Monte Carlo free energy estimates using non-Boltzmann sampling: Application to the sub-critical Lennard-Jones fluid

The paper reports a Monte Carlo technique for estimation of the free energies of fluids by sampling on distributions designed for this purpose, rather than on the usual Boltzmann distribution. As an illustration of its use, the free energy of a Lennard-Jones fluid in the liquid-vapour coexistence region has been estimated by relating it to that of the inverse-twelve (soft sphere) fluid, which itself shows no condensation.     

Density functional calculations of surface free energies

We propose a general method of thermodynamic integration to find the free energy of a surface, where our integration parameter is taken to be the strain on the unit cell of the system (which in the example presented in this paper is simply the extension of the unit cell along the normal to the surface), and the integration is performed over the thermal average stress from a molecular dynamics run. In order to open up a vacuum gap in a continuous and reversible manner, an additional control interaction has been introduced. We also use temperature integration to find a linear relation for the temperature dependence of the free surface energy. These methods have been applied to the titanium dioxide (110) surface, using first principles density functional theory. A proof of principle calculation for zero temperature shows excellent agreement between the integral calculation and the difference in energy calculated by the DFT program. Calculations that have been performed at 295 and 1000 K give excellent agreement between the two integration methods.     

Surface tension and surface free energy of polymers

The curent state of problems connected with the definition and experimental determination of surface free energy and surface tension of polymers is discussed. An analysis of the application of some equations based on classical and modern thermodynamics of polymer solutions shows that present theories need an essential improvement to fit experimental data. The Zisman concept of critical surface tension and Fowkers' hypothesis of additivity in the contribution of polar and dispersion forces to surface tension are criticized and a new approach to the problem is proposed.     

Some estimates of the surface tension of curved surfaces using density functional theory

Density functional theory is used to calculate the surface tension of planar and slightly curved surfaces, which can be written as gamma(R)=gamma(infinity)(1-2delta(infinity)R), where R is the radius of curvature of the surface. Calculations are performed for a Lennard-Jones fluid, split into a hard-sphere repulsive potential and an attractive part. The repulsive part is treated using the local density approximation. The attractive part is treated using a high temperature approximation (HTA) in which the pair correlation function is approximated by the Percus-Yevick pair correlation function of a uniform hard-sphere fluid evaluated at a position-dependent average density. An expression relating the Tolman length delta(infinity) to the density profile of the planar surface is derived. Numerical results are presented for the planar surface tension gamma(infinity) and for delta(infinity) and are compared with those using mean field theory (MFT) and with those using the square-gradient approximation. Values for gamma(infinity) using the HTA are 30%-40% higher than those using MFT. Values for delta(infinity) using the HTA are around -0.1 (in units of the Lennard-Jones parameter sigma) and only weakly dependent on temperature. These values are less negative than the values from MFT. The square-gradient approximation gives reasonable estimates of the more accurate nonlocal results for both the MFT and the HTA.     

Absolute Helmholtz free energy of highly anharmonic crystals: theory vs Monte Carlo

We discuss the problem of the quantitative theoretical prediction of the absolute free energy for classical highly anharmonic solids. Helmholtz free energy of the Lennard-Jones (LJ) crystal is calculated accurately while accounting for both the anharmonicity of atomic vibrations and the pair and triple correlations in displacements of the atoms from their lattice sites. The comparison with most precise computer simulation data on sublimation and melting lines revealed that theoretical predictions are in excellent agreement with Monte Carlo simulation data in the whole range of temperatures and densities studied.     

Potential energy surface of the reaction of imidazole with peroxynitrite: Density functional theory study

