BOND LENGTHS AND BOND ANGLES IN OCTAHEDRAL, TRIGONAL- BIPYRAMIDAL, AND RELATED MOLECULES OF THE NON-TRANSITION ELEMENTS

1961 ◽  
Vol 39 (2) ◽  
pp. 318-323 ◽  
Author(s):  
R. J. Gillespie
Keyword(s):  
Central Atom ◽  
Lone Pair ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Transition Elements ◽  
Electron Pairs ◽  
Bond Angles ◽  
Bond Lengths ◽  
Trigonal Bipyramidal ◽  
The Difference

The stereochemistry of molecules in which there are five or six pairs of electrons in the valency shell of a central atom is discussed in terms of the repulsions that exist between pairs of electrons in the valency shell as a consequence of the operation of the Pauli exclusion principle. An explanation is given for the difference in lengths of the axial and equatorial bonds in molecules such as PCl5 and ClF3 whose structures are based on the trigonal-bipyramidal arrangement of five valency-shell electron pairs. The fact that in molecules with a central atom with a valency shell of six electron pairs, one of which is a lone pair and which have the structure of a square pyramid, the central atom always lies below rather than in, or above, the base of the square pyramid, is also accounted for.

Conformationally induced and conjugatively amplified doubly degenerate uneven sulfuranes

1994 ◽  
Vol 72 (10) ◽  
pp. 2153-2158
Author(s):  
Elizabeth A. Innes ◽  
Imre G. Csizmadia ◽  
Jean-Louis Rivail ◽  
Michel Loos ◽  
Árpád Kucsman
Keyword(s):  
Potential Energy Surfaces ◽  
Valence Electron ◽  
Lone Pair ◽  
Equatorial Position ◽  
Electron Pairs ◽  
Bond Lengths ◽  
The Difference ◽  
Torsional Angles ◽  
Energy Surfaces ◽  
The Ideal

Sulfuranes, containing hypervalent or 10 valence electron central sulfur atoms of the type CH3(H)SCl2 (I), H2N(H)SCl2 (II), HO(H)SCl2 (III), (H2N)2SCl2 (IV), and (HO)2SCl2 (V) have been studied by ab initio MO computations. All sulfuranes exhibited pseudo trigonal bipyramide structure as appropriate 5 valence electron pairs. The two chlorine atoms were in apical positions and the other two ligands were in equatorial position. The fifth electron pair was a lone pair, also located in an equatorial position. The lone pair "pushed away" the S—Cl bonds from the ideal axis of the trigonal bipyramide and therefore the ClSCl bond angle was always less than 180°. With the changing conformations of the equatorial groups the axial bond lengths are varied. Even though the compounds had constitutionally identical S—Cl bonds at certain torsional angles of the equatory ligands the two S—Cl bond lengths became unequal. The difference between the two bond lengths was used as a measure of the extent of unevenness of the sulfurane structures. This led to the creation and annihilation of certain critical points on the conformational Potential Energy Surfaces.

The duodecet rule: Part 3. Fluoro species of the third period elements

1992 ◽  
Vol 70 (6) ◽  
pp. 1696-1705 ◽  
Author(s):  
E. A. Robinson
Keyword(s):  
Bond Length ◽  
Molecular Species ◽  
Central Atom ◽  
Covalent Radius ◽  
Valence Shell ◽  
Single Bond ◽  
Electron Pairs ◽  
Bond Lengths ◽  
The Third

On the basis of the suggested new value of 54 pm for the single bond covalent radius of fluorine, the previously established duodecetrule for period 3 elements in molecular species with highly electronegative ligands is extended to fluorides. It is shown, for species such as SiF4, (F3Si)2O, F3SiNH2, F3PO, and PF5, that the observed bond lengths are consistent with significant partial double bonding involving all the ligands, including fluorine, and with a total of six electron pairs in the valence shell of the central atom. Empirical rules based on d/d1, the ratio of an observed bond length to the corresponding single bond length calculated from the sum of covalent radii, are developed as a simple approximate guide to the extent of partial double bonding in bonds to third period elements. It is also shown that bond lengths in species such as Al2F5, AlO45−, and Al(NH2)4− are consistent with a duodecet rule.

