Electrostatic Point Charge Fitting as an Inverse Problem: Revealing the Underlying Ill-Conditioning

Atom-centered point charge model of the molecular electrostatics---a major workhorse of the atomistic biomolecular simulations---is usually parameterized by least-squares (LS) fitting of the point charge values to a reference electrostatic potential, a procedure that suffers from numerical instabilities due to the ill-conditioned nature of the LS problem. Here, to reveal the origins of this ill-conditioning, we start with a general treatment of the point charge fitting problem as an inverse problem, and construct an analytically soluble model with the point charges spherically arranged according to Lebedev quadrature naturally suited for the inverse electrostatic problem. This analytical model is contrasted to the atom-centered point-charge model that can be viewed as an irregular quadrature poorly suited for the problem. This analysis shows that the numerical problems of the point charge fitting are due to the decay of the curvatures corresponding to the eigenvectors of LS sum Hessian matrix. In part, this ill-conditioning is intrinsic to the problem and related to decreasing electrostatic contribution of the higher multipole moments, that are, in the case of Lebedev grid model, directly associated with the Hessian eigenvectors. For the atom-centered model, this association breaks down beyond the first few eigenvectors related to the high-curvature monopole and dipole terms; this leads to even wider spread-out of the Hessian curvature values. Using these insights, it is possible to alleviate the ill-conditioning of the LS point-charge fitting without introducing external restraints and/or constraints. Also, as the analytical Lebedev grid PC model proposed here can reproduce multipole moments up to a given rank, it may provide a promising alternative to including explicit multipole terms in a force field

Macroscopic effects in attosecond pulse generation

We examine how the generation and propagation of high-order harmonics in a partly ionized gas medium affect their strength and synchronization. The temporal properties of the resulting attosecond pulses generated in long gas targets can be significantly influenced by macroscopic effects, in particular by the intensity in the medium and the degree of ionization. Under some conditions, the use of gas targets longer than the absorption length can lead to the generation of self-compressed attosecond pulses. We show this effect experimentally, using long argon-filled gas cells as generating medium.Comment: 5 pages 4 figure

A New Model of Chemical Bonding in Ionic Melts

We developed a new physical model to predict macroscopic properties of inorganic molten systems using a realistic description of inter-atomic interactions. Unlike the conventional approach, which tends to overestimate viscosity by several times, our systems consist of a set of ions with an admixture of neutral atoms. The neutral atom subsystem is a consequence of the covalent/ionic state reduction, occurring in the liquid phase. Comparison of the calculated macroscopic properties (shear viscosity and self-diffusion constants) with the experiment demonstrates good performance of our model. The presented approach is inspired by a significant degree of covalent interaction between the alkali and chlorine atoms, predicted by the coupled cluster theory

Soft Manifold Dynamics Behind Negative Thermal Expansion

Minimal models are developed to examine the origin of large negative thermal expansion (NTE) in under-constrained systems. The dynamics of these models reveals how underconstraint can organize a thermodynamically extensive manifold of low-energy modes which not only drives NTE but extends across the Brillioun zone. Mixing of twist and translation in the eigenvectors of these modes, for which in ZrW2O8 there is evidence from infrared and neutron scattering measurements, emerges naturally in our model as a signature of the dynamics of underconstraint.Comment: 5 pages, 3 figure