This article presents a theoretical investigation of the reaction mechanism of imidazole nitration by peroxynitrite using density functional theory calculations. Understanding this reaction mechanism will help in elucidating the mechanism of guanine nitration by peroxynitrite, which is one of the assumed chemical pathways for damaging DNA in cells. This work focuses on the analysis of the potential energy surface (PES) for this reaction in the gas phase. Calculations were carried out using Hartree–Fock (HF) and density functional theory (DFT) Hamiltonians with double‐zeta basis sets ranging from 6‐31G(d) to 6‐31++G(d,p), and the triple‐zeta basis set 6‐311G(d). The computational results reveal that the reaction of imidazole with peroxynitrite in gas phase produces the following species: (i) hydroxide ion and 2‐nitroimidazole, (ii) hydrogen superoxide ion and 2‐nitrosoimidazole, and (iii) water and 2‐nitroimidazolide. The rate‐determining step is the formation of a short‐lived intermediate in which the imidazole C₂ carbon is covalently bonded to peroxynitrite nitrogen. Three short‐lived intermediates were found in the reaction path. These intermediates are involved in a proton‐hopping transport from C₂ carbon to the terminal oxygen of the ? O? O moiety of peroxynitrite via the nitroso (ON? ) oxygen. Both HF and DFT calculations (using the Becke3–Lee–Yang–Parr functional) lead to similar reaction paths for proton transport, but the landscape details of the PES for HF and DFT calculations differ. This investigation shows that the reaction of imidazole with peroxynitrite produces essentially the same types of products (nitro‐ and nitroso‐) as observed experimentally in the reaction of guanine with peroxynitrite, which makes the former reaction a good model to study by computation the essential characteristics of the latter reaction. Nevertheless, the computationally determined activation energy for imidazole nitration by peroxynitrite in the gas phase is 84.1 kcal/mol (calculated at the B3LYP/6‐31++G(d,p) level), too large for an enzymatic reaction. Exploratory calculations on imidazole nitration in solution, and on the reaction of 9‐methylguanine with peroxynitrite in the gas phase and solution, show that solvation increases the activation energy for both imidazole and guanine, and that the modest decrease (15 kcal mol^?1) in the activation energy, due to the adjacent six member ring of guanine, is counterbalanced by solvation. These results lead to the speculation that proton tunneling may be at the origin of experimentally observed high reaction rate of guanine nitration by peroxynitrite in solution. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

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.     

Density functional theory studies of N-protonation of the free base phthalocyanine

The structures and relative energies of twenty-two N-protonated species of the free base phthalocyanine (H₂Pc) have been systematically studied with the density functional theory at the B3LYP/6-31G(d) level of theory. The calculations demonstrated that the N-protonation tends to increase the N–C bonds and the C–N–C angles on the protonation sites. The inner protonation at the isoindole-nitrogen atoms causes significant out-of-plane deformation of the macrocycle, ascribed to the steric hindrance of the central cavity. The relative energies of various protonated species were calculated and compared to deduce the preferred sites for protonation. It was revealed that the outer protonation at the meso-nitrogen atoms is energetically more favorable than the inner protonation at the isoindole-nitrogen atoms. Among the studied twenty-two protonated species, the most stable one is H₆Pc⁴⁺(IS1), for which all the outer meso-nitrogen atoms are protonated. TDDFT calculations have been performed for selected species, and the results were used to analysis the UV–visible spectrum of the concentrated sulfuric acid solution of the free base phthalocyanine.     

白藜芦醇清除自由基活性的密度泛函理论研究

采用密度泛函理论(DFT)方法,从静态与动态两大方面分析了白藜芦醇分子酚羟基在不同溶剂中清除自由基活性的能力大小.通过白藜芦醇的结构参数、前线轨道理论、3种抽氢反应机制等方面分析了分子活性位与其性质的关系.探讨了白藜芦醇分子不同位置酚羟基清除·OH和·OOH的抗氧化机理,得到了该分子与·OOH发生抽氢反应时的过渡态结构.计算结果表明,在任何溶剂中白藜芦醇分子C(4')位上酚羟基活性最高,发生抽氢反应时反应热最小,是高活性位点.     

Density functional theory for the recognition of polymer at nanopatterned surface

The recognition of homopolymer at nanopatterned surface has been investigated by density functional theory (DFT). Chain conformation and pattern transfer parameter predicted from the DFT are in good agreement with Monte Carlo simulation results. The theory describes satisfactorily the transition from depletion at low packing fractions to adsorption and double-layer adsorption at high packing fractions and also accounts for the crucial effect of the segment-wall interaction. It is found that homopolymer is better recognized at a low bulk density and a stronger interaction with the surface. The polymer can not only recognize the surface but also invert the surface at high bulk densities. The chain in the solution-wall interface exhibits a typical "brush" conformation with a length approximated by half the length of polymer chain.     

Confinement and deposition of solution droplets on solvophilic surfaces using a flat high surface energy guide

A method of depositing small amounts of solution on flat micron scale surface areas on a hydrophilic substrate or die was developed. This method utilizes the capillarity of a flat, high surface free energy guide. Interfacial forces confine the solution between the guide and the substrate surface. The liquid follows the movement of the guide along the surface and can be moved to the desired area. The thermodynamic background of the method is given and its application to coat one arm of a gold plasmonic Mach-Zehnder interferometer with bovine serum albumin is described. This method, which is related to but different from microcontact printing and dip-pen microlithography, can be utilized in the manufacturing of biosensors and other lab-on-a-chip structures, and is particularly suitable to development stage devices.     

