Ab initio dynamics with wave-packets and density matrices

Efficient methodologies to conduct simultaneous dynamics of electrons and nuclei are discussed. Particularly, attention is directed to a recent development that combines quantum dynamics with ab initio molecular dynamics. The two components of the methodology, namely, quantum dynamics and ab initio molecular dynamics, are harnessed together using a time-dependent self-consistent field-like coupling procedure. An approach to conduct quantum dynamics using an accurate banded, sparse and Toeplitz representation for the discrete free propagator is highlighted with suitable review of other related approaches. One notable feature of the method is that all important quantum dynamical effects including zero-point effects, tunneling as well as over-barrier reflections are accurately treated. Computational methodologies for improved efficiency of the quantum dynamics are also discussed. There exists a number of ways to carry out simultaneous ab initio molecular dynamics (such as Born–Oppenheimer dynamics and extended Lagrangian dynamics, Car–Parrinello dynamics being a prime example of the latter); our prime focus remains on atom-centered density-matrix propagation and Born–Oppenheimer dynamics. The electronic degrees of freedom are handled at accurate levels of density functional theory, using hybrid or gradient corrected approximations. Benchmark calculations are provided for a prototypical proton transfer system. Future generalizations and goals are discussed.     

Improving the convergence of closed and open path integral molecular dynamics via higher order Trotter factorization schemes

Higher order factorization schemes are developed for path integral molecular dynamics in order to improve the convergence of estimators for physical observables as a function of the Trotter number. The methods are based on the Takahashi-Imada and Susuki decompositions of the Boltzmann operator. The methods introduced improve the averages of the estimators by using the classical forces needed to carry out the dynamics to construct a posteriori weighting factors for standard path integral molecular dynamics. The new approaches are straightforward to implement in existing path integral codes and carry no significant overhead. The Suzuki higher order factorization was also used to improve the end-to-end distance estimator in open path integral molecular dynamics. The new schemes are tested in various model systems, including an ab initio path integral molecular dynamics calculation on the hydrogen molecule and a quantum water model. The proposed algorithms have potential utility for reducing the cost of path integral molecular dynamics calculations of bulk systems.     

Quantum wave packet ab initio molecular dynamics: an approach to study quantum dynamics in large systems

A methodology to efficiently conduct simultaneous dynamics of electrons and nuclei is presented. The approach involves quantum wave packet dynamics using an accurate banded, sparse and Toeplitz representation for the discrete free propagator, in conjunction with ab initio molecular dynamics treatment of the electronic and classical nuclear degree of freedom. The latter may be achieved either by using atom-centered density-matrix propagation or by using Born-Oppenheimer dynamics. The two components of the methodology, namely, quantum dynamics and ab initio molecular dynamics, are harnessed together using a time-dependent self-consistent field-like coupling procedure. The quantum wave packet dynamics is made computationally robust by using adaptive grids to achieve optimized sampling. One notable feature of the approach is that important quantum dynamical effects including zero-point effects, tunneling, as well as over-barrier reflections are treated accurately. The electronic degrees of freedom are simultaneously handled at accurate levels of density functional theory, including hybrid or gradient corrected approximations. Benchmark calculations are provided for proton transfer systems and the dynamics results are compared with exact calculations to determine the accuracy of the approach.     

Algorithms for sampling a quantum microcanonical ensemble of harmonic oscillators at potential minima and conical intersections

Algorithms are presented for sampling quantum microcanonical ensembles for a potential energy minimum and for the conical intersection at the minimum energy crossing point of two coupled electronic states. These ensembles may be used to initialize trajectories for chemical dynamics simulations. The unimolecular dynamics of a microcanonical ensemble about a potential energy minimum may be compared with the dynamics predicted by quantum Rice-Ramsperger-Kassel-Marcus (RRKM) theory. If the dynamics is non-RRKM, it will be of particular interest to determine which states have particularly long lifetimes. Initializing a microcanonical ensemble for the electronically excited state at a conical intersection is a model for electronic nonadiabatic dynamics. The trajectory surface-hopping approach may be used to study the ensuing chemical dynamics. A strength of the model is that zero-point energy conditions are included for the initial nonadiabatic dynamics at the conical intersection.     