ELECTRON CORRELATION AND MOLECULAR SHAPE

1960 ◽  
Vol 38 (6) ◽  
pp. 818-826 ◽  
Author(s):  
R. J. Gillespie
Keyword(s):  
Electron Correlation ◽  
Polyatomic Molecule ◽  
Central Atom ◽  
Molecular Shape ◽  
Electron Pairs ◽  
Bond Lengths ◽  
Inverse Square Law ◽  
Lone Pairs ◽  
Electrostatic Repulsions

It is proposed that the arrangements of the electron pairs in the valency shell of a central atom of a polyatomic molecule can be predicted by considering the equilibrium arrangements of similar particles on the surface of a sphere with an appropriate law of force between the particles. The arrangements resulting from an inverse square law of force, corresponding to electrostatic repulsions, and a force which is proportional to 1/rn where n is large, corresponding to Pauli forces, are considered specifically. It is shown that the arrangements predicted agree with those found experimentally for molecules containing only non-transitional elements. The possible arrangements for seven, eight, and nine pairs of electrons in a valency shell are discussed in detail. A method is suggested for predicting the arrangements of electron pairs in valency shells containing lone pairs which can occupy alternative non-equivalent positions. The effect of the interactions of electron pairs on bond lengths in certain molecules is discussed. The extension of the same principles to molecules containing transitional elements is briefly outlined.

scholarly journals Cosmic space and Pauli exclusion principle in a system of M0-branes

2017 ◽  
Vol 14 (06) ◽  
pp. 1750095 ◽  
Author(s):  
Salvatore Capozziello ◽  
Emmanuel N. Saridakis ◽  
Kazuharu Bamba ◽  
Alireza Sepehri ◽  
Farook Rahaman ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Scalar Fields ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Gauge Fields ◽  
High Symmetry ◽  
Cosmic Space ◽  
The Difference ◽  
The One ◽  
The Universe

An emergence of cosmic space has been suggested by Padmanabhan [Emergence and expansion of cosmic space as due to the quest for holographic equipartition, arXiv:hep-th/1206.4916] where he proposed that the expansion of the universe originates from a difference between the number of degrees of freedom on a holographic surface and the one in the emerged bulk. Now, a natural question that arises is how this proposal would explain the production of fermions and an emergence of the Pauli exclusion principle during the evolution of the universe? We try to address this issue in a system of [Formula: see text]-branes. In this model, there is a high symmetry and the system is composed of [Formula: see text]-branes to which only scalar fields are attached that represent scalar modes of the graviton. Then, when [Formula: see text]-branes join each other and hence form [Formula: see text]-branes, this symmetry is broken and gauge fields are formed. Therefore, these [Formula: see text]-branes interact with the anti-[Formula: see text]-branes and the force between them leads to a break of a symmetry such as the lower and upper parts of these branes are not the same. In these conditions, gauge fields which are localized on [Formula: see text]-branes and scalars which are attached to them symmetrically, decay to fermions with upper and lower spins which attach to the upper and lower parts of the [Formula: see text]-branes anti-symmetrically. The curvature produced by the coupling of identical spins has the opposite sign of the curvature produced by non-identical spins which lead to an attractive force between anti-parallel spins and a repelling force between parallel spins and hence an emergence of the Pauli exclusion principle. By approaching [Formula: see text]-branes to each other, the difference between curvatures of parallel spins and curvatures of anti-parallel spins increases, which leads to an inequality between the number of degrees of freedom on the surface and the one in the emerged bulk and hence lead to an occurrence of the cosmic expansion. By approaching [Formula: see text]-branes to each other, the square of the energy of the system becomes negative and hence tachyonic states arise. To remove these states, [Formula: see text]-branes compactify, the sign of gravity changes and anti-gravity emerges which leads to the branes moving away from each other. By joining [Formula: see text]-branes, [Formula: see text]-branes are produced which are similar to an initial system that oscillates between compacting and opening branches. Our universe is placed on one of these [Formula: see text]-branes and by changing the difference between the amount of couplings between identical and non-identical spins, it contracts or expands.

