A canonical averaging in the second-order quantized Hamilton dynamics

Quantized Hamilton dynamics (QHD) is a simple and elegant extension of classical Hamilton dynamics that accurately includes zero-point energy, tunneling, dephasing, and other quantum effects. Formulated as a hierarchy of approximations to exact quantum dynamics in the Heisenberg formulation, QHD has been used to study evolution of observables subject to a single initial condition. In present, we develop a practical solution for generating canonical ensembles in the second-order QHD for position and momentum operators, which can be mapped onto classical phase space in doubled dimensionality and which in certain limits is equivalent to thawed Gaussian. We define a thermal distribution in the space of the QHD-2 variables and show that the standard beta=1/kT relationship becomes beta'=2/kT in the high temperature limit due to an overcounting of states in the extended phase space, and a more complicated function at low temperatures. The QHD thermal distribution is used to compute total energy, kinetic energy, heat capacity, and other canonical averages for a series of quartic potentials, showing good agreement with the quantum results.     

Direct probing of zwitterion formation in unsolvated peptides

Molecular beam electric deflection measurements have been used to determine electric susceptibilities for small unsolvated alanine-based peptides. The electric susceptibility provides information about the charge distribution within the peptide and can be used to distinguish between zwitterionic and canonical forms. Measured electric susceptibilities for WAn peptides (n = 1-5) are similar to those for capped Ac-WAn-NH2 peptides (which cannot form zwitterions). Susceptibilities calculated using a simulated tempering-based approach are substantially larger for the zwitterionic form than for the canonical form. The measured susceptibilities are in good agreement with those calculated for the canonical form. For the larger peptides, the lowest potential energy structure found in the simulations is hairpin-like, while the lowest free energy structure found at room temperature is extended. The zwitterionic form is constrained by intramolecular interactions which make it entropically unfavorable.     

Direct dynamics study of the hydrogen abstraction reaction of CF3CH2Cl + Cl → CF3CHCl + HCl

The hydrogen abstraction reaction of Cl atoms with CF₃CH₂Cl (HCFC‐133a) is investigated by using density function theory and ab initio approach, and the rate constants are calculated by using the dual‐level direct dynamics method. Optimized geometries and frequencies of reactants, transition state, and products are computed at the B3LYP/6‐311+G(2d,2p) level. To refine the energetic information along the minimum energy path, single‐point energy calculations are carried out at the G3(MP2) level of theory. The interpolated single‐point energy method is employed to correct the energy profiles for the title reaction. The rate constants are evaluated by using the canonical variational transition state theory with a small‐curvature tunneling correction over a wide range of temperature, 200–2000 K. The variational effect for the reaction is moderate at low temperatures and very small at high temperatures. However, the tunneling correction has an important contribution in the lower temperature range. The agreement between calculated rate constants and available experimental values is good at lower temperatures but diverges significantly at higher temperatures. © 2012 Wiley Periodicals, Inc. Int J Chem Kinet 44: 661–667, 2012     

Hydrogen storage in porous structures of adamantane‐based nitrogen‐heterocyclic ring with diamond‐like structure

Using the density functional theory and molecular mechanics methods, we calculated the binding energy and parameters about the primitive cell designed by us with the adamantane and the nitrogen heterocyclic ring, the vibrational frequencies about the small complexes. Grand canonical Monte Carlo simulations were performed to predict the capacities for the hydrogen storage and adsorption isotherms. The results show the positive effects of bigger specific surface area and pore volume on hydrogen storage and isosteric heat. The gravimetric hydrogen uptake of adamantane‐based nitrogen‐heterocyclic ring of quaterpyridyl can reach 9.02 wt % at room temperature and 100 bar. But the volumetric H₂ capacities of the four materials are low at T = 298 K because of weak interaction between the materials and H₂ molecule. © 2014 Wiley Periodicals, Inc.     

