Two-state model of energy dissipation at metal surfaces.

The rates and pathways of chemical reactions at metal surfaces can be strongly influenced by energy dissipation due to the nonadiabatic excitation of metallic conduction electrons. The introduction of frictional forces to account for this dissipation has been quite successful in situations for which the nonadiabatic coupling is weak. However, in cases where nonadiabatic coupling is strong, such as when electron transfer occurs, the friction model is likely to break down. Ryabinkin and Izmaylov have proposed 2-state and 3-state alternatives to the friction model for introducing electronic dissipation in molecular dynamics simulations. Here, we examine their 2-state model using some simple examples of atom-surface scattering. We find that, with the addition of decoherence, the 2-state model can produce quite promising results.

Mode Specific Electronic Friction in Dissociative Chemisorption on Metal Surfaces: H_{2} on Ag(111).

Electronic friction and the ensuing nonadiabatic energy loss play an important role in chemical reaction dynamics at metal surfaces. Using molecular dynamics with electronic friction evaluated on the fly from density functional theory, we find strong mode dependence and a dominance of nonadiabatic energy loss along the bond stretch coordinate for scattering and dissociative chemisorption of H_{2} on the Ag(111) surface. Exemplary trajectories with varying initial conditions indicate that this mode specificity translates into modulated energy loss during a dissociative chemisorption event. Despite minor nonadiabatic energy loss of about 5%, the directionality of friction forces induces dynamical steering that affects individual reaction outcomes, specifically for low-incidence energies and vibrationally excited molecules. Mode-specific friction induces enhanced loss of rovibrational rather than translational energy and will be most visible in its effect on final energy distributions in molecular scattering experiments.

Erratum: Role of Tensorial Electronic Friction in Energy Transfer at Metal Surfaces [Phys. Rev. Lett. 116, 217601 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.116.217601.

Probing the remarkable thermal kinetics of visual rhodopsin with E181Q and S186A mutants.

We recently reported a very unusual temperature dependence of the rate of thermal reaction of wild type bovine rhodopsin: the Arrhenius plot exhibits a sharp "elbow" at 47 °C and, in the upper temperature range, an unexpectedly large activation energy (114 ± 8 kcal/mol) and an enormous prefactor (1072±5 s-1). In this report, we present new measurements and a theoretical model that establish convincingly that this behavior results from a collective, entropy-driven breakup of the rigid hydrogen bonding networks (HBNs) that hinder the reaction at lower temperatures. For E181Q and S186A, two rhodopsin mutants that disrupt the HBNs near the binding pocket of the 11-cis retinyl chromophore, we observe significant decreases in the activation energy (∼90 kcal/mol) and prefactor (∼1060 s-1), consistent with the conclusion that the reaction rate is enhanced by breakup of the HBN. The results provide insights into the molecular mechanism of dim-light vision and eye diseases caused by inherited mutations in the rhodopsin gene that perturb the HBNs.

Unusual kinetics of thermal decay of dim-light photoreceptors in vertebrate vision.

We present measurements of rate constants for thermal-induced reactions of the 11-cis retinyl chromophore in vertebrate visual pigment rhodopsin, a process that produces noise and limits the sensitivity of vision in dim light. At temperatures of 52.0-64.6 °C, the rate constants fit well to an Arrhenius straight line with, however, an unexpectedly large activation energy of 114 ± 8 kcal/mol, which is much larger than the 60-kcal/mol photoactivation energy at 500 nm. Moreover, we obtain an unprecedentedly large prefactor of 10(72±5) s(-1), which is roughly 60 orders of magnitude larger than typical frequencies of molecular motions! At lower temperatures, the measured Arrhenius parameters become more normal: Ea = 22 ± 2 kcal/mol and Apref = 10(9±1) s(-1) in the range of 37.0-44.5 °C. We present a theoretical framework and supporting calculations that attribute this unusual temperature-dependent kinetics of rhodopsin to a lowering of the reaction barrier at higher temperatures due to entropy-driven partial breakup of the rigid hydrogen-bonding network that hinders the reaction at lower temperatures.

Role of Tensorial Electronic Friction in Energy Transfer at Metal Surfaces.

