scholarly journals Real space electron delocalization, resonance, and aromaticity in chemistry

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Leonard Reuter ◽  
Arne Lüchow
Keyword(s):  
First Principles ◽  
Valence Bond ◽  
Real Space ◽  
Wave Functions ◽  
High Probability Density ◽  
Hückel Rule ◽  
Bond Theory ◽  
Planar Systems ◽  
The Many ◽  
Lewis Structures

AbstractChemists explaining a molecule’s stability and reactivity often refer to the concepts of delocalization, resonance, and aromaticity. Resonance is commonly discussed within valence bond theory as the stabilizing effect of mixing different Lewis structures. Yet, most computational chemists work with delocalized molecular orbitals, which are also usually employed to explain the concept of aromaticity, a ring delocalization in cyclic planar systems which abide certain number rules. However, all three concepts lack a real space definition, that is not reliant on orbitals or specific wave function expansions. Here, we outline a redefinition from first principles: delocalization means that likely electron arrangements are connected via paths of high probability density in the many-electron real space. In this picture, resonance is the consideration of additional electron arrangements, which offer alternative paths. Most notably, the famous 4n + 2 Hückel rule is generalized and derived from nothing but the antisymmetry of fermionic wave functions.

scholarly journals Decoding the Chemical Bond—On the Connection between Probability Density Analysis, QTAIM, and VB Theory

2020 ◽  
Author(s):  
Leonard Reuter ◽  
Arne Lüchow
Keyword(s):  
Probability Density ◽  
First Principles ◽  
Valence Bond ◽  
Chemical Compounds ◽  
Wave Functions ◽  
Basis Set ◽  
Density Analysis ◽  
Bond Theory ◽  
Lewis Structures

Classification of bonds is essential for understanding and predicting the reactivity of chemical compounds. This classification mainly manifests in the bond order and the contribution of different Lewis resonance structures. Here, we outline a first principles approach to obtain these orders and contributions for arbitrary wave functions in a manner that is both, related to the quantum theory of atoms in molecules and consistent with valence bond theory insight: the Lewis structures arise naturally as attractors of the all-electron probability density |Ψ|². Doing so, we introduce valence bond weight definitions that do not collapse in the basis set limit.

Decoding the Chemical Bond—On the Connection between Probability Density Analysis, QTAIM, and VB Theory

2020 ◽  
Author(s):  
Leonard Reuter ◽  
Arne Lüchow
Keyword(s):  
Probability Density ◽  
First Principles ◽  
Valence Bond ◽  
Chemical Compounds ◽  
Wave Functions ◽  
Basis Set ◽  
Density Analysis ◽  
Bond Theory ◽  
Lewis Structures

Classification of bonds is essential for understanding and predicting the reactivity of chemical compounds. This classification mainly manifests in the bond order and the contribution of different Lewis resonance structures. Here, we outline a first principles approach to obtain these orders and contributions for arbitrary wave functions in a manner that is both, related to the quantum theory of atoms in molecules and consistent with valence bond theory insight: the Lewis structures arise naturally as attractors of the all-electron probability density |Ψ|². Doing so, we introduce a valence bond weight definition that does not collapse in the basis set limit.

scholarly journals Decoding the Chemical Bond—On the Connection between Probability Density Analysis, QTAIM, and VB Theory

2020 ◽  
Author(s):  
Leonard Reuter ◽  
Arne Lüchow
Keyword(s):  
Probability Density ◽  
First Principles ◽  
Valence Bond ◽  
Chemical Compounds ◽  
Wave Functions ◽  
Basis Set ◽  
Density Analysis ◽  
Bond Theory ◽  
Lewis Structures

Classification of bonds is essential for understanding and predicting the reactivity of chemical compounds. This classification mainly manifests in the bond order and the contribution of different Lewis resonance structures. Here, we outline a first principles approach to obtain these orders and contributions for arbitrary wave functions in a manner that is both, related to the quantum theory of atoms in molecules and consistent with valence bond theory insight: the Lewis structures arise naturally as attractors of the all-electron probability density |Ψ|². Doing so, we introduce a valence bond weight definition that does not collapse in the basis set limit.

scholarly journals Real Space Delocalization, Resonance and Aromaticity

2020 ◽  
Author(s):  
Leonard Reuter ◽  
Arne Lüchow
Keyword(s):  
Electronic Structure ◽  
Probability Density ◽  
Saddle Points ◽  
Valence Bond ◽  
Special Kind ◽  
Real Space ◽  
Structure Framework ◽  
Chemical Concepts ◽  
Bond Theory ◽  
The Many

