Increased-Valence or Electronic Hypervalence for a Diatomic One-Electron Bond

2005 ◽  
Vol 58 (10) ◽  
pp. 753 ◽  
Author(s):  
Richard D. Harcourt
Keyword(s):  
Excited State ◽  
Molecular Orbital ◽  
Valence Bond ◽  
Ground States ◽  
Bond Valence ◽  
Atomic Orbitals ◽  
Valence Bond Structure ◽  
The One ◽  
Increased Valence

With a and b as overlapping atomic orbitals to form the A–B bonding molecular orbital ψab = a + kb, it is deduced that for k ≠ 0, 1, or ∞, either the A atom or the B atom in the one-electron bond valence bond structure (A · B) exhibits increased-valence or electronic hypervalence, namely its valence exceeds unity. The result is illustrated using the results of STO-6G valence bond calculations for the one-electron bond of LiH+ and an excited state for H2CN. Valencies for the ground-states of H2+, H2, and H2− are also considered.

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.

Three-electron bonds and a valence-bond study of the rotation barrier for N2O4

1978 ◽  
Vol 31 (8) ◽  
pp. 1635 ◽  
Author(s):  
RD Harcourt
Keyword(s):  
Molecular Orbital ◽  
Significant Contribution ◽  
Valence Bond ◽  
Rotation Barrier ◽  
Atomic Orbitals ◽  
Planar Conformation ◽  
Valence Bond Structure ◽  
Oxygen Atoms

From molecular orbital studies, a number of previous workers have concluded that a most significant contribution to the barrier to rotation around the NN bond of N2O4 arises from the overlap of pairs of atomic orbitals located on the cis oxygen atoms of the planar conformation. A valence-bond study of this overlap contribution is reported. It is calculated that the 'long OO bond' formed by overlap of singly occupied 2pπ-orbitals in the valence-bond structure (3) for the planar conformation has negligible strength, and that insufficient stabilization is obtained when this structure participates in resonance with ionic structures of the type (5a). Diagram The primary overlap stabilization for the planar conformation is calculated to arise from resonance between structures of the types (2a) and (7). The O. :O ↔ 0: .O resonance that pertains here is equivalent to the formation of a Pauling 'three-electron bond' O...O between the two atoms. Therefore, the development of this type of bond in the planar conformation can be associated with the cis OO overlap contribution to the barrier to rotation around the NN bond. Another type of Pauling three-electron bond resonance, namely (4) ↔ (6), is calculated to produce a smaller but not insignificant stabilization of the planar conformation.

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.

Resolving the Quadruple Bonding Conundrum in C2 Using Insights Derived from Excited State Potential Energy Surfaces: A Molecular Orbital Perspective

2019 ◽  
Author(s):  
Ishita Bhattacharjee ◽  
Debashree Ghosh ◽  
Ankan Paul
Keyword(s):  
Excited State ◽  
Potential Energy ◽  
Molecular Orbital ◽  
High Spin ◽  
Potential Energy Surfaces ◽  
Valence Bond ◽  
Deep Minimum ◽  
State Potential ◽  
Energy Surfaces ◽  
Mo Theory

The question of quadruple bonding in C<sub>2</sub> has emerged as a hot button issue, with opinions sharply divided between the practitioners of Valence Bond (VB) and Molecular Orbital (MO) theory. Here, we have systematically studied the Potential Energy Curves (PECs) of low lying high spin sigma states of C<sub>2</sub>, N<sub>2</sub> and Be<sub>2</sub> and HC≡CH using several MO based techniques such as CASSCF, RASSCF and MRCI. The analyses of the PECs for the<sup> 2S+1</sup>Σ<sub>g/u</sub> (with 2S+1=1,3,5,7,9) states of C<sub>2</sub> and comparisons with those of relevant dimers and the respective wavefunctions were conducted. We contend that unlike in the case of N<sub>2</sub> and HC≡CH, the presence of a deep minimum in the <sup>7</sup>Σ state of C<sub>2</sub> and CN<sup>+</sup> suggest a latent quadruple bonding nature in these two dimers. Hence, we have struck a reconciliatory note between the MO and VB approaches. The evidence provided by us can be experimentally verified, thus providing the window so that the narrative can move beyond theoretical conjectures.

