Performance of reservoir discretizations in quantum transport simulations.

Quantum transport simulations often use explicit, yet finite, electronic reservoirs. These should converge to the correct continuum limit, albeit with a trade-off between discretization and computational cost. Here, we study this interplay for extended reservoir simulations, where relaxation maintains a bias or temperature drop across the system. Our analysis begins in the non-interacting limit, where we parameterize different discretizations to compare them on an even footing. For many-body systems, we develop a method to estimate the relaxation that best approximates the continuum by controlling virtual transitions in Kramers turnover for the current. While some discretizations are more efficient for calculating currents, there is little benefit with regard to the overall state of the system. Any gains become marginal for many-body, tensor network simulations, where the relative performance of discretizations varies when sweeping other numerical controls. These results indicate that typical reservoir discretizations have little impact on numerical costs for certain computational tools. The choice of a relaxation parameter is nonetheless crucial, and the method we develop provides a reliable estimate of the optimal relaxation for finite reservoirs.

Open System Tensor Networks and Kramers' Crossover for Quantum Transport.

Tensor networks are a powerful tool for many-body ground states with limited entanglement. These methods can nonetheless fail for certain time-dependent processes-such as quantum transport or quenches-where entanglement growth is linear in time. Matrix-product-state decompositions of the resulting out-of-equilibrium states require a bond dimension that grows exponentially, imposing a hard limit on simulation timescales. However, in the case of transport, if the reservoir modes of a closed system are arranged according to their scattering structure, the entanglement growth can be made logarithmic. Here, we apply this ansatz to open systems via extended reservoirs that have explicit relaxation. This enables transport calculations that can access steady states, time dynamics and noise, and periodic driving (e.g., Floquet states). We demonstrate the approach by calculating the transport characteristics of an open, interacting system. These results open a path to scalable and numerically systematic many-body transport calculations with tensor networks.

Topology, landscapes, and biomolecular energy transport.

While ubiquitous, energy redistribution remains a poorly understood facet of the nonequilibrium thermodynamics of biomolecules. At the molecular level, finite-size effects, pronounced nonlinearities, and ballistic processes produce behavior that diverges from the macroscale. Here, we show that transient thermal transport reflects macromolecular energy landscape architecture through the topological characteristics of molecular contacts and the nonlinear processes that mediate dynamics. While the former determines transport pathways via pairwise interactions, the latter reflects frustration within the landscape for local conformational rearrangements. Unlike transport through small-molecule systems, such as alkanes, nonlinearity dominates over coherent processes at even quite short time- and length-scales. Our exhaustive all-atom simulations and novel local-in-time and space analysis, applicable to both theory and experiment, permit dissection of energy migration in biomolecules. The approach demonstrates that vibrational energy transport can probe otherwise inaccessible aspects of macromolecular dynamics and interactions that underly biological function.

A spin-1 representation for dual-funnel energy landscapes.

The interconversion between the left- and right-handed helical folds of a polypeptide defines a dual-funneled free energy landscape. In this context, the funnel minima are connected through a continuum of unfolded conformations, evocative of the classical helix-coil transition. Physical intuition and recent conjectures suggest that this landscape can be mapped by assigning a left- or right-handed helical state to each residue. We explore this possibility using all-atom replica exchange molecular dynamics and an Ising-like model, demonstrating that the energy landscape architecture is at odds with a two-state picture. A three-state model-left, right, and unstructured-can account for most key intermediates during chiral interconversion. Competing folds and excited conformational states still impose limitations on the scope of this approach. However, the improvement is stark: Moving from a two-state to a three-state model decreases the fit error from 1.6 kBT to 0.3 kBT along the left-to-right interconversion pathway.

Communication: Master equations for electron transport: The limits of the Markovian limit.

Master equations are increasingly popular for the simulation of time-dependent electronic transport in nanoscale devices. Several recent Markovian approaches use "extended reservoirs"-explicit degrees of freedom associated with the electrodes-distinguishing them from many previous classes of master equations. Starting from a Lindblad equation, we develop a common foundation for these approaches. Due to the incorporation of explicit electrode states, these methods do not require a large bias or even "true Markovianity" of the reservoirs. Nonetheless, their predictions are only physically relevant when the Markovian relaxation is weaker than the thermal broadening and when the extended reservoirs are "sufficiently large," in a sense that we quantify. These considerations hold despite complete positivity and respect for Pauli exclusion at any relaxation strength.

Visible-Light-Responsive Graphitic Carbon Nitride: Rational Design and Photocatalytic Applications for Water Treatment.