<div>When chemists want to explain a molecule’s stability and reactivity, they often refer to the concepts of delocalization, resonance, and aromaticity. Resonance is commonly discussed within the electronic structure framework of valence bond theory as the stabilizing effect of mixing different Lewis structures. Yet, most computational chemists work with delocalized molecular orbitals, which are also usually employed to explain the concept of aromaticity, a special kind of ring delocalization that shows up in cyclic planar systems which abide certain number rules. As an intuitive picture for aromaticity, an electronic ring current has been hypothesized. However, all three concepts lack a real space definition, that is not reliant on orbitals or specific wave function expansions. Here, we outline a redefinition from first principles: the concepts are of kinetic nature and related to saddle points of the all-electron probability density |Ψ|². Delocalization means that likely electron arrangements are connected via paths of high probability density in the many-electron real space. In this picture, resonance is the consideration of additional electron arrangements, which offer alternative paths of higher probability. Most notably, the concept of aromatic ring currents in absence of a magnetic field is rejected and the famous 4n+2 Hückel rule is derived from nothing but the antisymmetry of fermionic wave functions. The analysis developed in this work allows for a quantitative discussion of important chemical concepts that were previously only accessible qualitatively or restricted to specific electronic structure frameworks.</div>

scholarly journals Real Space Delocalization, Resonance and Aromaticity

2020 ◽  
Author(s):  
Leonard Reuter ◽  
Arne Lüchow
Keyword(s):  
Electronic Structure ◽  
Probability Density ◽  
Saddle Points ◽  
Valence Bond ◽  
Special Kind ◽  
Real Space ◽  
Structure Framework ◽  
Chemical Concepts ◽  
Bond Theory ◽  
The Many

<div>When chemists want to explain a molecule’s stability and reactivity, they often refer to the concepts of delocalization, resonance, and aromaticity. Resonance is commonly discussed within the electronic structure framework of valence bond theory as the stabilizing effect of mixing different Lewis structures. Yet, most computational chemists work with delocalized molecular orbitals, which are also usually employed to explain the concept of aromaticity, a special kind of ring delocalization that shows up in cyclic planar systems which abide certain number rules. As an intuitive picture for aromaticity, an electronic ring current has been hypothesized. However, all three concepts lack a real space definition, that is not reliant on orbitals or specific wave function expansions. Here, we outline a redefinition from first principles: the concepts are of kinetic nature and related to saddle points of the all-electron probability density |Ψ|². Delocalization means that likely electron arrangements are connected via paths of high probability density in the many-electron real space. In this picture, resonance is the consideration of additional electron arrangements, which offer alternative paths of higher probability. Most notably, the concept of aromatic ring currents in absence of a magnetic field is rejected and the famous 4n+2 Hückel rule is derived from nothing but the antisymmetry of fermionic wave functions. The analysis developed in this work allows for a quantitative discussion of important chemical concepts that were previously only accessible qualitatively or restricted to specific electronic structure frameworks.</div>

Electronic levels in simple conjugated systems, I. Configuration interaction in cyclobutadiene

1950 ◽  
Vol 202 (1071) ◽  
pp. 498-506 ◽  
Keyword(s):  
Molecular Orbital ◽  
Configuration Interaction ◽  
Energy Levels ◽  
Valence Bond ◽  
Wave Functions ◽  
The Other ◽  
Orbital Theory ◽  
Valence Bond Theory ◽  
Symmetry Properties ◽  
Bond Theory

In the simplest cyclic system of π-electrons, cyclobutadiene, a non-empirical calculation has been made of the effects of configuration interaction within a complete basis of antisymmetric molecular orbital configurations. The molecular orbitals are made up from atomic wave functions and all the interelectron repulsion integrals which arise are included, although those of them which are three- and four-centre integrals are only known approximately. In this system configuration interaction is a large effect with a strongly differential action between states of different symmetry properties. Thus the 1 A 1g state is several electron-volts lower than the lowest configuration of that symmetry, whereas for 1 B 1g the comparable figure is about one-tenth of an electron-volt. The other two states examined, 1 B 2g and 3 A 2g are affected by intermediate amounts. The result is a drastic change in the energy-level scheme compared with that based on configuration wave functions. Neither the valence-bond theory nor the molecular orbital theory (in which the four states have the same energy) gives a satisfactory account of the energy levels according to these results. One conclusion from the valence-bond theory which is, however, confirmed, is the somewhat unexpected one that the non-totally symmetrical 1 B 2g state is more stable than the totally symmetrical 1 A 1g . On the other hand, it is clear that the valence-bond theory, with the usual value for its exchange integral, grossly exaggerates the resonance splitting of the states, giving separations between them several times too great. Thus the valence-bond theory leads to large values of the resonance energy (larger, per π-electron, than in benzene) and so associates with the molecule a considerable π-electron stabilization. This expectation has no support in the present more detailed and non-empirical calculations.

