Amphetamine-type stimulants (ATS) drug classification using shallow one-dimensional convolutional neural network.

Amphetamine-type stimulants (ATS) drug analysis and identification are challenging and critical nowadays with the emergence production of new synthetic ATS drugs with sophisticated design compounds. In the present study, we proposed a one-dimensional convolutional neural network (1DCNN) model to perform ATS drug classification as an alternative method. We investigate as well as explore the classification behavior of 1DCNN with the utilization of the existing novel 3D molecular descriptors as ATS drugs representation to become the model input. The proposed 1DCNN model is composed of one convolutional layer to reduce the model complexity. Besides, pooling operation that is a standard part of traditional CNN is not applied in this architecture to have more features in the classification phase. The dropout regularization technique is employed to improve model generalization. Experiments were conducted to find the optimal values for three dominant hyper-parameters of the 1DCNN model which are the filter size, transfer function, and batch size. Our findings found that kernel size 11, exponential linear unit (ELU) transfer function and batch size 32 are optimal for the 1DCNN model. A comparison with several machine learning classifiers has shown that our proposed 1DCNN has achieved comparable performance with the Random Forest classifier and competitive performance with the others.

Divagations about the periodic table: Boolean hypercube and quantum similarity connections.

In this study, several simple aspects associated with the periodic table (PT) of the elements are commented. First, the connection of the PT with the structure of a seven-dimensional Boolean hypercube leads afterward to discuss the nature of those PT elements bearing prime atomic numbers. Second, the use of quantum similarity (QS) to obtain an alternative insight on the PT element relations will be also developed. The foundation of the second part starts admitting that any element of the PT can be attached to a schematic electronic density function, constructed with a single Gaussian function: a Gaussian atomic density function, allowing to consider the PT elements as a set of quantum objects, and permits a straightforward construction of a QS matrix. Such QS scheme can be applied to the whole PT or to any subset of it. Manipulation of the QS matrices attached to any quantum object set allows the evaluation of statistical-like values, acting as coordinates to numerically or graphically represent the chosen PT atomic element sets. © 2019 Wiley Periodicals, Inc.

Nine questions on energy decomposition analysis.

The paper collects the answers of the authors to the following questions: Is the lack of precision in the definition of many chemical concepts one of the reasons for the coexistence of many partition schemes? Does the adoption of a given partition scheme imply a set of more precise definitions of the underlying chemical concepts? How can one use the results of a partition scheme to improve the clarity of definitions of concepts? Are partition schemes subject to scientific Darwinism? If so, what is the influence of a community's sociological pressure in the "natural selection" process? To what extent does/can/should investigated systems influence the choice of a particular partition scheme? Do we need more focused chemical validation of Energy Decomposition Analysis (EDA) methodology and descriptors/terms in general? Is there any interest in developing common benchmarks and test sets for cross-validation of methods? Is it possible to contemplate a unified partition scheme (let us call it the "standard model" of partitioning), that is proper for all applications in chemistry, in the foreseeable future or even in principle? In the end, science is about experiments and the real world. Can one, therefore, use any experiment or experimental data be used to favor one partition scheme over another? © 2019 Wiley Periodicals, Inc.

Statistical-like signature of molecular basis sets.

This paper defines the construction of a sequence of functions that might be used to geometrically characterize any GTO set employed in any molecular calculation. Such functions characterizing a basis set act as molecular statistical-like elements: the arithmetic mean or centroid of the basis set, and also variance, skewness, and kurtosis, corresponding to the first terms of a possibly larger sequence of descriptor moments. Once the moment functions are built, then they can be integrated over their electron variables. In this manner, a set of statistical-like scalars can be obtained, which will be uniquely associated with a chosen basis set. Therefore, such condensed moment scalars provide a unique numerical signature, which can be attached to any basis set employed in a molecular environment. Once obtained, basis set condensed statistical-like signatures could be used for comparison purposes. The overlap matrix of the basis set, which acts as a Gram matrix and a metric matrix, appears as the fundamental reference from where the statistical-like information can be obtained for a given basis set. Several numerical examples are provided.

Aromaticity, quantum multimolecular polyhedra, and quantum QSPR fundamental equation.

A causal relation connecting aromaticity with the current aromaticity descriptors used in the literature and compliant with a quantum mechanics theoretical background is described.

