In single-molecule electronics, 4,4 '-bipyridine is a well-characterized molecule that serves both as a fundamental testbed for developing experimental methodologies and showcases the complex behaviors expected from molecular electronic components. In break junction experiments, it is generally understood to exhibit a high- and a low-conductance state that are attributed to a tilted and stretched single-molecule configuration. Despite this established view, we suggest a supramolecular origin for these conductance states that has not previously been considered. Our findings indicate that the high- and low-conductance states may arise from the presence of two molecules and one molecule, respectively, challenging the conventional interpretation. Using a state-of-the-art machine learning force field called the neuroevolution potential, we find that the conventional interpretation of a tilted and stretched configuration is inconsistent with our simulations. Instead, our results suggest that the presence of two molecules promotes junction geometries and gold rearrangements that stabilize a high-conductance state whose transmission exceeds twice that of the low-conductance state. Furthermore, we compare this interpretation to the existing literature of diverse experimental data on 4,4 '-bipyridine in break junctions and find that it is consistent with the broader body of experimental evidence. Our results highlight the structural complexity of molecular behavior within break junctions, suggesting even more complex dynamics than originally anticipated. In this light, a broader examination of the dynamics of molecules in single-molecule break junctions with machine learning-assisted molecular dynamics is warranted.

ABSTRACT The efficiency of organic electronic devices relies on application of organic gate dielectric materials. Such organic films should exhibit high chemical/thermal stability, aromatic functionality compatible with organic semiconductors, and low gate leakage currents in combination with low thickness to reduce the operating voltage. An interesting class of materials for such applications are self‐assembled monolayers (SAMs) among which the N ‐heterocyclic carbenes (NHC) are known for their high chemical/thermal stability. The conductivity of NHC SAMs, however, has been sparsely explored and their electrical properties remain controversial. Here we report conductivity analysis for a well‐defined series of aromatic NHC SAMs. Our data show that all analyzed monolayers are highly insulating and in particular the shortest possible NHC of just ∼3.3 Å is by 5 orders of magnitude more insulating than standard insulators based on alkanethiolate SAM of the same length. Our calculations indicate the absence of destructive quantum interference (DQI) effect which has been considered responsible for suppression of conductivity in aromatic molecules. The suppression of SAMs conductivity just via selection of the imidazolium‐based bonding group is conceptually simpler opening possibility of using NHC SAMs as an ultra‐thin, and exceptionally insulating, aromatic monolayers for functionalization of the gate electrodes.

Classical simulation of quantum computers is essential for designing and benchmarking quantum algorithms. Here we present phase2, a full-state-vector simulator optimised for sequences of many-qubit Pauli rotations on distributed CPU and GPU clusters. Exploiting the common-suffix structure of Pauli-rotation circuits, the implementation reduces inter-node communication and achieves two orders of magnitude speedup for grouped rotations. We demonstrate weak and strong scaling to 40 qubits across 512 NVIDIA H100 GPUs using 32 TB of distributed memory. Applying the simulator to Hamiltonian time evolution of ruthenium-ligand active spaces up to 40 qubits, we find that the empirical Trotter error lies more than two orders of magnitude below the rigorous analytic upper bound for every active space in which the fit converged (up to 32 qubits). Practical circuit depths and simulation costs are therefore substantially smaller than the conservative estimates suggest.

Broad terms in the literature, such as nonstatistical reactivity or nontraditional luminescence, emerge when standard theories fail to explain experimental results. In the case of nonstatistical and dynamic effects, reaction rates and product ratios may vary wildly from transition state theory (TST) predictions and are commonly accompanied by a lack of temperature dependence. In this Tutorial, we explain how to use modern and freely available computational chemistry tools to model apparently nonstatistical reactions in relatively large organic molecules, using a concrete example of the thermal Garratt-Braverman/[1,5]-H shift of an ene-diallene, such that a non-expert can easily replicate our approach by following our steps. As a team of synthetic organic chemists and computational chemists, we aim to promote the use of preparatory computational work that can aid in reaction design during the experimental process rather than merely serving as complementary data to finished experimental studies. For this reason, we also offer an overview of the literature leading into more advanced computational techniques. Working through the example of the thermal Garratt-Braverman/[1,5]-H shift, we illustrate how theory and experiment can be used together to investigate the possibility of parallel light-enabled reactions and the role of tunneling effects and to perform careful variable temperature analysis when it becomes necessary. As the motifs of reactive π-π* absorptions, hydrogen transfers, and diradical intermediates are quite common, the points presented in this Tutorial are broadly applicable and indicative of the underlying complexity behind many chemical reactions that exhibit unexpected rates and ratios. The failure of TST also underscores a critical limitation of massive reaction network discovery schemes that heavily rely on calculated ground-state activation energies as well as the potential pitfalls of the conventional free energy diagram mindset.

