Evaluation of phenomenological one-phase criteria for the melting and freezing of softly repulsive particles

We test the validity of some widely used phenomenological criteria for the localization of the fluid-solid transition thresholds against the phase diagrams of particles interacting through the exp-6, inverse-power-law, and Gaussian potentials. We find that one-phase rules give, on the whole, reliable estimates of freezing/melting points. The agreement is ordinarily better for a face-centered-cubic solid than for a body-centered-cubic crystal, even more so in the presence of a pressure-driven reentrant transition of the solid into a denser fluid phase, as found in the Gaussian-core model.     

Evaluation of site-site bridge diagrams for molecular fluids

The presence of bridge functions in formally exact integral equation theories is the primary obstacle preventing the extraction of exact fluid structure from these theories. The bridge functions are typically neglected but in many fluids their impact may be significant. Each bridge function can be subdivided into bridge diagrams, which are well defined but difficult to evaluate. The calculation of bridge diagrams for the Chandler-Silbey-Ladanyi (CSL) integral equation theory is the subject of this paper. In particular, we evaluate the diagrams required to yield an exact theory up to the first power in density [O(rho(1))] and provide algorithms that remain feasible for any molecule. Further, the bridge diagrams are evaluated and compared with the f-bond and h-bond formulations. Exact bridge diagrams are numerically evaluated for several chiral molecules, for two polar dimers, and for SPC/E water. The quality of the diagrams is assessed in two ways: First, the predicted interatomic distributions are compared with those obtained from Monte Carlo simulations. Second, the connectivity constraints are evaluated and the errors in satisfying these exact relationships are compared for the f-bond and h-bond formulations. For apolar fluids, a clear improvement in CSL theory is evident with the inclusion of O(rho(0)) and O(rho(1)) diagrams. In contrast, for polar fluids, the inclusion of bridge diagrams does not lead to improvement in the structural predictions.     

Ab initio quasirelativistic calculations on electronic transitions in ICl by the multireference many‐body perturbation theory

A quasirelativistic perturbative method of ab initio calculations on ground and excited molecular electronic states and transition properties within the relativistic effective core potential approximation is presented and discussed. The method is based on the construction of a state‐selective many‐electron effective Hamiltonian in the model space spanned by an appropriate set of Slater determinants by means of the second‐order many‐body multireference perturbation theory. The neglect of effective spin–orbit interactions outside of the model space allows the exploitation of relatively high nonrelativistic symmetry during the evaluation of perturbative corrections and therefore dramatic reduction of the cost of computations without any contraction of the model‐space functions. One‐electron transition properties are evaluated via the perturbative construction of spin‐free transition density matrices. Illustrative calculations on the X0⁺ ? A1, B0⁺, and (ii)1 transitions in the ICl molecule are reported. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Conservation of connectivity of model-space effective interactions under a class of similarity transformation

Effective interaction operators usually act on a restricted model space and give the same energies (for Hamiltonian) and matrix elements (for transition operators, etc.) as those of the original operators between the corresponding true eigenstates. Various types of effective operators are possible. Those well defined effective operators have been shown to be related to each other by similarity transformation. Some of the effective operators have been shown to have connected-diagram expansions. It is shown in this paper that under a class of very general similarity transformations, the connectivity is conserved. The similarity transformation between Hermitian and non-Hermitian Rayleigh-Schrodinger perturbative effective operators is one of such transformations and hence the connectivity can be deducted from each other.     

Transformation diagrams for the collapse of a phospholipid monolayer

The kinetics of phase transitions in three-dimensional bulk materials are commonly presented in transformation diagrams. Time-temperature transformation (TTT) and continuous-cooling-transformation (CCT) diagrams plot the time required to transform specific fractions of the material to the new phase by cooling below a transition temperature. Transformation occurs isothermally for the TTT diagrams and during continuous cooling through a range of temperatures for CCT curves. Here we present analogous transformation diagrams for two-dimensional monolayers, which collapse at the equilibrium spreading pressure (pi e) to form a three-dimensional bulk phase. Time-surface pressure-transformation (TpiT) diagrams give the time required for specific fractions of the film to collapse when surface pressure is constant, and continuous-compression-transformation diagrams give the same information when surface pressure varies continuously. The diagrams, constructed here from previously reported data for 1-palmitoyl-2-oleoyl phosphatidylcholine, provide insights into the behavior of the films. The TpiT diagrams successfully predict the existence and approximate magnitude of a threshold rate for compressing the films to high surface pressures above pi e and the approximate shape of isotherms obtained with different rates of interfacial compression. The diagrams also caution that the behavior of mixed monolayers, explained previously in terms of compositional changes, can instead result from collapse that varies with surface pressure. Finally, the similarity between the shapes of the TTT and TpiT diagrams, with the time for transformation passing through a minimum and then increasing as the systems deviate further from equilibrium, suggests that analogous mechanisms determine the behavior of both systems.     