Softened electrostatic molecular potentials.

Electrostatic molecular potentials (EMPs) are studied from two points of view. First, a softened EMP (SEMP) approach is proposed, consisting in the substitution of a positive point charge as the entity with which an electronic density function (DF) interacts electrostatically to generate a classical EMP for a Gaussian charge distribution. Second, the performance of this SEMP approach under the Atomic Shell Approximation (ASA) is described and compared with classical EMP at the same ASA level. Several sample applications are presented to describe the general features of this new method of studying electrostatic interactions in molecules. The net result is a family of SEMPs that encompass EMPs as special cases but do not possess their infinite discontinuities. The features of SEMPs are quite similar to those of EMPs distant from nuclei, and the absence of infinity values makes them good candidates to be employed in molecular similarity calculations.

Notes on quantitative structure-property relationships (QSPR), part 3: density functions origin shift as a source of quantum QSPR algorithms in molecular spaces.

A general algorithm implementing a useful variant of quantum quantitative structure-property relationships (QQSPR) theory is described. Based on quantum similarity framework and previous theoretical developments on the subject, the present QQSPR procedure relies on the possibility to perform geometrical origin shifts over molecular density function sets. In this way, molecular collections attached to known properties can be easily used over other quantum mechanically well-described molecular structures for the estimation of their unknown property values. The proposed procedure takes quantum mechanical expectation value as provider of causal relation background and overcomes the dimensionality paradox, which haunts classical descriptor space QSPR. Also, contrarily to classical procedures, which are also attached to heavy statistical gear, the present QQSPR approach might use a geometrical assessment only or just some simple statistical outline or both. From an applied point of view, several easily reachable computational levels can be set up. A Fortran 95 program: QQSPR-n is described with two versions, which might be downloaded from a dedicated web site. Various practical examples are provided, yielding excellent results. Finally, it is also shown that an equivalent molecular space classical QSPR formalism can be easily developed.

Stereographic Projection of Density Functions (DF) and the Holographic Electronic Density Theorem (HEDT).

Mezey's holographic electronic density theorem is discussed from the point of view of stereographic projection techniques. Such a mathematical procedure is analyzed in depth from the point of view of first-order density functions; the procedure is then extended to any relevant quantum chemical function. This endeavor provides the background to construct a Holographic General Function Theorem (HGFT) for multivariate well-behaved functions. Stereographic projections, applied first as a way to obtain pictures of molecular quantum chemical functions, are shown to provide a flexible and original vantage point for visualizing, from any location and any chosen perspective, the form of any well-behaved function, irrespective of the number of variables involved. The pictographic possibilities of the HGFT are explored and exploited in several examples.

The Fukui matrix: a simple approach to the analysis of the Fukui function and its positive character.

The Fukui matrix is introduced as the derivative of the one-electron reduced density matrix with respect to a change in the number of electrons under constant external potential. The Fukui matrix extends the Fukui function concept: the diagonal of the Fukui matrix is the Fukui function. Diagonalizing the Fukui matrix gives a set of eigenvectors, the Fukui orbitals, and accompanying eigenvalues. At the level of theory used, there is always one dominant eigenvector, with an eigenvalue equal to 1. The remaining eigenvalues are either zero or come in pairs with eigenvalues of the same magnitude but opposite sign. Analysis of the frontier molecular orbital coefficient in the eigenvector with eigenvalue 1 gives information on the quality of the frontier molecular orbital picture. The occurrence of negative Fukui functions can be easily interpreted in terms of the nodal character of the dominant eigenvector versus the characteristics of the remaining eigenvectors and eigenvalues.

Communications on quantum similarity, part 3: a geometric-quantum similarity molecular superposition algorithm.

This work describes a new procedure to obtain optimal molecular superposition based on quantum similarity (QS): the geometric-quantum similarity molecular superposition (GQSMS) algorithm. It has been inspired by the QS Aufbau principle, already described in a previous work, to build up coherently quantum similarity matrices (QSMs). The cornerstone of the present superposition technique relies upon the fact that quantum similarity integrals (QSIs), defined using a GTO basis set, depend on the squared intermolecular atomic distances. The resulting QSM structure, constructed under the GQSMS algorithm, becomes not only optimal in terms of its QSI elements but can also be arranged to produce a positive definite matrix global structure. Kruskal minimum spanning trees are also discussed as a device to order molecular sets described in turn by means of QSM. Besides the main subject of this work, focused on MS and QS, other practical considerations are also included in this study: essentially the use of elementary Jacobi rotations as QSM refinement tools and inward functions as QSM scaling methods.

