A novel non-adiabatic spin relaxation mechanism in molecular qubits.

The interaction of electronic spin and molecular vibrations mediated by spin-orbit coupling governs spin relaxation in molecular qubits. We derive an extended molecular spin Hamiltonian that includes both adiabatic and non-adiabatic spin-dependent interactions, and we implement the computation of its matrix elements using state-of-the-art density functional theory. The new molecular spin Hamiltonian contains a novel spin-vibrational orbit interaction with a non-adiabatic origin, together with the traditional molecular Zeeman and zero-field splitting interactions with an adiabatic origin. The spin-vibrational orbit interaction represents a non-Abelian Berry curvature on the ground-state electronic manifold and corresponds to an effective magnetic field in the electronic spin dynamics. We further develop a spin relaxation rate model that estimates the spin relaxation time via the two-phonon Raman process. An application of the extended molecular spin Hamiltonian together with the spin relaxation rate model to Cu(II) porphyrin, a prototypical S = 1/2 molecular qubit, demonstrates that the spin relaxation time at elevated temperatures is dominated by the non-adiabatic spin-vibrational orbit interaction. The computed spin relaxation rate and its magnetic field orientation dependence are in excellent agreement with experimental measurements.

Global Brassicaceae phylogeny based on filtering of 1,000-gene dataset.

The mustard family (Brassicaceae) is a scientifically and economically important family, containing the model plant Arabidopsis thaliana and numerous crop species that feed billions worldwide. Despite its relevance, most phylogenetic trees of the family are incompletely sampled and often contain poorly supported branches. Here, we present the most complete Brassicaceae genus-level family phylogenies to date (Brassicaceae Tree of Life or BrassiToL) based on nuclear (1,081 genes, 319 of the 349 genera; 57 of the 58 tribes) and plastome (60 genes, 265 genera; all tribes) data. We found cytonuclear discordance between the two, which is likely a result of rampant hybridization among closely and more distantly related lineages. To evaluate the impact of such hybridization on the nuclear phylogeny reconstruction, we performed five different gene sampling routines, which increasingly removed putatively paralog genes. Our cleaned subset of 297 genes revealed high support for the tribes, whereas support for the main lineages (supertribes) was moderate. Calibration based on the 20 most clock-like nuclear genes suggests a late Eocene to late Oligocene origin of the family. Finally, our results strongly support a recently published new family classification, dividing the family into two subfamilies (one with five supertribes), together representing 58 tribes. This includes five recently described or re-established tribes, including Arabidopsideae, a monogeneric tribe accommodating Arabidopsis without any close relatives. With a worldwide community of thousands of researchers working on Brassicaceae and its diverse members, our new genus-level family phylogeny will be an indispensable tool for studies on biodiversity and plant biology.

Microcanonical rates from ring-polymer molecular dynamics: Direct-shooting, stationary-phase, and maximum-entropy approaches.

We address the calculation of microcanonical reaction rates for processes involving significant nuclear quantum effects using ring-polymer molecular dynamics (RPMD), both with and without electronically non-adiabatic transitions. After illustrating the shortcomings of the naive free-particle direct-shooting method, in which the temperature of the internal ring-polymer modes is set to the translational energy scale, we investigate alternative strategies based on the expression for the microcanonical rate in terms of the inverse Laplace transform of the thermal reaction rate. It is shown that simple application of the stationary-phase approximation (SPA) dramatically improves the performance of the microcanonical rates using RPMD, particularly in the low-energy region where tunneling dominates. Using the SPA as a Bayesian prior, numerically exact RPMD microcanonical rates are then obtained using maximum entropy inversion of the thermal reaction rates for both electronically adiabatic and non-adiabatic model systems. Finally, the direct-shooting method is revisited using the SPA-determined temperature for the internal ring-polymer modes, leading to a simple, direct-simulation method with improved accuracy in the tunneling regime. This work suggests a general strategy for the extraction of microcanonical dynamical quantities from RPMD (or other approximate thermal) simulations.

Real-time density-matrix coupled-cluster approach for closed and open systems at finite temperature.

We extend the coupled-cluster method to correlated quantum dynamics of both closed and open systems at finite temperatures using the thermofield formalism. The approach expresses the time-dependent density matrix in an exponential ansatz and describes time-evolution along the Keldysh path contour. A distinct advantage of the approach is exact trace-preservation as a function of time, ensuring conservation of probability and particle number. Furthermore, the method avoids the computation of correlated bra-states, simplifying the computational implementation. We develop the method in a thermal quasiparticle representation, which allows seamless connection to the projection method and diagrammatic techniques of the traditional coupled-cluster formalism. For comparison, we also apply the thermofield framework to the density-matrix renormalization-group method to obtain reference results for closed and open systems at finite temperature. We test the singles and doubles approximation to the density-matrix coupled-cluster method on the correlated electronic dynamics of the single-impurity Anderson model, demonstrating that the new method successfully captures the correlated dynamics of both closed systems at finite temperature and driven-dissipative open systems. This encouraging performance motivates future applications to nonequilibrium quantum many-body dynamics in realistic systems.