Fundamental limits of the dispersion of the two-photon absorption cross section

We rigorously apply the sum rules to the sum-over-states expression to calculate the fundamental limits of the dispersion of the two-photon absorption cross section. A comparison of the theory with the data suggests that the truncated sum rules in the three-level model give a reasonable fundamental limit. Furthermore, we posit that the two-photon absorption cross section near the limit must have only three dominant states, so by default, the three-level model is appropriate. This ansatz is supported by a rigorous analytical calculation that the resonant term gets smaller as more states are added. We also find that the contributions of the nonexplicitly resonant terms cannot be neglected when analyzing real molecules with many excited states, even near resonance. However, puzzling as it may be, extrapolating an off-resonant result to resonance using only the resonant term of the three-level model is shown to be consistent with the exact result. In addition, the off-resonant approximation is shown to scale logarithmically when compared with the full three-level model. This scaling can be used to simplify the analysis of measurements. We find that existing molecules are still far from the fundamental limit; so, there is room for improvement. But, reaching the fundamental limit would require precise control of the energy-level spacing, independently of the transition dipole moments-a task that does not appear possible using today's synthetic approaches. So, we present alternative methods that can still lead to substantial improvements which only require the control of the transition moment to the first excited state. While it is best to normalize measured two-photon absorption cross sections to the fundamental limits when comparing molecules, we show that simply dividing by the square of the number of electrons per molecule yields a good metric for comparison.     

Flow-alignment and viscosity rules for single-phase binary mesomorphic mixtures

A macroscopic model for incompressible homogeneous (single phase) binary nematic mixtures, under isothermal conditions is given. The rheological model is a generalization of the standard Ericksen's nematorheological model for single component uniaxial rod-like nematic liquid crystals. Its special cases include single component orthorhombic biaxial nematics and single component uniaxial nematics. The theory is used to formulate rules for the rotational viscosity and the reactive parameter of nematic mixtures in the presence of weak flows. The predicted mixture rules for the reactive parameter and rotational viscosity are analysed as a function of concentration and rotational viscosity ratio for various monomeric and polymeric mixtures, and for rod-rod, disc-disc, and rod-disc nematic mixtures. The mixture rules are used to compute alignment phase diagrams and alignment transition (orientational instability) thresholds.     

Transition state barriers in multidimensional Marcus theory

Multidimensional Marcus theory is the extension of traditional Marcus theory to systems in which multiple particles are transferred. Rather than the intersecting parabolas of Marcus theory, multidimensional Marcus theory involves the intersection of paraboloids. In this paper, we examine the conditions under which a full multidimensional treatment of these paraboloids is necessary and when it is possible to use a simpler one-dimensional formalism. In particular, we examine transition state barrier energies, which are essential parameters in many reaction rate equations, and which depend on the formalism used. We find, based on both analytic calculations and numerical simulation, that the reduced one-dimensional treatment yields excellent agreement with the exact, multidimensional results over a wide variety of conditions for one particular choice of the single collective reaction coordinate. We also outline a procedure for calculating accurate multidimensional transition state barrier energies and apply it to a two-dimensional model of proton-coupled electron transfer.     

Department of Physics,Shaoxing College of Arts and Sciences,Shaoxing 312000

A simplified method, Laplace transformation, is used to discuss the radial Schrodinger equation with the weakest bound electron potential model (WBEPM). Through using such method, the second-order differential equation is reduced to a first-order differential equation and the exact bound state solutions including energy spectrum and normalized wave functions are obtained by making use of the integral. The results agree with those obtained by Zheng. It is most important that the two kinds of new recursion relations of radial wave functions are derived by the same method. These new recursion relations are the relations between the effective principal and angular-momentum quantum numbers, and are comprehensive in application to the calculations of transition probabilities in atomic and molecular physics.     

Re-entrant phase behaviour of network fluids: a patchy particle model with temperature-dependent valence

We study a model consisting of particles with dissimilar bonding sites ("patches"), which exhibits self-assembly into chains connected by Y-junctions, and investigate its phase behaviour by both simulations and theory. We show that, as the energy cost ε(j) of forming Y-junctions increases, the extent of the liquid-vapour coexistence region at lower temperatures and densities is reduced. The phase diagram thus acquires a characteristic "pinched" shape in which the liquid branch density decreases as the temperature is lowered. To our knowledge, this is the first model in which the predicted topological phase transition between a fluid composed of short chains and a fluid rich in Y-junctions is actually observed. Above a certain threshold for ε(j), condensation ceases to exist because the entropy gain of forming Y-junctions can no longer offset their energy cost. We also show that the properties of these phase diagrams can be understood in terms of a temperature-dependent effective valence of the patchy particles.     