Stereospecific reactions of aryltellurium(IV) trichlorides with 3-cyclohexene-1-methanol and 3-cyclohexene-1,1-dimethanol: the X-ray crystal structure of 2′,4′-dimethoxyphenyl(trans-6-oxabicyclo[3.2.1]oct-4-yl)tellurium(IV) dichloride

1995 ◽  
Vol 73 (2) ◽  
pp. 255-263 ◽  
Author(s):  
Bozena Borecka ◽  
T. Stanley Cameron ◽  
M. Azad Malik ◽  
Barry C. Smith
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Lone Pair ◽  
Monoclinic Space Group ◽  
Space Group ◽  
X Ray ◽  
Bond Lengths ◽  
Trigonal Bipyramidal ◽  
Compound C ◽  
Stereospecific Reactions

Aryltellurium(IV) trichlorides react with 3-cyclohexene-1-methanol and 3-cyclohexene-1,1-dimethanol to give aryl(trans-6-oxabicyclo[3.2.1]oct-4-yl)tellurium(IV) dichlorides and aryl(cis-1-hydroxymethyl-trans-6-oxabicyclo[3.2.1]oct-4-yl)tellurium(IV) dichlorides. The structure of 2′,4′-dimethoxyphenyl(trans-6-oxabicyclo[3.2.1]oct-4-yl)tellurium(IV) dichloride has been determined by single crystal X-ray analysis. The compound C15H20Cl2O3Te, Mr = 446.8, crystallizes in the monoclinic space group P21/c with a = 9.626(2) Å, b = 15.768(5) Å, c = 11.176(3) Å, β = 92.08(1)°, V = 1695.2(5) Å3 and D(calc) = 1.751 for Z = 4. Tellurium is bonded axially to two chlorines and equatorially to aryl carbon and carbon from the cyclohexyl portion of oxabicyclo[3.2.1]oct-4-yl in a pseudo-trigonal-bipyramidal arrangement having an equatorial lone pair of electrons. Bond lengths are Te—Cl(1) = 2.492(3) Å, Te—Cl(2) = 2.539(3) Å, Te—C(4) = 2.175(10) Å, and Te—C(9) = 2.090(10) Å. Keywords: organotellurium(IV), 3-cyclohexene-1-methanol, 3-cyclohexene-1, 1-dimethanol.

Die Kristallstrukturen von PPh4[AsCl4(THF)2] und PPh4[AsBr4(THF)2] / The Crystal Structures of PPh4[AsCl4(THF)2] and PPh4[AsBr4(THF)2]

1992 ◽  
Vol 47 (5) ◽  
pp. 680-684 ◽  
Author(s):  
Birgit Siewert ◽  
Ulrich Müller
Keyword(s):  
Crystal Structures ◽  
Uv Irradiation ◽  
Octahedral Coordination ◽  
Trans Configuration ◽  
X Ray Diffraction ◽  
Electron Pairs ◽  
X Ray ◽  
Bond Angles ◽  
Bond Lengths ◽  
Stereochemical Activity

In the effort to react W(CO)6 with (PPh4)2[As2Cl8] and Cr(CO)6 with PPh4[As2SBr5] in tetrahydrofurane under UV irradiation the title compounds were obtained as main products. Their crystal structures were determined by X-ray diffraction. PPh4[AsCl4(THF)2], monoclinic, P2/c, Z = 2, a = 881.6(3), b = 809.0(6), c = 2418.6(9) pm, β = 99.44(4)°, R = 0.086 for 1619 observed unique reflexions. PPh4[AsBr4(THF)2], monoclinic, C 2/c, Z = 4, a = 2459.2(5), b = 748.2(3), c = 1784.3(4) pm, β = 94.02(2)°, R = 0.080 for 1513 reflexions. In both compounds ions [AsX4(THF)2]- are located on inversion centers; they have octahedral coordination with trans configuration; the stereochemical activity of the lone electron pairs does not show up in deviations of the bond angles, but in increased bond lengths. The PPh4+ ions are stacked to columns in the b direction.

