Valence Bond Structures for the N3- Anion, the N3 Radical and the N6- Radical Anion

2012 ◽  
Vol 67 (9) ◽  
pp. 935-943 ◽  
Author(s):  
Richard D. Harcourta ◽  
Thomas M. Klapötke
Keyword(s):  
Radical Anion ◽  
Electron Pair ◽  
Atomic Orbital ◽  
Valence Bond ◽  
Wave Functions ◽  
The One ◽  
Lewis Structures ◽  
Increased Valence ◽  
Polarity Parameters

With Heitler-London atomic orbital-type formulations of the wave functions for (fractional) electron-pair πx(NN) and πy(NN) bonds, increased-valence structures for the N3- anion and N3- radical are equivalent to resonance between familiar standard Lewis structures and singlet diradical (or “long-bond”) Lewis structures. Theory is developed for the calculation of the polarity parameters that are associated with the one-electron πx(NN) and πy(NN) bonds in the increased-valence structures, and illustrative STO-6G estimates of their values are reported. They show that the πx and πy electrons of these bonds are strongly charge-correlated relative to each other. The increased-valence structures for the N3- anion and the N3- radical are used to help construct increased-valence structures for the N6- radical anion with C2h symmetry

Some wave functions for the four-electron threecentre bonding of four- and eight-π-electron systems

1974 ◽  
Vol 27 (4) ◽  
pp. 691 ◽  
Author(s):  
RD Harcourt ◽  
JF Sillitoe
Keyword(s):  
Molecular Orbital ◽  
Configuration Interaction ◽  
Electron Pair ◽  
Valence Bond ◽  
Pair Bond ◽  
Wave Functions ◽  
Electron Systems ◽  
Numerical Evidence ◽  
The One ◽  
Increased Valence

For symmetrical four-electron three-centre bonding units, the standard valence-bond (VB), delocalized molecular orbital (MO), increased-valence (IV) and non-paired spatial orbital (NPSO) representations of the electrons are Diagram O3, NO2- and CF2 with four π-electrons, and N3-, CO2 and NO2+ with eight π-electrons, have respectively one and two four-electron three-centre bonding units for these n-electrons. By means of Pople-Parr-Pariser type approximations, the MO, standard VB, IV and NPSO wave functions for these systems are compared with complete VB (or best configuration interaction) wave functions for the ground states. Similar studies are reported for the n-electrons of N2O. Further demonstration is given for the important result obtained elsewhere that the IV formulae must always have energies which are lower than those of the standard VB formulae, provided that the same technique is used to construct electron-pair bond wave functions. The extra stability arises because IV formulae summarize resonance between the standard VB formulae and long-bond formulae of the type Diagram As has been discussed elsewhere, the latter structure can make appreciable contributions to the complete VB resonance when its atomic formal charges are either zero or small in magnitude.If two-centre bond orbitals are used to construct the wave functions for the one-electron bond(s) and the two-electron bond(s) of IV formulae, then the IV and MO wave functions are almost identical for the symmetrical systems. Further numerical evidence is provided for this near-equivalence.

Valence-bond studies of 4-electron 3-centre bonding units. I. The π-electrons of O3, NO2−, and CH2N2

1978 ◽  
Vol 56 (8) ◽  
pp. 1093-1101 ◽  
Author(s):  
Richard D. Harcourt ◽  
Walter Roso
Keyword(s):  
Electronic Structure ◽  
Ab Initio ◽  
Valence Bond ◽  
Ground States ◽  
Wave Functions ◽  
Dipolar Cycloaddition ◽  
Cycloaddition Reactions ◽  
Electronic Mechanism ◽  
Increased Valence

Some ab-initio valence-bond wave-functions are reported for the π-electrons of the ground-states of O3, NO2−, and CH2N2. Examination of these wave-functions provides further support for the hypothesis that, for the ground-states of many electron-excess molecules, important valence-bond structures are those that are compatible with the electroneutrality principle, i.e. they carry either small or zero formal charges on each of the atoms. For O3 and CH2N2, the important valence-bond structures with zero atomic formal charges are [Formula: see text]Each of these structures has a 'long-bond' between non-adjacent atoms. The significance of 'long-bond' (or spin-paired diradical) structures for the electronic mechanism of 1,3-dipolar cycloaddition reactions is discussed and 'increased-valence' descriptions of the electronic structure of each molecule are presented. Some comments on the utility of 'increased-valence' structures are provided.

Corrigendum to: Valence Bond Formulations of Mechanisms for the Formation and Decomposition of N2O5

2006 ◽  
Vol 3 (6) ◽  
pp. 457 ◽  
Author(s):  
Richard D. Harcourt ◽  
Thomas M. Klapötke
Keyword(s):  
Thermal Decomposition ◽  
Gas Phase ◽  
Phase Formation ◽  
Electronic Structures ◽  
Electron Pair ◽  
Valence Bond ◽  
Pair Bonds ◽  
Normal Electron ◽  
Stratospheric Clouds ◽  
Increased Valence

Environmental Context. N2O5 is an important nitrogen reservoir in polar stratospheric clouds found in Antarctica and involved with the ozone hole. Here we provide valence bond representations for the gas-phase formation and decomposition of this molecule. Abstract. Qualitative valence bond considerations are used to suggest how electronic reorganization could proceed for (a) the formation of N2O5 via the reactions NO2 + O3 → NO3 + O2, and NO2 + NO3 → N2O5, and (b) the thermal decomposition of N2O5 via the following sets of reactions: (i) N2O5 → NO2 + NO3, 2NO3 → O2NOONO2 → 2NO2 + O2; (ii) NO2 + NO3 → ONOONO2 → NO + O2 + NO2, NO + NO3 → 2NO2. Increased-valence structures, which possess one-electron bonds and fractional electron-pair bonds as well as 'normal' electron-pair bonds, are used to represent the electronic structures of the molecules.