An accurate description of nonadiabatic energy relaxation is crucial for modeling atomistic dynamics at metal surfaces. Interfacial energy transfer due to electron-hole pair excitations coupled to motion of molecular adsorbates is often simulated by Langevin molecular dynamics with electronic friction. Here, we present calculations of the full electronic friction tensor by using first order time-dependent perturbation theory at the density functional theory level. We show that the friction tensor is generally anisotropic and nondiagonal, as found for hydrogen atom on Pd(100) and CO on Cu(100) surfaces. This implies that electron-hole pair induced nonadiabatic coupling at metal surfaces leads to friction-induced mode coupling, therefore, opening an additional channel for energy redistribution. We demonstrate the robustness and accuracy of our results by direct comparison to established methods and experimental data.

Communication: Charge-population based dispersion interactions for molecules and materials.

We introduce a system-independent method to derive effective atomic C6 coefficients and polarizabilities in molecules and materials purely from charge population analysis. This enables the use of dispersion-correction schemes in electronic structure calculations without recourse to electron-density partitioning schemes and expands their applicability to semi-empirical methods and tight-binding Hamiltonians. We show that the accuracy of our method is en par with established electron-density partitioning based approaches in describing intermolecular C6 coefficients as well as dispersion energies of weakly bound molecular dimers, organic crystals, and supramolecular complexes. We showcase the utility of our approach by incorporation of the recently developed many-body dispersion method [Tkatchenko et al., Phys. Rev. Lett. 108, 236402 (2012)] into the semi-empirical density functional tight-binding method and propose the latter as a viable technique to study hybridorganic-inorganic interfaces.

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.

Perspective: Nonadiabatic dynamics theory.

Nonadiabatic dynamics--nuclear motion evolving on multiple potential energy surfaces--has captivated the interest of chemists for decades. Exciting advances in experimentation and theory have combined to greatly enhance our understanding of the rates and pathways of nonadiabatic chemical transformations. Nevertheless, there is a growing urgency for further development of theories that are practical and yet capable of reliable predictions, driven by fields such as solar energy, interstellar and atmospheric chemistry, photochemistry, vision, single molecule electronics, radiation damage, and many more. This Perspective examines the most significant theoretical and computational obstacles to achieving this goal, and suggests some possible strategies that may prove fruitful.

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.

Vibrational Fano resonances in dipole-bound anions.

This paper explores Fano resonances due to non-adiabatic coupling of vibrational modes and the electron continuum in dipole-bound anions. We adopt a simple one-electron model consisting of a point dipole and an auxiliary potential to represent the electron interaction with the neutral core. Nuclear motion is added by assuming that harmonic vibrations modulate the dipole moment. When the model is parameterized to simulate key features of the water tetramer anion, the resultant photodetachment lineshape closely resembles that observed experimentally and analyzed as a Fano resonance with a parameter q close to -1. Other parameterizations are explored for the model and it is found that large changes in the auxiliary potential are required to change the sign of q. This is consistent with the experimental finding that q is negative for all water cluster sizes studied.

Multiquantum vibrational excitation of NO scattered from Au(111): quantitative comparison of benchmark data to ab initio theories of nonadiabatic molecule-surface interactions.

Surface phenomena: measurements of absolute probabilities are reported for the vibrational excitation of NO(v=0→1,2) molecules scattered from a Au(111) surface. These measurements were quantitatively compared to calculations based on ab initio theoretical approaches to electronically nonadiabatic molecule-surface interactions. Good agreement was found between theory and experiment (see picture; T(s) =surface temperature, P=excitation probability, and E=incidence energy of translation).

A tiered approach to Monte Carlo sampling with self-consistent field potentials.

A "tiered" approach to Monte Carlo sampling of nuclear configurations is presented for ab initio, self-consistent field (SCF)-based potentials, including Hartree-Fock and density functional theory. Rather than Metropolis testing only the final SCF energy, individual cycle energies are tested in a tiered fashion, without approximation. Accordingly, rejected configurations are terminated early in the SCF procedure. The method is shown to properly obey detailed balance, and effective modifications are presented for cases in which the initial SCF guess is particularly poor. Demonstrations on simple systems are provided, including an assessment of the thermal properties of the neutral water dimer with B3LYP/6-31++G**. Cost analysis indicates a factor-of-two reduction in SCF cycles, which makes the method competitive with accelerated molecular dynamics sampling techniques, without the need for forces.

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.

Nonequilibrium Fermi golden rule for electronic transitions through conical intersections.