ABSTRACT We report a robust redox‐active N‐heterocyclic carbene (NHC) monolayer that exhibits synapse‐like behavior driven by proton‐coupled electron transfer (PCET). Our quinone‐functionalized NHC (Rex–NHC) forms densely packed, upright self‐assembled monolayers (SAMs) on Au, confirmed by cyclic voltammetry, x‐ ray photoelectron spectroscopy, sum‐frequency generation spectroscopy, and infrared reflection absorption spectroscopy. Molecular junctions built as Au–Rex–NHC//Ga 2 O 3 /EGaIn operate over ± 2 V and can withstand electric fields up to 3.3 GV/m. Bias‐induced PCET toggles between quinone (off) and hydroquinone (on) states, yielding reversible hysteresis with on/off ratios up to 1.9 × 10 2 . The devices exhibit spike‐timing and spike‐rate‐dependent plasticity, demonstrating for the first time molecular‐level neuromorphic behavior using NHCs as anchoring groups.

The concept of aromaticity is one of the most fundamental principles for understanding the properties and reactivities of organic molecules. However, in molecular electronics research, it has been shown that aromaticity is not necessarily advantageous for electron transmission across electrode-molecule-electrode junctions. In this work, we introduce formally antiaromatic, yet planar N,N'-disubstituted dihydrophenazines as a compelling building block for exploring molecular conductance properties beyond the scope of classical aromatic molecules and compare anchor group-modified dihydrophenazines and structurally closely related anthracenes. We find that molecular conductance increases by 1.5 orders of magnitude from aromatic anthracenes to their phenazine congeners, where the central ring attains partially antiaromatic character. Oxidation of the dihydrophenazine core results accordingly in conductance attenuation.

The compilation of an algorithm can vary significantly with the choice of physical hardware platform and error correction model. Yet, current compilation frameworks typically commit to a single architecture-hardware configuration, making it difficult to assess resource estimates across platforms. We present a platform-aware compilation framework that re-compiles a quantum circuit into a hardware-compatible instruction set as well as fault-tolerant operations and provides end-to-end resource estimates in terms of physical-qubit count, time-to-solution, and classical processing time. We benchmark the framework by obtaining end-to-end resource estimates for different compilers, each tailored to the functionalities of specific hardware modalities: connectivity, clock speed, and noise model. As part of this framework, we introduce a transversal active volume (t-AV) compilation architecture designed for the efficient execution of fault-tolerant operations in platforms supporting long-range logical connectivity. We benchmark the framework for Hamiltonian simulation of the 2D Fermi Hubbard model as well as for eigenenergy estimation of a small molecule (trimethylenemethane) as a candidate for early fault-tolerant demonstration of quantum chemistry. For the latter, we show that end-to-end quantum simulations can be achieved with ∼10^4 physical qubits and runtimes ranging from 10^2 ms (photonics, superconducting) to 10^5 ms (neutral atoms).

The semi-empirical Pariser–Parr–Pople (PPP) Hamiltonian is reviewed for its ability to provide a minimal model of the chemistry of conjugated π-electron systems, and its current applications and limitations are discussed. Since its inception, the PPP Hamiltonian has helped in the development of new computational approaches in instances where compute is constrained due to its inherent approximations that allow for an efficient representation and calculation of many systems of chemical and technological interest. The crucial influence of electron correlation on the validity of these approximations is discussed, and we review how PPP full configuration interaction-type calculations have enabled a deeper understanding of conjugated polymer systems. More recent usage of the PPP Hamiltonian includes its application in high-throughput screening activities to the inverse design problem, which we illustrate here for two specific fields of technological interest: singlet fission and singlet–triplet inverted energy gap molecules. Finally, we conjecture how utilizing the PPP model in quantum computing applications could be mutually beneficial.

Fault-tolerant quantum computing is a promising tool for simulating molecules and materials, but frequently-considered applications require substantial resources, and the gap between hardware capabilities and requirements remains significant. We propose quantum simulation of nanographene π-systems as relevant and scalable problems to span the gap between early and large-scale fault-tolerant quantum computing. We examine the efficiency of Trotterized quantum simulation, present a detailed analysis of worst-case, average-case and energy eigenvalue Trotter errors, and show that these Trotter error estimates vary by orders of magnitude. Trotter eigenvalue errors are obtained from a novel tensor-network-based approach which allows spectral analysis of product formulas for systems beyond brute-force calculation. Notably, we observe a Trotter error cancellation phenomenon whereby the Trotter error for energy differences between low-lying eigenstates is significantly smaller than the Trotter error for absolute energies, resulting in approximately an order of magnitude circuit depth reduction for quantum phase estimation calculation of energy gaps. This is a significant result because for most chemical applications, only energy differences are of practical relevance. We estimate that calculation of energy gaps to chemical accuracy between the ground- and excited-states within the Pariser–Parr–Pople model for large 2D nanographenes (up to 140 spin orbitals) requires circuits with < 3.2 × 10^7 Toffoli gates. This work shows that considering details of chemically-relevant applications and exploiting error cancellation can lead to substantial reductions in resource requirements.

