Criticality of a liquid-vapor interface from an inhomogeneous integral equation theory

A microscopic theory is developed to study the liquid-vapor interfacial properties of simple fluids with ab initio treatment of the inhomogeneous two-body correlation functions, without any interpolation. It consists of the inhomogeneous Ornstein-Zernike equation coupled with the Duh-Henderson-Verlet closure and the Lovett-Mou-Buff-Wertheim equation. For the liquid-vapor interface of the Lennard-Jones fluid, we obtained the density profile and the surface tension, as well as their critical behaviour. In particular, we identified non-classical critical exponents. The theory accurately predicts the phase diagram and the interfacial properties in a very good agreement with simulations. We also showed that the method leads to true capillary-wave asymptotics in the macroscopic limit.     

Temperature dependence of coarse-grained potentials for liquid hexane

The present molecular dynamics study is an investigation of the temperature (T) dependence of liquid hexane coarse-grained potentials optimized with the Iterative Boltzmann Inversion method. An approach for the derivation of coarse-grained potentials at temperatures T different from the optimization temperature T(0) has recently been proposed for ethylbenzene. This method is based on the use of a T-dependent scaling factor f(T) to generate ethylbenzene potentials at T≠T(0). The approach is here extended to hexane, considering different reference temperatures T(0) and functional forms for f(T). From our simulations, it appears that the accuracy of the temperature transferability depends simultaneously on the T(0) chosen and the analytic form of f(T). Such a behavior is suppressed by the use of a new 2-point interpolation formula to generate coarse-grained potentials as a function of T. This scheme employs a linear interpolation based on the optimization of coarse-grained potentials at two reference temperatures, T(L) and T(U), with T(L)≤T≤T(U). Accurate coarse-grained simulations of liquid hexane can be performed using the new interpolation scheme. The results are encouraging for the use of potential interpolations as a practical means for devising coarse-grained potentials within a wider temperature range.     

A practical integral equation for the structure and thermodynamics of hard sphere Coulomb fluids

A closure for the Ornstein-Zernike equation is presented, applicable for fluids of charged, hard spheres. From an exact, but intractable closure, we derive the radial distribution function of nonlinearized Debye-Hückel theory by subsequent approximations, and use the information to formulate a new closure by an extension of the mean spherical approximation. The radial distribution functions of the new closure, coined Debye-Hückel-extended mean spherical approximation, are in excellent agreement with those resulting from the hyper-netted chain approximation and molecular dynamics simulations, in the regime where the latter are applicable, except for moderately dilute systems at low temperatures where the structure agrees at most qualitatively. The method is numerically more efficient, and more important, convergent in the entire temperature-density plane. We demonstrate that the method is accurate under many conditions for the determination of the structural and thermodynamic properties of homogeneous, symmetric hard-sphere Coulomb systems, and estimate it to be a valuable basis for the formulation of density functional theories for inhomogeneous or highly asymmetric systems.     

Molecular orbital propagation to accelerate self-consistent-field convergence in an ab initio molecular dynamics simulation

Based on the idea of molecular orbital (MO) propagation, we propose a novel effective method for predicting initial guesses for the self-consistent-field calculations in direct ab initio molecular dynamics (AIMD) simulations. This method, called LIMO, adopts the Lagrange interpolation (LI) polynomial technique and predicts initial MO coefficients at the next AIMD step by using several previous results. Taking into account the crossing and/or mixing of MOs leads to orbital invariant formulas for the LIMO method. We also propose a simple method for determining the optimal degree of the LI polynomial, which corresponds to the number of previous steps. Numerical tests confirm that this proposed method is both effective and feasible.     

Improved High Performance Liquid Chromatographic Method for the Quantification of 3-Methylhistidine in Serum and Urine

Abstract

We optimized an high-performance liquid chromatographic (HPLC) method for the determination of 3-methylhistidine (3-MeHis) in biological fluids. After pre-column derivatization with OPA, analytical separation was achieved on a reversed-phase C18 column by a simple gradient between sodium propionate buffer and acetonitrile. the method is accurate, reproducible and sensitive, and allows the determination of urinary 3-MeHis levels in about 55 min. Other additional 16 amino acids may be easily quantified while the 3-MeHis peak is well resolved from an unknown urinary compound potentially interfering.     

