Ramon Carbó-Dorca

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.

Quantum similarity measures under atomic shell approximation: First order density fitting using elementary Jacobi rotations

The elementary Jacobi rotations technique is proposed as a useful tool to obtain fitted electronic density functions expressed as linear combinations of atomic spherical shells, with the additional constraint that all coefficients are kept positive. Moreover, a Newton algorithm has been implemented to optimize atomic shell exponents, minimizing the quadratic error integral function between ab initio and fitted electronic density functions. Although the procedure is completely general, as an application example both techniques have been used to compute a 1S‐type Gaussian basis for atoms H through Kr, fitted from a 3‐21G basis set. Subsequently, molecular electronic densities are modeled in a promolecular approximation, as a simple sum of parameterized atomic contributions. This simple molecular approximation has been employed to show, in practice, its usefulness to some computational examples in the field of molecular quantum similarity measures. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 2023–2039, 1997

A general survey of molecular quantum similarity

Abstract A comprehensive survey of the theoretical foundations and definitions associated with quantum similarity is given. In this task care has been taken to determine the primary mathematical structure which can be associated with quantum similarity measures. Due to this, the concept of a tagged set is defined to demonstrate how molecular sets can be described systematically. The definition of quantum object, a notion introduced by our laboratory and employed for a long time in quantum similarity studies, is clarified by means of a blend involving quantum theory and the tagged set structure formalism, and used afterwards as the cornerstone of the subsequent development of the theory. In the definition of quantum objects, density functions play a fundamental role. To formally construct the quantum similarity measure, it is very interesting to study the main algorithmic ideas, which may serve to compute approximate density forms, accurate enough to be employed in the practical calculation of nuclear, atomic and molecular quantum similarity measures. Thus, the atomic shell approximation is defined accompanied by all the implied computational constraints and the consequences they have in the whole theory development as well as to the physical interpretation of the results. A wide and complex field appears from all these ideas, where convex sets play a fundamental role, and a new definition emerges: one associated with vector semispaces, where the main numerical formalism of quantum similarity seems perfectly adapted. Applications of this development embrace quantum taxonomy, visual representation of molecular sets, QSAR and QSPR, topological indices, molecular alignment, etc., and among this range of procedures and fields, there appears with distinct importance the discrete representation of molecular structures.

Toward a Global Maximization of the Molecular Similarity Function: Superposition of Two Molecules

A quantum similarity measure between two molecules is normally identified with the maximum value of the overlap of the corresponding molecular electron densities. The electron density overlap is a function of the mutual positioning of the compared molecules, requiring the measurement of similarity, a solution of a multiple‐maxima problem. Collapsing the molecular electron densities into the nuclei provides the essential information toward a global maximization of the overlap similarity function, the maximization of which, in this limit case, appears to be related to the so‐called assignment problem. Three levels of approach are then proposed for a global search scanning of the similarity function. In addition, atom—atom similarity Lorentzian potential functions are defined for a rapid completion of the function scanning. Performance is tested among these three levels of simplification and the Monte Carlo and simplex methods. Results reveal the present algorithms as accurate, rapid, and unbiased techniques for density‐based molecular alignments.

Negative Fukui functions: new insights based on electronegativity equalization

Fukui functions have been calculated for large numbers of organic molecules, and were found to always be positive. Numeric and algebraic considerations allowed the identification of several boundary conditions for negative values for Fukui functions. Negative Fukui functions are found to be very unlikely, except when very short interatomic distances are present. Recent hypotheses concerning the occurrence of negative Fukui functions are strongly supported by the present approach.

Three-dimensional quantitative structure-activity relationships from tuned molecular quantum similarity measures: prediction of the corticosteroid-binding globulin binding affinity for a steroid family.

Predictive models based on tuned molecular quantum similarity measures and their application to obtain quantitative structure-activity relationships (QSAR) are described. In the present paper, the corticosteroid-binding globulin binding affinity of a 31 steroid family is studied by means of a multilinear regression using molecular descriptors derived from mixed steric-electrostatic quantum similarity matrixes as parameters, obtaining satisfactory predictions. A systematic procedure to treat outliers by using triple-density quantum similarity measures is also presented. This method depicts an alternative to the grid-based QSAR techniques, providing a consistent approach that avoids problematic result dependency on the grid parameters.

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

Fundamentals of Molecular Similarity

1. Prediction of Boiling Points of Organic Compounds from Molecular Descriptors by Using Backpropagation Neural Network.- 2. Some Relationships between Molecular Energy-Topology and Symmetry.- 3. Database Organization and Similarity Searching with E-State Indices.- 4. Similarity Searching in Chemical Databases Using Molecular Fields and Data Fusion.- 5. Topological Pharmacophore Description of Chemical Structures Using Mab-Force-Field-Derived Data and Corresponding Similarity Measures.- 6. Dissimilarity Measures: Introducing a Novel Methodology.- 7. Quantum-Mechanical Theory of Atoms in Molecules: A Relativistic Formulation.- 8. Topological Similarity of Molecules and the Consequences of the Holographic Electron Density Theorem, an Extension of the Hohenberg-Kohn Theorem.- 9. Quantum Chemical Reactivity: Beyond the Study of Small Molecules.- 10. Partitioning of Free Energies of Solvation into Fragment Contributions: Applications in Drug Design.- 11. Confronting Modern Valence Bond Theory with Momentum-Space Quantum Similarity and with Pair Density Analysis.- 12. Quantum Molecular Similarity: Theory and Applications to the Evaluation of Molecular Properties, Biological Activities and Toxicity.- 13. Self-Organizing Molecular Field Analysis (Somfa): A Tool for Structure-Activity Studies.- 14. Similarity Analysis of Molecular Interaction Potential Distributions. The Mipsim Software.

Molecular basis of quantitative structure-properties relationships (QSPR): A quantum similarity approach

Since the dawn of quantitative structure-properties relationships (QSPR), empirical parameters related to structural, electronic and hydrophobic molecular properties have been used as molecular descriptors to determine such relationships. Among all these parameters, Hammett σ constants and the logarithm of the octanol- water partition coefficient, log P, have been massively employed in QSPR studies. In the present paper, a new molecular descriptor, based on quantum similarity measures (QSM), is proposed as a general substitute of these empirical parameters. This work continues previous analyses related to the use of QSM to QSPR, introducing molecular quantum self-similarity measures (MQS-SM) as a single working parameter in some cases. The use of MQS-SM as a molecular descriptor is first confirmed from the correlation with the aforementioned empirical parameters. The Hammett equation has been examined using MQS-SM for a series of substituted carboxylic acids. Then, for a series of aliphatic alcohols and acetic acid esters, log P values have been correlated with the self-similarity measure between density functions in water and octanol of a given molecule. And finally, some examples and applications of MQS-SM to determine QSAR are presented. In all studied cases MQS-SM appeared to be excellent molecular descriptors usable in general QSPR applications of chemical interest.

A mathematical discussion on density and shape functions, vector semispaces and related questions

Density and shape functions are studied from the point of view of vector semispace structure and properties. Useful characteristics based on the shell structure of vector semispaces are used to analyze some properties of both functions. Fukui functions and quantum similarity indices are also studied when basic applications of the theory are discussed. Construction of approximate density functions and pseudo wave functions is also outlined. Finally, the original DFT variational theorem is reformulated within the frame of the shape function.