticle non-equilibrium Green function method to that obtained from an approximate mixed quantum-classical calculation, where correlations between the channels are taken into account through either the averaged rates or the averaged energy. We find, for the steady state current, that the approximation based on the averaged rates works well in most of the voltage regime, with marked deviations from the full quantum results only at the threshold for charging the weekly coupled level. These deviations are important for accurate description of the negative differential conduction behavior that often characterizes redox molecular junctions in the neighborhood of this threshold.

Stochastic and mixed density functional theory within the projector augmented wave formalism for simulation of warm dense matter.

Stochastic density functional theory (DFT) and mixed stochastic-deterministic DFT are burgeoning approaches for the calculation of the equation of state and transport properties in materials under extreme conditions. In the intermediate warm dense matter regime, a state between correlated condensed matter and kinetic plasma, electrons can range from being highly localized around nuclei to delocalized over the whole simulation cell. The plane-wave basis pseudopotential approach is thus the typical tool of choice for modeling such systems at the DFT level. Unfortunately, stochastic DFT methods scale as the square of the maximum plane-wave energy in this basis. To reduce the effect of this scaling and improve the overall description of the electrons within the pseudopotential approximation, we present stochastic and mixed DFT approaches developed and implemented within the projector augmented wave formalism. We compare results between the different DFT approaches for both single-point and molecular dynamics trajectories and present calculations of self-diffusion coefficients of solid density carbon from 1 to 50 eV.

Inelastic transport: a pseudoparticle approach.

We discuss a pseudoparticle NEGF approach as a tool to describe transport in molecular junctions in the language of many-body states of the molecule. A method developed by Oh et al. [Phys. Rev. B, 2011, 83, 205302] is applied to inelastic transport in the case of strong electron-vibron interaction. The approach can be seen as a generalization of the exact mapping developed by Bonca and Trugman [Phys. Rev. Lett., 1995, 75, 2566] which includes information on the Pauli exclusion principle and Fermi electron distribution in the leads. Within simple model calculations of inelastic transport in junctions, we compare the pseudoparticle approach to other approximate NEGF schemes.

Mixed stochastic-deterministic time-dependent density functional theory: application to stopping power of warm dense carbon.

Warm dense matter (WDM) describes an intermediate phase, between condensed matter and classical plasmas, found in natural and man-made systems. In a laboratory setting, WDM is often created dynamically. It is typically laser or pulse-power generated and can be difficult to characterize experimentally. Measuring the energy loss of high energy ions, caused by a WDM target, is both a promising diagnostic and of fundamental importance to inertial confinement fusion research. However, electron coupling, degeneracy, and quantum effects limit the accuracy of easily calculable kinetic models for stopping power, while high temperatures make the traditional tools of condensed matter, e.g. time-dependent density functional theory (TD-DFT), often intractable. We have developed a mixed stochastic-deterministic approach to TD-DFT which provides more efficient computation while maintaining the required precision for model discrimination. Recently, this approach showed significant improvement compared to models when compared to experimental energy loss measurements in WDM carbon. Here, we describe this approach and demonstrate its application to warm dense carbon stopping across a range of projectile velocities. We compare direct stopping-power calculation to approaches based on combining homogeneous electron gas response with bound electrons, with parameters extracted from our TD-DFT calculations.

An Ab Initio Multiple Cloning Method for Non-Adiabatic Excited-State Molecular Dynamics in NWChem.

The recently developed ab initio multiple cloning (AIMC) approach based on the multiconfigurational Ehrenfest (MCE) method provides a powerful and accurate way of describing the excited-state dynamics of molecular systems. The AIMC method is a controlled approximation to nonadiabatic dynamics with a particular strength in the proper description of decoherence effects because of the branching of vibrational wavepackets at a level crossing. Here, we report a new implementation of the AIMC algorithm in the open source NWChem computational chemistry program. The framework combines linear-response time-dependent density functional theory with Ehrenfest mean-field theory to determine the equations of motion for classical trajectories. The multidimensional wave function is decomposed into a superposition of Gaussian coherent states guided by Ehrenfest trajectories (i.e., MCE approach), which can clone with fully quantum mechanical amplitudes and phases. By using an efficient time-derivative based nonadiabatic coupling approach within the AIMC method, all observables are calculated on-the-fly in the nonadiabatic molecular dynamics process. As a representative example, we apply our implementation to study the ultrafast photoinduced electronic and vibrational energy transfer in a pyridine molecule. The effects of the cloning procedure on electronic and vibrational coherence, relaxation and unidirectional energy transfer are discussed. This new AIMC implementation provides a high-level nonadiabatic molecular dynamics framework for simulating photoexcited dynamics in complex molecular systems and experimentally relevant ultrafast spectroscopic probes, such as nonlinear coherent optical and X-ray signals.

