Molecular Geometry & Bonding
what the shape decides
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Series — page 2

A field says what an essay is about. A series follows one idea essay by essay — from the question that introduces it to the one that assumes all the others.
Four scales, four orderings. Each column ranks the elements by one electronegativity scale, most electronegative at the top, with a line joining each element across the columns. Every crossing is a pair of elements that two scales order differently.

Electronegativity

  1. 1 Electronegativity is not one quantity
  2. 2 A ranking is not a difference
  3. 3 A difference does not make a transfer
  4. 4 The quantity no scale prints
  5. 5 The value that only exists in the bond
  6. +8 more
13 essays · wrong sp3 hybrids. The directions the hybrids point, with the angle between them computed from the coefficients rather than quoted. The set is an orthogonal transformation of the atomic orbitals, so it describes the same space in different coordinates.

Hybrids

  1. 1 Hybrids are a basis
  2. 2 Hybridisation does not explain
  3. 3 The localisation transformation, demonstrated
  4. 4 The angle does not fix the hybridisation
  5. 5 Hybrids that were never orthogonal
  6. +8 more
13 essays · bonding The 2pz orbital. The 2pz orbital at the contour enclosing 90 per cent of its density — a level solved for by integration rather than chosen. The two colours are the two signs of the wavefunction, which is what distinguishes a bonding interaction from an antibonding one. Contours drawn: 2pz at 90% of its density, |ψ| = 9.48e-3.

Orbital

  1. 1 What an orbital is
  2. 2 Nodes
  3. 3 Where the electron is
  4. 4 The radial distribution across the periodic table
  5. 5 Complex harmonics against real ones
  6. +8 more
13 essays · orbitals A chain of 100 is more stable alternating. The electronic energy gained by alternating the bonds of a half-filled chain, the elastic cost of doing it, and their sum, all per site and all against the alternation. The sum has its best value away from zero, so the evenly spaced chain is not the stable structure.

Peierls distortion

  1. 1 A chain cannot stay even
  2. 2 The gap is not the band width
  3. 3 Copper is never quite octahedral
  4. 4 The distortion the filling chooses
  5. 5 A distortion needs two states
  6. +8 more
13 essays · solids A half-filled ring's cheapest excitation goes to zero. The energy of the smallest available excitation of a half-filled ring, against the number of atoms, on log axes. Every doubling at least halves it, so in the limit there is no smallest excitation — which is what a metal is, before any band picture is drawn.

Metal

  1. 1 What a metal actually is
  2. 2 Counting electrons in an extended structure
  3. 3 A half-filled band is not always a metal
  4. 4 The insulator band theory cannot see
  5. 5 A full band is not an insulator
  6. +7 more
12 essays · solids Orbitals at the 90 per cent contour. Several orbitals drawn at the same enclosed fraction and, unless stated otherwise, at the same scale — so the sizes on the page are the sizes. Each contour was solved for separately by integrating that orbital's own density. Contours drawn: 1s at 90% of its density, |ψ| = 3.94e-2; 2s at 90% of its density, |ψ| = 7.40e-3; 2pz at 90% of its density, |ψ| = 9.48e-3.

Approximation

  1. 1 Orbitals are not where the electron is
  2. 2 The aufbau order is not a property of the atom
  3. 3 A better energy is not a better answer
  4. 4 The atoms are not at the points
  5. 5 The bond length that depends on the isotope
  6. +6 more
11 essays · wrong What holds matter together, per pair. Four kinds of interaction between two units of matter, each computed from the model named beside it, on a logarithmic energy scale. The range from top to bottom is a factor of several hundred, which is the number behind why a molecular solid melts hundreds of degrees below a covalent one.

Cohesion

  1. 1 What holds a solid together
  2. 2 The lattice sum that depends on the order of adding
  3. 3 The bond that weakens as neighbours multiply
  4. 4 A surface is not a count of broken bonds
  5. 5 Two structures with the same neighbours
  6. +6 more
11 essays · solids Two sites, two electrons, every level exactly. The four states of a two-site Hubbard model against the on-site repulsion, in units of the hopping. The left-hand edge is the one-electron answer — -2t — and the dashed line is the lowest state with the spins parallel, which cannot hop at all and so does not move with U.

Correlation

  1. 1 The smallest many-electron calculation
  2. 2 The hole that is not repulsion
  3. 3 A method that is not additive
  4. 4 Two kinds of correlation, and only one is small
  5. 5 A third kind of correlation
  6. +6 more
11 essays · bonding The state on a defect at site 31 of 60. The amplitude of one eigenvector at each site of a 60-site chain whose site 31 has its energy raised by 1.6β. The two colours are the two signs. A state belonging to the whole chain would reach across it; this one does not.

Defect

  1. 1 A defect is a level in the gap
  2. 2 The end is the hardest place to bind
  3. 3 Two defects, and the level between them
  4. 4 A vacancy is not an impurity
  5. 5 One defect is a level, many are a band
  6. +6 more
11 essays · solids 4 sites, minimised. The arrangement of 4 points on a sphere that minimises their mutual repulsion. The angles printed were measured off the result rather than quoted, and the shape was not assumed.

VSEPR

  1. 1 VSEPR, computed
  2. 2 Five sites are not alike
  3. 3 Why water is bent
  4. 4 The shapes above six coordination
  5. 5 Bent's rule, against the substituent series
  6. +5 more
10 essays · shape NH₃: four states in a well the molecule does not sit at the bottom of. The umbrella coordinate of NH₃ — the signed distance of the N atom from the plane of its three H atoms — with the quartic well that has its minima at the measured 0.3816 ångström and its barrier at the quoted 2020 wavenumbers. The lowest 4 states are drawn at their computed energies. The lowest sits 587 wavenumbers above the bottom, which is 29.1 per cent of the way up the barrier, so the state is far from the harmonic bottom that a drawing of a pyramid implies.

Inversion

  1. 1 A barrier is not what a splitting measures
  2. 2 The exponent that runs both ways
  3. 3 It was never the mass
  4. 4 The mass nobody chose
  5. 5 An ordering worth half a per cent
  6. +3 more
8 essays · shape

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