Density Functional Theory Of Freezing Research Articles

Structures and freezing transitions in two-dimensional colloids with tunable repulsive interactions

We have used density functional theory of freezing and hypernetted chain(HNC) integral equation theory to investigate the effects of gradual softening of inverse-power repulsive interaction on the structure and fluid-triangular-solid freezing transition of a one component system of particles confined to a two-dimensional plane and interacting via core-softened potential. We have also performed Monte Carlo simulation to test the accuracy of the pair-structures obtained by HNC theory and to see the equilibrium configuration of particle in different thermodynamic conditions. The pair-structures are found to compare well with those obtained by MC results, particularly in high softness parameter region. The radial distribution given by HNC exhibits a non-monotonous behavior with the change in particle density in addition to the emergence of a new peak at shorter distance. In contrast to HNC, the RDF, obtained by MC simulation for high-softness parameter, display a splitting of the second peak at high density.

Electron transfer and spin dynamics of the radical-pair in the cryptochrome from Chlamydomonas reinhardtii by computational analysis

In an effort to elucidate the origin of avian magnetoreception, it was postulated that a radical-pair formed in a cryptochrome upon light activation provided the basis for the mechanism that enables an inclination compass sensitive to the geomagnetic field. Photoreduction in this case involves formation of a flavin adenine dinucleotide (FAD)-tryptophan (TRP) radical-pair, following electron transfer within a conserved TRP triad in the cryptochrome. Recently, an animal-like cryptochrome from Chlamydomonas reinhardtii (CraCRY) was analyzed, demonstrating the role of a fourth aromatic residue, which serves as a terminal electron donor in the photoreduction pathway, resulting in the creation of a more distal radical-pair and exhibiting fast electron transfer. In this work, we investigated the electron transfer in CraCRY with a combination of free energy molecular dynamics (MD) simulations, frozen density functional theory, and QM/MM MD simulations, supporting the suggestion of a proton coupled electron transfer mechanism. Spin dynamics simulations discerned details on the dependence of the singlet yield on the direction of the external magnetic field for the [FAD•- TYRH•+] and [FAD•- TYR•] radical-pairs in CraCRY, in comparison with the previously modeled [FAD•- TRPH•+] radical-pair.

Density functional theory of freezing of a system of highly elongated ellipsoidal oligomer solutions

ABSTRACTWe have used the density functional theory of freezing to study the liquid crystalline phase behavior of a system of highly elongated ellipsoidal conjugated oligomers dispersed in three different solvents namely chloroform, toluene and their equimolar mixture. The molecules are assumed to interact via solvent-implicit coarse-grained Gay–Berne potential. Pair correlation functions needed as input in the density functional theory have been calculated using the Percus–Yevick (PY) integral equation theory. Considering the isotropic and nematic phases, we have calculated the isotropic–nematic phase transition parameters and presented the temperature–density and pressure–temperature phase diagrams. Different solvent conditions are found not only to affect the transition parameters but also determine the capability of oligomers to form nematic phase in various thermodynamic conditions. In principle, our results are verifiable through computer simulations.

Density functional theory of freezing of a system of conjugated oligomers parameterised via Gay–Berne potential

ABSTRACTDensity functional theory (DFT) of freezing is used to study the isotropic–nematic, isotropic–smectic A and nematic–smectic A phase transitions in a system of large, semi-flexible conjugated oligomers parameterised within Gay–Berne (GB) potential. The pair correlation functions of the isotropic fluid, used as structural inputs in the DFT, are calculated by solving the Percus–Yevick integral equation theory. Large number of spherical harmonic coefficients of each orientation-dependent functions has been considered to ensure the numerical accuracy at different densities and temperatures for the system of these model GB ellipsoids having large aspect ratio (length-to-breadth ratio). We found that the system of GB ellipsoids parameterised for conjugated oligomers shows stable isotropic, nematic and smectic A phases. At low temperatures, on increasing the density, isotropic fluid makes a direct transition to smectic A phase. Nematic phase get stabilised in between the isotropic and smectic A phases on increasing the temperature. Using the transition parameter obtained through the DFT, we have plotted the temperature–density and pressure–temperature phase diagrams which are found to be qualitatively similar to the one obtained in simulations for the systems with low aspect ratio GB particles.