Molecular motion of ends of isolated poly(isobutylene) chains tethered on the poly(tetrafluoroethylene) surface in vacuo

Poly(isobutylene) (PIB) chains with a radical at the chain end were graft-copolymerized on the poly(tetrafluoroethylene) (PTFE) surface in vacuo at 77 K. The PIB chains tethered on the PTFE surface in vacuo were regarded as isolated chains from neighboring tethered PIB chains. The molecular motion of the ends of the isolated PIB chains was observed by an electron spin resonance (ESR) spectrometer in the temperature range from 3 to 125 K, which was lower than T_g of PIB, 200 K,¹ and two motion modes were found: One is a quantum tunneling of the methyl group located at the chain end at 3 K, and the other is an interconformation transition with freely rotating methyl group at the end at 77 K, where the transition rate was estimated to be 15 MHz at that temperature. The transition rate increased with an increase in temperature. The activation energy of the transition was estimated to be 370 J/mol. The high mobility and low activation energy was attributed to the isolation of PIB chains in vacuo. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2095–2102, 1998     

Thermodynamic study on the adsorption and micelle formation of long chain alkyltrimethylammonium chlorides

The surface tension of aqueous solutions of tetradecyl-trimethylammonium chloride (TTAC) and decyltrimethylammonium chloride (DeTAC) were measured as a function of temperature at concentrations below and above the critical micelle concentration under atmospheric pressure. The entropy and energy of adsorption from the monomeric state and from the micellar state and also the entropy and energy of micelle formation for TTAC were evaluated and compared with those of dodecyltrimethyl-ammonium chloride (DTAC). The values of Δ^M _W s and Δ^M _W u for TTAC and DTAC systems show that the micelle formation is driven by the entropy at low temperatures and by the energy at high temperatures. Received: 9 December 1997 Accepted: 4 March 1998     

MC(JBW): Simple but smart Monte Carlo algorithm for free energy simulations of multiconformational molecules

Many of the most common molecular simulation methods, including Monte Carlo (MC) and molecular or stochastic dynamics (MD or SD), have significant difficulties in sampling the space of molecular potential energy surfaces characterized by multiple conformational minima and significant energy barriers. In such cases improved sampling can be obtained by special techniques that lower such barriers or somehow direct search steps toward different low energy regions of space. We recently described a hybrid MC/SD algorithm [MC(JBW)/SD] incorporating such a technique that directed MC moves of selected torsion and bond angles toward known low energy regions of conformational space. Exploration of other degrees of freedom was left to the SD part of the hybrid algorithm. In the work described here, we develop a related but simpler simulation algorithm that uses only MC to sample all degrees of freedom (e.g., stretch, bend, and torsion). We term this algorithm MC(JBW). Using simulations on various model potential energy surfaces and on simple molecular systems (n-pentane, n-butane, and cyclohexane), MC(JBW) is shown to generate ensembles of states that are indistinguishable from the canonical ensembles generated by classical Metropolis MC in the limit of very long simulations. We further demonstrate the utility of MC(JBW) by evaluating the room temperature free energy differences between conformers of various substituted cyclohexanes and the larger ring hydrocarbons cycloheptane, cyclooctane, cyclononane, and cyclodecane. The results compare favorably with available experimental data and results from previously reported MC(JBW)/SD conformational free energy calculations. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1736–1745, 1998     

苯与丙烯在β分子筛上吸附行为的蒙特卡罗研究

采用巨正则统计系综蒙特卡罗模拟方法研究了β分子筛上苯与丙烯分子的吸附行为. 由分子筛内吸附质粒子云分布可知, 在100 kPa时, 丙烯在分子筛上的吸附量要远远大于苯的吸附量. 由吸附相互作用能分布来看, 苯与分子筛之间相互作用能比丙烯与分子筛之间的相互作用能更负, 这就使苯分子的吸附相对于丙烯分子稳定. 相对而言, 温度变化对丙烯吸附影响远大于对苯吸附的影响, 如100 kPa时, 温度由298 K升高至443 K导致丙烯分子吸附量明显减少, 由每8个晶胞吸附98个丙烯分子减少到80个; 而对苯分子吸附却没有显著的影响. β分子筛上存在着苯和丙烯的竞争吸附, 并且吸附分子之间存在相互作用使两者与分子筛之间的相互作用能分布改变. 在压力范围1×10－3～5.0 kPa, 不同温度下苯与丙烯在分子筛内吸附等温线的模拟结果表明, 在较高温度、较低压力下丙烯的吸附量要小于苯的吸附量.     