Stereographic projections and direct products

The concept of stereographic projections of point groups is reviewed. If the focus of attention is moved from the symmetry-equivalence of points to the symmetry operations inter-relating points, it is possible to give simple diagrams of irreducible representations, at least for many axial groups. This approach may be elaborated by the use of trigonometric basis functions, when these may be shown on similar stereographic-related diagrams. These two simple steps enable some insights into direct products; in particular, it is possible to give a diagrammatic representation of an antisymmetric direct product.     

At the boundary between reduced density-matrix and density-functional theories

Here, we revisit the problem of finding the ground-state energy of an N-fermion fluid under an external field, with molecular structure as the ultimate target. Density-functional methods only have to deal with electron density, but require an empirical functional; reduced density-matrix methods involve a matrix on pair space and do give exact bounds, but require very complex linear programming to achieve their results. The polydensity representation that we introduce has the advantage of dealing only with densities, requires no empirical information, and also gives exact bounds; the major problem is that of accumulating and utilizing conditions on the densities that iteratively improve their realizability in the class of N-fermion systems. We indicate several directions along these lines and make some primitive applications.     

The catalytic power of pyruvate decarboxylase. A stochastic model for the molecular evolution of enzymes.

Pyruvate decarboxylase (PDC) catalyzes the decarboxylation of pyruvate anion by a factor of around 10(12), compared with the non-enzymic decarboxylation by thiamine, under standard state conditions of 1 mM pyruvate and thiamine diphosphate (TDP), pH 6.2. Free-energy diagrams constructed on the basis of earlier measurements for the enzymic and non-enzymic reactions give some information on catalysis by PDC. PDC stabilizes the reactant state preceding TDP addition to pyruvate by 76 kJ mol-1 and the transition state for the addition by 83 kJ mol-1. PDC stabilizes the reactant state preceding decarboxylation (presumably alpha-lactyl-TDP) by 27 kJ mol-1 and the transition state for decarboxylation by 68 kJ mol-1. In addition, the free-energy diagrams reveal a leveling of reactant-state free energies in the enzymic reaction compared with the non-enzymic reaction, in that the former are nearly equal to each other. The enzyme-bound transition-state energies are similarly leveled. The energetic leveling of reactant states has been noted by Albery, Knowles and their coworkers in many enzymic reactions and termed 'matched internal thermodynamics.' They showed that the result would arise naturally (and inevitably) in the 'evolution to perfection' of enzymes, when the evolutionary process was treated by a deterministic model. The critical assumption of this model was the validity of a Marcus-type or Br?nsted-type linear free-energy relationship between rate and equilibrium constants for reactions occurring wholly within enzyme complexes. Here a completely stochastic simulation of molecular evolution, with no deterministic assumptions, is shown to reproduce both 'matched internal thermodynamics' and the 'matched internal kinetics' or leveling of transition-state energies noted here. The Albery-Knowles result is thus more general than might have been supposed.     

Voronoi-based detection of pockets in proteins defined by large and small probes

The function of enzymatic proteins is given by their ability to bind specific small molecules into their active sites. These sites can often be found in pockets on a hypothetical boundary between the protein and its environment. Detection, analysis, and visualization of pockets find its use in protein engineering and drug discovery. Many definitions of pockets and algorithms for their computation have been proposed. Kawabata and Go defined them as the regions of empty space into which a small spherical probe can enter but a large probe cannot and developed programs that can compute their approximate shape. In this article, this definition was slightly modified in order to capture the existence of large internal holes, and a Voronoi-based method for the computation of the exact shape of these modified regions is introduced. The method first puts a finite number of large probes on the protein exterior surface and then, considering both large probes and atomic balls as obstacles for the small probe, the method computes the exact shape of the regions for the small probe. This is all achieved with Voronoi diagrams, which help with the safe navigation of spherical probes among spherical obstacles. Detected regions are internally represented as graphs of vertices and edges describing possible movements of the center of the small probe on Voronoi edges. The surface bounding each region is obtained from this representation and used for visualization, volume estimation, and comparison with other approaches. © 2019 Wiley Periodicals, Inc.     

