Dimension-free path-integral molecular dynamics without preconditioning.

Convergence with respect to imaginary-time discretization (i.e., the number of ring-polymer beads) is an essential part of any path-integral-based molecular dynamics (MD) calculation. However, an unfortunate property of existing non-preconditioned numerical integration schemes for path-integral molecular dynamics-including essentially all existing ring-polymer molecular dynamics (RPMD) and thermostatted RPMD (T-RPMD) methods-is that for a given MD time step, the overlap between the exact ring-polymer Boltzmann-Gibbs distribution and that sampled using MD becomes zero in the infinite-bead limit. This has clear implications for hybrid Metropolis Monte Carlo/MD sampling schemes, and it also causes the divergence with bead number of the primitive path-integral kinetic-energy expectation value when using standard RPMD or T-RPMD. We show that these and other problems can be avoided through the introduction of "dimension-free" numerical integration schemes for which the sampled ring-polymer position distribution has non-zero overlap with the exact distribution in the infinite-bead limit for the case of a harmonic potential. Most notably, we introduce the BCOCB integration scheme, which achieves dimension freedom via a particular symmetric splitting of the integration time step and a novel implementation of the Cayley modification [R. Korol et al., J. Chem. Phys. 151, 124103 (2019)] for the free ring-polymer half-steps. More generally, we show that dimension freedom can be achieved via mollification of the forces from the external physical potential. The dimension-free path-integral numerical integration schemes introduced here yield finite error bounds for a given MD time step, even as the number of beads is taken to infinity; these conclusions are proven for the case of a harmonic potential and borne out numerically for anharmonic systems that include liquid water. The numerical results for BCOCB are particularly striking, allowing for nearly three-fold increases in the stable time step for liquid water with respect to the Bussi-Parrinello (OBABO) and Leimkuhler (BAOAB) integrators, while introducing negligible errors in the calculated statistical properties and absorption spectrum. Importantly, the dimension-free, non-preconditioned integration schemes introduced here preserve ergodicity and global second-order accuracy, and they remain simple, black-box methods that avoid additional computational costs, tunable parameters, or system-specific implementations.

Cayley modification for strongly stable path-integral and ring-polymer molecular dynamics.

Path-integral-based molecular dynamics (MD) simulations are widely used for the calculation of numerically exact quantum Boltzmann properties and approximate dynamical quantities. A nearly universal feature of MD numerical integration schemes for equations of motion based on imaginary-time path integrals is the use of harmonic normal modes for the exact evolution of the free ring-polymer positions and momenta. In this work, we demonstrate that this standard practice creates numerical artifacts. In the context of conservative (i.e., microcanonical) equations of motion, it leads to numerical instability. In the context of thermostated (i.e., canonical) equations of motion, it leads to nonergodicity of the sampling. These pathologies are generally proven to arise at integration time steps that depend only on the system temperature and the number of ring-polymer beads, and they are numerically demonstrated for the cases of conventional ring-polymer MD (RPMD) and thermostated RPMD (TRPMD). Furthermore, it is demonstrated that these numerical artifacts are removed via replacement of the exact free ring-polymer evolution with a second-order approximation based on the Cayley transform. The Cayley modification introduced here can immediately be employed with almost every existing integration scheme for path-integral-based MD-including path-integral MD (PIMD), RPMD, TRPMD, and centroid MD-providing strong symplectic stability and ergodicity to the numerical integration, at no penalty in terms of computational cost, algorithmic complexity, or accuracy of the overall MD time step. Furthermore, it is shown that the improved numerical stability of the Cayley modification allows for the use of larger MD time steps. We suspect that the Cayley modification will therefore find useful application in many future path-integral-based MD simulations.

Machine Learning Prediction of DNA Charge Transport.

First-principles calculations of charge transfer in DNA molecules are computationally expensive given that conducting charge carriers interact with intra- and intermolecular atomic motion. Screening sequences, for example, to identify excellent electrical conductors, is challenging even when adopting coarse-grained models and effective computational schemes that do not explicitly describe atomic dynamics. We present a machine learning (ML) model that allows the inexpensive prediction of the electrical conductance of millions of long double-stranded DNA (dsDNA) sequences, reducing computational costs by orders of magnitude. The algorithm is trained on short DNA nanojunctions with n = 3-7 base pairs. The electrical conductance of the training set is computed with a quantum scattering method, which captures charge-nuclei scattering processes. We demonstrate that the ML method accurately predicts the electrical conductance of varied dsDNA junctions tracing different transport mechanisms: coherent (short-range) quantum tunneling, on-resonance (ballistic) transport, and incoherent site-to-site hopping. Furthermore, the ML approach supports physical observations that clusters of nucleotides regulate DNA transport behavior. The input features tested in this work could be used in other ML studies of charge transport in complex polymers in the search for promising electronic and thermoelectric materials.

Reactions of Boron-Derived Radicals with Nucleophiles.

Reactions of phenanthrenedione- and pyrenedione-derived borocyclic radicals, CnH8O2B(C6F5)2• (n = 14 (1), 16 (3)), with a variety of nucleophiles have been studied. Reaction of 1 with P(t-Bu)3 affords the zwitterion 3-(t-Bu)3PC14H7O2B(C6F5)2 (5) in addition to the salt [HP(t-Bu)3][C14H8O2B(C6F5)2] (6). In contrast, the reaction of 1 with PPh3 proceeds to give two regioisomeric zwitterions, 1-(Ph3P)C14H7O2B(C6F5)2 (7a) and 3-(Ph3P)C14H7O2B(C6F5)2 (7b), as well as the related boronic ester C14H8O2B(C6F5) (2). In a similar fashion, 3 reacted with PPh3 to give 3-(Ph3P)C16H7O2B(C6F5)2 (8a), 1-(Ph3P)C16H7O2B(C6F5)2 (8b), and boronic ester C16H8O2B(C6F5) (4). Reactions of secondary phosphines Ph2PH and tBu2PH with 3 yield 3-(R2PH)C16H7O2B(C6F5)2 (R = Ph (9), t-Bu (10)). The reaction of 1 with N-heterocyclic carbene IMes afforded 3-(IMes)C14H7O2B(C6F5)2 (11) and [IMesH][C14H8O2B(C6F5)2] (12), while the reactions with quinuclidine and DMAP afforded the species 3-(C7H13N)C14H7O2B(C6F5)2 (13) and [H(NC7H13)2][C14H8O2B(C6F5)2] (14), and the salt [9,10-(DMAP)2C14H8O2B(C6F5)2][C14H8O2B(C6F5)2] (15), respectively. These products have been fully characterized, and the mechanism for the formation of these products is considered in the light of DFT calculations.

Thermopower of molecular junctions: Tunneling to hopping crossover in DNA.

We study the electrical conductance G and the thermopower S of single-molecule junctions and reveal signatures of different transport mechanisms: off-resonant tunneling, on-resonant coherent (ballistic) motion, and multi-step hopping. These mechanisms are identified by studying the behavior of G and S while varying molecular length and temperature. Based on a simple one-dimensional model for molecular junctions, we derive approximate expressions for the thermopower in these different regimes. Analytical results are compared to numerical simulations, performed using a variant of Büttiker's probe technique, the so-called voltage-temperature probe, which allows us to phenomenologically introduce environmentally induced elastic and inelastic electron scattering effects, while applying both voltage and temperature biases across the junction. We further simulate the thermopower of GC-rich DNA sequences with mediating A:T blocks and manifest the tunneling-to-hopping crossover in both the electrical conductance and the thermopower, in accord with measurements by Li et al. [Nat. Commun. 7, 11294 (2016)].