Role of Basic Surface Groups of Activated Carbon in Chlordecone and β-Hexachlorocyclohexane Adsorption: A Molecular Modelling Study

The influence of nitrogen-containing surface groups (SGs) onto activated carbon (AC) over the adsorption of chlordecone (CLD) and β-hexachlorocyclohexane (β-HCH) was characterized by a molecular modelling study, considering pH (single protonated SGs) and hydration effect (up to three water molecules). The interactions of both pollutants with amines and pyridine as basic SGs of AC were studied, applying the multiple minima hypersurface (MMH) methodology and using PM7 semiempirical Hamiltonian. Representative structures from MMH were reoptimized using the M06-2X density functional theory. The quantum theory of atoms in molecules (QTAIM) was used to characterize the interaction types in order understanding the adsorption process. A favorable association of both pesticides with the amines and pyridine SGs onto AC was observed at all pH ranges, both in the absence and presence of water molecules. However, a greater association of both pollutants with the primary amine was found under an acidic pH condition. QTAIM results show that the interactions of CLD and β-HCH with the SGs onto AC are governed by Cl···C interactions of chlorine atoms of both pesticides with the graphitic surface. Electrostatic interactions (H-bonds) were observed when water molecules were added to the systems. A physisorption mechanism is suggested for CLD and β-HCH adsorption on nitrogen-containing SGs of AC.

Data-driven analysis of the number of Lennard–Jones types needed in a force field

Force fields used in molecular simulations contain numerical parameters, such as Lennard–Jones (LJ) parameters, which are assigned to the atoms in a molecule based on a classification of their chemical environments. The number of classes, or types, should be no more than needed to maximize agreement with experiment, as parsimony avoids overfitting and simplifies parameter optimization. However, types have historically been crafted based largely on chemical intuition, so current force fields may contain more types than needed. In this study, we seek the minimum number of LJ parameter types needed to represent the key properties of organic liquids. We find that highly competitive force field accuracy is obtained with minimalist sets of LJ types; e.g., two H types and one type apiece for C, O, and N atoms. We also find that the fitness surface has multiple minima, which can lead to local trapping of the optimizer.

Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimization

We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed scheme is a stochastic zeroth-order optimization algorithm which demands only the capability to evaluate small subsets of components of the cost function. It can be depicted as a bank of samplers that generate particle approximations of several sequences of probability measures. These measures are constructed in such a way that they have associated probability density functions whose global maxima coincide with the global minima of the original cost function. The algorithm selects the best performing sampler and uses it to approximate a global minimum of the cost function. We prove analytically that the resulting estimator converges to a global minimum of the cost function almost surely and provide explicit convergence rates in terms of the number of generated Monte Carlo samples and the dimension of the search space. We show, by way of numerical examples, that the algorithm can tackle cost functions with multiple minima or with broad “flat” regions which are hard to minimize using gradient-based techniques.

The Cost-Sorted Distance Method for Identifying Minima Within Firefly Optimization Results: Application to Engineering Design

This paper provides a detailed description of the cost-sorted distance (CSD) method for visually and computationally identifying objective function minima within clustered population-based optimization results. CSD requires sorting the design vector population by cost and computing Euclidean distances between each pair of designs. It may be applied in conjunction with any population-based optimization method (e.g., particle swarm, genetic algorithm, simulated annealing, ant colony, firefly), but it is naturally compatible with the firefly algorithm (FA) because FA also requires the distances between each pair of design vectors and benefits from cost-sorting the population (the computational work required for CSD is a byproduct of FA). A modified FA is presented that uses CSD to more thoroughly search near potential minima and a systematic method for tuning the algorithm to reliably identify multiple minima is documented. The tuned algorithm's efficacy is demonstrated using a class of benchmark problems and a “real world” electromechanical design problem, where the identification of attractive design alternatives can be challenging.

Observation of an isomerizing double-well quantum system in the condensed phase

Molecular isomerization fundamentally involves quantum states bound within a potential energy function with multiple minima. For isolated gas-phase molecules, eigenstates well above the isomerization saddle points have been characterized. However, to observe the quantum nature of isomerization, systems in which transitions between the eigenstates occur—such as condensed-phase systems—must be studied. Efforts to resolve quantum states with spectroscopic tools are typically unsuccessful for such systems. An exception is CO adsorbed on NaCl(100), which is bound with the well-known OC–Na+ structure. We observe an unexpected upside-down isomer (CO–Na+) produced by infrared laser excitation and obtain well-resolved infrared fluorescence spectra from highly energetic vibrational states of both orientational isomers. This distinctive condensed-phase system is ideally suited to spectroscopic investigations of the quantum nature of isomerization.

Transformation Properties under the Operations of the Molecular Symmetry Groups G36 and G36(EM) of Ethane H3CCH3

In the present work, we report a detailed description of the symmetry propertiesof the eight-atomic molecule ethane, with the aim of facilitating the variational calculations ofrotation-vibration spectra of ethane and related molecules. Ethane consists of two methyl groupsCH3 where the internal rotation (torsion) of one CH3 group relative to the other is of large amplitudeand involves tunnelling between multiple minima of the potential energy function. The molecularsymmetry group of ethane is the 36-element group G36, but the construction of symmetrised basisfunctions is most conveniently done in terms of the 72-element extended molecular symmetrygroup G36(EM). This group can subsequently be used in the construction of block-diagonal matrixrepresentations of the ro-vibrational Hamiltonian for ethane. The derived transformation matricesassociated with G36(EM) have been implemented in the variational nuclear motion program TROVE(Theoretical ROVibrational Energies). TROVE variational calculations are used as a practical exampleof a G36(EM) symmetry adaptation for large systems with a non-rigid, torsional degree of freedom.We present the derivation of irreducible transformation matrices for all 36 (72) operations of G36(M)(G36(EM)) and also describe algorithms for a numerical construction of these matrices based on aset of four (five) generators. The methodology presented is illustrated on the construction of thesymmetry-adapted representations both of the potential energy function of ethane and of the rotation,torsion and vibration basis set functions.

The Short Path Algorithm Applied to a Toy Model

We numerically investigate the performance of the short path optimization algorithm on a toy problem, with the potential chosen to depend only on the total Hamming weight to allow simulation of larger systems. We consider classes of potentials with multiple minima which cause the adiabatic algorithm to experience difficulties with small gaps. The numerical investigation allows us to consider a broader range of parameters than was studied in previous rigorous work on the short path algorithm, and to show that the algorithm can continue to lead to speedups for more general objective functions than those considered before. We find in many cases a polynomial speedup over Grover search. We present a heuristic analytic treatment of choices of these parameters and of scaling of phase transitions in this model.

Optimizing the orbital occupation in the multiple minima problem of magnetic materials from the metaheuristic firefly algorithm

We present the use and implementation of the firefly algorithm to scan the multiple metastable minima of orbital occupations in density functional theory plus Hubbard U and to identify the ground state occupations in strongly correlated materials.