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 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

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.

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.

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.

Electronic levels in simple conjugated systems III. The significance of configuration interaction

1951 ◽  
Vol 206 (1086) ◽  
pp. 297-308 ◽  
Keyword(s):  
Configuration Interaction ◽  
Transition Probabilities ◽  
Electronic Energy ◽  
Wave Functions ◽  
Electron Systems ◽  
Molecular Systems ◽  
Self Consistent Field ◽  
The One ◽  
Configuration Interaction Calculations ◽  
Better Than

The features of configuration interaction calculations in π -electron systems so far reported are analyzed and compared with some atomic, and diatomic molecular, systems. The interactions between configuration wave functions are not negligible in atoms and are important in molecules bound either by σ - or π -electrons. In the one case where comparison is possible, viz. in H 2 (Coulson 1938), the magnitude of the effect is reduced to one-half when the configurations refer to self-consistent field orbitals rather than to linear combinations of atomic orbitals. The situation in which a consideration of configuration interaction is inescapable is for the configurations of a shell of molecular electrons where, typically, the spread of the energies is small compared with the total electronic energy. In cyclobutadiene, butadiene, benzene and naphthalene, i. e. in all cases so far reported, even the order of some of the states is changed. The wave functions derived in these calculations are markedly better than single-configuration ones, as judged by the much better agreement between calculated and experimental spectral transition probabilities.

Semi-empirical Molecular Orbital Energy Levels of the Hexammine and Chloroammine Complexes of Co(IV)

1967 ◽  
Vol 22 (2) ◽  
pp. 170-175 ◽  
Author(s):  
Walter A. Yeranos ◽  
David A. Hasman
Keyword(s):  
Molecular Orbital ◽  
Energy Levels ◽  
Empirical Evaluation ◽  
Wave Functions ◽  
Electronic Transitions ◽  
Orbital Energy ◽  
Molecular Orbital Energy ◽  
The One ◽  
Semi Empirical

Using the recently proposed reciprocal mean for the semi-empirical evaluation of resonance integrals, as well as approximate SCF wave functions for Co3+, the one-electron molecular energy levels of Co (NH3) 3+, Co (NH3) 5Cl2+, and Co (NH3) 4Cl21+ have been redetermined within the WOLFSBERG–HELMHOLZ approximation. The outcome of the study fits remarkably well with the observed electronic transitions in the u.v. spectra of these complexes and prompts different band assignments than previously suggested.

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.

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