Publisher Correction: Direct dioxygen evolution in collisions of carbon dioxide with surfaces.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Direct dioxygen evolution in collisions of carbon dioxide with surfaces.

The intramolecular conversion of CO2 to molecular oxygen is an exotic reaction, rarely observed even with extreme optical or electronic excitation means. Here we show that this reaction occurs readily when CO2 ions scatter from solid surfaces in a two-step sequential collision process at hyperthermal incidence energies. The produced O2 is preferentially ionized by charge transfer from the surface over the predominant atomic oxygen product, leading to direct detection of both O2+ and O2-. First-principles simulations of the collisional dynamics reveal that O2 production proceeds via strongly-bent CO2 configurations, without visiting other intermediates. Bent CO2 provides dynamic access to the symmetric dissociation of CO2 to C+O2 with a calculated yield of 1 to 2% depending on molecular orientation. This unexpected collision-induced transformation of individual CO2 molecules provides an accessible pathway for generating O2 in astrophysical environments and may inspire plasma-driven electro- and photo-catalytic strategies for terrestrial CO2 reduction.

Simple Flux-Side Formulation of State-Resolved Thermal Reaction Rates for Ring-Polymer Surface Hopping.

Employing the recently developed isomorphic Hamiltonian framework for including nuclear quantum effects in mixed quantum-classical nonadiabatic dynamics, we present a flux-side formulation of state-resolved thermal reaction rates for ring-polymer surface hopping (iso-RPSH). An appealing aspect of the new approach is that calculation of multiple state-resolved nonadiabatic thermal reaction rates is enabled with only a single free-energy surface calculation, whereas previous nonadiabatic flux-side formulations for surface hopping involve multiple free-energy surface calculations. The method is shown to be robust and straightforwardly implemented, and numerical results reveal that RPSH in the isomorphic Hamiltonian framework leads to better dividing surface independence than alternative RPSH methods due to improved preservation of the path-integral statistics.

Resolving the backbone of the Brassicaceae phylogeny for investigating trait diversity.

The Brassicaceae family comprises c. 4000 species including economically important crops and the model plant Arabidopsis thaliana. Despite their importance, the relationships among major lineages in the family remain unresolved, hampering comparative research. Here, we inferred a Brassicaceae phylogeny using newly generated targeted enrichment sequence data of 1827 exons (> 940 000 bases) representing 63 species, as well as sequenced genome data of 16 species, together representing 50 of the 52 currently recognized Brassicaceae tribes. A third of the samples were derived from herbarium material, facilitating broad taxonomic coverage of the family. Six major clades formed successive sister groups to the rest of Brassicaceae. We also recovered strong support for novel relationships among tribes, and resolved the position of 16 taxa previously not assigned to a tribe. The broad utility of these phylogenetic results is illustrated through a comparative investigation of genome-wide expression signatures that distinguish simple from complex leaves in Brassicaceae. Our study provides an easily extendable dataset for further advances in Brassicaceae systematics and a timely higher-level phylogenetic framework for a wide range of comparative studies of multiple traits in an intensively investigated group of plants.

Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics.

We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. We present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.

A Robust and Accurate Tight-Binding Quantum Chemical Method for Structures, Vibrational Frequencies, and Noncovalent Interactions of Large Molecular Systems Parametrized for All spd-Block Elements (Z = 1-86).

We propose a novel, special purpose semiempirical tight binding (TB) method for the calculation of structures, vibrational frequencies, and noncovalent interactions of large molecular systems with 1000 or more atoms. The functional form of the method is related to the self-consistent density functional TB scheme and mostly avoids element-pair-specific parameters. The parametrization covers all spd-block elements and the lanthanides up to Z = 86 using reference data at the hybrid density functional theory level. Key features of the Hamiltonian are the use of partially polarized Gaussian-type orbitals, a double-ζ orbital basis for hydrogen, atomic-shell charges, diagonal third-order charge fluctuations, coordination number-dependent energy levels, a noncovalent halogen-bond potential, and the well-established D3 dispersion correction. The accuracy of the method, called Geometry, Frequency, Noncovalent, eXtended TB (GFN-xTB), is extensively benchmarked for various systems in comparison with existing semiempirical approaches, and the method is applied to a few representative structural problems in chemistry.

Synthesis and Dynamics of Nanosized Phenylene-Ethynylene-Butadiynylene Rotaxanes and the Role of Shape Persistence.

