Performance evaluation of third-order thermodynamic perturbation theory and comparison with existing liquid state theories

To evaluate the performance of a recently proposed third-order thermodynamic perturbation theory (TPT), we employ the third TPT for calculation of thermodynamic properties such as compressibility factor, internal energy, excess chemical potential, gas-liquid coexistence curve, and critical properties of several fluids. By comparing the third-order TPT results with corresponding simulation data available in literature and supplied in the present report and theoretical results from several other theoretical approaches, one concludes that the third-order TPT is, in general, more accurate than other approaches such as Barker-Henderson second-order TPT using a macroscopic compressibility approximation (MCA-TPT), self-consistent Ornstein-Zernike approach, Monte Carlo perturbation theory, and a specially devised equation of state. Specifically, the third-order TPT can predict quantitatively a double critical phenomena of gas-liquid transition and a low-density liquid (LDL)-high-density liquid (HDL) transition associated with a soft core (SC) potential fluid very satisfactorily, but the predictions for the LDL-HDL transition based on the second-order MCA-TPT are quantitatively very bad or qualitatively incorrect. The failure of the second-order MCA-TPT for the SC fluid can be ascribed to the facts that for the SC potential the second-order and third-order terms of the perturbation expansion are not small quantities and that the second-order term is underestimated by the MCA. It is concluded that the present third-order version of the TPT is reliable for varying model fluids.     

Insights into the dynamics of HIV-1 protease: a kinetic network model constructed from atomistic simulations

The conformational dynamics in the flaps of HIV-1 protease plays a crucial role in the mechanism of substrate binding. We develop a kinetic network model, constructed from detailed atomistic simulations, to determine the kinetic mechanisms of the conformational transitions in HIV-1 PR. To overcome the time scale limitation of conventional molecular dynamics (MD) simulations, our method combines replica exchange MD with transition path theory (TPT) to study the diversity and temperature dependence of the pathways connecting functionally important states of the protease. At low temperatures the large-scale flap opening is dominated by a small number of paths; at elevated temperatures the transition occurs through many structurally heterogeneous routes. The expanded conformation in the crystal structure 1TW7 is found to closely mimic a key intermediate in the flap-opening pathways at low temperature. We investigated the different transition mechanisms between the semi-open and closed forms. The calculated relaxation times reveal fast semi-open ? closed transitions, and infrequently the flaps fully open. The ligand binding rate predicted from this kinetic model increases by 38-fold from 285 to 309 K, which is in general agreement with experiments. To our knowledge, this is the first application of a network model constructed from atomistic simulations together with TPT to analyze conformational changes between different functional states of a natively folded protein.     

Solid phase thermodynamic perturbation theory: test and application to multiple solid phases

A simple procedure for the determination of hard sphere (HS) solid phase radial distribution function (rdf) is proposed, which, thanks to its physical foundation, allows for extension to other crystal structures besides the fcc structure. The validity of the procedure is confirmed by comparing (1) the predicted HS solid phase rdf's with corresponding simulation data and (2) the predicted non-HS solid phase Helmholtz free energy by the present solid phase first-order thermodynamic perturbation theory (TPT) whose numerical implementation depends on the HS solid phase rdf's as input, with the corresponding predictions also by the first-order TPT but the required HS solid phase rdf is given by an "exact" empirical simulation-fitted formula. The present solid phase first-order TPT predicts isostructural fcc-fcc transition of a hard core attractive Yukawa fluid, in very satisfactory agreement with the corresponding simulation data and is far more accurate than a recent thermodynamically consistent density functional perturbation theory. The present solid phase first-order TPT is employed to investigate multiple solid phases. It is found that a short-ranged potential, even if it is continuous and differentiable or is superimposed over a long-ranged potential, is sufficient to induce the multiple solid phases. When the potential range is short enough, not only isostructural fcc-fcc transition but also isostructural bcc-bcc transition, simple cubic (sc)-sc transition, or even fcc-bcc, fcc-sc, and bcc-sc transitions can be induced. Even triple point involving three solid phases becomes possible. The multiple solid phases can be stable or metastable depending on the potential parameters.     

