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Amorphous graphene or amorphous monolayer carbon (AMC) is a family of carbon films that exhibit a surprising sensitivity of electronic conductance to morphology. We combine deep learning-enhanced simulation techniques with percolation theory to analyze three morphologically distinct mesoscale AMCs. Our approach avoids the pitfalls of applying periodic boundary conditions to these fundamentally aperiodic systems or equating crystalline inclusions with conducting sites. We reproduce the previously reported dependence of charge conductance on morphology and explore the limitations of partial morphology descriptors in witnessing conductance properties. Finally, we perform crystallinity analysis of conductance networks along the electronic energy spectrum and show that they metamorphose from being localized on crystallites at band edges to localized on defects around the Fermi energy opening the possibility of control through gate voltage.

Amorphous solids form an enormous and underutilized class of materials. In order to drive the discovery of new useful amorphous materials further we need to achieve a closer convergence between computational and experimental methods. In this review, we highlight some of the important gaps between computational simulations and experiments, discuss popular state-of-the-art computational techniques such as the Activation Relaxation Technique nouveau (ARTn) and Reverse Monte Carlo (RMC), and introduce more recent advances: machine learning interatomic potentials (MLIPs) and generative machine learning for simulations of amorphous matter, e.g., the Morphological Autoregressive Protocol (MAP). Examples are drawn from the amorphous silicon and silica literature as well as from molecular glasses. Our outlook stresses the need for new computational methods to extend the time- and length- scales accessible through numerical simulations.

Signed Particle Monte Carlo (SPMC) approach has been used in the past to model steady-state and transient dynamics of the Wigner quasi-distribution for electrons in low dimensional semiconductors. Here we make a step towards high-dimensional quantum phase-space simulation in chemically relevant scenarios by improving the stability and memory demands of SPMC in 2D. We do so by using an unbiased propagator for SPMC to improve trajectory stability and by applying machine learning to reduce memory demands for storage and manipulation of the Wigner potential. We perform computational experiments on a 2D double-well toymodel of proton transfer and demonstrate stable pico-second-long trajectories that require only a modest computational effort.

Disordered molecular systems such as amorphous catalysts, organic thin films, electrolyte solutions, and water are at the cutting edge of computational exploration today. Traditional simulations of such systems at length-scales relevant to experiments in practice require a compromise between model accuracy and quality of sampling. To remedy the situation, we have developed an approach based on generative machine learning called the Morphological Autoregressive Protocol (MAP) which provides computational access to mesoscale disordered molecular configurations at linear cost at generation for materials in which structural correlations decay sufficiently rapidly. The algorithm is implemented using an augmented PixelCNN deep learning architecture that we previously demonstrated produces excellent results in 2 dimensions (2D) for mono-elemental molecular systems. Here, we extend our implementation to multielemental 3D and demonstrate performance using water as our test system in two scenarios: 1. liquid water, and 2. a sample conditioned on the presence of a rare motif. We trained the model on small-scale samples of liquid water produced using path-integral molecular dynamics simulation including nuclear quantum effects under ambient conditions. MAP-generated water configurations are shown to accurately reproduce the properties of the training set and to produce stable trajectories when used as initial conditions in classical and quantum dynamical simulations. We expect our approach to perform equally well on other disordered molecular systems while offering unique advantages in situations when the disorder is quenched rather than equilibrated.

Inverse design of short single-stranded RNA and DNA sequences (aptamers) is the task of finding sequences that satisfy a set of desired criteria. Relevant criteria may be, for example, the presence of specific folding motifs, binding to molecular ligands, sensing properties, etc. Most practical approaches to aptamer design identify a small set of promising candidate sequences using high-throughput experiments (e.g. SELEX), and then optimize performance by introducing only minor modifications to the empirically found candidates. Sequences that possess the desired properties but differ drastically in chemical composition will add diversity to the search space and facilitate the discovery of useful nucleic acid aptamers. Systematic diversification protocols are needed. Here we propose to use an unsupervised machine learning model known as the Potts model to discover new, useful sequences with controllable sequence diversity. We start by training a Potts model using the maximum entropy principle on a small set of empirically identified sequences unified by a common feature. To generate new candidate sequences with a controllable degree of diversity, we take advantage of the model's spectral feature: an energy bandgap separating sequences that are similar to the training set from those that are distinct. By controlling the Potts energy range that is sampled, we generate sequences that are distinct from the training set yet still likely to have the encoded features. To demonstrate performance, we apply our approach to design diverse pools of sequences with specified secondary structure motifs in 30-mer RNA and DNA aptamers.