Phenylacetylene-based [2]rotaxanes were synthesized by a covalent-template approach by aminolysis of the corresponding prerotaxanes. The wheel and the bulky stoppers are made of phenylene-ethynylene-butadiynylene macrocycles of the same size. The stoppers are large enough to enable the synthesis and purification of the rotaxane. However, the wheel unthreads from the axle at elevated temperatures. The deslipping kinetics and the activation parameters were determined. We described theoretically the unthreading by state-of-the-art DFT-based molecular-mechanics models and a string method for the simulation of rare events. This approach enabled us to characterize in detail the unthreading mechanism, which involves the folding of the stopper during its passage through the wheel opening, a process that defies intuitive geometrical considerations. The conformational and energetic features of the transition allowed us to infer the molecular residues controlling the disassembly timescale.

On the connection of semiclassical instanton theory with Marcus theory for electron transfer in solution.

We present a derivation of Marcus theory of electron transfer in solution starting from semiclassical instanton theory. The conventional semiclassical instanton theory provides an inadequate description of the electron transfer process in the inverted Marcus regime. This has been attributed to the lack of backscattering in the product region, which is represented as a semi-infinite continuum of states. For electron transfer processes in condensed phase, the electronic states in the acceptor well are bound, which violates the continuum assumption. We show by detailed analysis of the minimum action path of a model system for electron transfer that the proper tunneling coordinate is a delocalized, "bead-count" mode. The tunneling mode is analytically continued in the complex plane as in the traditional derivation. Unlike the traditional analysis where the method of steepest descent is used, the tunneling coordinate is treated as a quasi-zero mode. This feature allows including the influence of backscattering in the acceptor well and leads to the recovery of the Marcus formula for the rate of electron transfer. The results have implications on the performance of ring polymer molecular dynamics for the study of electron transfer dynamics.

Orthogonality constrained density functional theory for electronic excited states.

We report a novel scheme for computing electronic excitation energies within the framework of density functional theory (DFT) based on a time-independent variational formulation of DFT. The excited state density functional is recast as a Kohn-Sham functional, which is further simplified by an adiabatic approximation of the exchange-correlation functional. Under the adiabatic approximation, the minimization of the excited state Kohn-Sham functional is shown to be equivalent to a ground state DFT computation augmented with orthogonality constraints with respect to the ground state Kohn-Sham determinant. An algorithm for the optimization of the energy subject to orthogonality constraints, which does not suffer from variational collapse, is described and implemented. A benchmark test set containing 28 organic molecules (Schreiber, M. J. Chem. Phys. 2008, 128, 134110) was used to assess the quality of the excitation energies obtained. Two novel approaches to spin-adapt the resulting excitation energies are discussed and found to provide results with error metrics similar to those of time-dependent DFT. Similarities and differences with respect to other time-independent DFT approaches are highlighted and some of the advantages of our scheme-including the ability to correctly describe charge-transfer excitations-are critically assessed.

Ring polymer molecular dynamics with surface hopping.

We propose a ring polymer molecular dynamics method for the calculation of chemical rate constants that incorporates nonadiabatic effects by the surface-hopping approach. Two approximate ring polymer electronic Hamiltonians are formulated and the time-dependent Schrodinger equation for the electronic amplitudes is solved self-consistently with the ring polymer equations of motion. The beads of the ring polymer move on a single adiabatic potential energy surface at all times except for instantaneous surface hops. The probability for a hop is determined by the fewest-switches surface-hopping criterion. During a surface hop all beads switch simultaneously to the new potential energy surface with positions kept unchanged and momenta adjusted properly to conserve total energy. The approach allows the evaluation of total rate coefficients as well as electronic state-selected contributions. The method is tested against exact quantum mechanical calculations for a one-dimensional, two-state model system that mimics a prototypical nonadiabatic bimolecular chemical reaction. For this model system, the method reproduces quite accurately the tunneling contribution to the rate and the distribution of reactants between the electronic states.

Mixed time slicing in path integral simulations.

A simple and efficient scheme is presented for using different time slices for different degrees of freedom in path integral calculations. This method bridges the gap between full quantization and the standard mixed quantum-classical (MQC) scheme and, therefore, still provides quantum mechanical effects in the less-quantized variables. Underlying the algorithm is the notion that time slices (beads) may be "collapsed" in a manner that preserves quantization in the less quantum mechanical degrees of freedom. The method is shown to be analogous to multiple-time step integration techniques in classical molecular dynamics. The algorithm and its associated error are demonstrated on model systems containing coupled high- and low-frequency modes; results indicate that convergence of quantum mechanical observables can be achieved with disparate bead numbers in the different modes. Cost estimates indicate that this procedure, much like the MQC method, is most efficient for only a relatively few quantum mechanical degrees of freedom, such as proton transfer. In this regime, however, the cost of a fully quantum mechanical simulation is determined by the quantization of the least quantum mechanical degrees of freedom.