Commentaries on quantum similarity (1): Density gradient quantum similarity.

Computation of density gradient quantum similarity integrals is analyzed, while comparing such integrals with overlap density quantum similarity measures. Gradient quantum similarity corresponds to another kind of numerical similarity assessment between a pair of molecular frames, which contrarily to the usual up to date quantum similarity definitions are not measures, that is: strictly positive definite integrals. As the density gradient quantum similarity integrals are defined as scalar products of three real functions, they appear to possess a richer structure than the corresponding positive definite density overlap quantum similarity measures, while preserving the overall similarity trends, when the molecular frames are relatively moved in three-dimensional space. Similarity indices are also studied when simple cases are analyzed in order to perform more comparisons with density overlap quantum similarity. Multiple gradient quantum similarity integrals are also defined. General GTO formulae are given. Numerical results within the atomic shell approximation (ASA) framework are presented as simple examples showing the new performances of the gradient density quantum similarity. Fortran 90 programs illustrating the proposed theoretical development can be downloaded from appropriate websites.

Notes on quantitative structure-properties relationships (QSPR) part 2: the role of the number of atoms as a molecular descriptor.

A previous analysis performed in our laboratory about the polynomial dependency of the atomic quantum self-similarity measures on the atomic number, together with recent publications on quantitative structure-properties relationships (QSPR), based on the number of molecular atoms, published by various authors, have driven us to show here that a simplified form of the fundamental quantum QSPR (QQSPR) equation, permits to theoretically demonstrate the important, but obvious, role of the number of atoms in a molecule, as a possible molecular descriptor. A discussion of the practical use of the number of atoms in QSPR is also given at the end, which also contains a discussion on the role of Ockham's razor in descriptor simplification choices.

Notes on quantitative structure-properties relationships (QSPR) (1): A discussion on a QSPR dimensionality paradox (QSPR DP) and its quantum resolution.

Classical quantitative structure-properties relationship (QSPR) statistical techniques unavoidably present an inherent paradoxical computational context. They rely on the definition of a Gram matrix in descriptor spaces, which is used afterwards to reduce the original dimension via several possible kinds of algebraic manipulations. From there, effective models for the computation of unknown properties of known molecular structures are obtained. However, the reduced descriptor dimension causes linear dependence within the set of discrete vector molecular representations, leading to positive semi-definite Gram matrices in molecular spaces. To resolve this QSPR dimensionality paradox (QSPR DP) here is proposed to adopt as starting point the quantum QSPR (QQSPR) computational framework perspective, where density functions act as infinite dimensional descriptors. The fundamental QQSPR equation, deduced from employing quantum expectation value numerical evaluation, can be approximately solved in order to obtain models exempt of the QSPR DP. The substitution of the quantum similarity matrix by an empirical Gram matrix in molecular spaces, build up with the original non manipulated discrete molecular descriptor vectors, permits to obtain classical QSPR models with the same characteristics as in QQSPR, that is: possessing a certain degree of causality and explicitly independent of the descriptor dimension.

Modeling the structure-property relationships of nanoneedles: A journey toward nanomedicine.

Innovative biomedical techniques operational at the nanoscale level are being developed in therapeutics, including advanced drug delivery systems and targeted nanotherapy. Ultrathin needles provide a low invasive and highly selective means for molecular delivery and cell manipulation. This article studies the geometry and the stability of a family of packed carbon nanoneedles (CNNs) formed by units of 4, 6, and 8 carbons, by using quantum chemistry computational modeling methods. At the limit of infinite-length, these CNNs might act as semiconductors, especially when the number of terminal units is increased. CNNs are also potentially able to stabilize ions around their structure. Therefore, due to the apolar characteristics of CNNs and their ability to carry ionic species, they would be suitable to act as drug carriers through nonpolar biologic media.

Critical thoughts on computing atom condensed Fukui functions.