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.

Increased Valence or Electronic Hypervalence for Symmetrical Three-Centre Molecular Orbital Configurations

2007 ◽  
Vol 60 (9) ◽  
pp. 691 ◽  
Author(s):  
Richard D. Harcourt
Keyword(s):  
Molecular Orbital ◽  
Atomic Orbital ◽  
Additional Contribution ◽  
Electron Configuration ◽  
Electron Charge ◽  
Atomic Orbitals ◽  
Maximum Value ◽  
Orbital Configuration ◽  
The One ◽  
Increased Valence

With ψ1 = y + k1a + b, ψ2 = y – b, and ψ3 = y – k3a + b as Y–A and A–B bonding, non-bonding, and antibonding three-centre molecular orbitals for a symmetrical Y–A–B type bonding unit with overlapping atomic orbitals y, a, and b, it is deduced that the maximum value for the A atom valence, (VA = Vab + Vay), is (a) 4(3 – 2√2) = 0.6863 for the one-electron and five-electron configurations Φ(1) = (ψ1)1 and Φ(5) = (ψ1)2ψ2)2(ψ3)1; (b) 8(3 – 2√2) = 1.3726 for the two-electron and four-electron configurations Φ(2) = (ψ1)2 and Φ(4) = (ψ1)2(ψ2)2; and (c) 4/3 for the three-electron configuration Φ(3) = (ψ1)2(ψ2)1. Thus for each of the three-centre molecular orbital configurations, the A-atom can exhibit increased valence, or electronic hypervalence, relative to the valence for an A-atom in a two-centre molecular orbital configuration. When k1 ≠ 0 for Φ(1) and k3 ≠ 0 for Φ(5), the A-atom odd-electron charge is not equal to zero. This odd-electron charge is available for (fractional) electron-pair bonding to a fourth atom X, to give an additional contribution, Va, to the valence. The resulting maximum value for the A-atom valence (VA = Vab + Vay + Va) is equal to 1.2020 for each of Φ(1) and Φ(5). A-atom valencies are calculated for the three-centre bonding units for several molecules and ions. The expressions for VA = Vab + Vay were derived with atomic orbital overlap integrals omitted. The present paper shows how the theory is modified when these integrals are included.

Valence Bond Studies of N5+

2002 ◽  
Vol 57 (9) ◽  
pp. 983-992 ◽  
Author(s):  
Richard D. Harcourta ◽  
Thomas M. Klapötkeb
Keyword(s):  
Valence Bond ◽  
Molecular Orbital Calculations ◽  
Energy Minimum ◽  
Localized Molecular Orbitals ◽  
Bond Lengths ◽  
Formal Charge ◽  
Valence Structure ◽  
Valence Bond Structure ◽  
Lewis Structures ◽  
Increased Valence

The results of STO-6G valence-bond studies are reported for the six π-electrons of C2v symmetry N5+, with π-electron core charges determined from the valence bond structures. Important types of canonical Lewis structures are calculated to carry either three atomic formal charges, arranged spatially as (+), (-) and (+) , as in or a single (+) atomic formal charge, as in the “long-bond” structure When localized molecular orbitals are used to accommodate bonding electrons between pairs of adjacent atoms, each of these types of Lewis structures, and others, are components of the increased-valence structure whose bond properties are in qualitative accord with experimental estimates of the bond lengths for N5+. Consideration is also given to other types of valence bond representations for N5+, and the results of MP2 molecular orbital calculations for the hypothetical N82+ are reported. For the latter species, a stable energy minimum with C2 symmetry is obtained. Its bond lengths are related to those implied by a Lewis-type valence-bond structure

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.

Molecular orbital, increased valence, valence bond and non-pairing spatial orbital formulae for three-centre bonding

1969 ◽  
Vol 22 (2) ◽  
pp. 279 ◽  
Author(s):  
RD Harcourt
Keyword(s):  
Molecular Orbital ◽  
Valence Bond ◽  
Wave Functions ◽  
Bond Orders ◽  
Increased Valence

The simple valence-bond and molecular orbital formulae for three-centre bonding involving four electrons and three atoms Y, A, and B are Y 4-B - Y-A 'P, and Y---A---B Increased-valence formulae that have been developed recently are Y-A . B and Y . A-B If Y and B are the same type of atom, and bond-orbitals are used as wave functions for Y-A and A-B bonds, then the near-equivalence of the molecular orbital and increased-valence wave functions is demonstrated. Bond-orders (or numbers) for these and Linnett's5s6 non-pairing spatial orbital formula Y . A . B are calculated.

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