Homogeneous nucleation in vapor-liquid phase transition of Lennard-Jones fluids: a density functional theory approach

Density functional theory (DFT) with square gradient approximation for the free energy functional and a model density profile are used to obtain an analytical expression for the size-dependent free energy of formation of a liquid drop from the vapor through the process of homogeneous nucleation, without invoking the approximations used in classical nucleation theory (CNT). The density of the liquid drop in this work is not the same as the bulk liquid density but it corresponds to minimum free energy of formation of the liquid drop. The theory is applied to study the nucleation phenomena from supersaturated vapor of Lennard-Jones fluid. The barrier height predicted by this theory is significantly lower than the same in CNT which is rather high. The density at the center of the small liquid drop as obtained through optimization is less than the bulk density which is in agreement with other earlier works. Also proposed is a sharp interface limit of the proposed DFT of nucleation, which is as simple as CNT but with a modified barrier height and this modified classical nucleation theory, as we call it, is shown to lead to improved results.     

Density functional theory study on the hydrolysis process of COS and CS2 on a graphene surface

Research on Chemical Intermediates - The adsorption behavior and hydrolysis mechanism of COS and CS2 on a graphene surface were studied by using density functional theory. It could be concluded...     

Thermodynamic perturbation theory of simple liquids: Monte Carlo simulation of a hard sphere system and the Helmholtz free energy of SW fluids

The Monte Carlo method is used to simulate similar sized hard sphere systems in a wide range of densities (from η 0.005 to 0.530 with a step of η = 0.005). The models are used to calculate the coefficients of the thermodynamic perturbation theory series for SW fluids up to the fourth order. The width of the attraction zone of the SW potential λ is varied from 1 to 2.5 sphere diameters. The analytical expressions approximating the obtained coefficients by polynomials with respect to the variables η and λ are determined. The absolute accuracy of the approximation is estimated to be better than ±0.001. All the necessary data for the calculation of the Helmholtz free energy of SW fluids up to the fourth-order perturbation theory are given.     

咪唑菌酮的密度泛函理论计算模拟及表面增强拉曼光谱快速测定EI北大核心CSCD

Density functional theory （DFT） was used to identify and assign the Raman spectra of fenamidone, and a simple and rapid surface-enhanced Raman spectroscopy （SERS）detection method for fenamidone was established. Gold nanoparticles （AuNPs）were synthesized via an improved reduction method of chloroauric acid with the trisodium citrate. DFT was used to optimize the geometric configuration of fenamidone, so as to identify and assign the vibration modes of SERS spectra. The simulated spectra were compared to that of the standard solution as well as the tobacco matrix spiked solution.The SERS detection limit of fenamidone was 0.01 mg/kg in the standard solution and 0.02 mg/kg in tobacco matrix spiked solution. In the range of 0.1-5 mg/L, there was a good linear response between SERS intensity and the logarithm of fenamidone concentrations, with the correlation coefficient （R2） of 0.9658. The relative standard deviations （RSDs）were less than 2.6%. This method is suitable for the determination of fenamidone residues in tobacco samples. © 2023 the authors.     

Density functional theory of homopolymer mixtures confined in a slit

A density functional theory (DFT) is developed for polymer mixtures with shorted-ranged attractive interparticle interactions confined in a slit. Different weighting functions are used separately for the repulsive part and the attractive part of the excess free energy functional by applying the weighted density approximation. The predicted results by DFT are in good agreement with the corresponding simulation data indicating the reliability of the theory. Furthermore, the center-of-mass profiles and the end-to-end distance distributions are obtained by the single chain simulation; the predictions also agree well with simulation data. The results reveal that both the attraction of the slit wall and the temperature has stronger effect on longer chains than on shorter ones because the intrasegment correlation of chains increases with increasing chain length.     

Density functional theory for adsorption of HCHO on the FeO（100） surface

The density functional theory (DFT) and periodic slab model were used to get information concerning the adsorption of HCHO on the FeO(100) surface. A preferred η2-(C,O)-di-σ four-membered ring adsorption conformation on the Fe-top site was found to be the most favorable structure with the predicted adsorption energy of 210.7 kJ/mol. The analysis of density of states, Mulliken population, and vibrational frequencies before and after adsorption showed clear weakening of the carbonyl bond, and high sp3 charact...     

Calculation of free energy surfaces using the methods of thermodynamic perturbation theory

A molecular dynamics method for determining the free energy difference between systems separated in configuration space has been developed. With this new approach, which is based on thermodynamic perturbation techniques, potentials of mean force for conformational changes may be calculated. As a test of the method, the potential of mean force and radial distribution function for liquid argon have been computed. The results are in good agreement with those obtained from an ordinary simulation.