Ab initio 3-21 G Calculations of Push-Pull Interactions of Substituents at Imino-Nitrogen in Formamidines. Non-Equivalence of NO-Bonds of the Nitro-Substituent

1992 ◽  
Vol 47 (10) ◽  
pp. 1480-1490 ◽  
Author(s):  
Günter Häfelinger ◽  
Tadeusz Marek Krygowski ◽  
Frank K. H. Kuske
Keyword(s):  
Charge Density ◽  
Ab Initio ◽  
Amino Nitrogen ◽  
Lone Pair ◽  
Molecular Structures ◽  
Electron Charge Density ◽  
Imino Nitrogen ◽  
Bond Lengths ◽  
Mechanism Of Interaction ◽  
The Difference

Full ab initio 3-21 G optimization of molecular structures of twelve planar formamidines substituted by X in Ε-configuration at imino nitrogen (N2) (X = H, CH3, NH2, C6H5, OH, F, CHO, CN, BH2, NO (four isomers), NO2 (planar and perpendicular conformations), and CH2+) yielded the following conclusions: (1) as was found earlier experimentally, an increase of the shorter CN2 bond lengths is associated linearly with a decrease of the longer CN1 bond; (2) the difference of both CN distances (Δ CN) is related linearly to the Mulliken π-electron charge density at amino nitrogen (N1); (3) a decrease of Mulliken π-charge density (Δ qπ) at N1 is linearly related to a corresponding increase of Δ qπ at N2. The scatter and a slope of –0.54 indicate a mixed mechanism of interaction between NH2 and the substituents at amino nitrogen composed of n-π-conjugation and through conjugation; (4) an increase of σ-charge density at H2 is correlated with an increase of N1 – H2 bond lengths. As a result of interaction between the lone pair at N2 and the cis-bond of the nitro substituent this bond is calculated to be significantly shorter than the other one by 0.042 A. The same effect is calculated for the E-isomer of C-nitro substituted formamidine (Δ = 0.037 A) in contrast to the corresponding Z-isomer (Δ = 0.004 Å). A selection of experimental X-ray determinations of nitro-substituted compounds confirm this effect.

Hardness and HOMO-LUMO Gap Probed by the Helium Atom Pushing the Molecular Surface of the First-Row Hydride Molecules

2003 ◽  
Vol 68 (12) ◽  
pp. 2344-2354 ◽  
Author(s):  
Edyta Małolepsza ◽  
Lucjan Piela
Keyword(s):  
Helium Atom ◽  
Pauli Exclusion Principle ◽  
Structure Change ◽  
Molecular Surface ◽  
Exclusion Principle ◽  
Probe Position ◽  
Repulsion Energy ◽  
Ionic Dissociation ◽  
Probe Site ◽  
Homo Lumo

A molecular surface defined as an isosurface of the valence repulsion energy may be hard or soft with respect to probe penetration. As a probe, the helium atom has been chosen. In addition, the Pauli exclusion principle makes the electronic structure change when the probe pushes the molecule (at a fixed positions of its nuclei). This results in a HOMO-LUMO gap dependence on the probe site on the isosurface. A smaller gap at a given probe position reflects a larger reactivity of the site with respect to the ionic dissociation.

Identical Particles and Second Quantization: Occupation Number Representation

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Occupation Number ◽  
Annihilation Operator ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Number Representation ◽  
Second Quantization ◽  
Identical Particles ◽  
Fundamental Properties ◽  
Minimum Uncertainty ◽  
Creation Operators

Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized into “creation” and “annihilation” operators, whose fundamental properties and commutation/anticommutation relations are derived in conjunction with the Pauli exclusion principle. This leads to “second quantization” with the Hamiltonian, number, linear and angular momentum operators expressed in terms of the annihilation and creation operators, as well as the occupation number representation. Finally, the concept of coherent states, as eigenstates of the annihilation operator, having minimum uncertainty, is introduced and discussed in detail.

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