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.

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

Resolving the Quadruple Bonding Conundrum in C2 Using Insights Derived from Excited State Potential Energy Surfaces: A Molecular Orbital Perspective

2019 ◽  
Author(s):  
Ishita Bhattacharjee ◽  
Debashree Ghosh ◽  
Ankan Paul
Keyword(s):  
Excited State ◽  
Potential Energy ◽  
Molecular Orbital ◽  
High Spin ◽  
Potential Energy Surfaces ◽  
Valence Bond ◽  
Deep Minimum ◽  
State Potential ◽  
Energy Surfaces ◽  
Mo Theory

The question of quadruple bonding in C<sub>2</sub> has emerged as a hot button issue, with opinions sharply divided between the practitioners of Valence Bond (VB) and Molecular Orbital (MO) theory. Here, we have systematically studied the Potential Energy Curves (PECs) of low lying high spin sigma states of C<sub>2</sub>, N<sub>2</sub> and Be<sub>2</sub> and HC≡CH using several MO based techniques such as CASSCF, RASSCF and MRCI. The analyses of the PECs for the<sup> 2S+1</sup>Σ<sub>g/u</sub> (with 2S+1=1,3,5,7,9) states of C<sub>2</sub> and comparisons with those of relevant dimers and the respective wavefunctions were conducted. We contend that unlike in the case of N<sub>2</sub> and HC≡CH, the presence of a deep minimum in the <sup>7</sup>Σ state of C<sub>2</sub> and CN<sup>+</sup> suggest a latent quadruple bonding nature in these two dimers. Hence, we have struck a reconciliatory note between the MO and VB approaches. The evidence provided by us can be experimentally verified, thus providing the window so that the narrative can move beyond theoretical conjectures.

scholarly journals STABILITY OF GROUND STATES IN SECTORS AND ITS APPLICATION TO THE WIGNER–WEISSKOPF MODEL

2001 ◽  
Vol 13 (04) ◽  
pp. 513-528 ◽  
Author(s):  
ASAO ARAI ◽  
MASAO HIROKAWA
Keyword(s):  
Excited State ◽  
Scalar Field ◽  
Ground State ◽  
Adjoint Operator ◽  
Ground States ◽  
The Other ◽  
Coupling Constant ◽  
A Value ◽  
First Excited State ◽  
The One

We consider two kinds of stability (under a perturbation) of the ground state of a self-adjoint operator: the one is concerned with the sector to which the ground state belongs and the other is about the uniqueness of the ground state. As an application to the Wigner–Weisskopf model which describes one mode fermion coupled to a quantum scalar field, we prove in the massive case the following: (a) For a value of the coupling constant, the Wigner–Weisskopf model has degenerate ground states; (b) for a value of the coupling constant, the Wigner–Weisskopf model has a first excited state with energy level below the bottom of the essential spectrum. These phenomena are nonperturbative.

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.

A molecular orbital treatment of diborane as a four-centre, four-electron problem

1956 ◽  
Vol 235 (1202) ◽  
pp. 395-407 ◽  
Keyword(s):  
Molecular Orbital ◽  
Valence Bond ◽  
Field Equations ◽  
Net Charge ◽  
Atomic Orbitals ◽  
Plane Normal ◽  
Self Consistent Field ◽  
Actual Configuration ◽  
Resonance Hybrid ◽  
Better Than

The Roothaan self-consistent field equations in their linear combination of atomic orbitals form have been solved for a system composed of four electrons in the field of a framework of two asymmetric boron cores of net charge +1 each and two protons in the 'bridge' positions as in diborane. Exact values for all one and two-centre integrals were used, and approximations were made for three- and four-centre integrals. The molecular orbitals of lowest energy are the completely symmetric orbital and the π -orbital with a nodal plane normal to the line between the protons. In terms of the molecular-orbital coefficients, there is a small residual net negative charge on the hydrogens, i. e. the bridge hydrogens have a hydridic character. In terms of configurational expansions, a localized three-centre bond description of the molecule is very close to the actual configuration and is somewhat better than a description as a resonance hybrid between either ordinary covalent valence bond structures or localized two-centre molecular orbital structures.

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