Features of chemical bonds based on the overlap polarizabilities: diatomic and solid-state systems with the frozen-density embedding approach.

The chemical bond overlap properties were obtained for alkali halides NaY (Y = F, Cl, Br), alkaline-earth chalcogenides MX (M = Ca, Mg and X = O, S, Se) and alkali and alkali-earth metals (Li, Na, and Mg) in diatomic and solid-state systems using an embedding approach based on the frozen density functional theory to simulate the crystalline effects. The computational protocol established provides errors for bond distances smaller than 1%. The results indicate that larger chemical bond covalency leads to larger absorption or scattering by the overlap region. The ionic specific valence and overlap polarizability are closely related to the valence orbital compactness measured by the sum of Mulliken electronegativities. The embedding approach used in this work makes it possible to quantify the effects of the crystalline environment on the chemical bond overlap properties. In the solid-state, the bond overlap charges are less polarizable, in cases of well-known ionic systems (provided by electronegativity differences), leading to smaller chemical bond covalency in solids than in diatomics. The spectroscopic properties of the polarizability of the electron density in the overlap region of a chemical bond could be measured in the 1-20 eV spectral region and could be used to characterize some bands in several spectra whose assignments are ambiguous or not available.

Density functional theory of freezing for binary mixtures of 2D superparamagnetic colloids

Density functional theory of freezing is used to study the phase diagram of a binary mixture of superparamagnetic colloidal particles in two dimensions. The particles interact via a purely repulsive potential that scales as the inverse cube of the inter-particle separation. This corresponds to a magnetic dipole interaction where the dipoles are induced by an external magnetic field applied normal to the plane. The pair correlation functions needed as input information in the density functional theory are calculated by the hypernetted chain integral equation closure. Considering the freezing into a disordered triangular solid phase, a spindle phase diagram is found for the susceptibility ratio 0.9 of the species, which changes to an azeotrope at a ratio 0.8. A eutectic-like phase diagram with an intervening solid phase emerges for the susceptibility ratio 0.7. The results are verifiable in real-space experiments on superparamagnetic colloids in external magnetic fields.

Origin of Linear Free Energy Relationships: Exploring the Nature of the Off-Diagonal Coupling Elements in SN2 Reactions

Understanding the relationship between the adiabatic free energy profiles of chemical reactions and the underlining diabatic states is central to the description of chemical reactivity. The diabatic states form the theoretical basis of Linear Free Energy Relationships (LFERs) and thus play a major role in physical organic chemistry and related fields. However, the theoretical justification for some of the implicit LFER assumptions has not been fully established by quantum mechanical studies. This study follows our earlier works(1,2) and uses the ab initio frozen density functional theory (FDFT) method(3) to evaluate both the diabatic and adiabatic free energy surfaces and to determine the corresponding off-diagonal coupling matrix elements for a series of S(N)2 reactions. It is found that the off-diagonal coupling matrix elements are almost the same regardless of the nucleophile and the leaving group but change upon changing the central group. Furthermore, it is also found that the off diagonal elements are basically the same in gas phase and in solution, even when the solvent is explicitly included in the ab initio calculations. Furthermore, our study establishes that the FDFT diabatic profiles are parabolic to a good approximation thus providing a first principle support to the origin of LFER. These findings further support the basic approximation of the EVB treatment.

Colloidal Crystal Growth at Externally Imposed Nucleation Clusters

We study the conditions under which and how an imposed cluster of fixed colloidal particles at prescribed positions triggers crystal nucleation from a metastable colloidal fluid. Dynamical density functional theory of freezing and Brownian dynamics simulations are applied to a two-dimensional colloidal system with dipolar interactions. The externally imposed nucleation clusters involve colloidal particles either on a rhombic lattice or along two linear arrays separated by a gap. Crystal growth occurs after the peaks of the nucleation cluster have first relaxed to a cutout of the stable bulk crystal.

