The Electron Pair in Chemistry

The reality of the electron pair as a fundamental unit in the electronic structure of molecular systems is evidenced by calculations which show that the most probable partitioning of a system is the one which localizes pairs of electrons in well-defined spatial regions or loges. The loges in turn, correspond to those regions of space generally associated with core, bonded, and non-bonded electrons. In terms of information theory, they yield the maximum amount of information concerning the localizability of the electrons. The most probable three-loge partitioning of the six-electron BH(X1∑+) system, for example, is dominated by the event which places two electrons in each of three loges, the location and shape of the loges being such as to justify the labelling of the electron pairs they localize as core, bonded and nonbonded. Since the loges are defined in real space and are totally nonoverlapping, one may define the volume of space occupied by pairs of electrons. In BH, for example, the volume of space required to contain 95% of the nonbonded pair of electrons is over two times larger than that required to contain 95% of the bonded pair. It is possible to define core loges which exhibit pair occupation probabilities ranging in value from 95% in LiH+ to 85% in BH. Corresponding probabilities ranging in value from 75% to 90% are obtained for bonded and nonbonded loges. In the set of molecules studied here, the occurrence of events with such high probabilities is found only for loges which maximize the probability of a pair occupation.

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Electron states and electron transport in quasi-one-dimensional molecular systems

Canadian Journal of Chemistry ◽

10.1139/v85-314 ◽

1985 ◽

Vol 63 (7) ◽

pp. 1899-1903 ◽

Cited By ~ 2

Author(s):

Alexandr S. Davydov ◽

Ivan I. Ukrainskii

Keyword(s):

Electron Pair ◽

Electron System ◽

Linear Potential ◽

Electron Wave ◽

Electron Pairs ◽

One Dimensional ◽

Molecular Systems ◽

Fermi Statistics ◽

Causative Factors ◽

The Many

It is shown that the concept of electron pairs may be introduced in conducting quasi-one-dimensional systems with electron delocalization such as (CH)x and the stacks of molecule-donors and acceptors of electrons TMTSF, TTT, TCNQ, etc. The introduction of pairing proves to be useful and electronic structure and electronic processes can be easily visualized. The two causative factors in the appearance of pairs in a many-electron system with repulsion are pointed out. The first one is the electron Fermi-statistics that does not allow a spatial region to be occupied by more than two electrons. The second one is the interaction of electrons with a soft lattice. The first of these factors is important at large and intermediate electron densities ρ ≥ 1, the second one dominates at [Formula: see text]. The kink-type excitation parameters in (CH)x are considered with a non-linear potential obtained in an electron-pair approach for the many-electron wave function of (CH)x.

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Energetics of Electron Pairs in Electrophilic Aromatic Substitutions

Molecules ◽

10.3390/molecules26020513 ◽

2021 ◽

Vol 26 (2) ◽

pp. 513

Author(s):

Julen Munárriz ◽

Miguel Gallegos ◽

Julia Contreras-García ◽

Ángel Martín Pendás

Keyword(s):

Electron Pair ◽

Valence Bond ◽

Substituent Effects ◽

Relevant Information ◽

Real Space ◽

Reactive Force ◽

Electron Pairs ◽

Exchange Correlation ◽

Reactive Force Fields ◽

Interacting Quantum Atoms

The interacting quantum atoms approach (IQA) as applied to the electron-pair exhaustive partition of real space induced by the electron localization function (ELF) is used to examine candidate energetic descriptors to rationalize substituent effects in simple electrophilic aromatic substitutions. It is first shown that inductive and mesomeric effects can be recognized from the decay mode of the aromatic valence bond basin populations with the distance to the substituent, and that the fluctuation of the population of adjacent bonds holds also regioselectivity information. With this, the kinetic energy of the electrons in these aromatic basins, as well as their mutual exchange-correlation energies are proposed as suitable energetic indices containing relevant information about substituent effects. We suggest that these descriptors could be used to build future reactive force fields.

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Electron detachment from anions in aqueous solutions studied by two- and three-pulse femtosecond spectroscopy

Pure and Applied Chemistry ◽

10.1351/pac-con-09-12-04 ◽

2010 ◽

Vol 82 (10) ◽

pp. 1919-1926 ◽

Cited By ~ 8

Author(s):

Hristo Iglev ◽

Martin K. Fischer ◽

Alfred Laubereau

Keyword(s):

Diffusion Coefficients ◽

Strong Influence ◽

Electron Pair ◽

Hydrated Electron ◽

The Other ◽

Electron Detachment ◽

Electron Pairs ◽

Electron Photodetachment ◽

Relaxation Channel ◽

The One

The electron photodetachment of the aqueous halides and hydroxide is studied after resonant excitation in the lowest charge-transfer-to-solvent (CTTS) state. The initially excited state is followed by an intermediate assigned to a donor-electron pair that displays a competition of recombination and separation. Using pump–repump–probe (PREP) spectroscopy, the pair species is verified via a secondary excitation with separation of the pairs so that the yield of released electrons is increased. The observed recombination process on the one hand and the similar absorptions of the intermediate and the hydrated electron on the other hand suggest that the donor-electron pairs incorporate only few if not just one water molecule. The geminate dynamics measured in the various CTTS systems reveal a strong influence of the parent radical. The electron survival probability decreases significantly from 0.77 to 0.29 going from F– to OH–. The extracted dissociation rates of the halogen-electron pairs seem to be proportional to the mutual diffusion coefficients of the geminate particles, while such a relation between the recombination rate and the diffusion coefficient is not found. Results for I– show that excitation of a higher-lying CTTS state opens a new relaxation channel, which directly leads to a fully hydrated electron, while the relaxation channel discussed above is not significantly affected.