Design of de novo biological sequences with desired properties, like protein and DNA sequences, often involves an active loop with several rounds of molecule ideation and expensive wet-lab evaluations. These experiments can consist of multiple stages, with increasing levels of precision and cost of evaluation, where candidates are filtered. This makes the diversity of proposed candidates a key consideration in the ideation phase. In this work, we propose an active learning algorithm leveraging epistemic uncertainty estimation and the recently proposed GFlowNets as a generator of diverse candidate solutions, with the objective to obtain a diverse batch of useful (as defined by some utility function, for example, the predicted anti-microbial activity of a peptide) and informative candidates after each round. We also propose a scheme to incorporate existing labeled datasets of candidates, in addition to a reward function, to speed up learning in GFlowNets. We present empirical results on several biological sequence design tasks, and we find that our method generates more diverse and novel batches with high scoring candidates compared to existing approaches., Comment: ICML 2022. 15 pages, 3 figures. Code available at: https://github.com/MJ10/BioSeq-GFN-AL. Updated GFP results

In molecular electronic conduction, exotic lattice morphologies often give rise to exotic behaviors. Among 2D systems, graphene is a notable example. Recently, a stable amorphous version of graphene called Monolayer Amorphous Carbon (MAC) was synthesized. MAC poses a new set of questions regarding the effects of disorder on conduction. In this Letter, we perform ensemble-level computational analysis of the coherent electronic transmission through MAC nano-fragments in search of defining characteristics. Our analysis, relying on a semi-empirical Hamiltonian (Pariser-Parr-Pople) and Landauer theory, showed that states near the Fermi energy ($E_F$) in MAC inherit partial characteristics of analogous surface states in graphene nano-fragments. Away from $E_F$, current is carried by a set of delocalized states which transition into a subset of insulating interior states at the band edges. Finally, we also found that quantum interference between the frontier orbitals is a common feature among MAC nano-fragments.

Coarse-grained simulations of conjugated polymers have become a popular way of investigating the device physics of organic photovoltaics. While UV-Vis spectroscopy remains one of key experimental methods for the interrogation of these devices, a rigorous bridge between coarse-grained simulations and spectroscopy has never been established. Here we address this challenge by developing a method that predicts spectra of conjugated polymers directly from coarse-grained representations while avoiding ad-hoc procedures such as back-mapping from coarse-grained to atomistic representations followed by computing the spectra using standard quantum chemistry methods. Our approach is based on a generative deep learning model: the long-short-term memory recurrent neural network (LSTM-RNN) and it is suggested by the apparent similarity between natural languages and the mathematical structure of the perturbative expansions of the excited state energies due to small fluctuations of the polymer conformation. We use this model to demonstrate a dangerous discrepancy between the spectra obtained in the coarse-grained representation and after the back-mapping. This indicates that standard protocols may require additional fine-tuning in order to become reliable and that our model presents a novel tool uniquely suited for improving the back-mapping protocols and for including spectral data in the development of coarse-grained potentials.

The optoelectronic properties of amorphous conjugated polymers are sensitive to conformational disorder and spectroscopy provides the means for structural characterization of the fragments of the chain which interact with light - "chromophores". A faithful interpretation of spectroscopic conformational signatures, however, presents a key challenge. We investigate the relationship between the ground state optical gaps, the properties of the excited states, and the structural features of chromophores of a single molecule poly(3-hexyl)-thiophene (P3HT), using quantum-classical atomistic simulations. Our results demonstrate that chromophoric disorder reflects an interplay between excited state de-localization and electron-hole polarization, and is controlled by torsional disorder that is specifically associated with the presence of side chains. Within this conceptual framework, we predict and explain a counter-intuitive spectral signature of P3HT: a red-shifted absorption, despite shortening of chromophores, with increasing temperature.