Phase-field crystal modeling and classical density functional theory of freezing

In this paper the relationship between the classical density functional theory of freezing and phase-field modeling is examined. More specifically a connection is made between the correlation functions that enter density functional theory and the free energy functionals used in phase-field crystal modeling and standard models of binary alloys (i.e., regular solution model). To demonstrate the properties of the phase-field crystal formalism a simple model of binary alloy crystallization is derived and shown to simultaneously model solidification, phase segregation, grain growth, elastic and plastic deformations in anisotropic systems with multiple crystal orientations on diffusive time scales.

Density functional theory of vortex lattice melting in layered superconductors: A mean-field substrate approach

We study the melting of the pancake vortex lattice in a layered superconductor in the limit of vanishing Josephson coupling. Our approach combines the methodology of a recently proposed mean-field substrate model for such systems with the classical density functional theory of freezing. We derive a free-energy functional in terms of a scalar order-parameter profile and use it to derive a simple formula describing the temperature dependence of the melting field. Our theoretical predictions are in good agreement with simulation data. The theoretical framework proposed is thermodynamically consistent and thus capable of describing the negative magnetization jump obtained in experiments. Such consistency is demonstrated by showing the equivalence of our expression for the density discontinuity at the transition with the corresponding Clausius-Clapeyron relation.

Using the Constrained DFT Approach in Generating Diabatic Surfaces and Off Diagonal Empirical Valence Bond Terms for Modeling Reactions in Condensed Phases

The empirical valence bond (EVB) model provides an extremely powerful way for modeling and analyzing chemical reactions in solutions and proteins. However, this model is based on the unverified assumption that the off diagonal elements of the EVB Hamiltonian do not change significantly upon transfer of the reacting system from one phase to another. This ad hoc assumption has been rationalized by its consistency with empirically observed linear free energy relationships, as well as by other qualitative considerations. Nevertheless, this assumption has not been rigorously established. The present work explores the validity of the above EVB key assumption by a rigorous numerical approach. This is done by exploiting the ability of the frozen density functional theory (FDFT) and the constrained density functional theory (CDFT) models to generate convenient diabatic states for QM/MM treatments, and thus to examine the relationship between the diabatic and adiabatic surfaces, as well as the corresponding effective off diagonal elements. It is found that, at least for the test case of S(N)()2 reactions, the off diagonal element does not change significantly upon moving from the gas phase to solutions and thus the EVB assumption is valid and extremely useful.

Theoretical approaches to the glass transition in simple liquids

Theoretical approaches to the development of an understanding of the behaviour of simple supercooled liquids near the structural glass transition are reviewed and our work on this problem, based on the density functional theory of freezing and replicated liquid state theory, are summarized in this context. A few directions for further work on this problem are suggested.

Density Functional Theory of Freezing of Superfluid Helium 4

We discuss freezing of superfluid helium 4 in the frame of density functional theory. We first review the previous attempts made with different inputs for the liquid properties. We then present a new calculation based on a more recent input. Our resugt confirms the finding by Likos et al. [C. N. Likos, S. Moroni, and G. Senatore, Phys. Rev. B, 55, 8867 (1997)] that the solid is always too stable. However, a slight rescaling leads to freezing parameters and an equation of state for the solid consistent with the experiments. We discuss the physical origin of this rescaling.

Melting in two dimensions: first-order versus continuous transition

In the framework of the theory, based on the density functional theory of freezing, the melting of the system with Yukawa potential and the hard-disk system with square-well attraction is considered. It is shown that melting scenario crucially depends on the shape of the potential. For the soft-core Yukawa potential melting mainly occurs by means of two continuous transitions, however, there is the critical value of the radius of the potential where the crossover from two continuous to one first-order transition occurs. It should be noted that the first-order transition exists only for very short-range interaction. In the case of hard-core square-well potential situation is more complex, and there are several crossover points, where the melting scenario changes from continuous to first-order transition, and vice versa.

