Cold collisions of complex polyatomic molecules

We introduce a method for classical trajectory calculations to simulate collisions between atoms and large rigid asymmetric-top molecules. We investigate the formation of molecule-helium complexes in buffer-gas cooling experiments at a temperature of 6.5 K for molecules as large as naphthalene. Our calculations show that the mean lifetime of the naphthalene-helium quasi-bound collision complex is not long enough for the formation of stable clusters under the experimental conditions. Our results suggest that it may be possible to improve the efficiency of the production of cold molecules in buffer-gas cooling experiments by increasing the density of helium. In addition, we find that the shape of molecules is important for the collision dynamics when the vibrational motion of molecules is frozen. For some molecules, it is even more crucial than the number of accessible degrees of freedom. This indicates that by selecting molecules with suitable shape for buffer-gas cooling, it may be possible to cool molecules with a very large number of degrees of freedom.     

Effects of classical nonlinear resonances in grazing diatom-surface collisions

Energy transfer between vibrational, rotational, and translational degrees of freedom of a molecule during a collision process is enhanced when the classical frequencies associated with the initial state are in the proximity of nonlinear resonance conditions. We present an analysis of the classical resonant effects in the collisions of light diatoms with periodic surfaces, and discuss the initial conditions in which these effects can be observed. In particular, we find that for grazing incidence and resonant initial values of the classical frequencies, corresponding to specific vibro-rotational molecular states and translational energies, an efficient energy transfer between the intramolecular vibro-rotational degrees of freedom and the translational degree of freedom along a symmetry direction on the surface can be found. This efficient energy transfer manifests itself in the emergence of specific peaks in the molecular diffraction patterns. The predictions of the resonance analysis are contrasted with the results of classical trajectory calculations obtained in a diatom-rigid surface collision model.     

Theoretical modeling of vibroelectronic quantum states in complex molecular systems: solvated carbon monoxide, a test case

In this paper we extend the perturbed matrix method by explicitly including the nuclear degrees of freedom, in order to treat quantum vibrational states in a perturbed molecule. In a previous paper we showed how to include, in a simple way, nuclear degrees of freedom for the calculation of molecular polarizability. In the present work we extend and generalize this approach to model vibroelectronic transitions, requiring a more sophisticated treatment.     

The role of solvent fluctuations in hydrophobic assembly

We use a coarse-grained solvent model to study the self-assembly of two nanoscale hydrophobic particles in water. We show how solvent degrees of freedom are involved in the process. By using tools of transition path sampling, we elucidate the reaction coordinates describing the assembly. In accord with earlier expectations, we find that fluctuations of the liquid-vapor-like interface surrounding the solutes are significant, in this case leading to the formation of a vapor tunnel between the two solute particles. This tunnel accelerates assembly. While considering this specific model system, the approach we use illustrates a methodology that is broadly applicable.     

Computational methods in coupled electron-ion Monte Carlo simulations.

In the last few years, we have been developing a Monte Carlo simulation method to cope with systems of many electrons and ions in the Born-Oppenheimer approximation: the coupled electron-ion Monte Carlo method (CEIMC). Electronic properties in CEIMC are computed by quantum Monte Carlo rather than by density functional theory (DFT) based techniques. CEIMC can, in principle, overcome some of the limitations of the present DFT-based ab initio dynamical methods. The new method has recently been applied to high-pressure metallic hydrogen. Herein, we present a new sampling algorithm that we have developed in the framework of the reptation quantum Monte Carlo method chosen to sample the electronic degrees of freedom, thereby improving its efficiency. Moreover, we show herein that, at least for the case of metallic hydrogen, variational estimates of the electronic energies lead to an accurate sampling of the proton degrees of freedom.     

Semiclassical initial value representation study of internal conversion rates

Internal conversion is an inherently quantum mechanical process. To date, "on the fly" computation of internal conversion rates is limited to harmonic approximations, which would seem to be especially unsuitable, given that the typical transition to the ground electronic state occurs at energies which are far from the harmonic limit. It is thus of interest to study the applicability of the semiclassial initial value representation (SCIVR) approach which is in principle amenable to on the fly studies even with "many" degrees of freedom. In this paper we study the applicability of the Herman-Kluk (HK) SCIVR to a model system with two coupled and anharmonic degrees of freedom. We find that (a) the HK SCIVR is a good approximation to the exact quantum dynamics; (b) computation of the first order correction to the HK-SCIVR approximation corroborates the accuracy; (c) by studying a large parameter range, we find that the harmonic approximation is mostly unsatisfactory; and (d) for the specific model used, the coupling between the modes was found to be relatively unimportant. These results imply that the HK-SCIVR methodology is a good candidate for on the fly studies of internal conversion processes of "large" molecules.     