Spectrofluorometric determination of ketorolac tromethamine via its oxidation with cerium(IV) in pharmaceutical preparations and biological fluids

A simple and sensitive fluorometric method for determination of ketorolac tromethamine was studied. The method depends on oxidation of the drug with cerium(IV) and subsequent monitoring of the fluorescence of the induced cerium(III) at lambda(em) 365 nm after excitation at 255 nm. Different variables affecting the reaction conditions, such as the concentrations of cerium(IV), sulfuric acid concentration, reaction time, and temperature, were carefully studied and optimized. Under the optimum conditions, a linear relationship was found between the relative fluorescence intensity and the concentration of the investigated drug in the range of 0.1-0.8 microg/mL. No interferences could be observed from the excipients commonly present in dosage forms. The proposed method was successfully applied to the analysis of the investigated drug in its pure form, pharmaceutical preparations, and biological fluids with good accuracy and precision. The recoveries for pharmaceutical formulations ranged from 99.8-101.0 +/- 0.6% for tablets, 98.5-101.0 +/- 1.0% for ampoules, and 99.0-100.5 +/- 0.7% for eye drops. The results obtained by the proposed method were satisfactory compared with those obtained by the official method. The recoveries for biological fluids were 99.1-100.4 +/- 0.7 and 99.0-100.0 +/- 0.5% for plasma and urine, respectively.     

Efficient exploration of reaction paths via a freezing string method

The ability to efficiently locate transition states is critically important to the widespread adoption of theoretical chemistry techniques for their ability to accurately predict kinetic constants. Existing surface walking techniques to locate such transition states typically require an extremely good initial guess that is often beyond human intuition to estimate. To alleviate this problem, automated techniques to locate transition state guesses have been created that take the known reactant and product endpoint structures as inputs. In this work, we present a simple method to build an approximate reaction path through a combination of interpolation and optimization. Starting from the known reactant and product structures, new nodes are interpolated inwards towards the transition state, partially optimized orthogonally to the reaction path, and then frozen before a new pair of nodes is added. The algorithm is stopped once the string ends connect. For the practical user, this method provides a quick and convenient way to generate transition state structure guesses. Tests on three reactions (cyclization of cis,cis-2,4-hexadiene, alanine dipeptide conformation transition, and ethylene dimerization in a Ni-exchanged zeolite) show that this "freezing string" method is an efficient way to identify complex transition states with significant cost savings over existing methods, particularly when high quality linear synchronous transit interpolation is employed.     

A study of the anisotropy of stress in a fluid confined in a nanochannel

We present molecular dynamics simulations of planar Poiseuille flow of a Lennard-Jones fluid at various temperatures and body forces. Local thermostatting is used close to the walls to reach steady-state up to a limit body force. Macroscopic fields are obtained from microscopic data by time- and space-averaging and smoothing the data with a self-consistent coarse-graining method based on kernel interpolation. Two phenomena make the system interesting: (i) strongly confined fluids show layering, i.e., strong oscillations in density near the walls, and (ii) the stress deviates from the Newtonian fluid assumption, not only in the layered regime, but also much further away from the walls. Various scalar, vectorial, and tensorial fields are analyzed and related to each other in order to understand better the effects of both the inhomogeneous density and the anisotropy on the flow behavior and rheology. The eigenvalues and eigendirections of the stress tensor are used to quantify the anisotropy in stress and form the basis of a newly proposed objective, inherently anisotropic constitutive model that allows for non-collinear stress and strain gradient by construction.     