Reorientation dynamics of nanoconfined water: power-law decay, hydrogen-bond jumps, and test of a two-state model

The reorientation dynamics of water confined within nanoscale, hydrophilic silica pores are investigated using molecular dynamics simulations. The effect of surface hydrogen-bonding and electrostatic interactions are examined by comparing with both a silica pore with no charges (representing hydrophobic confinement) and bulk water. The OH reorientation in water is found to slow significantly in hydrophilic confinement compared to bulk water, and is well-described by a power-law decay extending beyond one nanosecond. In contrast, the dynamics of water in the hydrophobic pore are more modestly affected. A two-state model, commonly used to interpret confined liquid properties, is tested by analysis of the position-dependence of the water dynamics. While the two-state model provides a good fit of the orientational decay, our molecular-level analysis evidences that it relies on an over-simplified picture of water dynamics. In contrast with the two-state model assumptions, the interface dynamics is markedly heterogeneous, especially in the hydrophilic pore and there is no single interfacial state with a common dynamics.     

Dynamics of nanoscopic water: vibrational echo and infrared pump-probe studies of reverse micelles

The dynamics of water in nanoscopic pools 1.7-4.0 nm in diameter in AOT reverse micelles were studied with ultrafast infrared spectrally resolved stimulated vibrational echo and pump-probe spectroscopies. The experiments were conducted on the OD hydroxyl stretch of low-concentration HOD in the H2O, providing a direct examination of the hydrogen-bond network dynamics. Pump-probe experiments show that the vibrational lifetime of the OD stretch mode increases as the size of the reverse micelle decreases. These experiments are also sensitive to hydrogen-bond dissociation and reformation dynamics, which are observed to change with reverse micelle size. Spectrally resolved vibrational echo data were obtained at several frequencies. The vibrational echo data are compared to data taken on bulk water and on a 6 M NaCl solution, which is used to examine the role of ionic strength on the water dynamics in reverse micelles. Two types of vibrational echo measurements are presented: the vibrational echo decays and the vibrational echo peak shifts. As the water nanopool size decreases, the vibrational echo decays become slower. Even the largest nanopool (4 nm, approximately 1000 water molecules) has dynamics that are substantially slower than bulk water. It is demonstrated that the slow dynamics in the reverse micelle water nanopools are a result of confinement rather than ionic strength. The data are fit using time-dependent diagrammatic perturbation theory to obtain the frequency-frequency correlation function (FFCF) for each reverse micelle. The results are compared to the FFCF of water and show that the largest differences are in the slowest time scale dynamics. In bulk water, the slowest time scale dynamics are caused by hydrogen-bond network equilibration, i.e., the making and breaking of hydrogen bonds. For the smallest nanopools, the longest time scale component of the water dynamics is approximately 10 times longer than the dynamics in bulk water. The vibrational echo data for the smallest reverse micelle displays a dependence on the detection wavelength, which may indicate that multiple ensembles of water molecules are being observed.     

Fluorescence probing of temperature-dependent dynamics and friction in ionic liquid local environments

The solvation dynamics and local orientational friction for a series of four ionic liquids have been probed using coumarin 153 (C153) as a function of temperature. These ionic liquids are comprised of nonaromatic organic cations paired with a common anion, bis(trifluoromethylsulfonyl)imide (NTf(2)-). The specific liquids are as follows: N-methyl-tri-N-butylammonium NTf(2)- (N(1444)+/NTf(2)-), N-hexyl-tri-N-butylammonium NTf(2)- (N(6444)+/NTf(2)-), N-methyl-N-butylpyrrolidinium NTf(2)- (Pyrr(14)+/NTf(2)-), and N-methyl-N-ethoxyethylpyrrolidinium NTf(2)- (Pyrr(1(2O2))+/NTf(2)-). The observed solvation dynamics and fluorescence depolarization dynamics occur over a broad range of time scales that can only be adequately fit by functions including three or more exponential components. Stretched exponential distributions cannot adequately fit our data. The solvation and reorientational dynamics of the C153 probe are studied over a range of temperatures from 278.2 to 353.2 K. For both the solvation dynamics and the probe reorientational dynamics, the observed temperature dependence is well fit by a Vogel-Tammann-Fulcher law. To correlate the observed microscopic dynamics with macroscopic physical properties, temperature-dependent viscosities are also measured. Differential scanning calorimetry is used to study the thermodynamics of the phase transitions from the liquid to supercooled liquid to glassy states. For the two tetraalkylammonium liquids, the observed melting transitions occur near 300 K, so we are able to study the dynamics in a clearly supercooled regime. Very long time scale orientational relaxation time constants dynamics on the order of 100 ns are observed in the C153 fluorescence anisotropy. These are interpreted to arise from long-lived local structures in the environment surrounding the C153 probe.     