We look for manifestations of quantum interference effects in the Seebeck coefficient of a molecular junction, when the electronic conductance exhibits pronounced destructive interference features due to the presence of quasi-degenerate electronic states which differ in their spatial symmetry. We perform our analysis by considering three separate limits for electron transport: coherent, fully dephased, and suffering inelastic scattering with molecular vibrations. We find that while the conductance displays strong signatures of the underling transport mechanisms: destructive quantum interference features in the coherent case and thermal activation characteristics in the inelastic limit, the Seebeck coefficient conceals details of electron dynamics while it robustly reveals information about the energy characteristics of the junction. We provide closed-form expressions for the electronic conductance and the thermopower of our system as a function of temperature, gate voltage and hybridization energy in different transport limits, then exemplify our analysis on a specific conjugated molecule with quasi-degenerate orbitals of different spatial symmetry.

We study electron transport in nanojunctions in which an electron on a quantum dot or a molecule is interacting with an N-state local impurity, a harmonic ("Holstein") mode, or a two-state system ("spin"). These two models, the Anderson-Holstein model and the spin-fermion model, can be conveniently transformed by a shift transformation into a form suitable for a perturbative expansion in the tunneling matrix element. We explore the current-voltage characteristics of the two models in the limit of high temperature and weak electron-metal coupling using a kinetic rate equation formalism, considering both the case of an equilibrated impurity, and the unequilibrated case. Specifically, we show that the analog of the Franck-Condon blockade physics is missing in the spin-fermion model. We complement this study by considering the low-temperature quantum adiabatic limit of the dissipative spin-fermion model, with fast tunneling electrons and a slow impurity. While a mean-field analysis of the Anderson-Holstein model suggests that nonlinear functionalities, bistability and hysteresis may develop, such effects are missing in the spin-fermion model at the mean-field level.

We study Landau-Zener transitions between two states with the addition of a shared discretized continuum. The continuum allows for population decay from the initial state as well as indirect transitions between the two states. The probability of nonadiabatic transition in this multichannel model preserves the standard Landau-Zener functional form except for a shift in the usual exponential factor, reflecting population transfer into the continuum. We provide an intuitive explanation for this behavior assuming independent individual transitions between pairs of states. In contrast, the probability of survival in the ground state at long time shows a novel, non-monotonic, functional form, with an oscillatory behavior in the sweep rate at low sweep rate values. We contrast the behavior of this open-multistate model to other generalized Landau-Zener models incorporating an environment: the stochastic Landau-Zener model and the dissipative case, where energy dissipation and thermal excitations affect the adiabatic region. Finally, we present evidence that the continuum of states may act to shield the two-state Landau-Zener transition probability from the effect of noise.

We expand iterative numerically-exact influence functional path-integral tools and present a method capable of following the nonequilibrium time evolution of subsystems coupled to multiple bosonic and fermionic reservoirs simultaneously. Using this method, we study the real-time dynamics of charge transfer and vibrational mode excitation in an electron conducting molecular junction. We focus on nonequilibrium vibrational effects, particularly, the development of vibrational instability in a current-rectifying junction. Our simulations are performed by assuming large molecular vibrational anharmonicity (or low temperature). This allows us to truncate the molecular vibrational mode to include only a two-state system. Exact numerical results are compared to perturbative Master equation calculations demonstrating an excellent agreement in the weak electron-phonon coupling regime. Significant deviations take place only at strong coupling. Our simulations allow us to quantify the contribution of different transport mechanisms, coherent dynamics and inelastic transport, in the overall charge current. This is done by studying two model variants: The first admits inelastic electron transmission only, while the second one allows for both coherent and incoherent pathways.

It is known that quantum systems yield non-exponential (power law) decay on long time scales, associated with continuum threshold effects contributing to the survival probability for a prepared initial state. For an open quantum system consisting of a discrete state coupled to continuum, we study the case in which a discrete bound state of the full Hamiltonian approaches the energy continuum as the system parameters are varied. We find in this case that at least two regions exist yielding qualitatively different power law decay behaviors; we term these the long time `near zone' and long time `far zone.' In the near zone the survival probability falls off according to a $t^{-1}$ power law, and in the far zone it falls off as $t^{-3}$. We show that the timescale $T_Q$ separating these two regions is inversely related to the gap between the discrete bound state energy and the continuum threshold. In the case that the bound state is absorbed into the continuum and vanishes, then the time scale $T_Q$ diverges and the survival probability follows the $t^{-1}$ power law even on asymptotic scales. Conversely, one could study the case of an anti-bound state approaching the threshold before being ejected from the continuum to form a bound state. Again the $t^{-1}$ power law dominates precisely at the point of ejection., Comment: 15 pages, 9 figures