Constant-NTμ simulations: Free energy difference method for excess adsorption

We describe a new method to simulate confined fluids in equilibrium with a bulk. The equilibrium is first located at a low density, where conventional methods relying upon real or virtual particle exchanges are reliable. Thereafter, the chemical potential of the fluid is increased by the same amount in both systems using a variation of a recently developed free energy difference method in an isobaric (isotension) ensemble. The method, illustrated here for a simple fluid in a planar slit, is shown to be reliable up to high densities. As the method does not rely upon particle exchanges it is ideally suited to the simulation of equilibria in complex fluids, e.g., molecular liquids and polymers. © 1996 by John Wiley & Sons, Inc.     

Pulse shaping for optimal control of molecular processes

In this paper, a new method is proposed to design optimized control fields with desired temporal and/or spectral properties. The method is based on penalizing the difference between an optimized field obtained from an iterative scheme and a reference field with desired temporal and/or spectral properties. Compared with the standard optimal control theory, the current method allows a simple, experimentally accessible field be found on the fly; while compared with parameter space searching optimization, the iterative nature of this method allows automatic exploration of the intrinsic mechanism of the population transfer. The method is illustrated by examing the optimal control of vibrational excitation of the Cl-O bond with both temporally and spectrally restricted pulses.     

Rotational symmetry of the molecular potential energy in the Cartesian coordinates

We consider the molecular Born-Oppenheimer potential energy as a function of atomic Cartesian coordinates and discuss the non-stationary Hessian properties arising due to rotational symmetry. A connection with the extended Hessian theory is included. New applications of Cartesian representation for examining and correcting raw numerical Hessian data and a simple formulation of harmonic vibrational analysis of partially optimized systems are proposed. Exemplary calculations for the porphyrin molecule with an internal proton transfer are reported. We also develop the normal transformation method to incorporate the rotational symmetry into the approximate analytical potentials, which are parametrized in the Cartesian coordinates. The transformation converts the coordinates from the space fixed frame to the frame which translates and rotates with the molecule and is determined by the Eckart conditions. New simple analytical formulas for the first and second derivatives of the transformed potential are derived. This fast method can be used to calculate the potential and its derivatives in the simulations of chemical reaction dynamics in the space fixed Cartesian frame without the need to constrain the molecular rotation or to define the local non-redundant internal coordinates.     

Direct Determination of Azathioprine in Human Fluids and Pharmaceutical Formulation Using Flow Injection Chemiluminescence Analysis

A simple, sensitive and inexpensive flow injection chemiluminescence method for the determination of azathioprine had been discovered. It was based on the fact that the weak chemiluminescent reaction of cerium(IV) with azathioprine in acidic medium, which was enhanced by the addition of rhodamine 6G. A lot of optimized experimental conditions had been studied in detail. The CL intensity was linearly related to the concentration of azathioprine in the range of 0.1–10.0 μM and the detection limit was 45.0 nM (3σ). The relative standard deviation (RSD) for the technique was 2.1% (n = 11). The method had high selectivity, sensitivity and good repeatability. The proposed method had been triumphantly applied to the determination of azathioprine in human fluids and pharmaceutical formulation with satisfactory results.     

Uniform quality gaussian basis sets for molecular calculations,I. C1 hydrocarbons

The optimality of MO basis sets of Gaussian functions, when constructed from AO basis sets optimized for the neutral atom or for atom ions, is investigated. A formal charge parameter Q is defined and used to adjust the AO basis sets to the molecular environment, by virtue of a simple quadratic expression. Calculations on a series of C₁ hydrocarbons (CH₂, CH₃, CH₃⁺, CH₃^?, CH₄) using 3G basis sets indicate considerable variations in the optimum Q value with the molecular species. The proposed method offers a simple alternative technique to a full molecular basis set optimization.     