Graphitic carbon nitride (g-C3N4) has recently emerged as a promising visible-light-responsive polymeric photocatalyst; however, a molecular-level understanding of material properties and its application for water purification were underexplored. In this study, we rationally designed nonmetal doped, supramolecule-based g-C3N4 with improved surface area and charge separation. Density functional theory (DFT) simulations indicated that carbon-doped g-C3N4 showed a thermodynamically stable structure, promoted charge separation, and had suitable energy levels of conduction and valence bands for photocatalytic oxidation compared to phosphorus-doped g-C3N4. The optimized carbon-doped, supramolecule-based g-C3N4 showed a reaction rate enhancement of 2.3-10.5-fold for the degradation of phenol and persistent organic micropollutants compared to that of conventional, melamine-based g-C3N4 in a model buffer system under the irradiation of simulated visible sunlight. Carbon-doping but not phosphorus-doping improved reactivity for contaminant degradation in agreement with DFT simulation results. Selective contaminant degradation was observed on g-C3N4, likely due to differences in reactive oxygen species production and/or contaminant-photocatalyst interfacial interactions on different g-C3N4 samples. Moreover, g-C3N4 is a robust photocatalyst for contaminant degradation in raw natural water and (partially) treated water and wastewater. In summary, DFT simulations are a viable tool to predict photocatalyst properties and oxidation performance for contaminant removal, and they guide the rational design, fabrication, and implementation of visible-light-responsive g-C3N4 for efficient, robust, and sustainable water treatment.

Computational modeling of self-trapped electrons in rutile TiO2.

In conjunction with the constrained density functional theory, a valence-bond representation has been employed to model the migration of anionic polaron in bulk rutile TiO2. It was found that the charge delocalization of a self-trapped electron proceeded predominately along the c crystal axis of rutile, thus exhibiting pronounced directional heterogeneity of polaron migration. As a result, the extrapolated polaron activation energies are 0.026 eV and 0.195 eV along the [001] and [111] lattice vectors, respectively. According to the Holstein theory, the difference on the activation energy makes the polaron drift over 100 times faster along the c crystal axis than on the ab crystal plane at room temperature. The notable anisotropy of the anionic polaron was also reflected through the electron paramagnetic resonance (EPR) g-matrix, whose principal component along [001] is substantially smaller than that along [110] or [11̅0]. Finally, the extent of polaron charge was probed by our calculated isotropic hyperfine coupling constants on two groups of crystallographically inequivalent (17)O atoms, which manifest distinct strengths of spin-orbit interaction with the unpaired electron.

Ab initio dynamics of the cytochrome P450 hydroxylation reaction.

The iron(IV)-oxo porphyrin π-cation radical known as Compound I is the primary oxidant within the cytochromes P450, allowing these enzymes to affect the substrate hydroxylation. In the course of this reaction, a hydrogen atom is abstracted from the substrate to generate hydroxyiron(IV) porphyrin and a substrate-centered radical. The hydroxy radical then rebounds from the iron to the substrate, yielding the hydroxylated product. While Compound I has succumbed to theoretical and spectroscopic characterization, the associated hydroxyiron species is elusive as a consequence of its very short lifetime, for which there are no quantitative estimates. To ascertain the physical mechanism underlying substrate hydroxylation and probe this timescale, ab initio molecular dynamics simulations and free energy calculations are performed for a model of Compound I catalysis. Semiclassical estimates based on these calculations reveal the hydrogen atom abstraction step to be extremely fast, kinetically comparable to enzymes such as carbonic anhydrase. Using an ensemble of ab initio simulations, the resultant hydroxyiron species is found to have a similarly short lifetime, ranging between 300 fs and 3600 fs, putatively depending on the enzyme active site architecture. The addition of tunneling corrections to these rates suggests a strong contribution from nuclear quantum effects, which should accelerate every step of substrate hydroxylation by an order of magnitude. These observations have strong implications for the detection of individual hydroxylation intermediates during P450 catalysis.

Spin equilibrium and O2-binding kinetics of Mycobacterium tuberculosis CYP51 with mutations in the histidine-threonine dyad.

The acidic residues of the "acid-alcohol pair" in CYP51 enzymes are uniformly replaced with histidine. Herein, we adopt the Mycobacterium tuberculosis (mt) enzyme as a model system to investigate these residues' roles in finely tuning the heme conformation, iron spin state, and formation and decay of the oxyferrous enzyme. Properties of the mtCYP51 and the T260A, T260V, and H259A mutants were interrogated using UV-Vis and resonance Raman spectroscopies. Evidence supports that these mutations induce comprehensive changes in the heme environment. The heme iron spin states are differentially sensitive to the binding of the substrate, dihydrolanosterol (DHL). DHL and clotrimazole perturb the local environments of the heme vinyl and propionate substituents. Molecular dynamics (MD) simulations of the DHL-enzyme complexes support that the observed perturbations are attributable to changes in the DHL binding mode. Furthermore, the rates of the oxyferrous formation were measured using stopped-flow methods. These studies demonstrate that both HT mutations and DHL modulate the rates of oxyferrous formation. Paradoxically, the binding rate to the H259A mutant-DHL complex was approximately four-fold that of mtCYP51, a phenomenon that is predicted to result from the creation of an additional diffusion channel from loss of the H259-E173 ion pair in the mutant. Oxyferrous enzyme auto-oxidation rates were relatively constant, with the exception of the T260V-DHL complex. MD simulations lead us to speculate that this behavior may be attributed to the distortion of the heme macrocycle by the substrate.