Structural relaxation and glass transition behavior of binary hard-ellipse mixtures

Structural relaxation and glass transition in binary hard-spherical particle mixtures have been reported to exhibit unusual features depending on the size disparity and composition. However, the mechanism by which the mixing effects lead to these features and whether these features are universal for particles with anisotropic geometries remains unclear. Here, we employ event-driven molecular dynamics simulation to investigate the dynamical and structural properties of binary two-dimensional hard-ellipse mixtures. We find that the relaxation dynamics for translational degrees of freedom exhibit equivalent trends as those observed in binary hard-spherical mixtures. However, the glass transition densities for translational and rotational degrees of freedom present different dependencies on size disparity and composition. Furthermore, we propose a mechanism based on structural properties that explain the observed mixing effects and decoupling behavior between translational and rotational motions in binary hard-ellipse systems.     

Introducing phase transitions to quantum chemistry: from Trouton's rule to first principles vaporization entropies

In the present study, we employ quantum cluster equilibrium calculations on a small water cluster set in order to derive thermochemical equilibrium properties of the liquid phase as well as the liquid-vapor phase transition. The focus is set on the calculation of liquid phase entropies, from which entropies of vaporization at the normal boiling point of water are derived. Different electronic structure methods are compared and the influences of basis set size and of cooperative effects are discussed. In line with a previous study on the subject [B. Kirchner, J. Chem. Phys. 123, 204116 (2005)], we find that the neglect of cooperativity leads to large errors in the equilibrium cluster populations as well as in the obtained entropy values. In contrast, a correct treatment of the intermolecular many-body interaction yields liquid phase entropies and phase transition entropies being in very good agreement with the experimental reference, thus demonstrating that the quantum cluster equilibrium partition function intrinsically accounts for the shortcomings of the ideal gas partition function often employed in first principles entropy calculations. Comparing the calculated vaporization entropies to the value predicted by Trouton's rule, it is observed that for entropy calculations the consideration of intracluster cooperative effects is more important than the explicit treatment of the intercluster association even in a highly associated liquid such as water. The decomposition of entropy into contributions due to different degrees of freedom implies the need for the accurate treatment of particle indistinguishability and free volume of translation, whereas minor influences should be expected from the vibrational and rotational degrees of freedom and none from the electronic degrees of freedom.     

The electronic mean-field configuration interaction method. I. Theory and integral formulas

In this article, we introduce a new method for solving the electronic Schrodinger equation. This new method follows the same idea followed by the mean-field configuration interaction method already developed for molecular vibrations; i.e., groups of electronic degrees of freedom are contracted together in the mean field of the other degrees. If the same partition of electronic degrees of freedom is iterated, a self-consistent field method is obtained. Making coarser partitions (i.e., including more degrees in the same groups) and discarding the high energy states, the full configuration interaction limit can be approached. In contrast with the usual group function theory, no strong orthogonality condition is enforced. We have made use of a generalized version of the fundamental formula defining a Hopf algebra structure to derive Hamiltonian and overlap matrix element expressions which respect the group structure of the wave function as well as its fermionic symmetry. These expressions are amenable to a recursive computation.     

Application of the projection operator formalism to non-hamiltonian dynamics

Reconstruction of equations of motion from incomplete or noisy data and dimension reduction are two fundamental problems in the study of dynamical systems with many degrees of freedom. For the latter, extensive efforts have been made, but with limited success, to generalize the Zwanzig-Mori projection formalism, originally developed for hamiltonian systems close to thermodynamic equilibrium, to general non-hamiltonian systems lacking detailed balance. One difficulty introduced by such systems is the lack of an invariant measure, needed to define a statistical distribution. Based on a recent discovery that a non-hamiltonian system defined by a set of stochastic differential equations can be mapped to a hamiltonian system, we develop such general projection formalism. In the resulting generalized Langevin equations, a set of generalized fluctuation-dissipation relations connect the memory kernel and the random noise terms, analogous to hamiltonian systems obeying detailed balance. Lacking of these relations restricts previous application of the generalized Langevin formalism. Result of this work may serve as the theoretical basis for further technical developments on model reconstruction with reduced degrees of freedom. We first use an analytically solvable example to illustrate the formalism and the fluctuation-dissipation relation. Our numerical test on a chemical network with end-product inhibition further demonstrates the validity of the formalism. We suggest that the formalism can find wide applications in scientific modeling. Specifically, we discuss potential applications to biological networks. In particular, the method provides a suitable framework for gaining insights into network properties such as robustness and parameter transferability.     