Pair correlation function integrals: computation and use

We describe a method for extending radial distribution functions obtained from molecular simulations of pure and mixed molecular fluids to arbitrary distances. The method allows total correlation function integrals to be reliably calculated from simulations of relatively small systems. The long-distance behavior of radial distribution functions is determined by requiring that the corresponding direct correlation functions follow certain approximations at long distances. We have briefly described the method and tested its performance in previous communications [R. Wedberg, J. P. O'Connell, G. H. Peters, and J. Abildskov, Mol. Simul. 36, 1243 (2010); Fluid Phase Equilib. 302, 32 (2011)], but describe here its theoretical basis more thoroughly and derive long-distance approximations for the direct correlation functions. We describe the numerical implementation of the method in detail, and report numerical tests complementing previous results. Pure molecular fluids are here studied in the isothermal-isobaric ensemble with isothermal compressibilities evaluated from the total correlation function integrals and compared with values derived from volume fluctuations. For systems where the radial distribution function has structure beyond the sampling limit imposed by the system size, the integration is more reliable, and usually more accurate, than simple integral truncation.     

Finite element interpolation for combined classical/quantum mechanical molecular dynamics simulations

A method is presented to interpolate the potential energy function for a part of a system consisting of a few degrees of freedom, such as a molecule in solution. The method is based on a modified finite element (FE) interpolation scheme. The aim is to save computer time when expensive methods such as quantum-chemical calculations are used to determine the potential energy function. The expensive calculations are only carried out if the molecule explores new unknown regions of the conformation space. If the molecule resides in regions previously explored, a cheap interpolation is performed instead of an expensive calculation, using known neighboring points. We report the interpolation techniques for the energies and the forces of the molecule, the handling of the FE mesh, and an application to a simple test example in molecular dynamics (MD) simulations. Good performance of the method was obtained (especially for MD simulations with a preceding Monte Carlo mesh generation) without losing accuracy. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1484–1495, 1997     

Equilibrium properties of dense hydrogen isotope gases based on the theory of simple fluids

We present a new method for the prediction of the equilibrium properties of dense gases containing hydrogen isotopes. The proposed approach combines the Feynman-Hibbs effective potential method and a deconvolution scheme introduced by Weeks et al. The resulting equations of state and the chemical potentials as functions of pressure for each of the hydrogen isotope gases depend on a single set of Lennard-Jones parameters. In addition to its simplicity, the proposed method with optimized Lennard-Jones potential parameters accurately describes the equilibrium properties of hydrogen isotope fluids in the regime of moderate temperatures and pressures. The present approach should find applications in the nonlocal density functional theory of inhomogeneous quantum fluids and should also be of particular relevance to hydrogen (clean energy) storage and to the separation of quantum isotopes by novel nanomaterials.     

Invited Lecture. Columnar ordering as an excluded-volume effect

The nature of the possible liquid-crystalline phases that a molecular or colloidal system may exhibit depends sensitively on the shape of the constituent particles. Recent computer simulations on fluids of consisting of non-spherical hard-core molecules suggest that, in order to predict the relative stability of isotropic, nematic, smectic and columnar phases in such very simple model fluids, it is not enough to characterize the molecular shape by an overall length-to-width ratio. New results of computer simulations on a model for disc-like molecules clearly illustrate this point.     

Invited Lecture. Columnar ordering as an excluded-volume effect

The nature of the possible liquid-crystalline phases that a molecular or colloidal system may exhibit depends sensitively on the shape of the constituent particles. Recent computer simulations on fluids of consisting of non-spherical hard-core molecules suggest that, in order to predict the relative stability of isotropic, nematic, smectic and columnar phases in such very simple model fluids, it is not enough to characterize the molecular shape by an overall length-to-width ratio. New results of computer simulations on a model for disc-like molecules clearly illustrate this point.     

Density functional theory of inhomogeneous liquids. I. The liquid-vapor interface in Lennard-Jones fluids

A simple model is proposed for the direct correlation function (DCF) for simple fluids consisting of a hard-core contribution, a simple parametrized core correction, and a mean-field tail. The model requires as input only the free energy of the homogeneous fluid, obtained, e.g., from thermodynamic perturbation theory. Comparison to the DCF obtained from simulation of a Lennard-Jones fluid shows this to be a surprisingly good approximation for a wide range of densities. The model is used to construct a density functional theory for inhomogeneous fluids which is applied to the problem of calculating the surface tension of the liquid-vapor interface. The numerical values found are in good agreement with simulation.