Vibrational spectral diffusion and hydrogen bond dynamics in heavy water from first principles

We present a first-principles theoretical study of vibrational spectral diffusion and hydrogen bond dynamics in heavy water without using any empirical model potentials. The calculations are based on ab initio molecular dynamics simulations for trajectory generation and a time series analysis using the wavelet method for frequency calculations. It is found that, in deuterated water, although a one-to-one relation does not exist between the instantaneous frequency of an OD bond and the distance of its associated hydrogen bond, such a relation does hold on average. The dynamics of spectral diffusion is investigated by means of frequency-time correlation and spectral hole dynamics calculations. Both of these functions are found to have a short-time decay with a time scale of approximately 100 fs corresponding to dynamics of intact hydrogen bonds and a slower long-time decay with a time constant of approximately 2 ps corresponding to lifetimes of hydrogen bonds. The connection of the slower time scale to the dynamics of local structural relaxation is also discussed. The dynamics of hydrogen bond making is shown to have a rather fast time scale of approximately 100 fs; hence, it can also contribute to the short-time dynamics of spectral diffusion. A damped oscillation is also found at around 150-200 fs, which is shown to have come from underdamped intermolecular vibrations of a hydrogen-bonded water pair. Such assignments are confirmed by independent calculations of power spectra of intermolecular motion and hydrogen bond kinetics using the population correlation function formalism. The details of the time constants of frequency correlations and spectral shifts are found to depend on the frequencies of chosen OD bonds and are analyzed in terms of the dynamics of hydrogen bonds of varying strengths and also of free non-hydrogen-bonded OD groups.     

The phase-dependent photochemical reaction dynamics of halooxides and nitrosyl halides

Recent progress in understanding the phase-dependent reactivity of halooxides and nitrosyl halides is outlined. Halooxide reactivity is represented by the photochemistry of chlorine dioxide (OClO) and dichlorine monoxide (ClOCl). The gas phase photochemical dynamics of OClO are contrasted with the dynamics in condensed environments. The role of excited-state symmetry in defining the reaction dynamics and the observation of photoisomerization resulting in the production of ClOO are discussed. The current understanding of the excited-state reaction dynamics of ClOCl and evidence for photoisomerization of this species resulting in the production of ClClO are outlined. Finally, the photochemical reaction dynamics of the nitrosyl halide ClNO are presented. The main difference between the gas and condensed phase reaction dynamics of this species is that whereas photodissociation to form Cl and NO dominates the gas phase reaction dynamics, photoisomerization resulting in ClON production occurs to an appreciable extent in condensed environments. The observation of photoisomerization for OClO, ClOCl and ClNO suggests that this process is a general feature of the condensed phase reaction dynamics for smaller halooxides and nitrosyl halides. Finally, future areas for study in both halooxide and nitrosyl halide photoreactivity are outlined.     

Effects of disordered interchain interactions on polaron dynamics in semiconducting polymers

Polaron dynamics in a system of two randomly coupled polymer chains is simulated using a nonadiabatic evolution method. The simulations are performed within the framework of the Su-Schrieffer-Heeger model modified to include disordered interchain interactions and an external electric field. By analysing the polaron velocity statistically, we find that the polaron motion is determined by the competition between the electric field and the disordered interchain interactions. Polaron dynamics are classified into two types, weak-coupling dynamics and strong-coupling dynamics. It is found that the strength of interchain interactions is the dominant factor controlling charge propagation in weak-coupling dynamics, whereas the effects of disorder are dominant in strong-coupling dynamics. The charge carriers tend to have higher mobility for stronger interchain coupling, and interchain coupling disorder can be favorable for charge transport depending on the coupling strength and the electric field.     

Hydrogen bond dynamics at water/organic liquid interfaces

Hydrogen bond dynamics at the neat interface between water and a series of organic liquids are studied with molecular dynamics computer simulation. The organic liquids are nonpolar (carbon tetrachloride), weakly polar (1,2-dichloroethane), and polar (nitrobenzene). The effect of surface polarity and surface roughness is examined. The dynamics are expressed in terms of the hydrogen bond population autocorrelation functions and are found to be nonexponential and strongly dependent on the nature of the organic phase. In particular, at all interfaces, the dynamics are slower at the interface than in the bulk and sensitive to the location of the water molecules along the interface normal.     

