Atomic-defect engineering in thin membranes provides opportunities for ionic and molecular filtration and analysis. While molecular-dynamics (MD) calculations have been used to model conductance through atomic vacancies, corresponding experiments are lacking. We create sub-nanometer vacancies in suspended single-layer molybdenum disulfide (MoS) via Ga ion irradiation, producing membranes containing ∼300 to 1200 pores with average and maximum diameters of ∼0.5 and ∼1 nm, respectively. Vacancies exhibit missing Mo and S atoms, as shown by aberration-corrected scanning transmission electron microscopy (AC-STEM). The longitudinal acoustic band and defect-related photoluminescence were observed in Raman and photoluminescence spectroscopy, respectively. As the irradiation dose is increased, the median vacancy area remains roughly constant, while the number of vacancies (pores) increases. Ionic current versus voltage is nonlinear and conductance is comparable to that of ∼1 nm diameter single MoS pores, proving that the smaller pores in the distribution display negligible conductance. Consistently, MD simulations show that pores with diameters <0.6 nm are almost impermeable to ionic flow. Atomic pore structure and geometry, studied by AC-STEM, are critical in the sub-nanometer regime in which the pores are not circular and the diameter is not well-defined. This study lays the foundation for future experiments to probe transport in large distributions of angstrom-size pores.

Coarse-grained molecular-dynamics simulations offer a dramatic extension of the time-scale of simulations compared to all-atom approaches. In this article, we describe the use of the physics-based united-residue (UNRES) force field, developed in our laboratory, in protein-structure simulations. We demonstrate that this force field offers about a 4000-times extension of the simulation time scale; this feature arises both from averaging out the fast-moving degrees of freedom and reduction of the cost of energy and force calculations compared to all-atom approaches with explicit solvent. With massively parallel computers, microsecond folding simulation times of proteins containing about 1000 residues can be obtained in days. A straightforward application of canonical UNRES/MD simulations, demonstrated with the example of the N-terminal part of the B-domain of staphylococcal protein A (PDB code: 1BDD, a three-α-helix bundle), discerns the folding mechanism and determines kinetic parameters by parallel simulations of several hundred or more trajectories. Use of generalizedensemble techniques, of which the multiplexed replica exchange method proved to be the most effective, enables us to compute thermodynamics of folding and carry out fully physics-based prediction of protein structure, in which the predicted structure is determined as a mean over the most populated ensemble below the folding-transition temperature. By using principal component analysis of the UNRES folding trajectories of the formin-binding protein WW domain (PDB code: 1E0L; a three-stranded antiparallel β-sheet) and 1BDD, we identified representative structures along the folding pathways and demonstrated that only a few (low-indexed) principal components can capture the main structural features of a protein-folding trajectory; the potentials of mean force calculated along these essential modes exhibit multiple minima, as opposed to those along the remaining modes which are unimodal. In addition, a comparison, between the structures that are representative of the minima in the free-energy profile along the essential collective coordinates of protein folding (computed by principal component analysis) and the free-energy profile projected along the virtualbond dihedral angles γ of the backbone, revealed the key residues involved in the transitions between the different basins of the folding free-energy profile, in agreement with existing experimental data for 1E0L.

A new Hirshfeld partitioning of cluster polarizability into intrinsic polarizabilities and charge delocalization contributions is presented. For water clusters, density-functional theory calculations demonstrate that the total polarizability of a water molecule in a cluster depends upon the number and type of hydrogen bonds the molecule makes with its neighbors. The intrinsic contribution to the molecular polarizability is transferable between water molecules displaying the same H-bond scheme in clusters of different sizes, and geometries, while the charge delocalization contribution also depends on the cluster size. These results could be used to improve the existing force fields.

The exact equations for the variations of the electronic density induced by an adiabatic external potential are derived to an arbitrary perturbation order in the framework of density-functional-theory. The formal solutions of these density perturbation equations are given and the exact relations between the electronic response functions and the Hohenberg–Kohn functional are derived. Using these relations, the static nonlinear electronic response functions are constructed from the linear one. Nonconserving electron number perturbations are also directly included in the formalism to all perturbation orders. In this way the well-known results of the density-functional reactivity theory are generalized beyond the first and the second-order. This makes it possible to derive the exact relations between the Hohenberg–Kohn functional and the linear and nonlinear Fukui responses, the nonlinear Fukui functions and the nonlinear hardnesses. These relations allow us to reformulate all the derivatives of the electronic energy relative to the external potential and to the particle number in terms of the linear response kernel and in terms of the linear Fukui function. The formalism is applied to the Thomas–Fermi–Dirac-λ von Weiszäcker model of the Hohenberg–Kohn functional.

In a recent paper [J. Chem. Phys. 105, 6471 (1996)], nonlinear chemical responses of a system to a simultaneous change of its external potential and of its number of electrons have been formulated in terms of the ground-state electronic density for a given model of the Hohenberg-Kohn functional. In the present work, an exact one-electron formulation of all the chemical responses is derived in terms of the Kohn-Sham orbitals of the unperturbed system. The present formulation encompasses the band-structure formulation of the linear Fukui function derived recently [M.H. Cohen, M.V. Ganduglia-Pirovano, and J. Kudrnovský, J. Chem. Phys. 101, 8988 (1994)] and provides an exact orbital expression of the linear hardness. The latter is compared to the hardness matrix used in the construction of ab initio pseudo-potentials [M. Teter, Phys. Rev. B 48, 5031 (1993)]. In addition, the relation between the covalent radius of atoms and the linear and nonlinear hardnesses is discussed.

The structure and phonons of an ordered ice surface, prepared in situ under ultra high vacuum conditions, have been studied by high resolution helium atom scattering. The angular distributions are dominated by sharp hexagonal (1×1) diffraction peaks characteristic of a full bilayer terminated ice Ih crystal. Additional, very broad and weak, p(2.1×2.1) peaks may indicate the presence of small domains of antiphase oriented molecules. An eikonal analysis of the 1×1 peaks is compatible with either a proton disordered or a proton ordered surface with corrugations of 0.76 Å and 0.63 Å, respectively. Inelastic time-of-flight spectra reveal not only a dispersionless phonon branch reported previously at 5.9 meV, but also the first evidence for the surface Rayleigh phonons, which are reproduced well by a Born–von Kármán simulation of a full bilayer terminated ice surface using the unmodified force constants derived from neutron scattering bulk phonon measurements. Since the lattice dynamics simulations do not reproduce the dispersionless branch, it is attributed to the vibrations of single water molecules on the ice surface.

Density functional theory (DFT) calculations with different exchangecorrelation functionals, Becke's three-parameter exchange functional and the gradientcorrected functional of Lee, Yang, and Paar (B3LYP) and Becke's three-parameter functional with Perdew-Wang correlational functional (B3PW91), are performed to study the dielectric properties of small and medium-sized water clusters. For these Hbonded systems, we optimize the geometries and compute the dipole moments and polarizabilities using a supermolecule approach. The corresponding properties of the individual water molecules in the clusters are extracted from the molecular properties using the Hirshfeld expansion of the electronic density. Calculations at Hartree-Fock and second-order Møller-Plesset (MP2) levels are also presented for a comparison with the DFT results. The dependence of the dielectric properties on the cluster structure and size is given for both clusters and individual molecules and is compared with the available experimental data. The intermolecular interactions and their influences on the dielectric properties are discussed. The current results could serve to improve existing polarizable force fields for water.

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