Broad terms in the literature, such as nonstatistical reactivity or nontraditional luminescence, emerge when standard theories fail to explain experimental results. In the case of nonstatistical and dynamic effects, reaction rates and product ratios may vary wildly from transition state theory (TST) predictions and are commonly accompanied by a lack of temperature dependence. In this tutorial, we explain how to use modern and freely available computational chemistry tools to model a reported nonstatistical reaction of a relatively large organic molecule, the thermal Garratt–Braverman/[1,5]-H shift of an ene-diallene, such that a non-expert can easily replicate our approach by following our steps. As a team of synthetic organic chemists and computational chemists, we also hope to encourage the use of preparatory computational work that may aid in reaction design during the experimental process, not just as complementary data to finished experimental studies. Through this approach, we discover that the thermal Garratt–Braverman/[1,5]-H shift exhibits a parallel light-enabled reaction that bypasses the rate-limiting first step. Additionally, when tunneling effects are accounted for, TST predictions return to realistic values, only to be disproved again by careful variable temperature experiments. As the motifs of reactive π−π∗ absorptions, hydrogen transfers, and diradical intermediates are quite common, the points presented in this paper are broadly applicable and indicative of the underlying complexity behind many chemical reactions that exhibit unexpected rates and ratios. The failure of TST also underscores a critical limitation of massive reaction network discovery schemes that heavily rely on calculated ground state activation energies and the potential pitfalls of the conventional free energy diagram.

This work experimentally investigates a mechanism of rectification in molecular junctions proposed by van Dyck and Ratner, supported by theoretical modeling. The defining feature of the mechanism is the spatial separation of frontier molecular orbitals such that each tracks the two leads independently. We achieve this orbital separation in oligophenyleneethylene molecular wires with electron-rich thiols and electron-poor pyridines at their termini. Density functional theory (DFT) calculations show localization of the frontier molecular orbitals at these termini that increases with the molecular length. Measurements of rectification ratios in molecular ensemble junctions using eutectic Ga-In (EGaIn) top-contacts and Au bottom-contacts reveal a length dependence that is almost completely insensitive to the insertion of a nonconjugated methylene spacer between the thiol anchor and conjugated backbone. Simulations using nonequilibrium Green's function + DFT methods show that transport is dominated by the lowest unoccupied molecular orbitals, which track the EGaIn electrode, leading to rectification. These results validate the approach of creating molecular rectifiers by spatially separating the frontier molecular orbitals and show an approach to modeling their behavior under bias in ensemble junctions.

Thermal management in molecular systems presents challenges that require a deeper understanding of phonon transport, an essential aspect of heat conduction in single molecule junctions. Our work introduces the use of heavy atoms as a strategy for suppressing phonon transport in organic molecules. Starting with a 1D force-constant model and density functional theory calculations of model chemical systems, we illustrate how increasing the mass of a central atom affects the phonon transmission and conductance. Following this, we turn our attention to the chemically accessible systems of metallapolyynes and extended metal atom chains (EMACs). Our findings suggest that several of the studied EMACs exhibit thermal conductance either near or below a recently proposed threshold of 10 pW/K – a crucial step towards reaching high thermoelec- tric figure of merits. Specifically, we predict that the molecule MoMoNi(npo)4 (NCS)2 has a thermal conductance of just 8.3 pW/K at 300 K. Our results demonstrate that conceptually simple chemical modifications can markedly reduce the thermal conductance of single molecules; these results both deepens our understanding of the mechanisms driving single-molecule phonon thermal conductance and suggest a path towards using single molecules as thermoelectric materials.

In single-molecule junctions (SMJs), functional substitution or doping generally has only a modest impact on the conductance. To achieve significant conductance modulation, harnessing the quantum interference (QI) effect becomes essential, which requires significant changes in the structural topology, charge state, or redox reactions. This raises a key question: Can chemical substitution or doping alone be strong enough to alter QI behavior and considerably modulate conductance? To explore this, we studied the effect of isoelectronic B-N substitution on QI in synthetically relevant coronene-based SMJs by selectively replacing C═C bonds with B-N pairs at various positions and patterns, employing a combination of density functional theory and non-equilibrium Green's function methods. Calculations reveal that position- and pattern-dependent B-N substitutions can strongly perturb the molecular orbital symmetry, phases, and energies that switch QI characteristics and finally modulate the conductance remarkably. This work demonstrates a novel design strategy to harness the QI effect in polyaromatic hydrocarbon-based SMJs.