TheRate: Program for ab initio direct dynamics calculations of thermal and vibrational-state-selected rate constants

We introduce TheRate (THEoretical RATEs), a complete application program with a graphical user interface (GUI) for calculating rate constants from first principles. It is based on canonical variational transition-state theory (CVT) augmented by multidimensional semiclassical zero and small curvature tunneling approximations. Conventional transition-state theory (TST) with one-dimensional Wigner or Eckart tunneling corrections is also available. Potential energy information needed for the rate calculations are obtained from ab initio molecular orbital and/or density functional electronic structure theory. Vibrational-state-selected rate constants may be calculated using a diabetic model. TheRate also introduces several technical advancements, namely the focusing technique and energy interpolation procedure. The focusing technique minimizes the number of Hessian calculations required by distributing more Hessian grid points in regions that are critical to the CVT and tunneling calculations and fewer Hessian grid points elsewhere. The energy interpolation procedure allows the use of a computationally less demanding electronic structure theory such as DFT to calculate the Hessians and geometries, while the energetics can be improved by performing a small number of single-point energy calculations along the MEP at a more accurate level of theory. The CH₄+H↔CH₃+H₂ reaction is used as a model to demonstrate usage of the program, and the convergence of the rate constants with respect to the number of electronic structure calculations. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1039–1052, 1998     

A dual‐level direct dynamics study on the hydrogen abstraction reaction of oxygen atom with methylhydrazine

The mechanism of the multichannel reaction CH₃NHNH₂ (SC₁ and SC₂) + O → products is investigated theoretically using ab initio and density functional theory, and dynamics properties are explored by a dual‐level direct dynamics method. The calculation of the potential energy surface is carried out at the BMC‐CCSD//MPW1K/6‐311G(d,p) level. Using canonical variational transition state theory with a small‐curvature tunneling correction, the rate constants of each channel are evaluated over a wide temperature range of 200–2000 K on the basis of obtained electronic structures and energy information. The total rate constants are calculated from the sum of the individual rate constants taking into account the Boltzmann distribution of two conformers. The reactivity of the H atom located in different groups is compared. © 2013 Wiley Periodicals, Inc.     

On the interfacial energy of extended-chain crystals from polyethylene melt by revised Flory equations of fusion

To analyze extended-chain crystalline systems composed of linear polyethylene, Flory's conventional theory of fusion is reconsidered by introducing a new concept of crystallinity. When this new treatment is applied to a melting case of a low molecular weight polyethylene fraction (M_n = 5600) isothermally bulk crystallized, a certain result that very large lamellar thickness was caused by a very small increase in crystallization temperature can satisfactorily be explained by a significant change in interfacial free energy of the crystallite end. Further, it shows 14–17 kJ/mol as a nonequilibrium value range of interfacial free energy for highly crystalline polyethylene fractions of low molecular weight M_n ≦ 5600 by using the previous data presented by other workers. A similar result is also obtained on the M_n = 5600 fraction by analyzing from a standpoint of equilibrium crystallinity. In either case, the estimated range of interfacial free energy is consistent with the conventional range. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1293–1303, 1998     

Variable Temperature Single‐Molecule Dynamics of MEH‐PPV

Herein, we continue our investigation of the single‐molecule spectroscopy of the conjugated polymer poly[2‐methoxy,5‐(2′‐ethylhexyloxy)‐p‐phenylene‐vinylene] (MEH‐PPV) at cryogenic temperatures. First, the low temperature microsecond dynamics of single MEH‐PPV conjugated polymer molecules are compared to the dynamics at room temperature revealing no detectible temperature dependence. The lack of temperature dependence is consistent with the previous assignment of the dynamics to a mechanism that involves intersystem crossing and triplet–triplet annihilation. Second, the fluorescence spectra of single MEH‐PPV molecules at low temperature are studied as a function of excitation wavelength (i.e. 488, 543, and 568 nm). These results exhibit nearly identical fluorescence spectra for different excitation wavelengths. This strongly suggests that electronic energy transfer occurs efficiently to a small number of low‐energy sites in the multichromophoric MEH‐PPV chains.     

