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. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

A quantum similarity matrix (QSM) Aufbau procedure

An Aufbau recursive algorithm, leading to the construction of molecular Quantum similarity matrices (QSM) with positive definite structure is described. As a consequence, Molecular Quantum Similarity measures optimization has to be restricted by a recursive constraint, related to the Euclidian norm of the QSM column elements in Quantum Object density tag reciprocal space.     

General trends in atomic and nuclear quantum similarity measures

Simple and accurate relationships between atomic and nuclear quantum similarity measures and their constituent elements were found. These results complement findings in previous studies in which quantum self‐similarity measures in atoms and nuclei were linked to the atomic and mass numbers, respectively. The models were validated on a large test set, and the general trends in the behavior of the quantum similarity measures for these quantum objects were made clear. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 685–692, 2000     

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. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Second-order quantum similarity measures from intracule and extracule densities

The calculation of quantum similarity measures from second-order density functions contracted to intracule and extracule densities obtained at the Hartree-Fock level is presented and applied to a series of atoms, (He, Li, Be, and Ne), isoelectronic molecules (C₂H₂, HCN, CNH, CO, and N₂), and model hydrogen-transfer processes (H₂/H⁺, H₂/Hot, H₂/H⁻). Second-order quantum similarity measures and indices are found to be suitable measures for quantitatively analyzing electron-pair density reorganizations in atoms, molecules, and chemical processes. For the molecular series, a comparative analysis between the topology of pairwise similarity functions as computed from one-electron, intracule, and extracule densities is carried out and the assignment of each particular local similarity maximum to a molecular alignment discussed. In the comparative study of the three hydrogen-transfer reactions considered, second-order quantum similarity indices are found to be more sensitive than first-order indices for analyzing the electron-density reorganization between the reactant complex and the transition state, thus providing additional insights for a better understanding of the mechanistic aspects of each process. Received: 7 July 1997 / Accepted: 29 October 1997     

Quantum fidelity for analyzing atoms and fragments in molecule: Application to similarity,chirality, and aromaticity

Quantum information theory is applied to formulate a new technique for dealing with molecular similarity problems. In this technique, the so‐called quantum fidelity appears to be a counterpart of the conventional similarity measure due to Carbo (Carbo, R.; Leyda, L.; Arnau, M. Int J Quantum Chem 1980, 17, 1185). We define many‐body spin‐free density matrices for atoms and fragments in molecule, and compute corresponding fidelity measures for molecular subsystems. It allows us to treat the problem from the beginning within a many‐electron setting. The approach is employed for analyzing similarity between free atoms and atoms in molecule. A new chirality index, as based on the fidelity between molecule and its mirror image, is suggested to be an approximately additive nonnegative quantity. We also examine a local aromaticity by computing the fidelity measures for benzenoid fragments in polyaromatic hydrocarbons. A detailed study of the proposed indices is reported at the ab initio or semiempirical levels. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Fitted electronic density functions from H to Rn for use in quantum similarity measures: cis-diamminedichloroplatinum(II) complex as an application example

A consistent set of fitted electronic density functions was generated for the elements from hydrogen to radon using an algorithm based on the elementary Jacobi rotations (EJR) technique. The main distinguishing attribute of this fitting procedure is the production of approximated electronic density functions with positive definite expansion coefficients; in this way, the statistical meaning of the probability distribution is preserved. The methodology, which was fully described previously, was modified in this work to improve and accelerate the fitting procedure. This variation concerns the optimization method employed to obtain the optimal angle of the EJR, implementing an algorithm based on a Taylor series expansion. Additionally, a new 1S-Type Gaussian basis set for atoms H to Rn is presented, that was fitted from a primitive basis set of Huzinaga. Fitted density functions facilitate theoretical calculations over large molecules and may be employed in many areas of computational chemistry, for example, in quantum similarity measures (QSM). To verify the basis set, a sound example related to QSM applications is given. This corresponds to the comparison of experimental structures obtained from X-ray determination for cis-diamminedichloroplatinum(II) complex with optimized molecular geometries using several theoretical methods to quantify the differences between the analyzed levels of theory. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 911–920, 1999     

Communications on quantum similarity (2): A geometric discussion on holographic electron density theorem and confined quantum similarity measures

The so‐called holographic electron density theorem (HEDT) is analyzed from an algebraic perspective, and a brief analytical point of view is also given. The connection of the HEDT with quantum similarity measures (QSM) over electronic density functions (DF) is studied using GTO functions, atomic ASA DF, and promolecular ASA DF. Restricted integration of QSM over a box of finite side length is discussed for all this DF. This work emphasizes the geometric aspects of HEDT, but for the sake of completeness, some analytical insight based on a general Taylor series expansion is also given at the end. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

On the Topological Sub-Structural Molecular Design (TOSS-MODE) in QSPR/QSAR and Drug Design Research

Abstract

A recently introduced graph-theoretical approach to the study of structure-property-activity relationships is presented. The theoretical approach and the computational strategy for the use of the TOSS-MODE approach are given with details. Several QSPR and QSAR applications are reviewed including the study of physical properties of organic compounds, diamagnetic susceptibilities, and biological properties. The applications of the TOSS-MODE approach to discrimination of active/inactive compounds, the virtual screening of compounds with a desired property from databases of chemical structures, identification of active/inactive fragments and its relationships with 2D/3D pharmacophores, and to the design of novel compounds with desired biological activities are also reviewed.