Large-scale classical simulation of quantum computers is crucial for benchmarking quantum algorithms, establishing boundaries of quantum advantage and exploring heuristic quantum algorithms. We present a full-state vector simulation algorithm and software implementation designed to perform HPC simulation of layers of rotations around a string of Pauli operators. We demonstrate robust scalability of the simulation method on large distributed CPU and GPU systems. Our distributed computation harnessed up to 16 384 CPU cores and 512 NVIDIA H100 GPUs, using 32 TB of memory. The simulator significantly outperforms other high-performance libraries, showing a typical speedup of 10-100 for large-scale multi-GPU workloads. As a first application of our approach, we report a numerical experiment aimed at simulating exactly Hamiltonian dynamics of up to 40 qubits to investigate the Trotter error for a quantum chemistry problem. Bounding the Trotter error is important for evaluating the cost of quantum algorithms for chemistry, and rigorous bounds are often conservative, as our simulations confirm. Our software, specifically designed for quantum time evolution applications, is also well equipped to manage circuits that utilize standard gate sets.

Quantum algorithms have the potential to revolutionize our understanding of open quantum systems in chemistry. In this work, we demonstrate that a repeated interaction model, which could serve as the foundation for a digital quantum algorithm, can effectively reproduce non-Markovian electron transfer dynamics under four different donor-acceptor parameter regimes and for a donor-bridge-acceptor system. We systematically explore how the model scales for the regimes. Notably, our approach exhibits favorable scaling in the required repeated interaction duration as the electronic coupling, temperature, damping rate, and system size increase. Furthermore, a single Trotter step per repeated interaction leads to an acceptably small error, and high-fidelity initial states can be prepared with a short time evolution. This efficiency highlights the potential of the model for tackling increasingly complex systems. When fault-tolerant quantum hardware becomes available, algorithms based on this model could be extended to incorporate structured baths, additional energy levels, or more intricate coupling schemes, enabling the simulation of real-world open quantum systems that remain beyond the reach of classical computation.

Quantum simulations of strongly interacting fermionic systems, such as those described by the Hubbard model, are promising candidates for useful early fault-tolerant quantum computing applications. This paper presents tile Trotterization, a generalization of plaquette Trotterization, which uses a set of tiles to construct Trotter decompositions of arbitrary lattice Hubbard models. The tile Trotterization scheme also enables the simulation of more complex models, including the extended Hubbard model. We improve previous Hubbard-model commutator bounds, further provide tight commutator bounds for periodic extended Hubbard models, and demonstrate the use of tensor network methods for this task. We consider applications of tile Trotterization to simulate hexagonal lattice Hubbard models and compare the resource requirements of tile Trotterization for performing quantum phase estimation to a qubitization-based approach, demonstrating that tile Trotterization scales more efficiently with system size. These advancements significantly broaden the potential applications of early fault-tolerant quantum computers to models of practical interest in materials research and organic chemistry.

When a small electric bias is applied to a single-molecule junction, current will flow through the molecule via a tunneling mechanism. In molecules with a cyclic or helical structure there may be circular currents, giving rise to a uni-directional magnetic field. Here, we implement the Biot Savart law and calculate the magnetic field resulting from the ballistic current density for a selection of molecules. We find that three prerequisites are important for achieving a substantial magnetic field in a single-molecule junction. (1) The current must be high, (2) the ring current must be unidirectional within the bias window, and (3) the diameter of the ring current must be small. We identify both cyclic and linear molecules that potentially fulfill these requirements. In cyclic annulenes with bond-length alternation the current-induced magnetic field can approach the mT-range whereas archetypical cyclic molecules, such as benzene, are not suitable candidates for the generation of a substantial magnetic field. In linear carbon chains with circular currents due to their helical π-systems, the magnetic field is in the mT-range. When the bias window is gated closer to resonance, we show that the magnetic field can potentially reach the sub-Tesla range. Our results provide proof-of-concept for achieving experimentally relevant current-induced magnetic fields in molecular wires at low bias.

The properties and dynamics of gold nanowires have been studied for decades as an important testbed for several physical phenomena. Gold nanowires forming at contacts are an integral part of molecular junctions used to study the electronic and thermal properties of single molecules. However, the huge discrepancy in time scales between experiments and simulations, compounded by the limited accuracy of classical force fields, has posed a challenge in accurately simulating realistic junctions. Here, we show that machine-learning force fields uncover phenomena not captured by classical force fields when modeling Au-Au pulling junctions. Our simulations show a dependency of the average breaking distance on the pulling speed, highlighting a more complex behavior than previously thought. Our results demonstrate that the use of more accurate force fields to simulate metallic nanowires is essential for capturing the complexity of their structural evolution in break junction experiments. Our developments advance the modeling accuracy of molecular junctions, bridging the gap between experimental and simulation time scales.