Critical energy-density profile near walls.

We examine critical adsorption for semi-infinite thermodynamic systems of the Ising universality class when they are in contact with a wall of the so-called normal surface universality class in spatial dimension d=3 and in the mean-field limit. We apply local-functional theory and Monte Carlo simulations in order to quantitatively determine the properties of the energy density as the primary scaling density characterizing the critical behaviors of Ising systems besides the order parameter. Our results apply to the critical isochore, near two-phase coexistence, and along the critical isotherm if the surface and the weak bulk magnetic fields are either collinear or anticollinear. In the latter case, we also consider the order parameter, which so far has yet to be examined along these lines. We find the interface between the surface and the bulk phases at macroscopic distances from the surface, i.e., the surface is "wet." It turns out that in this case the usual property of monotonicity of primary scaling densities with respect to the temperature or magnetic field scaling variable does not hold for the energy density due to the presence of this interface.

First-principles study of large-amplitude dynamic Jahn-Teller effects in vanadium tetrafluoride.

Transition metal tetrahalides are a class of highly symmetric molecules for which very few spectroscopic data exist. Exploratory ab initio calculations of electronic potential energy functions indicate that the equilibrium molecular geometries of the vanadium, niobium, and tantalum tetrafluorides (i.e., VF4, NbF4, and TaF4) exhibit strong distortions from the tetrahedral configuration in their electronic ground state (2E) and first excited state (2T2) along the nuclear displacement coordinates of e symmetry. The distortions result from the E × e and T2 × e Jahn-Teller (JT) effects, respectively. In addition, there are weaker distortions in the 2T2 state along the coordinates of t2 symmetry due to the T2 × t2 JT effect. The description of the large-amplitude dynamics induced by these JT effects requires the construction of JT Hamiltonians beyond the standard model of JT theory, which is based on Taylor expansions up to second order in normal-mode displacements. These higher-order JT Hamiltonians were constructed in this work by expansions of the electronic potentials of the title molecule in terms of symmetry invariant polynomials in symmetry-adapted nuclear displacement coordinates for the bending modes of VF4. A multi-configuration electronic structure method was employed to determine the coefficients of these high-order polynomial expansions from first principles. Using these large-amplitude Jahn-Teller Hamiltonians, the vibronic spectra of VF4 were computed. The spectra illustrate the effects of large-amplitude fluxional nonadiabatic dynamics due to exceptionally strong E × e and T2 × e JT couplings. In addition, the vibronic spectrum of the T2 × (e + t2) JT effect, including the bending mode of t2 symmetry, was computed. The spectrum displays strong inter-mode coupling effects exhibiting a vibronic structure, which is substantially different from that predicted by independent-mode approximation. These results represent the first ab initio study of dynamical Jahn-Teller effects in VF4.

Inverse patchy colloids with two and three patches. Analytical and numerical study.

We propose an analytical solution of the multi-density Ornstein-Zernike equation supplemented by the associative Percus-Yevick closure relations specifically designed to describe the equilibrium properties of the novel class of patchy colloidal particles represented by the inverse patchy colloids with arbitrary number of patches. Using Baxter's factorization method, we reduce solution of the problem to the solution of one nonlinear algebraic equation for the fraction of the particles with one non-bonded patch. We present closed-form expressions for the structure (structure factor) and thermodynamic (internal energy) properties of the system in terms of this fraction (and parameters of the model). We perform computer simulation studies and compare theoretical and computer simulation predictions for the pair distribution function, internal energy, and number of single and double bonds formed in the system, for two versions of the model, each with two and three patches. We consider the models with formation of the double bonds blocked by the patch-patch repulsion and the models without patch-patch repulsion. In general very good agreement between theoretical and computer simulation results is observed.

Critical Casimir interactions between spherical particles in the presence of bulk ordering fields.

The spatial suppression of order parameter fluctuations in a critical media produces critical Casimir forces acting on confining surfaces. This scenario is realized in a critical binary mixture near the demixing transition point that corresponds to the second-order phase transition of the Ising universality class. Due to these critical interactions similar colloids, immersed in a critical binary mixture near the consolute point, exhibit attraction. The numerical method for computation of the interaction potential between two spherical particles using Monte Carlo simulations for the Ising model is proposed. This method is based on the integration of the local magnetization over the applied local magnetic field. For the stronger interaction the concentration of the component of the mixture that does not wet colloidal particles should be larger than the critical concentration. The strongest amplitude of the interactions is observed below the critical point.

Critical Casimir torques and forces acting on needles in two spatial dimensions.

We investigate the universal orientation-dependent interactions between nonspherical colloidal particles immersed in a critical solvent by studying the instructive paradigm of a needle embedded in bounded two-dimensional Ising models at bulk criticality. For a needle in an Ising strip, the interaction on mesoscopic scales depends on the width of the strip and the length, position, and orientation of the needle. By lattice Monte Carlo simulations we evaluate the free-energy difference between needle configurations being parallel and perpendicular to the strip. We concentrate on small but nonetheless mesoscopic needle lengths for which analytic predictions are available for comparison. All combinations of boundary conditions for the needles and boundaries are considered which belong to either the "normal" or the "ordinary" surface universality class, i.e., which induce local order or disorder, respectively. We also derive exact results for needles of arbitrary mesoscopic length, in particular for needles embedded in a half plane and oriented perpendicularly to the corresponding boundary as well as for needles embedded at the center line of a symmetric strip with parallel orientation.