We consider photoinduced electronic transitions through conical intersections in large molecules. Starting from the linear vibronic model Hamiltonian and treating linear diabatic couplings within the second order cumulant expansion, we have developed a simple analytical expression for the time evolution of electronic populations at finite temperature. The derived expression can be seen as a nonequilibrium generalization of the Fermi golden rule due to a nonequilibrium character of the initial photoinduced nuclear distribution. All parameters in our model are obtained from electronic structure calculations followed by a diabatization procedure. The results of our model are found to agree well with those of quantum dynamics for a test set of systems: fulvene molecule, 2,6-bis(methylene) adamantyl cation, and its dimethyl derivative.

Excited State Intramolecular Proton Transfer with Nuclear-Electronic Orbital Ehrenfest Dynamics.

The recent development of the Ehrenfest dynamics approach in the nuclear-electronic orbital (NEO) framework provides a promising way to simulate coupled nuclear-electronic dynamics. Our previous study showed that the NEO-Ehrenfest approach with a semiclassical traveling proton basis method yields accurate predictions of molecular vibrational frequencies. In this work, we provide a more thorough analysis of the semiclassical traveling proton basis method to elucidate its validity and convergence behavior. We also conduct NEO-Ehrenfest dynamics simulations to study an excited state intramolecular proton transfer process. These simulations reveal that nuclear quantum effects influence the predictions of proton transfer reaction rates and kinetic isotope effects due to the intrinsic delocalized nature of the quantum nuclear wave function. This work illustrates the importance of nuclear quantum effects in coupled nuclear-electronic dynamical processes and shows that the NEO-Ehrenfest approach can be a powerful tool for providing insights and predictions for these processes.

Ab initio molecular dynamics with dual basis set methods.

On-the-fly, ab initio classical molecular dynamics are demonstrated with an underlying dual basis set potential energy surface. Dual-basis self-consistent field (Hartree-Fock and density functional theory) and resolution-of-the-identity second-order Møller-Plesset perturbation theory (RI-MP2) dynamics are tested for small systems, including the water dimer. The resulting dynamics are shown to be faithful representations of their single-basis analogues for individual trajectories, as well as vibrational spectra. Computational cost savings of 58% are demonstrated for SCF methods, even relative to Fock-extrapolated dynamics, and savings are further increased to 71% with RI-MP2. Notably, these timings outperform an idealized estimate of extended-Lagrangian molecular dynamics. The method is subsequently demonstrated on the vibrational absorption spectrum of two NO(+)(H2O)3 isomers and is shown to recover the significant width of the shared-proton bands observed experimentally.

Relativistic interactions in the radical pair model of magnetic field sense in CRY-1 protein of Arabidopsis thaliana.

Experimentally, it has been shown that magnetic field sensitivity in living organisms is connected to the presence of blue-light photoreceptor cryptochromes. Cryptochromes transduce a light signal through a chain of chemical reactions involving the formation of intermediate biradicals. It was proposed that an external magnetic field affects the interconversion between singlet and triplet states of biradicals and thus interferes with the signal transduction chain. Theoretical modeling of this process requires an accurate evaluation of all interactions important for singlet-triplet interconversion: electron-electron, spin-orbit, spin-spin, hyperfine, and Zeeman. In the current study we investigate these interactions at the CIS level of theory applied to representative fragments of the CRY-1 protein in the plant Arabidopsis thaliana. We find, in contrast to previous simplified modeling (O. Efimova, O.; Hore, P. J. Biophys. J. 2008, 94, 1565), that the spin-spin interaction is significantly larger than the "exchange" interaction. Thus it is not canceled by the latter but rather dies off with the inter-radical separation. Also, we find that the spin-orbit interaction can play a significant role in singlet-triplet interconversion for short inter-radical distances, and the hyperfine interaction becomes the only coupling interaction for long inter-radical distances.

Nonadiabatic dynamics at metal surfaces: independent-electron surface hopping.

Recent experiments have shown convincing evidence for nonadiabatic energy transfer from adsorbate degrees of freedom to surface electrons during the interaction of molecules with metal surfaces. In this paper, we propose an independent-electron surface hopping algorithm for the simulation of nonadiabatic gas-surface dynamics. The transfer of energy to electron-hole pair excitations of the metal is successfully captured by hops between electronic adiabats. The algorithm is able to account for the creation of multiple electron-hole pairs in the metal due to nonadiabatic transitions. Detailed simulations of the vibrational relaxation of nitric oxide on a gold surface, employing a multistate potential energy surface fit to density functional theory calculations, confirm that our algorithm can capture the underlying physics of the inelastic scattering process.