Exciton coherence lifetimes from electronic structure

We model the coherent energy transfer of an electronic excitation within covalently linked aromatic homodimers from first-principles. Our results shed light on whether commonly used models of the bath calculated via detailed electronic structure calculations can reproduce the key dynamics. For the systems we model, the time scales of coherent transport are experimentally known from time-dependent polarization anisotropy measurements, and so we can directly assess whether current techniques are predictive for modeling coherent transport. The coupling of the electronic degrees of freedom to the nuclear degrees of freedom is calculated from first-principles rather than assumed, and the fluorescence anisotropy decay is directly reproduced. Surprisingly, we find that although time-dependent density functional theory absolute energies are routinely in error by orders of magnitude more than the coupling energy between monomers, the coherent transport properties of these dimers can be semi-quantitatively reproduced from these calculations. Future directions which must be pursued to yield predictive and reliable models of coherent transport are suggested.     

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.     

Communication: Exciton-phonon information flow in the energy transfer process of photosynthetic complexes

Non-Markovian and nonequilibrium phonon effects are believed to be key ingredients in the energy transfer in photosynthetic complexes, especially in complexes which exhibit a regime of intermediate exciton-phonon coupling. In this work, we utilize a recently developed measure for non-Markovianity to elucidate the exciton-phonon dynamics in terms of the information flow between electronic and vibrational degrees of freedom. We study the measure in the hierarchical equation of motion approach which captures strong coupling effects and nonequilibrium molecular reorganization. We propose an additional trace distance measure for the information flow that could be extended to other master equations. We find that for a model dimer system and for the Fenna-Matthews-Olson complex the non-Markovianity is significant under physiological conditions.     

Evolutionary method for the assembly of rigid protein fragments

Genetic algorithms constitute a powerful optimization method that has already been used in the study of the protein folding problem. However, they often suffer from a lack of convergence in a reasonably short time for complex fitness functions. Here, we propose an evolutionary strategy that can reproducibly find structures close to the minimum of a potential function for a simplified protein model in an efficient way. The model reduces the number of degrees of freedom of the system by treating the protein structure as composed of rigid fragments. The search incorporates a double encoding procedure and a merging operation from subpopulations that evolve independently of one another, both contributing to the good performance of the full algorithm. We have tested it with protein structures of different degrees of complexity, and present our conclusions related to its possible application as an efficient tool for the analysis of folding potentials.     

Multiple steps and multiple excitations in photoisomerization of azobenzene

Detailed understanding of femtosecond-scale photochemical processes requires dynamical simulations that are complementary to interpretations based on transitions between energy surfaces. For cis to trans photoisomerization of azobenzene following a 100 fs laser pulse, we find that the mechanism is rotation about the central NN bond, and the process is complete in less than 1 ps. The initial excitation and subsequent de-excitation are each achieved via multiple steps, with the molecule always in a superposition of electronic states, as the 3N nuclear degrees of freedom are excited by the laser pulse.     

Sampling of slow diffusive conformational transitions with accelerated molecular dynamics

Slow diffusive conformational transitions play key functional roles in biomolecular systems. Our ability to sample these motions with molecular dynamics simulation in explicit solvent is limited by the slow diffusion of the solvent molecules around the biomolecules. Previously, we proposed an accelerated molecular dynamics method that has been shown to efficiently sample the torsional degrees of freedom of biomolecules beyond the millisecond timescale. However, in our previous approach, large-amplitude displacements of biomolecules are still slowed by the diffusion of the solvent. Here we present a unified approach of efficiently sampling both the torsional degrees of freedom and the diffusive motions concurrently. We show that this approach samples the configuration space more efficiently than normal molecular dynamics and that ensemble averages converge faster to the correct values.