Minimum energy pathways of brittle and ductile deformation/fracture processes

An alternative approach to exploring deformation and fracture processes from molecular dynamics simulations is presented. The underlying concept is based on the transition path sampling scheme which was proven powerful for unprejudiced mechanistic analyses of rare reaction events and phase transitions. Transferring this method to deformation and fracture is particularly rewarding for the study of brittle materials. Similar to unbiased investigations of nucleation events in first order phase transitions, our simulations do not require the preparation of cavities to induce fracture processes. The mechanisms of cavitation and fracture propagation are instead obtained as simulation results. As two case studies, transition path sampling related to brittle fracture of ZnO nanorods and to ductile deformation of Al nanoblocks is compared to conventional simulations imposing constant-strain rates.     

PyRETIS: A well‐done,medium‐sized python library for rare events

Transition path sampling techniques are becoming common approaches in the study of rare events at the molecular scale. More efficient methods, such as transition interface sampling (TIS) and replica exchange transition interface sampling (RETIS), allow the investigation of rare events, for example, chemical reactions and structural/morphological transitions, in a reasonable computational time. Here, we present PyRETIS, a Python library for performing TIS and RETIS simulations. PyRETIS directs molecular dynamics (MD) simulations in order to sample rare events with unbiased dynamics. PyRETIS is designed to be easily interfaced with any molecular simulation package and in the present release, it has been interfaced with GROMACS and CP2K, for classical and ab initio MD simulations, respectively. © 2017 Wiley Periodicals, Inc.     

Phase behavior of density-dependent pair potentials

Phase diagram is calculated by a recently proposed third-order thermodynamic perturbation theory (TPT) for fluid phase and a recently proposed first-order TPT for solid phases; the underlying interparticle potential consists of a hard sphere repulsion and a perturbation tail of an attractive inverse power law type or Yukawa type whose range varies with bulk densities. It is found that besides usual phase transitions associated with density-independent potentials, the density dependence of the perturbation tail evokes some additional novel phase transitions including isostructural solid-solid transition and liquid-liquid transition. Novel triple points are also exhibited which includes stable fluid (vapor or liquid)-face-centered cubic(fcc)-fcc and liquid-liquid-fcc, metastable liquid-body-centered cubic(bcc)-bcc. It also is found that the phase diagram sensitively depends on the density dependence and the concrete mathematical form of the underlying potentials. Some of the disclosed novel transitions has been observed experimentally in complex fluids and molecular liquids, while others still remain to be experimentally verified.     

How critical fluctuations influence adsorption properties of a van der Waals fluid onto a spherical colloidal particle

A recently proposed 3rd-order thermodynamic perturbation theory (TPT) is extended to its 5th-order version and non-uniform counterpart by supplementing with density functional theory (DFT) and a number of ansatzs for a bulk 2nd-order direct correlation function (DCF). Employment of the ansatzs DCF enables the resultant non-uniform formalism devoid of any adjustable parameter and free from numerically solving an Ornstein–Zernike integral equation theory. Density profiles calculated by the present non-uniform formalism for a hard core attractive Yukawa (HCAY) fluid near a spherical geometry are favorably compared with corresponding simulation data available in literature, and are more accurate than those based on a previous 3rd + 2nd-order perturbation DFT. The non-uniform 5th-order TPT is employed to investigate adsorption of the HCAY fluid onto a colloidal particle; it is disclosed that a depletion adsorption can be induced when the coexistence bulk fluid is situated in neighborhood of a critical point or near a bulk vapor–liquid coexistence gaseous phase or liquid phase density. A physical interpretation is given for such depletion adsorption and for its connection with parameters of the potential under consideration, which is ascribed to critical density fluctuations existing within a wide region of the bulk diagram. For a large spherical external potential inducing wetting transition, it is found that only round wetting transition is found instead of 1st-order pre-wetting transition in the case of a planar wall external potential, and the wetting transition temperature increases relative to that for the planar wall external potential. The present theoretical results for wetting transitions are supported by previous investigation based on thermodynamic considerations and a phenomenological Landau mean field theory, and are also in conformity with the present qualitative physical interpretation.     