Solvatochromism and the solvation structure of benzophenone.

Many complex molecular phenomena, including macromolecular association, protein folding, and chemical reactivity, are determined by the nuances of their electrostatic landscapes. The measurement of such electrostatic effects is nonetheless difficult, and is typically accomplished by exploiting a spectroscopic probe within the system of interest, such as through the vibrational Stark effect. Raman spectroscopy and solvatochromism afford an alternative to this method, circumventing the limitations of infrared spectroscopy, providing a lower detection limit, and permitting measurement in a native chemical environment. To explore this possibility, the solvatochromism of the C=O and aromatic C-H stretching modes of benzophenone are investigated using Raman spectroscopy. In conjunction with density functional theory calculations, these observations are sufficient to determine the probe electrostatic environment as well as contributions from halogen and hydrogen bonding. Further analysis using a detailed Kubo-Anderson lineshape model permits the detailed assignment of distinct hydrogen bonding configurations for water in the benzophenone solvation shell. These observations reinforce the use of benzophenone as an effective electrostatic probe for complex chemical systems.

Cytochrome P450 compound I in the plane wave pseudopotential framework: GGA electronic and geometric structure of thiolate-ligated iron(IV)-oxo porphyrin.

The cytochromes P450 constitute a ubiquitous family of metalloenzymes, catalyzing manifold reactions of biological and synthetic importance via a thiolate-ligated iron-oxo (IV) porphyrin radical species denoted compound I (Cpd I). Experimental investigations have implicated this intermediate in a broad spectrum of biophysically interesting phenomena, further augmenting the importance of a Cpd I model system. Ab initio molecular dynamics, including Car-Parrinello and path integral methods, conjoin electronic structure theory with finite temperature simulation, affording tools most valuable to approach such enzymes. These methods are typically driven by density functional theory (DFT) in a plane-wave pseudopotential framework; however, existing studies of Cpd I have been restricted to localized Gaussian basis sets. The appropriate choice of density functional and pseudopotential for such simulations is accordingly not obvious. To remedy this situation, a systematic benchmarking of thiolate-ligated Cpd I is performed using several generalized-gradient approximation (GGA) functionals in the Martins-Troullier and Vanderbilt ultrasoft pseudopotential schemes. The resultant electronic and structural parameters are compared to localized-basis DFT calculations using GGA and hybrid density functionals. The merits and demerits of each scheme are presented in the context of reproducing existing experimental and theoretical results for Cpd I.

A GGA+U approach to effective electronic correlations in thiolate-ligated iron-oxo (IV) porphyrin.

High-valent oxo-metal complexes exhibit correlated electronic behavior on dense, low-lying electronic state manifolds, presenting challenging systems for electronic structure methods. Among these species, the iron-oxo (IV) porphyrin denoted Compound I occupies a privileged position, serving a broad spectrum of catalytic roles. The most reactive members of this family bear a thiolate axial ligand, exhibiting high activity toward molecular oxygen activation and substrate oxidation. The default approach to such systems has entailed the use of hybrid density functionals or multi-configurational/multireference methods to treat electronic correlation. An alternative approach is presented based on the GGA+U approximation to density functional theory, in which a generalized gradient approximation (GGA) functional is supplemented with a localization correction to treat on-site correlation as inspired by the Hubbard model. The electronic structure of thiolate-ligated iron-oxo (IV) porphyrin and corresponding Coulomb repulsion U are determined both empirically and self-consistently, yielding spin-distributions, state level splittings, and electronic densities of states consistent with prior hybrid functional calculations. Comparison of this detailed electronic structure with model Hamiltonian calculations suggests that the localized 3d iron moments induce correlation in the surrounding electron gas, strengthening local moment formation. This behavior is analogous to strongly correlated electronic systems such as Mott insulators, in which the GGA+U scheme serves as an effective single-particle representation for the full, correlated many-body problem.

Free energy landscape of the retinol/serum retinol binding protein complex: a biological host-guest system.

Small molecule host-guest complexes have traditionally provided model systems for biological ligand recognition. Nonetheless, direct extrapolation of these results is precluded by the comparative simplicity of these supramolecular assemblies. If energetic behavior analogous to small molecule host-guest chemistry exists, it is unclear how this would manifest for protein-small molecule interactions. To answer this question, we employ the retinol/serum retinol binding protein (sRBP) system as an analogue of a classical host-guest complex. Using a combination of molecular dynamics simulations and free energy methods, we decompose the potential of mean force for retinol unbinding from the sRBP into constituent interactions. Our calculations reveal an unexpected mechanism of host-guest complexation. Desolvation is sufficient to drive formation of an intermediate binding state; however, a combination of electrostatic and van der Waals interactions pull the intermediate into a stable configuration. Association is accompanied by a change in the conformational flexibility of the portal domains of sRBP and subsequent "stiffening" of the holo sRBP, reflecting an "order-disorder" transition in the protein.