Model hysteresis dimer molecule II: deductions from probability profile due to system coordinates

The hysteresis dimer reaction of the first sequel is applied to test the Gibbs density-in-phase hypothesis for a canonical distribution at equilibrium. The probability distribution of variously defined internal and external variables is probed using the algorithms described, in particular the novel probing of the energy states of a labeled particle where it is found that there is compliance with the Gibbs’ hypothesis for the stated equilibrium condition and where the probability data strongly suggests that an extended equipartition principle may be formulated for some specific molecular coordinates, whose equipartition temperature does not equal the mean system temperature and a conjecture concerning which coordinates may be suitable is provided. Evidence of violations to the mesoscopic nonequilibrium thermodynamics (MNET) assumptions used without clear qualifications for a canonical distribution for internal variables are described, and possible reasons outlined, where it is found that the free dimer and atom particle kinetic energy distributions agree fully with Maxwell–Boltzmann statistics but the distribution for the relative kinetic energy of bonded atoms does not. The principle of local equilibrium (PLE) commonly used in nonequilibrium theories to model irreversible systems is investigated through NEMD simulation at extreme conditions of bond formation and breakup at the reservoir ends in the presence of a temperature gradient, where for this study a simple and novel difference equation algorithm to test the divergence theorem for mass conservation is utilized, where mass is found to be conserved from the algorithm in the presence of flux currents, in contradiction to at least one aspect of PLE in the linear domain. It is concluded therefore that this principle can be a good approximation at best, corroborating previous purely theoretical results derived from the generalized Clausius Inequality, which proved that the PLE cannot be an exact principle for nonequilibrium systems.      

Canonical statistical adiabatic channel model calculations of the H + CH3 → CH4 recombination reaction on an ab initio potential energy surface. The role of the transitional modes

The canonical formalism of the statistical adiabatic channel model is used to calculate limiting high pressure rate constants for the H + CH₃ → CH₄ recombination reaction on a recently reported analytic potential energy surface based on ab initio calculations. An effective adiabatic channel potential which incorporates the G_?? matrix element of the twofold degenerate H₃C? H transitional bending mode, quartic anharmonicity, and state selected mode coupling effects is implemented. The rate constants calculated over the temperature range 200–1000 K are in very good agreement with recent canonical variational transition state theory calculations performed on the same surface. The comparison with experimental results is also discussed.     

Smoothing techniques of global optimization: Distance scaling method in searches for most stable Lennard–Jones atomic clusters

Spatial averaging of the potential energy function facilitates the search for the most stable configuration of a molecular system. Recently some global optimization methods of this kind have been designed in the literature that rely on physical phenomena such as diffusion, wave function evolution in quantum mechanics, Smoluchowski dynamics, evolution in temperature of canonical ensembles, etc. In the present article we highlight the fact that all these methods, when applied to the Gaussian distributions of an ensemble, represent special cases of a set of differential equations involving the spatially averaged potential energy. Their structure suggests that the nature's strategy to cope with the global optimization is robust and differs only in the details in particular applications. The strategy consists of going downhill of the averaged potential energy, removing the barriers, and hunting for low energy regions by a selective increasing of the spatial averaging. In this study we explore the deformation of the potential rather than its averaging. The deformation comes from scaling of atomic distances and reduces the barriers even more effectively than the Gaussian averaging. The position and widths of the Gaussian distribution evolve similarly to the Gaussian density annealing (GDA), but we allow elliptical instead of spherical Gaussians as well as branching of the single trajectory of the system into multiple ones. When the temperature reaches 0 K, one has a number of independent Gaussian distributions, each corresponding to a structure and (usually low) energy of the system. The multiple elliptic-Gaussian distance scaling method has been applied to clusters of argon atoms (N=5,…,31), a system serving usually as a benchmark domain. The method found the global minima for all but three clusters (of very low energy). The procedure is 20 or more times less expensive than the GDA one. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 2040–2049, 1997     

Repeated‐annealing sampling combined with multicanonical algorithm for conformational sampling of bio‐molecules

A novel conformational sampling method (repeated‐annealing sampling method) is proposed to execute an efficient conformational sampling at a reasonable computational cost. In the method, a molecular dynamics simulation is done with repeating an elemental process. An elemental process consists of four subprocesses: high‐temperature run, annealing, room‐temperature run, and fast heating. The sampling is done automatically according to a temperature‐control schedule. The room‐temperature run is treated with the multicanonical algorithm, and the other subprocesses are done with the conventional molecular dynamics algorithm. The method, differing from the generalized ensemble methods recently developed, is not warrantable to give the canonical ensemble because of the nonphysical process in the annealing. However, we observed that the slower the annealing and the longer the high‐temperature run, the closer the sampled conformations to those of the canonical ensemble. A test was performed with tri‐N‐acetyl‐D ‐glucosamine in vacuo, and the results were compared with those from the conventional multicanonical simulation. Not only the reweighted canonical distribution function but also the energy landscape were in good agreement with those from the conventional multicanonical simulation. The potential of mean force also showed a fairly good agreement with that from the conventional multicanonical simulation in the room‐temperature region. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1098–1106, 2001     