Exploring reaction pathways with transition path and umbrella sampling: application to methyl maltoside

The transition path sampling (TPS) method is a powerful approach to study chemical reactions or transitional properties on complex potential energy landscapes. One of the main advantages of the method over potential of mean force methods is that reaction rates can be directly accessed without knowledge of the exact reaction coordinate. We have investigated the complementary nature of these two differing approaches, comparing transition path sampling with the weighted histogram analysis method to study a conformational change in a small model system. In this case study, the transition paths for a transition between two rotational conformers of a model disaccharide molecule, methyl beta-D-maltoside, were compared with a free energy surface constrained by the two commonly used glycosidic (phi,psi) torsional angles. The TPS method revealed a reaction channel that was not apparent from the potential of mean force method, and the suitability of phi and psi as reaction coordinates to describe the isomerization in vacuo was confirmed by examination of the transition path ensemble. Using both transition state theory and transition path sampling methods, the transition rate was estimated. We have estimated a characteristic time between transitions of approximately 160 ns for this rare isomerization event between the two conformations of the carbohydrate. We conclude that transition path sampling can extract subtle information about the dynamics not apparent from the potential of mean force method. However, in calculating the reaction rate, the transition path sampling method required 27.5 times the computational effort than was needed by the potential of mean force method.     

Simulating rare events in equilibrium or nonequilibrium stochastic systems

We present three algorithms for calculating rate constants and sampling transition paths for rare events in simulations with stochastic dynamics. The methods do not require a priori knowledge of the phase-space density and are suitable for equilibrium or nonequilibrium systems in stationary state. All the methods use a series of interfaces in phase space, between the initial and final states, to generate transition paths as chains of connected partial paths, in a ratchetlike manner. No assumptions are made about the distribution of paths at the interfaces. The three methods differ in the way that the transition path ensemble is generated. We apply the algorithms to kinetic Monte Carlo simulations of a genetic switch and to Langevin dynamics simulations of intermittently driven polymer translocation through a pore. We find that the three methods are all of comparable efficiency, and that all the methods are much more efficient than brute-force simulation.     

Non-hard sphere thermodynamic perturbation theory

A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of f(ex-ref), chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established.     

Effect of critical fluctuations on adsorption of van der Waals fluid in a spherical cavity

A recently proposed non-uniform fifth-order thermodynamic perturbation theory (TPT) is employed to investigate the adsorption of a hard core attractive Yukawa (HCAY) fluid in a spherical cavity. Extensive comparison with available simulation data indicate that the non-uniform fifth-order TPT is sufficiently reliable in calculating the density profiles of the HCAY fluid in the highly confining geometry, and generally is more accurate than a previous third-order?+?second-order perturbation density functional theory. The non-uniform fifth-order TPT is free from numerically solving an Ornstein–Zernike integral equation, and also free of any adjustable parameter; consequently, it can be applied to both supercritical and subcritical temperature regions. The non-uniform fifth-order TPT is employed to investigate critical adsorption of the HCYA fluid in a single spherical cavity – it is disclosed that the critical fluctuations near the critical point induce depletion adsorption – quantitative theoretical calculation on relationship between the critical depletion adsorption, parameters of coexistence bulk phase and the responsible external field is in agreement with qualitative physical analysis.     

Solvation effects for polymers at an interface: a hybrid self-consistent field-density functional theory approach

Using polyatomic density functional theory of Kierlik and Rosinberg, we show that Wertheim's thermodynamic perturbation theory (TPT) incorporates solvation effects in a systematic, although simplified form. We derive two approximate solvation potentials, which require the knowledge of the correlation function in the reference unbonded fluid only. The theoretical predictions are tested against many-chain Monte Carlo simulations for moderate chain lengths. The predictions of the end-to-end distance in the bulk are in a reasonable agreement with simulations for the TPT(M-1) approximation, while the simpler TPT2_e approximation leads to the solvation potential that is shorter ranged and considerably less accurate. The resulting conformations are used in the subsequent self-consistent field theory calculations of hard-sphere polymers at a hard wall. While the incorporation of the solvation effects has little impact on the density profiles, the predictions of the components of the end-to-end distance vector as a function of the distance to the wall are much improved.     