Structural aspects of lipid monolayers: computer simulation analyses.

Extensive molecular dynamics simulations at room temperature were carried out for model films of two dissimilar lipids (DPPC and dicaprin) at the air/water interface. To study the peculiarities of the organization patterns at different average areas per molecule, surface concentrations corresponding to five almost equally spaced points along the isotherms of the two surfactants were considered. A variable of prime interest was the density distribution in a direction normal to the interface of the monolayer components: interfacial water and surfactant on one hand and the separate moieties of the lipids on the other hand. The packing pattern and cluster size dispersion were studied by means of Voronoi tessellation and radial distribution functions. Speculations regarding structural changes upon phase-state changes during film compression were made. Individual characteristics for surfactant heads and tails as well as for interfacial water were outlined and related to the available experimental data. An analysis of the diffusion coefficients revealed the limiting factors for lipid lateral and normal diffusion. Structural arguments in support of changes in monolayer dielectric properties with the area per molecule were provided.

Molecular dynamics study of the electric and dielectric properties of model DPPC and dicaprin insoluble monolayers: size effect.

Atomistic modeling of insoluble monolayers is currently used to inspect their organization and electric characteristics, providing a link between theory and experiment. Extensive molecular dynamics simulations at 300 K were carried out for model films of the lipids dipalmitoylphosphatidylcholine (DPPC) and dicaprin (DC) at the air/water interface. Surface concentrations corresponding to a set of points along the surface pressure/area isotherms of the surfactants were considered. The models contained 25 or 81 lipid molecules in hexagonal arrangement and explicit aqueous media (TIP3P) treated in periodic boundary conditions. Molecular dynamics simulations based on a classical force field (CHARMM27) were carried out and key characteristics of the studied films were estimated. The dielectric properties of the films in normal and tangential direction were quantified by means of dipole moment magnitude and orientation analysis and by monolayer dielectric permittivity. The contributions of lipids and interfacial water to each component of the considered characteristics were assessed and their variations upon film compression were discussed and compared for the two monolayers and to earlier results. The dielectric permittivity tensors were analyzed. Electrostatic potential profiles across the layers and surface pressure values were used for more detailed clarification of experimental measurements. The results show dissimilar behavior of the two lipids at the air-water interface. While the average electric and dielectric properties of DPPC monolayers result from opposite surfactant and water contributions, the two subsystems are synergetic in the DC films. The anisotropy of the monolayer dipole moment and dielectric permittivity is explained by domination of a different subsystem in the various components. Tangential characteristics turn out to be more sensitive to the size of the model and to the degree of film compression.

Systematic study of the influence of base-step parameters on the electronic coupling between base-pair dimers: comparison of A-DNA and B-DNA forms.

The electronic coupling is one of the key parameters governing electron hole transfer along DNA helices. In this study, we established the first comprehensive data base of electronic coupling elements, calculated at the ab initio level. The data set comprises all possible Watson-Crick base pair dimers, both in standard A-DNA and B-DNA geometries. We also quantified the sensitivity of the coupling elements with respect to geometry changes by varying each of the six standard base step parameters, which specify the relative orientation of neighboring base pairs. We compare the couplings in a systematic way by discussing variations in the coupling magnitude due to geometry or nucleotide sequence in the dimer, and we analyze how the structure affects the electronic coupling in terms of general and dimer-specific trends. Furthermore, we studied how the coupling changes when one introduces the chemically modified base 7-deazaguanine in the corresponding base-pair dimers. Finally, on the basis of the calculated coupling elements, we suggest a model duplex with an enhanced capacity for hole transfer.

Dielectric properties tangential to the interface in model insoluble monolayers: theoretical assessment.

Studies of insoluble monolayers built of phospholipids and various long-chained fatty acids or their glycerin esters are the major source for what is currently known about the relationship between monolayer composition and physicochemical properties. The surface pressure, dipole moment, dielectric permittivity, polarizability, refractivity, and other electrical and optical features are governed by the surfactant structural specificity and solvent organization at the microscopic level. To provide insight into the atomistic details of the interfacial structure, model monolayers at the air/water interface of two distinctly different in composition and isotherm profile surfactants are investigated by means of molecular dynamics all-atom simulations. Analysis of the computational results allows the estimation of empirically unattainable quantities such as tangential (di)electric properties, their decomposition to surfactant and water contributions, and their relationship with the changes in interfacial molecular organization at different surface concentrations. The employed theoretical approach provides a comprehensive description of interfacial phenomena at the molecular level where the traditional phenomenological investigations are ineffective.