Molecular Geometry & Bonding
what the shape decides
Depth

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.
Chains of 2, 4, 8, 16, 40: the levels crowd, the edges do not move. Every level of a chain of 2, 4, 8, 16, 40 sites, drawn at its computed energy on one axis. Adding sites adds levels inside a fixed interval rather than widening it, which is what makes the large system a band rather than a wider molecule.

Bands in a solid

  1. 1 A solid is a molecule that did not stop
  2. 2 The width of a band is a count of neighbours
  3. 3 A density of states is not a spectrum
  4. 4 A band with no structure in it
  5. 5 Where a molecule stops being one
  6. +9 more
14 essays · solids 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. +9 more
14 essays · solids What the group settles. For each molecule, the point group found from its coordinates and the two properties that follow from the group alone. Neither column required knowing anything about the bonds.

Dipole

  1. 1 The dipole is not a sum of bonds
  2. 2 One coordinate, three point groups
  3. 3 What a dipole cannot tell apart
  4. 4 The lone pair is not the missing term
  5. 5 Zero dipole is not no interaction
  6. +9 more
14 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. +9 more
14 essays · bonding A d shell in an octahedral field. The five d energies in octahedral coordination, computed and drawn in units of the octahedral splitting. The dashed line is the barycentre, which the five levels sum to whatever the arrangement.

Ligand field

  1. 1 The splitting is a symmetry statement
  2. 2 Two models, one ratio
  3. 3 The spectrochemical series is not electrostatics
  4. 4 Where a d–d band falls
  5. 5 The double hump and what removes it
  6. +9 more
14 essays · applied Splitting goes with overlap. For each pair, the atomic levels on the outside and the combinations they form in the middle, with the splitting drawn in proportion to the computed overlap. A pair that symmetry forbids does not split at all, because its overlap is exactly zero.

Models

  1. 1 Molecular orbital and valence bond
  2. 2 Where molecular orbital theory dissociates
  3. 3 Two pictures, one plane
  4. 4 A weight that depends on how it is weighed
  5. 5 One spectrum, a line of models
  6. +9 more
14 essays · bonding The largest angle each ring size can have. The ceiling on a bond angle in a closed ring of equal bonds, 180°(n−2)/n, which is the interior angle of the regular planar polygon and follows from a closed curve having to turn through a full circle. The line at 109.47° is the tetrahedral angle: rings of 3, 4, 5 atoms cannot reach it at any geometry whatever, and every larger ring can, by leaving the plane.

Strain

  1. 1 The angle a ring cannot have
  2. 2 The ring that cannot hold still
  3. 3 The double bond a ring cannot hold
  4. 4 The strain that is not in the angles
  5. 5 The atoms that meet across a ring
  6. +9 more
14 essays · shape 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. +8 more
13 essays · bonding 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. +8 more
13 essays · solids 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. +7 more
12 essays · solids 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. +6 more
11 essays · shape

All essays