Finite temperature string method for the study of rare events

A method is presented for the study of rare events such as conformational changes arising in activated processes whose reaction coordinate is not known beforehand and for which the assumptions of transition state theory are invalid. The method samples the energy landscape adaptively and determines the isoprobability surfaces for the transition: by definition the trajectories initiated anywhere on one of these surfaces has equal probability to reach first one metastable set rather than the other. Upon weighting these surfaces by the equilibrium probability distribution, one obtains an effective transition pathway, i.e., a tube in configuration space inside which conformational changes occur with high probability, and the associated rate. The method is first validated on a simple two-dimensional example; then it is applied to a model of solid-solid transformation of a condensed system.     

链状分子状态方程的推导及热容的推算

在Barker Henderson, Zhang以及Wertheim 等微扰理论的基础上,以方阱势硬球流体为参考体系,将Zhang的解析表达方法与Wertheim 的链成键自由能的处理方法结合起来,推导出自由链接的链状分子流体的Helmholtz自由能的解析表达式,并得到了压缩因子、内能、恒容热容等热力学性质的计算式.计算结果与MC(Monte Carlo)模拟结果吻合良好.对Zhang的解析表达式与“TPT D”(二阶Wertheim微扰理论)的结合也作了推导和计算.     

A quantum chemistry study of the Cl atom reaction with formaldehyde

The elementary vapor-phase reaction between Cl atoms and HCHO has been studied by ab initio methods. Calculations at the MP2, MP3, MP4(SDTQ), CCSD, CCSD(T), and MRD-CI levels of theory show that the reaction is characterized by a low electronic barrier; excluding the effects of spin-orbit splitting in Cl, our best estimate at the MRD-CI/aug-cc-pVTZ//RHF-RCCSD(T)/aug-cc-pVTZ level of theory predicts a Born-Oppenheimer barrier height of 0.7 kJ mol-1. The energies of the lowest six electronic states as resulting from MRD-CI calculations are presented at discrete points along the reaction path, and two avoided crossings are found in the transition state region. The spin-orbit splitting in Cl is also calculated along the reaction path; it is not negligible in the transition state region and is found to increase the barrier by only 1.4 kJ mol-1 at the RCCSD(T)/aug-cc-pVTZ transition state geometry. The minimum energy path of the reaction connects an energetically weakly stabilized adduct on the flat potential surface on the reactant side and an energetically strongly stabilized postreaction adduct. The reaction rate coefficient and the kinetic isotope effects were calculated using improved canonical variational theory with small curvature tunneling (ICVT/SCT), and the results were compared to experimental data. The experimental reaction rate coefficient is reproduced within its uncertainty limits by variational transition state theory with interpolated single-point energy corrections (ISPE) at the MP4(SDTQ) level of theory and by conventional transition state theory with interpolated optimized energies (IOE) at the MRD-CI//RCCSD(T) level of theory and interpolated optimized geometries at the RCCSD(T) level of theory on an MP2/aug-cc-pVTZ potential energy surface when employing scaled vibrational frequencies.     

Theoretical studies on the reaction path and dynamics of the reaction CH_3+H_2O→CH_4+OH

The reaction path, the dynamical properties along the reaction path and CVT rate constants are computed by the ab initio MO method, the reaction path Hamiltonian theory and the variational transition state theory. The results show that the effect of the electron correlation energy on activation barrier is large, the recrossing and tunneling effects exist in the reaction.     

