On the suitability of different representations of solid catalysts for combinatorial library design by genetic algorithms

Genetic algorithms are widely used to solve and optimize combinatorial problems and are more often applied for library design in combinatorial chemistry. Because of their flexibility, however, their implementation can be challenging. In this study, the influence of the representation of solid catalysts on the performance of genetic algorithms was systematically investigated on the basis of a new, constrained, multiobjective, combinatorial test problem with properties common to problems in combinatorial materials science. Constraints were satisfied by penalty functions, repair algorithms, or special representations. The tests were performed using three state-of-the-art evolutionary multiobjective algorithms by performing 100 optimization runs for each algorithm and test case. Experimental data obtained during the optimization of a noble metal-free solid catalyst system active in the selective catalytic reduction of nitric oxide with propene was used to build up a predictive model to validate the results of the theoretical test problem. A significant influence of the representation on the optimization performance was observed. Binary encodings were found to be the preferred encoding in most of the cases, and depending on the experimental test unit, repair algorithms or penalty functions performed best.     

The vibrational progressions of the N-->V electronic transition of ethylene: a test case for the computation of Franck-Condon factors of highly flexible photoexcited molecules

The vibrational progressions of the N-->V electronic transition of ethylene--a test case for the computation of Franck-Condon factors between electronic states exhibiting very different equilibrium geometries--have been calculated by using both the Cartesian and the curvilinear internal coordinate representations of the normal modes of vibration. The comparison of the theoretical spectra with the experimental one shows that the Cartesian representation yields vibrational progressions which are not observed in the experimental spectrum, whereas the curvilinear one gives a very satisfying agreement, even in harmonic approximation.     

Some notes on 2-D graphical representation of DNA sequence

Some 2-D and 3-D graphical representations of DNA sequences have been given by Nandy, Leong and Mogenthaler, and Randic et al., which give visual characterizations of DNA sequences. In this paper, we presented a novel graphical representation of DNA sequences by taking four special vectors in 2-D Cartesian coordinate system to represent the four nucleic acid bases in DNA sequences, so that a DNA sequence is denoted on a plane by a directed walk. It is shown that the new graphical representation of DNA sequences has lower or nondegeneracy.     

First and second derivative matrix elements for the stretching,bending, and torsional energy

Matrix elements for the first and second derivatives of the internal coordinates with respect to Cartesian coordinates are reported for stretching, linear, nonlinear, and out-of-plane bending and torsional motion. Derivatives of the energy with respect to the Cartesian coordinates are calculated with the chain rule. Derivatives of the energy with respect to the internal coordinates are straightforward, but the calculation of the derivatives of the internal coordinates with respect to the Cartesian coordinates can be simplified by the following two steps outlined in this article. First, the number of terms in the analytical functions can be reduced or will vanish when the derivatives of the bond length, bond angle, and torsion angle are reported in a local coordinate system in which one bond lies on an axis and an adjacent bond lies in the plane of two axes or is projected onto perpendicular planes for linear and out-of-plane bending motion. Second, a simple rotation transforms these derivatives to the appropriate orientation in the space-fixed molecular coordinate system. Functions of the internal coordinates are invariant with respect to translation and rotation. The translational invariance and the symmetry of the second derivatives for a system with L atoms are used to select L-1- and L(L-1)/2-independent first and second derivatives, respectively, of which approximately half of the latter vanish in the local coordinate system. The rotational invariance permits the transformation of the simplified derivatives in the local coordinate system to any orientation in space. The approach outlined in this article simplifies the formulas by expressing them in a local coordinate system, identifies the most convenient independent elements to compute, from which the dependent ones are calculated, and defines a transformation to the space-fixed molecular coordinate system.     

Reduced eigensystem representation of the linear density-density response function

The linear density-density response function represents a formulation of the generalized density response of a molecular (or extended) system to arbitrary perturbing potentials. We have recently established an approach for reducing the dimension of the (in principle infinite) eigenspace representation (the moment expansion) and generalized it to arbitrary self-adjoint, positive-definite, and compact linear operators. Here, we present a modified representation—the reduced eigensystem representation—which allows to define a trivial criterion for the convergence of the approximation to the density response. By means of this novel eigensystem-like structure, the remarkable reduction of the dimensionality becomes apparent for the calculation of the density-density response function.     