Freezing transition of the vortex liquid in anisotropic superconductors

We study the solid-liquid transition of a model of pancake vortices in laminar superconductors using a density functional theory of freezing. The physical properties of the system along the melting line are discussed in detail. We show that there is a very good agreement with experimental data in the shape and position of the first order transition in the phase diagram and in the magnitude and temperature dependence of the magnetic induction jump at the transition. We analyze the validity of the Lindemann melting criterion and the Hansen-Verlet freezing criterion. Both criteria are shown to predict well the phase diagram in the region where a first-order phase transition is experimentally observed.

Density functional theory for hard spherocylinders: phase transitions in the bulk and in the presence of external fields

The phase behaviour of hard spherocylinders is calculated using the classical density functional theory of freezing. In particular, we construct a modified weighted-density approximation and calculate the bulk phase diagram. While the stability regime of the isotropic, nematic and smectic-A phases is in reasonable agreement with computer simulation data, the theory fails to describe the correct stability of the crystalline phases. Furthermore, we investigate the phase behaviour in an external field coupling to the orientational degrees of freedom. As a result, bulk phases which have the same translational symmetry but a different orientational symmetry can be transformed continuously into each other above a critical strength of the external field.

A partitioned density functional theory of freezing: application to soft spheres

A non-perturbative density functional theory (DFT) for inhomogeneous fluids is developed by partitioning the functional into short range (‘entropic’) and long range (‘energetic’) contributions. The short range part is treated using standard weighted density functional techniques and the long range contribution is evaluated exactly. This method, which is a generalization of a method due to Likos, C., and Senatore, G., 1995, J. Phys.: Condens. Matter, 7, 6797, does not require the use of a reference system. Results are presented for the calculation of the crystal-/fluid phase coexistence for systems interacting with inverse-power potentials of the form r -n , where n = 4, 6 and 12. These results show that this non-perturbative DFT is capable of predicting the freezing of long range inverse power systems (n = 4, 6) into a body-centredcubic lattice. Improvements over earlier methods also are noted in the current results for the solid structure as measured by the Lindemann ratio.

A partitioned density functional theory of freezing: application to soft spheres

A non-perturbative density functional theory (DFT) for inhomogeneous fluids is developed by partitioning the functional into short range (‘entropic’) and long range (‘energetic’) contributions. The short range part is treated using standard weighted density functional techniques and the long range contribution is evaluated exactly. This method, which is a generalization of a method due to Likos, C., and Senatore, G., 1995, J. Phys.: Condens. Matter, 7, 6797, does not require the use of a reference system. Results are presented for the calculation of the crystal-/fluid phase coexistence for systems interacting with inverse-power potentials of the form r -n , where n = 4, 6 and 12. These results show that this non-perturbative DFT is capable of predicting the freezing of long range inverse power systems (n = 4, 6) into a body-centredcubic lattice. Improvements over earlier methods also are noted in the current results for the solid structure as measured by the Lindemann ratio.

Ab Initio Frozen Density Functional Calculations of Proton Transfer Reactions in Solution

The recently developed frozen density functional theory (FDFT) is extended to ab initio free energy calculations of chemical reactions in solution. This method treats the solute−solvent system as a supermolecule but constrains the electron density of the solvent molecules. Unlike hybrid quantum mechanical/molecular mechanics techniques, FDFT represents the solvent quantum mechanically. The quality of the solute−solvent interaction potential is examined by generating clusters of a reacting system and several solvent molecules and comparing the supermolecule DFT energies to the corresponding FDFT energies. The FDFT potential surfaces for solute−solvent systems provide a good approximation of the supermolecule DFT surfaces and require, in some cases, several orders of magnitude less computation time (in particular if one treats many solvent molecules quantum mechanically). The ab initio free energy surface for the F- + HF → FH + F- proton transfer reaction in solution is calculated using the corresponding “c...

Supercooling of surface modified liquids.

We present a simple model of surface modified first-order phase transitions, based on the density-functional theory of freezing. Motivated by recent experiments of surface induced freezing, we show how supercooling may in fact be inhibited below a certain temperature which depends on the lattice mismatch between the monolayer and the nucleated crystal, as well as on the macroscopic strength of the surface treatment. We also apply the model to systems which tend to surface-freeze above the melting point, and correlate their surface-freezing and supercooling temperatures. \textcopyright{} 1996 The American Physical Society.