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.

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.

A variational method for calculating magnetic shielding constants in molecules

1957 ◽  
Vol 243 (1233) ◽  
pp. 264-273 ◽  
Keyword(s):  
Variational Method ◽  
Molecular Orbital ◽  
Diamagnetic Susceptibility ◽  
Valence Bond ◽  
Wave Functions ◽  
Magnetic Shielding ◽  
Magnetic Nucleus ◽  
Shielding Constants ◽  
Good Agreement

The general variational method is applied to the problem of calculating magnetic shielding constants in molecules. Using approximate variation functions together with simple molecular-orbital and valence-bond wave functions calculations have been made for the molecules hydrogen, methane, ethylene and acetylene. An approximation using the calculated diamagnetic susceptibility is used for electrons which are not localized near the magnetic nucleus considered. The results are in good agreement with experiment and in particular it is shown that the shielding constant for acetylene should lie between those for methane and ethylene.

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.

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.

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