Nonlinear prediction of quantitative structure-activity relationships

Predicting the log of the partition coefficient P is a long-standing benchmark problem in Quantitative Structure-Activity Relationships (QSAR). In this paper we show that a relatively simple molecular representation (using 14 variables) can be combined with leading edge machine learning algorithms to predict logP on new compounds more accurately than existing benchmark algorithms which use complex molecular representations.     

Filter feature selectors in the development of binary QSAR models

The application of machine learning methods to the construction of quantitative structure–activity relationship models is a complex computational problem in which dimensionality reduction of the representation of the molecular structure plays a fundamental role in predicting a target activity. The feature selection pre-processing approach has been indicated to be effective in dimensionality reduction for building simpler and more understandable models. In this paper, a performance comparative study of 13 state-of-the-art feature selection filter methods is conducted. Structure–activity relationship models are constructed using three widely used classifiers and a diverse collection of datasets. The comparative study utilizes robust statistical tests to compare the algorithms. According to the experimental results, there are substantial differences in performance among the evaluated feature selection methods. The methods that exhibit the best performance are correlation-based feature selection, fast clustering-based feature selection and the set cover method.     

Geometric constraints in semiclassical initial value representation calculations in Cartesian coordinates: accurate reduction in zero-point energy

An approach for the inclusion of geometric constraints in semiclassical initial value representation calculations is introduced. An important aspect of the approach is that Cartesian coordinates are used throughout. We devised an algorithm for the constrained sampling of initial conditions through the use of multivariate Gaussian distribution based on a projected Hessian. We also propose an approach for the constrained evaluation of the so-called Herman-Kluk prefactor in its exact log-derivative form. Sample calculations are performed for free and constrained rare-gas trimers. The results show that the proposed approach provides an accurate evaluation of the reduction in zero-point energy. Exact basis set calculations are used to assess the accuracy of the semiclassical results. Since Cartesian coordinates are used, the approach is general and applicable to a variety of molecular and atomic systems.     

Moment expansion of the linear density‐density response function

We present a low rank moment expansion of the linear density‐density response function. The general interacting (fully nonlocal) density‐density response function is calculated by means of its spectral decomposition via an iterative Lanczos diagonalization technique within linear density functional perturbation theory. We derive a unitary transformation in the space of the eigenfunctions yielding subspaces with well‐defined moments. This transformation generates the irreducible representations of the density‐density response function with respect to rotations within SO(3). This allows to separate the contributions to the electronic response density from different multipole moments of the perturbation. Our representation maximally condenses the physically relevant information of the density‐density response function required for intermolecular interactions, yielding a considerable reduction in dimensionality. We illustrate the performance and accuracy of our scheme by computing the electronic response density of a water molecule to a complex interaction potential. © 2015 Wiley Periodicals, Inc.     

On the similarity of DNA primary sequences

We consider numerical characterization of graphical representations of DNA primary sequences. In particular we consider graphical representation of DNA of beta-globins of several species, including human, on the basis of the approach of A. Nandy in which nucleic bases are associated with a walk over integral points of a Cartesian x, y-coordinate system. With a so-generated graphical representation of DNA, we associate a distance/distance matrix, the elements of which are given by the quotient of the Euclidean and the graph theoretical distances, that is, through the space and through the bond distances for pairs of bases of graphical representation of DNA. We use eigenvalues of so-constructed matrices to characterize individual DNA sequences. The eigenvalues are used to construct numerical sequences, which are subsequently used for similarity/dissimilarity analysis. The results of such analysis have been compared and combined with similarity tables based on the frequency of occurrence of pairs of bases.     

Efficient representation of the linear density-density response function

We present a thorough derivation of the mathematical foundations of the representation of the molecular linear electronic density-density response function in terms of a computationally highly efficient moment expansion. Our new representation avoids the necessities of computing and storing numerous eigenfunctions of the response kernel by means of a considerable dimensionality reduction about from 10³ to 10¹. As the scheme is applicable to any compact, self-adjoint, and positive definite linear operator, we present a general formulation, which can be transferred to other applications with little effort. We also present an explicit application, which illustrates the actual procedure for applying the moment expansion of the linear density-density response function to a water molecule that is subject to a varying external perturbation potential. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.     