Plume Expansion Dynamics of Matrix‐Assisted Laser Desorption Ionization

High‐resolution angular and velocity distributions for neutral analytes (tryptophan and poly‐tryptophan) and matrix (2,4,6‐trihydroxyacetophenon, THAP) are measured by using 355 nm laser desorption. The information suggests that two separate mechanisms dominate the angular and velocity distributions at the beginning and before the end of desorption. A molecular jet‐like isentropic expansion dominates the plume expansion at the beginning of desorption. This only occurs at high surface temperature, thus resulting in a large velocity normal to the surface and a very narrow angular distribution. Most of the analytes are produced under these conditions. Before the end of desorption, the surface temperature decreases and the mechanism of thermal desorption at low vapor pressure takes over. The velocities become small and the angular distribution is close to cosθ. Only a very small amount of analytes are generated under these conditions. Compared to tryptophan, poly‐tryptophan has a much narrower angular distribution, thereby suggesting that it is only produced at the higher surface temperatures.     

Ab initio conformational analysis of cyclooctane molecule

The potential energy surface (PES) for the cyclooctane molecule was comprehensively investigated at the Hartree–Fock (HF) level of theory employing the 3–21G, 6–31G, and 6–31G* basis sets. Six distinct true minimum energy structures (named B, BB, BC, CROWN, TBC, and TCC₁), characterized through harmonic frequency analysis, were located on the multidimensional PES. Two transition state structures were also located on the PES for the cyclooctane molecule. Electron correlation effects were accounted for using the Møller–Plesset second-order perturbation theory (MP2) approach. The predicted global minimum energy structure on the ab initio PES for the cyclooctane molecule is the BC conformer. A gas phase electron diffraction study at 300 K suggested a conformational mixture while an NMR study in solution at 161.5 K predicted the BC conformer as the predominant form. The equilibrium constants reported in the present study, which were evaluated from the ab initio calculated total Gibbs free energy change values, were in good agreement with both experimental investigations. The ab initio results showed that the low temperature condition significantly favored the BC conformer while above room temperature both BC and CROWN structures can coexist. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 524–534, 1998     

Micellar properties of alkyldimethylphenylammonium bromides in water

The synthesis and methods applied for the purification of dodecyl-, tetradecyl-, and hexadecyldimethylphenylammonium bromides are described. The results of surface tension measurements of aqueous solutions of these surfactants show that slight amounts of strongly surface-active nonionic impurities are persistent in the crystalline materials presumably due to their low thermal stability. The Critical micelle concentration (cmc) and the degree of ionization (β) of the micelles of the salts studied in aqueous solutions were determined at 25 °C from specific conductivity versus molality plots. The temperature dependence of the cmc and of β of the tetradecyl homologue was measured in the range 4–34 °C. A minimum cmc amounting to 1.20 mmol/kg was determined at about 14 °C. The values of β were found to grow linearly with temperature. From these results, the standard Gibbs energy, the enthalpy and the entropy of the process of micellization were obtained by application of the pseudo-phase-separation model. Enthalpy and entropy show a compensation effect in their contribution to the Gibbs energy. At low temperatures the process of micellization is driven mainly by the entropic term, whereas with increasing temperature the enthalpic term becomes predominant. At the temperature of the minimum cmc, the value of the enthalpy is far from being zero because of the important contribution of the (β/T)R ln X _cmc term. Received: 27 July 1998 Accepted in revised form: 15 December 1998     

Zero-field mobilities in helium: highly accurate values for use in ion mobility spectrometry

The zero-field mobilities of 46 atomic ions in helium are calculated as functions of the gas temperature in an ion mobility spectrometer. The calculations are based on highly accurate, ab initio potential energy curves obtained in the last few years. In general, they start from a small value at low temperature, rise steadily to a maximum at some specific temperature, T _max , and then decline at higher temperatures. The ratio of T _max to the dissociation energy (well depth) of the ion-neutral interaction potential is shown to be approximation the same for all singly-charged ions and a few multiply-charged ions.