The theoretical basis of the first-principles molecular dynamics introduced by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)] is investigated. We elucidate how the classical dynamics generated by the Car-Parrinello Lagrangian approximates efficiently the quantum adiabatic evolution of a system and discuss the role played by the spectrum of the eigenvalues of the Hamiltonian of Kohn and Sham [Phys. Rev. 140, A1133 (1965)]. A detailed characterization of the statistical ensemble sampled in the numerical simulation is given. By combining theoretical arguments and numerical results we demonstrate that the motion of the electronic variables is a superposition of a direct drag due to the ions and of high-frequency normal modes. By making a connection with the averaging methods of classical mechanics, we argue that whenever it is possible to get a large separation between the time scales of these modes and the ionic frequencies, the dynamics of the ions closely approximates that resulting from the adiabatic approximation. We introduce simple n-level models, easily amenable to analytic treatment, to add clarity and study the possible mechanisms of broken adiabaticity encountered in the actual calculations.

We thoroughly investigate a simple model representative of the recently synthesized Janus particles, i.e., colloidal spherical particles whose surface is divided into two areas of different chemical composition. When the two surfaces are solvophilic and solvophobic, these particles constitute the simplest example of surfactants. The phase diagram includes a colloidal-poor (gas), colloidal-rich (liquid) demixing region, which is progressively suppressed by the insurgence of micelles, providing the first model in which micellization and phase separation are simultaneously observed. The coexistence curve is found to be negatively sloped in the temperature-pressure plane, suggesting that Janus particles can provide a colloidal system with anomalous thermodynamic behavior.

Molecular-dynamics simulations have been carried out on a ‘‘soft-sphere’’ model for binary alloys quenched into supercooled and amorphous states. The main emphasis of the work is on the static and dynamic characterization of the glass transition. A comparison between molecular-dynamics data and the results of a self-consistent integral equation shows that the equation of state bifurcates into ‘‘glass’’ and ‘‘fluid’’ branches below a glass transition temperature $T_g$. The static pair structures differ significantly along the two branches. The structurally relaxed ‘‘fluid’’ branch leads to a phase separation at very low temperatures. Close to the glass transition, the atomic mean-square displacements of the two species go over more and more slowly to the asymptotic diffusive regime, due to the emergence of an intermediate time scale linked to the slowing down of structural relaxation. The diffusion constants of the two species follow closely a scaling law, as predicted by mode-coupling theory, except in the immediate vicinity of the glass transition where activated processes lead to residual diffusion.

The existence of systematic variations of isobaric fragility in different supercooled Lennard-Jones binary mixtures is revealed by molecular dynamics simulations. The connection between fragility and local structures in the bulk is analyzed by means of a Voronoi construction. It is found that clusters of particles belonging to locally preferred structures form slow, long-lived domains, whose spatial extension increases with decreasing temperature. As a general rule, a more rapid growth, upon supercooling, of such domains is associated with a more pronounced super-Arrhenius behavior, and hence to a larger fragility.

Binary mixtures of additive (d ₁₂ = (d ₁ + d ₂)/2) and non-additive (d ₁₂ ≠ (d ₁ + d ₂)/2) hard spheres have been studied with new integral equations. Accurate Monte Carlo results for some non-additive cases have been generated and tables of radial distribution functions are explicitly given. Comparison of structural and thermodynamic results demonstrates that an approximate integral equation recently proposed by Martynov and Sarkisov for one-component hard spheres significantly improves on the Percus-Yevick approximation also in the mixture case, without introducing free parameters. A simple further generalization gives a very good parameterization of the computer experiment results. An analytical fit of the equation of state for symmetric non-additive systems is also given.

We perform numerical simulations of a simple model of one-patch colloidal particles to investigate: (i) the behavior of the gas–liquid phase diagram on moving from a spherical attractive potential to a Janus potential and (ii) the collective structure of a system of Janus particles. We show that, for the case where one of the two hemispheres is attractive and one is repulsive, the system organizes into a dispersion of orientationally ordered micelles and vesicles and, at low temperature (T), the system can be approximated as a fluid of such clusters, interacting essentially via excluded volume. The stability of this cluster phase generates a very peculiar shape of the gas and liquid coexisting densities, with a gas coexistence density that increases on cooling, approaching the liquid coexistence density at very low T.