A four-dimensional potential energy surface (PES) for the CO dimer consisting of rigid molecules has been calculated, using a scheme that combines density functional theory to describe the monomers and symmetry adapted perturbation theory for the interaction energy (DFT-SAPT). The potential is fitted in terms of analytic functions, and the fitted potential is used to compute the lowest rovibrat...

Transition state theory was introduced in 1930s to account for chemical reactions. Central to this theory is the idea of a potential energy surface (PES). It was assumed that such a surface could be constructed using eigensolutions of the Schrödinger equation for the molecular (Coulomb) Hamiltonian but at that time such calculations were not possible. Nowadays quantum mechanical ab initio elect...

We use Bott’s equivariant Morse theory to show that compact Riemannian three-manifolds with negative sectional curvature possess closed minimal surfaces of arbitrarily high Morse index. 1 Sources of noncompactness for parametrized minimal surfaces In this article, we apply the theory of parametrized two-dimensional minimal surfaces in a compact n-dimensional Riemannian manifold (M, 〈·, ·〉) to t...

Theoretical calculations based on density functional theory have made significant contributions to our understanding of metal oxides, their surfaces, and the binding of molecules at these surfaces. In this paper we investigate the binding of methanol at the α-Al2O3(0001) surface using first-principles density functional theory. We calculate the molecular adsorption energy of methanol to be E ad...

We evaluate the accuracy of Tully's surface hopping algorithm for the spin-boson model in the limit of small to moderate reorganization energy. We calculate transition rates between diabatic surfaces in the exciton basis and compare against exact results from the hierarchical equations of motion; we also compare against approximate rates from the secular Redfield equation and Ehrenfest dynamics...

The potential energy surface of an off-lattice model protein is characterized in detail by constructing a disconnectivity graph and by examining the organisation of pathways on the surface. The results clearly reveal the frustration exhibited by this system and explain why it does not fold efficiently to the global potential energy minimum. In contrast, when the frustration is removed by constr...

We propose and analyze a simple variational model for dislocations at semi-coherent interfaces. The energy functional describes the competition between two terms: a surface energy induced by dislocations and a bulk elastic energy, spent to decrease the amount of dislocations needed to compensate the lattice misfit. We prove that, for minimizers, the former scales like the surface area of the in...

This paper models the self-assembly dynamics of a two-phase monolayer on an elastic substrate. The two phases coarsen to reduce the phase boundary energy and refine to reduce the elastic energy. To minimize the total free energy, the two phases can order into nanoscale patterns. We combine the continuum phase field model of spinodal decomposition and the anisotropic surface stress. The numerica...

We resolve the long-standing controversy over the metal surface energy: Density-functional methods that require uniform-electron-gas input agree with each other, but not with high-level correlated calculations such as Fermi hypernetted chain and diffusion Monte Carlo calculations that predict the uniform-gas correlation energy. Here we apply the inhomogeneous Singwi-Tosi-Land-Sjölander method, ...