Nonadiabatic Excited-State Molecular Dynamics Methodologies: Comparison and Convergence.

Direct atomistic simulation of nonadiabatic molecular dynamics is a challenging goal that allows important insights into fundamental physical phenomena. A variety of frameworks, ranging from fully quantum treatment of nuclei to semiclassical and mixed quantum-classical approaches, were developed. These algorithms are then coupled to specific electronic structure techniques. Such diversity and lack of standardized implementation make it difficult to compare the performance of different methodologies when treating realistic systems. Here, we compare three popular methods for large chromophores: Ehrenfest, surface hopping, and multiconfigurational Ehrenfest with ab initio multiple cloning (MCE-AIMC). These approaches are implemented in the NEXMD software, which features a common computational chemistry model. The resulting comparisons reveal the method performance for population relaxation and coherent vibronic dynamics. Finally, we study the numerical convergence of MCE-AIMC algorithms by considering the number of trajectories, cloning thresholds, and Gaussian wavepacket width. Our results provide helpful reference data for selecting an optimal methodology for simulating excited-state molecular dynamics.

Efficient identification of novel mutations in patients with limb girdle muscular dystrophy.

Limb girdle muscular dystrophy type 2 (LGMD2) is a genetically heterogeneous autosomal recessive disorder caused by mutations in 15 known genes. DNA sequencing of all candidate genes can be expensive and laborious, whereas a selective sequencing approach often fails to provide a molecular diagnosis. We aimed to efficiently identify pathogenic mutations via homozygosity mapping in a population in which the genetics of LGMD2 has not been well characterized. Thirteen consanguineous families containing a proband with LGMD2 were recruited from Saudi Arabia, and for 11 of these families, selected individuals were genotyped at 10,204 single nucleotide polymorphisms. Linkage analysis excluded all but one or two known genes in ten of 11 genotyped families, and haplotype comparisons between families allowed further reduction in the number of candidate genes that were screened. Mutations were identified by DNA sequencing in all 13 families, including five novel mutations in four genes, by sequencing at most two genes per family. One family was reclassified as having a different myopathy based on genetic and clinical data after linkage analysis excluded all known LGMD2 genes. LGMD2 subtypes A and B were notably absent from our sample of patients, indicating that the distribution of LGMD2 mutations in Saudi Arabian families may be different than in other populations. Our data demonstrate that homozygosity mapping in consanguineous pedigrees offers a more efficient means of discovering mutations that cause heterogeneous disorders than comprehensive sequencing of known candidate genes.

Inefficient dystrophin expression after cord blood transplantation in Duchenne muscular dystrophy.

We report a boy who received two allogeneic stem cell transplantations from umbilical cord donors to treat chronic granulomatous disease (CGD). The CGD was cured after the second transplantation, but 2.5 years later he was diagnosed with Duchenne muscular dystrophy (DMD). Examinations of his DNA, muscle tissue, and myoblast cultures derived from muscle tissue were performed to determine whether any donor dystrophin was being expressed. The boy was found to have a large-scale deletion on the X chromosome that spanned the loci for CYBB and DMD. The absence of dystrophin led to muscle histology characteristic of DMD. Analysis of myofibers demonstrated no definite donor cell engraftment. This case suggests that umbilical cord-derived hematopoietic stem cell transplantation will not be efficacious in the therapy of DMD without additional interventions that induce engraftment of donor cells in skeletal muscle.

Static and dynamic properties of multi-ionic plasma mixtures.

Complex plasma mixtures with three or more components are often encountered in astrophysics or in inertial confinement fusion (ICF) experiments. For mixtures containing species with large differences in atomic number Z, the modeling needs to consider at the same time the kinetic theory for low-Z elements combined with the theory of strongly coupled plasma for high-Z elements, as well as all the intermediate situations that can appear in multicomponent systems. For such cases, we study the pair distribution functions, self-diffusions, mutual diffusion, and viscosity for ternary mixtures at extreme conditions. These quantities can be produced from first principles using orbital free molecular dynamics at the computational expense of very intensive simulations to reach good statistics. Utilizing the first-principles results as reference data, we assess the merit of a global analytic model for transport coefficients, "pseudo-ions in jellium" (PIJ), based on an isoelectronic assumption (iso-n_{e}). With a multicomponent hypernetted-chain integral equation, we verify the quality of the iso-n_{e} prescription for describing the static structure of the mixtures. This semianalytical modeling compares well with the simulation results and allows one to consider plasma mixtures not accessible to simulations. Applications are given for the mix of materials in ICF experiments. A reduction of a multicomponent mixture to an effective binary mixture is also established in the hydrodynamic limit and compared with PIJ estimations for ICF relevant mixtures.