Semi-analytic evaluation of morse oscillator energies and wavefunctions in excited rotational states

A simple technique for generating accurate semi-analytic solutions for the one-dimensional Morse oscillator is presented. This modified Morse technique retains the simplicity and form of the j = 0 Morse solution but still satisfactorily includes the rotational features of the cases where j ≠ 0. The modified Morse solutions are compored to rigid rotor and exact numerical calculations performed by the finite element method. The technique is shown to give an accurate representation of the true wavefunction, and this result should make the method particularly useful for the generation of vibration-rotation transition matrix elements.     

反相色谱法表征聚苯乙烯磺酸的转变现象

1969年,Smidsrφd和Guillet就应用反相色谱法(IGC)测量聚合物的玻璃化转变温度。十几年来许多科学工作者研究了IGC测量聚合物玻璃化转变现象的各种影响因素,但应用IGC研究离聚物还属罕见。离聚物分子上带有离子基闭,分子间的相互作用比较复杂,我们曾用热激放电电流法(TSDC)等测量了本实验所用的聚苯乙烯磺酸(PSSA)样品的玻璃化转变现象。应用IGC法,不仅能够比较精密地测出不同磺化度     

Electron Domains and the VSEPR Model of Molecular Geometry

The valence shell electron pair repulsion (VSEPR) model—also known as the Gillespie–Nyholm rules—has for many years provided a useful basis for understanding and rationalizing molecular geometry, and because of its simplicity it has gained widespread acceptance as a pedagogical tool. In its original formulation the model was based on the concept that the valence shell electron pairs behave as if they repel each other and thus keep as far apart as possible. But in recent years more emphasis has been placed on the space occupied by a valence shell electron pair, called the domain of the electron pair, and on the relative sizes and shapes of these domains. This reformulated version of the model is simpler to apply, and it shows more clearly that the Pauli principle provides the physical basis of the model. Moreover, Bader and his co-workers' analysis of the electron density distribution of many covalent molecules have shown that the local concentrations of electron density (charge concentrations) in the valence shells of the atoms in a molecule have the same relative locations and sizes as have been assumed for the electron pair domains in the VSEPR model, thus providing further support for the model. This increased understanding of the model has inspired efforts to examine the electron density distribution in molecules that have long been regarded as exceptions to the VSEPR model to try to understand these exceptions better. This work has shown that it is often important to consider not only the relative locations and sizes, but also the shapes, of both bonding and lone pair domains in accounting for the details of molecular geometry. It has also been shown that a basic assumption of the VSEPR model, namely that the core of an atom underlying its valence shell is spherical and has no influence on the geometry of a molecule, is normally valid for the nonmetals but often not valid for the metals, including the transition metals. The cores of polarizable metal atoms may be nonspherical because they include nonbonding electrons or because they are distorted by the ligands, and these nonspherical cores may have an important influence on the geometry of a molecule.     

Some efforts beyond the local density approximation

The exchange-correlation density functional can be expressed as a many-body perturbation series in terms of the Coulomb interaction using the exact Kohn-Sham orbitals as the basis. A self-consistent equation is derived for the exact exchangecorrelation potential. This perturbation approach forms a basis for going beyond the local density approximation (LDA ). The discontinuity in the exchange-correlation potential for semiconductors calculated by the perturbative approach gives a good account of the discrepancy of the band gap calculated in LDA . The discontinuity also plays an important role in the interface band diagrams. A theory to account for the interaction effects of localized d or f orbitals is reviewed and the physics of the applications to a model test, to some 3d transition metals, and to heavy fermions is discussed. The perturbative approach to improvement beyond LDA tends to be computation-intensive and to be system-specific. © 1995 John Wiley & Sons, Inc.     

Inherent structure versus geometric metric for state space discretization

Inherent structure (IS) and geometry‐based clustering methods are commonly used for analyzing molecular dynamics trajectories. ISs are obtained by minimizing the sampled conformations into local minima on potential/effective energy surface. The conformations that are minimized into the same energy basin belong to one cluster. We investigate the influence of the applications of these two methods of trajectory decomposition on our understanding of the thermodynamics and kinetics of alanine tetrapeptide. We find that at the microcluster level, the IS approach and root‐mean‐square deviation (RMSD)‐based clustering method give totally different results. Depending on the local features of energy landscape, the conformations with close RMSDs can be minimized into different minima, while the conformations with large RMSDs could be minimized into the same basin. However, the relaxation timescales calculated based on the transition matrices built from the microclusters are similar. The discrepancy at the microcluster level leads to different macroclusters. Although the dynamic models established through both clustering methods are validated approximately Markovian, the IS approach seems to give a meaningful state space discretization at the macrocluster level in terms of conformational features and kinetics. © 2016 Wiley Periodicals, Inc.