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.

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.

d- and s-orbital populations in the d block: unbound atoms in physical vacuum versus chemical elements in condensed matter. A Dronskowski-population analysis

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kaixuan Chen ◽  
Wan-Lu Li ◽  
W. H. Eugen Schwarz
Keyword(s):  
Density Functional ◽  
Chemical Elements ◽  
Population Analysis ◽  
Atomic Orbital ◽  
Orbital Energy ◽  
Physical Vacuum ◽  
Electron Configuration ◽  
Transition Elements ◽  
The One ◽  
Dominant Configuration

Abstract The electron configurations of Ca, Zn and the nine transition elements M in between (and their heavier homologs) are reviewed on the basis of density functional theory and experimental facts. The d-s orbital energy and population patterns are systematically diverse. (i) The dominant valence electron configuration of most free neutral atoms M0 of groups g = 2–12 is 3d g−2 4s 2 (textbook rule), or 3d g−14s 1. (ii) Formal M q+ cations in chemical compounds have the dominant configuration 3d g−q 4s 0 (basic concept of transition metal chemistry). (iii) M0 atoms in metallic phases [M∞] of hcp, ccp(fcc) and bcc structures have intermediate populations near 3d g−1 4s 1 (lower d populations for Ca (ca. ½) and Zn (ca. 10)). Including the 4p valence orbitals, the dominant metallic configuration is 3d g−δ 4(sp) δ with δ ≈ 1.4 (±0.2) throughout (except for Zn). (iv) The 3d,4s population of atomic clusters M m varies for increasing m smoothly from single-atomic 3d g−24s 2 toward metallic 3d g−14s 1. – The textbook rule for the one-electron energies, i.e., ns < (n−1)d, holds ‘in a broader sense’ for the s block, but in general not for the d block, and never for the p block. It is more important to teach realistic atomic orbital (AO) populations such as the ones given above.

Acrylonitrile (AN)–Cu9(100) interfaces: Electron distribution and nature of bonded interactions

2003 ◽  
Vol 81 (6) ◽  
pp. 542-554 ◽  
Author(s):  
Petar M Mitrasinovic
Keyword(s):  
Electron Density ◽  
Molecular Orbital ◽  
Density Functional ◽  
Electron Distribution ◽  
Atomic Orbital ◽  
Interfacial Interactions ◽  
Total Electron Density ◽  
Total Electron ◽  
Topological Features ◽  
The One

There is a fundamental interest in the investigation of the interfacial interactions and charge migration processes between organic molecules and metallic surfaces from a theoretical standpoint. Quantum mechanical (QM) concepts of bonding are contrasted, and the vital importance of using combined QM methods to explore the nature of the interfacial interactions is established. At the one-electron level, the charge distribution and nature of bonded interactions at the AN–Cu9(100) (neutral and charged (–1)) interfaces are investigated by both the Becke (B) – Vosko (V) – Wilk (W) – Nusair (N)/DZVP density functional theory (DFT) method and the MP2/6–31+G* strategy within the conceptual framework provided by natural bond orbital (NBO) – natural atomic orbital (NAO) population analysis and Atoms-In-Molecules (AIM) theory. By this approach, the interfacial interactions are given physical definitions free of any assumptions and are visualized by using the topological features of the total electron density. A natural link between the electron density on the one side and the shapes (not energies) of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) on the other side is clarified. The question of whether the spatial extents of the HOMO and LUMO resemble the corresponding spatial maps of the negative (charge locally concentrated) and positive (charge locally depleted) Laplacian of the total electron density in [AN–Cu9(100)]–1 is addressed.Key words: AN–Cu9(100) interfaces, NBO–NAO population, electron distribution, AIM, bonded interactions.

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

Ab initio band theory approach to electron energy loss near edge structures

1988 ◽  
Vol 46 ◽  
pp. 506-507
Author(s):  
Xudong Weng ◽  
O.F. Sankey ◽  
Peter Rez
Keyword(s):  
Ab Initio ◽  
Local Density ◽  
Interpolation Method ◽  
Atomic Orbital ◽  
Plane Waves ◽  
Large Set ◽  
Theory Approach ◽  
Band Theory ◽  
Atomic Orbitals ◽  
Pseudopotential Calculations

Single electron band structure techniques have been applied successfully to the interpretation of the near edge structures of metals and other materials. Among various band theories, the linear combination of atomic orbital (LCAO) method is especially simple and interpretable. The commonly used empirical LCAO method is mainly an interpolation method, where the energies and wave functions of atomic orbitals are adjusted in order to fit experimental or more accurately determined electron states. To achieve better accuracy, the size of calculation has to be expanded, for example, to include excited states and more-distant-neighboring atoms. This tends to sacrifice the simplicity and interpretability of the method.In this paper. we adopt an ab initio scheme which incorporates the conceptual advantage of the LCAO method with the accuracy of ab initio pseudopotential calculations. The so called pscudo-atomic-orbitals (PAO's), computed from a free atom within the local-density approximation and the pseudopotential approximation, are used as the basis of expansion, replacing the usually very large set of plane waves in the conventional pseudopotential method. These PAO's however, do not consist of a rigorously complete set of orthonormal states.

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.

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