Improved Ehrenfest Approach to Model Correlated Electron-Nuclear Dynamics.

Mixed quantum-classical mechanical descriptions are critical to modeling coupled electron-nuclear dynamics, i.e., nonadiabatic molecular dynamics, relevant to photochemical and photophysical processes. We introduce an efficient description of such dynamics in terms of an effective Hamiltonian that not only properly captures electron-nuclear correlation effects but also helps develop an efficient computational method. In particular, we introduce a coupled Gaussian wavepacket parametrization of the nuclear wave function, which generalizes the Ehrenfest approach to account for electron-nuclei correlations. We test this new approach, Ehrenfest-Plus, on a suite of model problems that probe electron-nuclear correlation in nonadiabatic transitions. The high accuracy of our approach, combined with mixed quantum-classical efficiency, opens a path for improved simulation of nonadiabatic molecular dynamics in realistic molecular systems.

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.

LGMD2I in a North American population.

BACKGROUND: There is a marked variation in clinical phenotypes that have been associated with mutations in FKRP, ranging from severe congenital muscular dystrophies to limb-girdle muscular dystrophy type 2I (LGMD2I). METHODS: We screened the FKRP gene in two cohorts totaling 87 patients with the LGMD phenotype. RESULTS: The c.826C>A, p.L276I mutation was present in six patients and a compound heterozygote mutation in a seventh patient. Six patients had a mild LGMD2I phenotype, which resembles that of Becker muscular dystrophy. The other patient had onset before the age of 3 years, and thus may follow a more severe course. CONCLUSION: These findings suggest that LGMD2I may be common in certain North American populations. This diagnosis should be considered early in the evaluation of LGMD.

Correlation and transport properties for mixtures at constant pressure and temperature.

Transport properties of mixtures of elements in the dense plasma regime play an important role in natural astrophysical and experimental systems, e.g., inertial confinement fusion. We present a series of orbital-free molecular dynamics simulations on dense plasma mixtures with comparison to a global pseudo ion in jellium model. Hydrogen is mixed with elements of increasingly high atomic number (lithium, carbon, aluminum, copper, and silver) at a fixed temperature of 100 eV and constant pressure set by pure hydrogen at 2g/cm^{3}, namely, 370 Mbars. We compute ionic transport coefficients, such as self-diffusion, mutual diffusion, and viscosity for various concentrations. Small concentrations of the heavy atoms significantly change the density of the plasma and decrease the transport coefficients. The structure of the mixture evidences a strong Coulomb coupling between heavy ions and the appearance of a broad correlation peak at short distances between hydrogen atoms. The concept of an effective one component plasma is used to quantify the overcorrelation of the light element induced by the admixture of a heavy element.

Fusion strategies for selecting multiple tuning parameters for multivariate calibration and other penalty based processes: A model updating application for pharmaceutical analysis.

New multivariate calibration methods and other processes are being developed that require selection of multiple tuning parameter (penalty) values to form the final model. With one or more tuning parameters, using only one measure of model quality to select final tuning parameter values is not sufficient. Optimization of several model quality measures is challenging. Thus, three fusion ranking methods are investigated for simultaneous assessment of multiple measures of model quality for selecting tuning parameter values. One is a supervised learning fusion rule named sum of ranking differences (SRD). The other two are non-supervised learning processes based on the sum and median operations. The effect of the number of models evaluated on the three fusion rules are also evaluated using three procedures. One procedure uses all models from all possible combinations of the tuning parameters. To reduce the number of models evaluated, an iterative process (only applicable to SRD) is applied and thresholding a model quality measure before applying the fusion rules is also used. A near infrared pharmaceutical data set requiring model updating is used to evaluate the three fusion rules. In this case, calibration of the primary conditions is for the active pharmaceutical ingredient (API) of tablets produced in a laboratory. The secondary conditions for calibration updating is for tablets produced in the full batch setting. Two model updating processes requiring selection of two unique tuning parameter values are studied. One is based on Tikhonov regularization (TR) and the other is a variation of partial least squares (PLS). The three fusion methods are shown to provide equivalent and acceptable results allowing automatic selection of the tuning parameter values. Best tuning parameter values are selected when model quality measures used with the fusion rules are for the small secondary sample set used to form the updated models. In this model updating situation, evaluation of all possible models, thresholding, and iterative SRD performed equivalently for the three fusion rules with TR and PLS performed worse. While the application is model updating, the fusion processes are applicable to other situations requiring selection of multiple tuning parameter values.