A DFT study of the pericyclic/pseudopericyclic character of cycloaddition reactions of ethylene and formaldehyde to buta-1,3-dien-1-one and derivatives

Cycloaddition reactions of ethylene and formaldehyde to buta-1,3-dien-1-one and derivatives were studied by performing a density functional theory study with the 6-31+G* basis set. Reactants, products, and transition states for each reaction were localized, and the path connecting reactants and products was also obtained. Magnetic properties were evaluated along the reaction path to elucidate the characteristics of the reactions studied. Also, a natural bond orbital analysis was performed to study the orbital interactions in the transition states. Calculations indicate that all reactions are pericyclic except three cases, which are pseudopericyclic reactions. In the latter, transition states are almost planar, and magnetic properties do not reveal aromatization enhancement in their transition states. Also, though the participation of lone pairs diminish the pericyclic character of the reactions, sometimes this participation is not enough to generate a change to a pseudopericyclic path. Overall, magnetic properties reveal as a good criterion to elucidate the characteristics of the reactions studied, though a combined application of several criteria is recommended.     

Conformational transition pathway of polymerase beta/DNA upon binding correct incoming substrate

The closing conformational transition of wild-type polymerase beta bound to DNA template/primer before the chemical step (nucleotidyl transfer reaction) is simulated using the stochastic difference equation (in length version, "SDEL") algorithm that approximates long-time dynamics. The order of the events and the intermediate states during pol beta's closing pathway are identified and compared to a separate study of pol beta using transition path sampling (TPS) (Radhakrishnan, R.; Schlick, T. Proc. Natl. Acad. Sci. USA 2004, 101, 5970-5975). Results highlight the cooperative and subtle conformational changes in the pol beta active site upon binding the correct substrate that may help explain DNA replication and repair fidelity. These changes involve key residues that differentiate the open from the closed conformation (Asp192, Arg258, Phe272), as well as residues contacting the DNA template/primer strand near the active site (Tyr271, Arg283, Thr292, Tyr296) and residues contacting the beta and gamma phosphates of the incoming nucleotide (Ser180, Arg183, Gly189). This study compliments experimental observations by providing detailed atomistic views of the intermediates along the polymerase closing pathway and by suggesting additional key residues that regulate events prior to or during the chemical reaction. We also show general agreement between two sampling methods (the stochastic difference equation and transition path sampling) and identify methodological challenges involved in the former method relevant to large-scale biomolecular applications. Specifically, SDEL is very quick relative to TPS for obtaining an approximate path of medium resolution and providing qualitative information on the sequence of events; however, associated free energies are likely very costly to obtain because this will require both successful further refinement of the path segments close to the bottlenecks and large computational time.     

Steepest descent reaction path integration using a first-order predictor-corrector method

The theoretical treatment of chemical reactions inevitably includes the integration of reaction pathways. After reactant, transition structure, and product stationary points on the potential energy surface are located, steepest descent reaction path following provides a means for verifying reaction mechanisms. Accurately integrated paths are also needed when evaluating reaction rates using variational transition state theory or reaction path Hamiltonian models. In this work an Euler-based predictor-corrector integrator is presented and tested using one analytic model surface and five chemical reactions. The use of Hessian updating, as a means for reducing the overall computational cost of the reaction path calculation, is also discussed.     

Transition path sampling for discrete master equations with absorbing states

Transition path sampling (TPS) algorithms have been implemented with deterministic dynamics, with thermostatted dynamics, with Brownian dynamics, and with simple spin flip dynamics. Missing from the TPS repertoire is an implementation with kinetic Monte Carlo (kMC), i.e., with the underlying dynamics coming from a discrete master equation. We present a new hybrid kMC-TPS algorithm and prove that it satisfies detailed balance in the transition path ensemble. The new algorithm is illustrated for a simplified Markov State Model of trp-cage folding. The transition path ensemble from kMC-TPS is consistent with that obtained from brute force kMC simulations. The committor probabilities and local fluxes for the simple model are consistent with those obtained from exact methods for simple master equations. The new kMC-TPS method should be useful for analysis of rare transitions in complex master equations where the individual states cannot be enumerated and therefore where exact solutions cannot be obtained.