The influence of different structure representations on the clustering of an RNA nucleotides data set

The last couple of years an overwhelming amount of data has emerged in the field of biomolecular structure determination. To explore information hidden in these structure databases, clustering techniques can be used. The outcome of the clustering experiments largely depends, among others, on the way the data is represented; therefore, the choice how to represent the molecular structure information is extremely important. This article describes what the influence of the different representations on the clustering is and how it can be analyzed by means of a dendrogram comparison method. All experiments are performed using a data set consisting of RNA trinucleotides. Besides the most basic structure representation, the Cartesian coordinates representation, several other structure representations are used.     

Few-body quantum and many-body classical hyperspherical approaches to reactions and to cluster dynamics

The hyperspherical method is a widely used and successful approach for the quantum treatment of elementary chemical processes. It has been mostly applied to three-atomic systems, and current progress is here outlined concerning the basic theoretical framework for the extension to four-body bound state and reactive scattering problems. Although most applications only exploit the advantages of the hyperspherical coordinate systems for the formulation of the few-body problem, the full power of the technique implies representations explicitly involving quantum hyperangular momentum operators as dynamical quantities and hyperspherical harmonics as basis functions. In terms of discrete analogues of these harmonics one has a universal representation for the kinetic energy and a diagonal representation for the potential (hyperquantization algorithm). Very recently, advances have been made on the use of the approach in classical dynamics, provided that a hyperspherical formulation is given based on “classical” definitions of the hyperangular momenta and related quantities. The aim of the present paper is to offer a retrospective and prospective view of the hyperspherical methods both in quantum and classical dynamics. Specifically, regarding the general quantum hyperspherical approaches for three- and four-body systems, we first focus on the basis set issue, and then we present developments on the classical formulation that has led to applications involving the implementations of hyperspherical techniques for classical molecular dynamics simulations of simple nanoaggregates.     

Pharmacophore alignment search tool: influence of the third dimension on text-based similarity searching

Previously (Hähnke et al., J Comput Chem 2010, 31, 2810) we introduced the concept of nonlinear dimensionality reduction for canonization of two‐dimensional layouts of molecular graphs as foundation for text‐based similarity searching using our Pharmacophore Alignment Search Tool (PhAST), a ligand‐based virtual screening method. Here we apply these methods to three‐dimensional molecular conformations and investigate the impact of these additional degrees of freedom on virtual screening performance and assess differences in ranking behavior. Best‐performing variants of PhAST are compared with 16 state‐of‐the‐art screening methods with respect to significance estimates for differences in screening performance. We show that PhAST sorts new chemotypes on early ranks without sacrificing overall screening performance. We succeeded in combining PhAST with other virtual screening techniques by rank‐based data fusion, significantly improving screening capabilities. We also present a parameterization of double dynamic programming for the problem of small molecule comparison, which allows for the calculation of structural similarity between compounds based on one‐dimensional representations, opening the door to a holistic approach to molecule comparison based on textual representations. © 2011 Wiley Periodicals, Inc. J Comput Chem , 2011.     

Modeling vibrational dephasing and energy relaxation of intramolecular anharmonic modes for multidimensional infrared spectroscopies

Starting from a system-bath Hamiltonian in a molecular coordinate representation, we examine an applicability of a stochastic multilevel model for vibrational dephasing and energy relaxation in multidimensional infrared spectroscopy. We consider an intramolecular anharmonic mode nonlinearly coupled to a colored noise bath at finite temperature. The system-bath interaction is assumed linear plus square in the system coordinate, but linear in the bath coordinates. The square-linear system-bath interaction leads to dephasing due to the frequency fluctuation of system vibration, while the linear-linear interaction contributes to energy relaxation and a part of dephasing arises from anharmonicity. To clarify the role and origin of vibrational dephasing and energy relaxation in the stochastic model, the system part is then transformed into an energy eigenstate representation without using the rotating wave approximation. Two-dimensional (2D) infrared spectra are then calculated by solving a low-temperature corrected quantum Fokker-Planck (LTC-QFP) equation for a colored noise bath and by the stochastic theory. In motional narrowing regime, the spectra from the stochastic model are quite different from those from the LTC-QFP. In spectral diffusion regime, however, the 2D line shapes from the stochastic model resemble those from the LTC-QFP besides the blueshifts caused by the dissipation from the colored noise bath. The preconditions for validity of the stochastic theory for molecular vibrational motion are also discussed.