Fluctuating charge normal modes: An algorithm for implementing molecular dynamics simulations with polarizable potentials

A new method for performing molecular dynamics simulations with fluctuating charge polarizable potentials is introduced. In fluctuating charge models, polarizability is treated by allowing the partial charges to be variables, with values that are coupled to charges on the same molecule as well as those on other molecules. The charges can be efficiently propagated in a molecular dynamics simulation using extended Lagrangian dynamics. By making a coordinate change from the charge variables to a set of normal mode charge coordinates for each molecule, a new method is constructed in which the normal mode charge variables uncouple from those on the same molecule. The method is applied to the TIP4P-FQ model of water and compared to other methods for implementing the dynamics. The methods are compared using different molecular dynamics time steps.     

多原子体系非绝热动力学的近似理论方法

非绝热动力学普遍存在于光物理和光化学过程中。描述非绝热跃迁需要处理电子-原子核间的相互耦合运动。由于计算量随体系尺度增大剧烈增长,准确的量子动力学计算目前只适用于描述小分子体系。为了研究多原子分子体系的非绝热过程,近年来发展了一些基于量子-经典动力学近似方法。本文将对典型的这类方法包括经典Ehrenfest方法、面跳跃方法、基于Wigner表示的混合量子-经典方法进行简要的介绍,并讨论如何将量子-经典动力学方法与电子结构从头算手段相结合,模拟非绝热过程。重点阐明各种方法的基本思想和优缺点,并对该领域的发展进行展望。     

High-pressure effect on the dynamics of solvated peptides

The dynamics of peptides has a direct connection to how quickly proteins can alter their conformations. The speed of exploring the free energy landscape depend on many factors, including the physical parameters of the environment, such as pressure and temperature. We performed a series of molecular dynamics simulations to investigate the pressure-temperature effects on peptide dynamics, especially on the torsional angle and peptide-water hydrogen bonding (H-bonding) dynamics. Here, we show that the dynamics of the omega angle and the H-bonding dynamics between water and the peptide are affected by pressure. At high temperature (500 K), both the dynamics of the torsional angle ω and H-bonding slow down significantly with increasing pressure, interestingly, at approximately the same rate. However, at a lower temperature of 300 K, the observed trend on H-bonding dynamics as a function of pressure reverses, i.e., higher pressure speeds up H-bonding dynamics.     

Mesoscopic description of solvent effects on polymer dynamics

Solvent effects on polymer dynamics and structure are investigated using a mesoscopic solvent model that accounts for hydrodynamic interactions among the polymer beads. The simulation method combines molecular dynamics of the polymer chain, interacting with the solvent molecules through intermolecular forces, with mesoscopic multiparticle collision dynamics for the solvent molecules. Changes in the intermolecular forces between the polymer beads and mesoscopic solvent molecules are used to vary the solvent conditions from those for good to poor solvents. Polymer collapse and expansion dynamics following changes in solvent conditions are studied for homopolymer and block copolymer solutions. The frictional properties of polymers are also investigated.     

Calculation of diffusion coefficients for carbon dioxide + solute system near the critical conditions by non-equilibrium molecular dynamics simulation

A non-equilibrium molecular dynamics simulation was adopted to calculate the diffusion coefficients for a pseudo-binary system of carbon dioxide and for a carbon dioxide + solute system at 308.2 and 318.2 K. The calculated results were compared with the self- and tracer diffusion coefficients calculated by an equilibrium molecular dynamics simulation. The simulated results for the pseudo-binary system of carbon dioxide by the non-equilibrium molecular dynamics simulation are in good agreement with the results of self diffusion coefficients for pure carbon dioxide by the equilibrium molecular dynamics simulation. The simulated results of mutual diffusion coefficients for the carbon dioxide + solute system by the non-equilibrium molecular dynamics simulation are slightly lower than the results of the tracer diffusion coefficients by the equilibrium molecular dynamics simulation. The anomalous behavior of diffusion coefficients near the critical concentration was represented by the results of the non-equilibrium molecular dynamics simulation.     

Molecular structure and dynamics of liquids: aqueous urea solutions

In this review a multi-technical approach to the analysis of the structure and dynamics of the urea/water system is described. The reorientational movement of the solute molecule is investigated by the analysis of spectral band-shapes, as well as with the use of the optical Kerr effect (OKE) and molecular dynamics simulation (MDS). The effect of solute concentration on the structure and dynamics of the aqueous solutions (aggregation, orientational distribution, solvation...) is studied by molecular dynamics simulation and neutron scattering. The results obtained by other techniques are included to provide a critical analysis. Finally, the low-frequency Raman spectra of the system are interpreted on the basis of the semi-quantitative information obtained by molecular dynamics simulation.