Different procedures to obtain atom condensed Fukui functions are described. It is shown how the resulting values may differ depending on the exact approach to atom condensed Fukui functions. The condensed Fukui function can be computed using either the fragment of molecular response approach or the response of molecular fragment approach. The two approaches are nonequivalent; only the latter approach corresponds in general with a population difference expression. The Mulliken approach does not depend on the approach taken but has some computational drawbacks. The different resulting expressions are tested for a wide set of molecules. In practice one must make seemingly arbitrary choices about how to compute condensed Fukui functions, which suggests questioning the role of these indicators in conceptual density-functional theory.

Critical analysis and extension of the Hirshfeld atoms in molecules.

The computational approach to the Hirshfeld [Theor. Chim. Acta 44, 129 (1977)] atom in a molecule is critically investigated, and several difficulties are highlighted. It is shown that these difficulties are mitigated by an alternative, iterative version, of the Hirshfeld partitioning procedure. The iterative scheme ensures that the Hirshfeld definition represents a mathematically proper information entropy, allows the Hirshfeld approach to be used for charged molecules, eliminates arbitrariness in the choice of the promolecule, and increases the magnitudes of the charges. The resulting "Hirshfeld-I charges" correlate well with electrostatic potential derived atomic charges.

Unrevealed structural requirements for auxin-like molecules by theoretical and experimental evidences.

An computational-biostatistical approach, supported by ab initio optimizations of auxin-like molecules, was used to find biologically meaningful relationships between quantum chemical variables and fresh bioassay's data. It is proven that the auxin-like recognition requires different molecular assembling states. We suggest that the carboxyl group is not the determining factor in explaining the biological auxin-like conduct. The biological effects depends essentially on the chemical condition of the ring system. The aim to find active molecules (quantum objects) via statistical grouping-analysis of molecular quantum similarity measures was verified by bioactivity assays. Next, this approach led to the discovery of a non-carboxylated active auxin-like molecule (2,6-dibromo-phenol). This is the first publication on structure activity relationship of auxin-like molecules, which relies on highly standardized bioassays of different auxins screened in parallel as well as analysed by multi-dimensional scaling.

Aromaticity in linear polyacenes: generalized population analysis and molecular quantum similarity approach.

The relative aromaticity of benzenoid rings in the linear polyacenes is investigated using two novel aromaticity approaches. According to the first, the aromaticity of individual benzene rings was gauged by the values of six-center bond indices (SCI) calculated within the so-called Generalized Population Analysis (GPA). In the second approach, the same goal is addressed using the theory of Molecular Quantum Similarity (MQS). Both independent approaches are found to correlate very well, and both point toward decreasing aromaticity in any linear polyacenes upon going from the outer to inner rings.

Select-divide-and-conquer method for large-scale configuration interaction.

A select-divide-and-conquer variational method to approximate configuration interaction (CI) is presented. Given an orthonormal set made up of occupied orbitals (Hartree-Fock or similar) and suitable correlation orbitals (natural or localized orbitals), a large N-electron target space S is split into subspaces S0,S1,S2,...,S(R). S0, of dimension d0, contains all configurations K with attributes (energy contributions, etc.) above thresholds tao 0 identical with{Tao 0(egy),Tao 0(etc.)}; the CI coefficients in S0 remain always free to vary. S1 accommodates Ks with attributes above tao 1 < or = tao 0. An eigenproblem of dimension d0 + d1 for S0 + S1 is solved first, after which the last d1 rows and columns are contracted into a single row and column, thus freezing the last d1 CI coefficients hereinafter. The process is repeated with successive Sj(j > or = 2) chosen so that corresponding CI matrices fit random access memory (RAM). Davidson's eigensolver is used R times. The final energy eigenvalue (lowest or excited one) is always above the corresponding exact eigenvalue in S. Threshold values {tao j;j = 0,1,2,...,R} regulate accuracy; for large-dimensional S, high accuracy requires S0 + S1 to be solved outside RAM. From there on, however, usually a few Davidson iterations in RAM are needed for each step, so that Hamiltonian matrix-element evaluation becomes rate determining. One mu hartree accuracy is achieved for an eigenproblem of order 24 x 10(6), involving 1.2 x 10(12) nonzero matrix elements, and 8.4 x 10(9) Slater determinants.