Centroid origin shift of quantum object sets and molecular point clouds description and element comparisons

Carbó‐Dorca, Ramon; Besalú, Emili

doi:10.1007/s10910-011-9960-y

Cited by 27 publications

(18 citation statements)

References 34 publications

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“…Origin shift, see for example Refs. [ ], performed on the elements of the set E produces, in fact, a unique function which might be defined as:

\begin{matrix} left \\ {normalρ}_{R} \to {normalτ}_{R} = {normalρ}_{R} - {normalρ}_{C} \land {normalρ}_{S} \to {normalτ}_{S} = {normalρ}_{S} - {normalρ}_{C} \Rightarrow \\ {normalτ}_{R} = \frac{1}{2} true({normalρ}_{R} - {normalρ}_{S} true) \land {normalτ}_{S} = \frac{1}{2} true({normalρ}_{S} - {normalρ}_{R} true) = - {normalτ}_{R} . \end{matrix}

…”

Section: Practical Example 1: Chiral Systems Quantum Similarity and mentioning

confidence: 99%

“…Recently, a basic concept for this endeavor appears grounded on the description of molecular quantum polyhedra . This is a linear algebra structure which defines, from the point of view of quantum mechanics, the collective description of molecular sets forming quantum object sets, a previous theoretical mathematical construct developed in this laboratory …”

Section: Introductionmentioning

confidence: 99%

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Toward a universal quantum QSPR operator

Carbó‐Dorca

2018

Int J of Quantum Chemistry

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This article presents a discussion about the formalism, which might be associated to a general Quantum quantitative structure–properties relations operator, appearing in a Boltzmann‐like exponential form, which is based in turn on the definition of the concept of thermal voltage, applied to thermally scaled electronic density functions. Three practical numerical examples are presented, corresponding to the calculation of the polarization angle in assorted chiral molecules, the estimation of fish toxicity for perchlorobenzene within the set of chlorobenzenes and a typical quantum QSAR study on the popular Cramer steroid set.

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“…Origin shift, see for example Refs. [ ], performed on the elements of the set E produces, in fact, a unique function which might be defined as:

\begin{matrix} left \\ {normalρ}_{R} \to {normalτ}_{R} = {normalρ}_{R} - {normalρ}_{C} \land {normalρ}_{S} \to {normalτ}_{S} = {normalρ}_{S} - {normalρ}_{C} \Rightarrow \\ {normalτ}_{R} = \frac{1}{2} true({normalρ}_{R} - {normalρ}_{S} true) \land {normalτ}_{S} = \frac{1}{2} true({normalρ}_{S} - {normalρ}_{R} true) = - {normalτ}_{R} . \end{matrix}

…”

Section: Practical Example 1: Chiral Systems Quantum Similarity and mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Toward a universal quantum QSPR operator

Carbó‐Dorca

2018

Int J of Quantum Chemistry

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“…In this sense, one of the most important properties in the MQS field used in this study is the definition of a centroid origin which shifts to choose a reference system within the MQS measures using the fact of their linear independence, according to Carbó-Dorca et al [68,69].…”

Section: Similarity Indexesmentioning

confidence: 99%

Understanding the Polar Character Trend in a Series of Diels-Alder Reactions Using Molecular Quantum Similarity and Chemical Reactivity Descriptors

Morales-Bayuelo

Vivas‐Reyes

2014

Journal of Quantum Chemistry

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In molecular similarity there is a premise "similar molecules tend to behave similarly"; however in the actual quantum similarity field there is no clear methodology to describe the similarity in chemical reactivity, and with this end an analysis of charge-transfer (CT) processes in a series of Diels-Alder (DA) reactions between cyclopentadiene (Cp) and cyano substitutions on ethylene has been studied. The CT analysis is performed in the reagent assuming a grand canonical ensemble and the considerations for an electrophilic system using B3LYP/6-31 ( ) and M06-2X/6-311 + ( , ) methods. An analysis for CT was performed in agreement with the experimental results with a good statistical correlation ( 2 = 0.9118) relating the polar character to the bond force constants in DA reactions. The quantum distortion analysis on the transition states (TS) was performed using molecular quantum similarity indexes of overlap and coulomb showing good correlation ( 2 = 0.8330) between the rate constants and quantum similarity indexes. In this sense, an electronic reorganization based on molecular polarization in terms of CT is proposed; therefore, new interpretations on the electronic systematization of the DA reactions are presented, taking into account that today such electronic systematization is an open problem in organic physical chemistry. Additionally, one way to quantify the similarity in chemical reactivity was shown, taking into account the dependence of the molecular alignment on properties when their position changes; in this sense a possible way to quantify the similarity of the CT in systematic form on these DA cycloadditions was shown.

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“…As mentioned in point (l), some preliminary rough work has been already performed on the PT.Now, the next purpose of this article is to set up a prospect using the state of the art in QS. Such new possibilities have been published not very far in time up to date …”

Section: Introductionmentioning

confidence: 99%

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

Carbó‐Dorca

Chakraborty

2019

J Comput Chem

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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.

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Centroid origin shift of quantum object sets and molecular point clouds description and element comparisons

Cited by 27 publications

References 34 publications

Toward a universal quantum QSPR operator

Toward a universal quantum QSPR operator

Understanding the Polar Character Trend in a Series of Diels-Alder Reactions Using Molecular Quantum Similarity and Chemical Reactivity Descriptors

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

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