Arbitrarily tight α BB underestimators of general non-linear functions over sub-optimal domains.

In this paper we explore the construction of arbitrarily tight α BB relaxations of C 2 general non-linear non-convex functions. We illustrate the theoretical challenges of building such relaxations by deriving conditions under which it is possible for an α BB underestimator to provide exact bounds. We subsequently propose a methodology to build α BB underestimators which may be arbitrarily tight (i.e., the maximum separation distance between the original function and its underestimator is arbitrarily close to 0) in some domains that do not include the global solution (defined in the text as "sub-optimal"), assuming exact eigenvalue calculations are possible. This is achieved using a transformation of the original function into a µ -subenergy function and the derivation of α BB underestimators for the new function. We prove that this transformation results in a number of desirable bounding properties in certain domains. These theoretical results are validated in computational test cases where approximations of the tightest possible µ -subenergy underestimators, derived using sampling, are compared to similarly derived approximations of the tightest possible classical α BB underestimators. Our tests show that µ -subenergy underestimators produce much tighter bounds, and succeed in fathoming nodes which are impossible to fathom using classical α BB.

Efficient Handling of Molecular Flexibility in Lattice Energy Minimization of Organic Crystals.

This paper presents a novel algorithm, CrystalOptimizer, for the minimization of the lattice energy of crystals formed by flexible molecules. The algorithm employs isolated-molecule quantum mechanical (QM) calculations of the intramolecular energy and conformation-dependent atomic multipoles in the course of the lattice energy minimization. The algorithm eliminates the need to perform QM calculations at each iteration of the minimization by using Local Approximate Models (LAMs), with a minimal impact on accuracy. Additional computational efficiencies are achieved by storing QM-derived components of the lattice energy model in a database and reusing them in subsequent calculations whenever possible. This makes the approach particularly well suited to applications that involve a sequence of lattice energy evaluations, such as crystal structure prediction. The algorithm is capable of handling efficiently complex systems with considerable conformational flexibility. The paper presents examples of the algorithm's application ranging from single-component crystals to cocrystals and salts of flexible molecules with tens of intramolecular degrees of freedom whose optimal values are determined by the interplay of conformational strain and packing forces. For any given molecule, the degree of flexibility to be considered can vary from a few torsional angles to relaxation of the entire set of torsion angles, bond angles, and bond lengths present in the molecule.

Transferable SAFT-VR models for the calculation of the fluid phase equilibria in reactive mixtures of carbon dioxide, water, and n-alkylamines in the context of carbon capture.

The amine functional groups are fundamental building blocks of many molecules that are central to life, such as the amino acids, and to industrial processes, such as the alkanolamines, which are used extensively for gas absorption. The modeling of amines and of mixtures of amines with water (H(2)O) and carbon dioxide (CO(2)) is thus relevant to a number of applications. In this contribution, we use the statistical associating fluid theory for potentials of variable range (SAFT-VR) to describe the fluid phase behavior of ammonia + H(2)O + CO(2) and n-alkyl-1-amine + H(2)O + CO(2) mixtures. Models are developed for ammonia (NH(3)) and n-alkyl-1-amines up to n-hexyl-1-amine (CH(3)NH(2) to C(6)H(13)NH(2)). The amines are modeled as homonuclear chain molecules formed from spherical segments with additional association sites incorporated to mediate the effect of hydrogen-bonding interactions. The SAFT-VR approach provides a representation of the pure component fluid phase equilibria, on average, to within 1.48% of the experimental data in relative terms for the saturated liquid densities and vapor pressures. A simple empirical correlation is derived for the SAFT-VR parameters of the n -alkylamine series as a function of molecular weight. Aqueous mixtures of the amines are modeled using a model of water taken from previous work. The models developed for the mixtures are of high fidelity and can be used to calculate the binary fluid phase equilibrium of these systems to within 2.28% in relative terms for the temperature or pressure and 0.027 in absolute terms for the mole fraction. Regions of both vapor-liquid and liquid-liquid equilibria are considered. We also consider the reactive mixtures of amines and CO(2) in aqueous solution. To model the reaction of CO(2) with the amine, an additional site is included on the otherwise nonassociating CO(2) model. The unlike interaction parameters for the NH(3) + H(2)O + CO(2) ternary mixture are obtained by comparison to the experimental data available for this system. The resulting model is found to correlate and predict the liquid-phase loading (moles of CO(2) per mole of amine) to within 0.091 of experimental data in absolute terms. The parameters describing the NH(3)-CO(2) interaction are then transferred to other n-alkyl-1-amines, and sample predictions of the fluid phase equilibria for the n-propyl-1-amine + H(2)O + CO(2), n-butyl-1-amine + H(2)O + CO(2), and n-hexyl-1-amine + H(2)O + CO(2) mixtures are presented. The latter mixture is found to exhibit regions of liquid-liquid immiscibility.

Global optimization and modeling techniques for planar multilayered dielectric structures.

We present a multilevel global optimization strategy for synthesizing planar multilayered dielectric structures. A low discrepancy sequence of sample points with uniform variable space coverage allows a global-level search while systematic refinement using gradient-based techniques identifies optima at the local level. Since efficient local optimization is important for this method, a fast calculation approach based on mode matching is presented; this also facilitates the compact derivation of analytical gradients. The approach is compared with genetic and simulated annealing algorithms through an antireflection coating design. The method proves to be competitive in terms of its performance, nonadaptive algorithm, and ability to track local solutions.