The molecular orbital theory of chemical valency XIII. Orbital wave functions for excited states of a homonuclear diatomic molecule

1953 ◽  
Vol 216 (1126) ◽  
pp. 424-433 ◽  
Keyword(s):  
Molecular Orbital ◽  
Excited States ◽  
Valence Bond ◽  
Present Theory ◽  
Wave Functions ◽  
Molecular Orbital Theory ◽  
Orbital Theory ◽  
Bond Theory ◽  
Homonuclear Diatomic Molecules ◽  
Approximate Wave

The expansions for the exact wave functions for excited states of homonuclear diatomic molecules derived in part XII are used as the basis for discussing various approximate wave functions of the orbital type. The states considered in detail are the lowest states of symmetries 1 Σ u + , 3 Σ u + . The calculus of variations is used to determine the optimum forms for the component orbital functions. A transformation to equivalent orbitals is used to bring out the physical significance of the various wave functions, and to relate the present theory to earlier theories, in particular the molecular orbital theory, the valence-bond theory and their generalizations.

scholarly journals The Valence-Bond (VB) Model and Its Intimate Relationship to the Symmetric or Permutation Group

Molecules ◽  
2021 ◽  
Vol 26 (15) ◽  
pp. 4524
Author(s):  
Marco Antonio Chaer Nascimento
Keyword(s):  
Permutation Group ◽  
Point Group ◽  
Valence Bond ◽  
Fundamental Difference ◽  
Wave Functions ◽  
Group Symmetry ◽  
Chemical Bonds ◽  
Permutation Symmetry ◽  
Independent Entity ◽  
The Many

VB and molecular orbital (MO) models are normally distinguished by the fact the first looks at molecules as a collection of atoms held together by chemical bonds while the latter adopts the view that each molecule should be regarded as an independent entity built up of electrons and nuclei and characterized by its molecular structure. Nevertheless, there is a much more fundamental difference between these two models which is only revealed when the symmetries of the many-electron Hamiltonian are fully taken into account: while the VB and MO wave functions exhibit the point-group symmetry, whenever present in the many-electron Hamiltonian, only VB wave functions exhibit the permutation symmetry, which is always present in the many-electron Hamiltonian. Practically all the conflicts among the practitioners of the two models can be traced down to the lack of permutation symmetry in the MO wave functions. Moreover, when examined from the permutation group perspective, it becomes clear that the concepts introduced by Pauling to deal with molecules can be equally applied to the study of the atomic structure. In other words, as strange as it may sound, VB can be extended to the study of atoms and, therefore, is a much more general model than MO.

The valence-bond theory of molecular structure - III. Cyclo butadiene and benzene

1955 ◽  
Vol 227 (1170) ◽  
pp. 288-312 ◽  
Keyword(s):  
Intrinsic Value ◽  
Energy Levels ◽  
Valence Bond ◽  
Wave Functions ◽  
Empirical Theory ◽  
Different Types ◽  
Rigorous Framework ◽  
Bond Theory ◽  
Complete Sets ◽  
The One

The revised valence-bond (VB) theory of previous papers is applied in non-empirical calculation of the lower π -electron levels of cyclo butadiene and benzene. For the first of these molecules, complete sets of all non-polar and polar, singlet and triplet structures are employed; for the second, 89 singlet and 69 triplet structures were selected from the complete sets of 175 singlet and 189 triplet structures. The calculations, which follow unfamiliar lines but which proved not too heavy, are outlined in some detail. The results for cyclo butadiene agree with those of Craig, who employed a complete MO basis; but previous calculations on benzene are surpassed in accuracy, except in the case of the ground state which is apparently well represented by a few MO configurations. The primary aim of the present work was, however, simply to exploit the valence-bond approach as a practicable alternative to the MO method, with exactly similar ‘non-empirical’ potentialities. Energy levels, wave functions and bond orders were calculated in a variety of approximations, numerical results converging slowly to their final values as configurations were added, so that the function of different types of structure should be revealed: and ‘higher’ structures—those, for instance, which are doubly -polar—were found to have an unexpected importance. This supports the view that calculations making any pretence of being non-empirical cannot easily be extended to systems which explicitly involve more than a few electrons. The orthodox VB approach is re-examined, within this rigorous framework, and is found to have less intrinsic value than might have been hoped; the shortcomings of the conventional empirical theory are further revealed. Semi-empirica! developments are briefly investigated. The revised VB theory contains only a few numerically large parameters: these are, in the first place, ‘resonance’ integrals (of the one-electron type encountered in MO theory) and, secondly, the energies of the various polar configurations relative to the non-polar; by adjusting the latter quantities empirically it is possible partly to overcome one of the principal defects of the non-empirical theory—namely, its use of the Hückel approximation in which changes in the σ-bonded framework, accompanying π -electron ‘polarizations’, are ignored. It seems likely that considerable progress can be made along these lines.

Sign in / Sign up

Export Citation Format

Share Document