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Tetrel Interactions from an Interacting Quantum Atoms Perspective

Molecules ◽

10.3390/molecules24122204 ◽

2019 ◽

Vol 24 (12) ◽

pp. 2204 ◽

Cited By ~ 7

Author(s):

José Luis Casals-Sainz ◽

Aurora Costales Castro ◽

Evelio Francisco ◽

Ángel Martín Pendás

Keyword(s):

Electron Pair ◽

Real Space ◽

Coupled Cluster ◽

Group 14 ◽

Electron Pairs ◽

Covalent Interaction ◽

Exchange Correlation ◽

Covalent Contribution ◽

Interacting Quantum Atoms ◽

Tetrel Bonds

Tetrel bonds, the purportedly non-covalent interaction between a molecule that contains an atom of group 14 and an anion or (more generally) an atom or molecule with lone electron pairs, are under intense scrutiny. In this work, we perform an interacting quantum atoms (IQA) analysis of several simple complexes formed between an electrophilic fragment (A) (CH3F, CH4, CO2, CS2, SiO2, SiH3F, SiH4, GeH3F, GeO2, and GeH4) and an electron-pair-rich system (B) (NCH, NCO-, OCN-, F-, Br-, CN-, CO, CS, Kr, NC-, NH3, OC, OH2, SH-, and N3-) at the aug-cc-pvtz coupled cluster singles and doubles (CCSD) level of calculation. The binding energy ( E bind AB ) is separated into intrafragment and inter-fragment components, and the latter in turn split into classical and covalent contributions. It is shown that the three terms are important in determining E bind AB , with absolute values that increase in passing from electrophilic fragments containing C, Ge, and Si. The degree of covalency between A and B is measured through the real space bond order known as the delocalization index ( δ AB ). Finally, a good linear correlation is found between δ AB and E xc AB , the exchange correlation (xc) or covalent contribution to E bind AB .

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Statistical analysis of classification

Symposium - International Astronomical Union ◽

10.1017/s0074180900053420 ◽

1966 ◽

Vol 24 ◽

pp. 188-189

Author(s):

T. J. Deeming

Keyword(s):

Multivariate Analysis ◽

Statistical Analysis ◽

Classification Scheme ◽

Analytical Procedure ◽

Narrow Band ◽

Scientific Research ◽

Maximum Amount ◽

Amount Of Information

If we make a set of measurements, such as narrow-band or multicolour photo-electric measurements, which are designed to improve a scheme of classification, and in particular if they are designed to extend the number of dimensions of classification, i.e. the number of classification parameters, then some important problems of analytical procedure arise. First, it is important not to reproduce the errors of the classification scheme which we are trying to improve. Second, when trying to extend the number of dimensions of classification we have little or nothing with which to test the validity of the new parameters.Problems similar to these have occurred in other areas of scientific research (notably psychology and education) and the branch of Statistics called Multivariate Analysis has been developed to deal with them. The techniques of this subject are largely unknown to astronomers, but, if carefully applied, they should at the very least ensure that the astronomer gets the maximum amount of information out of his data and does not waste his time looking for information which is not there. More optimistically, these techniques are potentially capable of indicating the number of classification parameters necessary and giving specific formulas for computing them, as well as pinpointing those particular measurements which are most crucial for determining the classification parameters.

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Quantum HF/DFT-embedding algorithms for electronic structure calculations: Scaling up to complex molecular systems

The Journal of Chemical Physics ◽

10.1063/5.0029536 ◽

2021 ◽

Vol 154 (11) ◽

pp. 114105

Author(s):

Max Rossmannek ◽

Panagiotis Kl. Barkoutsos ◽

Pauline J. Ollitrault ◽

Ivano Tavernelli

Keyword(s):

Electronic Structure ◽

Electronic Structure Calculations ◽

Scaling Up ◽

Molecular Systems ◽

Structure Calculations

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Multiscale real-space quantum-mechanical tight-binding calculations of electronic structure in crystals with defects using perfectly matched layers

Journal of Computational Physics ◽

10.1016/j.jcp.2016.07.024 ◽

2016 ◽

Vol 323 ◽

pp. 115-125 ◽

Cited By ~ 1

Author(s):

Hossein Pourmatin ◽

Kaushik Dayal

Keyword(s):

Electronic Structure ◽

Tight Binding ◽

Real Space ◽

Quantum Mechanical ◽

Perfectly Matched Layers ◽

Matched Layers

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Synthesis and electronic structure determination of uranium(vi) ligand radical complexes

Dalton Transactions ◽

10.1039/c6dt02089e ◽

2016 ◽

Vol 45 (31) ◽

pp. 12576-12586 ◽

Cited By ~ 15

Author(s):

Khrystyna Herasymchuk ◽

Linus Chiang ◽

Cassandra E. Hayes ◽

Matthew L. Brown ◽

Jeffrey S. Ovens ◽

...

Keyword(s):

Electronic Structure ◽

Structure Determination ◽

Salen Ligands ◽

The One

Pentagonal bipyramidal uranyl (UO22+) complexes of salen ligands were prepared and the electronic structure of the one-electron oxidized species[1a–c]+were investigated in solution.

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