Recently added

What's new

Essays arrive in groups rather than one at a time. The most recent group is below in full, and every earlier one after it, newest first.

Essays arrive in groups rather than one at a time, and a group usually opens up a subject not covered before. Between one group and the next nothing changes, so a reader who has seen the most recent group has seen everything.

1 November 2026

3 essays on when the molecule does not stop, bonding models and where the atoms go

Freeing the chain's length leaves every tail exponent where it was. The tail exponent p of a two-ended fit A·b^(−p)·e^(−b/λ) from bond 6, at ten stiffnesses, for the chain whose total length is held fixed and for the chain at zero tension. The fixed chain's middle is compressed by an amount that goes as one over its length; the free chain's is not compressed at all. The exponents differ by at most 0.0009 — the constraint was never in them.

When the molecule does not stop

The chain that pays for nothing

Held to a fixed length, a Peierls chain pays for its ends' extra alternation with a compression of every bond. Let the length go and nothing is paid: the middle is the free infinite chain to twelve figures, the ends adjust locally — and every tail exponent comes out where the fixed chain put it, to under a thousandth. The constraint was never in the exponents. Nor is the drift in them a missing 1/b term: fitting one makes the exponent wander three times further.

7 figures

Along the series one pair crosses the boundary, and it is the one nobody asks about. The two-orbital criterion's margin for each pair of the carbonyl-type trio as the heteroatom runs through carbon, nitrogen, oxygen and fluorine at one bond length. Above one the mixed description wins. The σ–π margin falls from far off the scale to 1.179 and never reaches the boundary; the π–n margin rises from 0.470 to 1.350 and crosses it between oxygen and fluorine. The σ–n margin is drawn faint because the criterion does not apply to that pair at all.

Bonding models

A verdict that flips and changes nothing

Run the two-orbital mixing criterion along H₂C=CH⁻, H₂C=NH, H₂C=O and H₂C=F⁺ and one pair finally crosses its boundary — the π and the lone pair, a third of the way from oxygen to fluorine. It is the first real test the criterion has had, and the localised orbitals on the far side of it are the ones on the near side: two bent bonds and a lone pair that stays itself.

7 figures

With the bonds free to stretch, which three are long depends on where the lone pair goes. The near three bonds' mean length over the far three's, minus one, against the lone-pair weight, with every bond on a spring of stiffness 20 and the six bonds stretched by about 8.7%. If the lone pair keeps its place among the bonds the long three are opposite the face below a weight of 0.725, as with lengths fixed by hand. If it stays where it was, or sits on a bond's spring, the long three are round the face across that range instead.

Where the atoms go

The lone pair has no bond to stretch

Put every one of xenon hexafluoride's bonds on a spring and let the repulsion set the six lengths, and which three come out long is decided by something the model has never had to say: how far from the xenon the lone pair sits once the bonds have moved. Three equally defensible answers give three different verdicts — and none of them produces a split within a factor of twenty of the measured one without stretching every bond beyond recognition.

6 figures

Before that

Everything published earlier, newest first. Titles only — the cards are on the full listing.

26 October 2026

6 essays on when the molecule does not stop, what the shape is for, what is taught wrongly, bonding models, beyond the octet and where the atoms go

The disc was a band with holes in it — when the molecule does not stop
The pair fold was the road to a tetrahedron — what the shape is for
The worst case measured the reference — what is taught wrongly
The angular factor belongs to the chain — bonding models
On an angular ring the carbon decides — beyond the octet
The model lengthens the wrong three — where the atoms go

14 October 2026

3 essays on what a spectrum settles, what symmetry decides and orbitals

The Coriolis constant was an isotope shift — what a spectrum settles
Two Coriolis constants are one number — what symmetry decides
The node a nodeless orbital has — orbitals

6 October 2026

2 essays on bonding models and orbitals

A root that moves when nothing else does — bonding models
The minimum belongs to the heavy atom's node — orbitals

3 October 2026

4 essays on what symmetry decides, what the shape is for, what a spectrum settles and what is taught wrongly

Potassium's turn was a fine-structure question — what symmetry decides
The blindness needed a single top level — what the shape is for
The fourth constant chose a curve, not a depth — what a spectrum settles
The limit was two chains at once — what is taught wrongly

30 September 2026

4 essays on when the molecule does not stop, what symmetry decides, where the atoms go and beyond the octet

The residual was the stiffness — when the molecule does not stop
The worst case was the loosest constant — what symmetry decides
A lone pair weaker than a bond — where the atoms go
Priced against the whole bond — beyond the octet

28 September 2026

7 essays on what a spectrum settles, what the shape is for, what is taught wrongly, bonding models, beyond the octet, where the atoms go and orbitals

The pyramid trades its pairs — what a spectrum settles
The spacing sets the constant — what the shape is for
Two measurements leave nothing to fit — what is taught wrongly
The agreement was hydrogen's energy — bonding models
Only a steep contact makes five square — beyond the octet
The lone pair goes through a face — where the atoms go
The lone pair sits where the floor was — orbitals

27 September 2026

4 essays on when the molecule does not stop, what symmetry decides, bonding models and beyond the octet

A ring is not the bulk — when the molecule does not stop
The shell was the wrong unit — what symmetry decides
Six electronvolts was a difference — bonding models
Five ligands, and no ideal to aim at — beyond the octet

25 September 2026

4 essays on when the molecule does not stop, what is taught wrongly, where the atoms go and orbitals

No moment sees the winner change — when the molecule does not stop
A repulsion the proton does not have — what is taught wrongly
The fluorines' range decides the ring — where the atoms go
The third function fills the floor — orbitals

24 September 2026

6 essays on what symmetry decides, what the shape is for, what a spectrum settles, bonding models and beyond the octet

Three ways to stretch a bond — what symmetry decides
The threshold belongs to the atom — what symmetry decides
The window sets the constant — what the shape is for
Three constants, two potentials — what a spectrum settles
Spin below zero — bonding models
What a missing orbital costs — beyond the octet

23 September 2026

11 essays on what the shape is for, when the molecule does not stop, what a spectrum settles, what is taught wrongly, bonding models, beyond the octet, where the atoms go and orbitals

Four lifts and one that matters — what the shape is for
The rate that turned back — when the molecule does not stop
The third mass that cannot help — what a spectrum settles
The excitation that raises the spin — what the shape is for
What a linewidth leaves of the probe — what a spectrum settles
The worst system in the square was the solver's — what is taught wrongly
Two changes that do not add — bonding models
The count needed no table — beyond the octet
The cage that averages like a sphere — beyond the octet
The ring held flat by its long bonds — where the atoms go
The shortfall was a length, not a strength — orbitals

20 September 2026

14 essays on when the molecule does not stop, what symmetry decides, what the shape is for, what a spectrum settles, what is taught wrongly, bonding models, where the atoms go and orbitals

The commonest runs reach it in a grain — when the molecule does not stop
The two coordinates a square plane was missing — what symmetry decides
A plane spends the same reach on a disc — when the molecule does not stop
Half the distance from a coin — what symmetry decides
One was a symmetry and one was not — what the shape is for
The shape was the group and the size was not — what a spectrum settles
The arms were the kindest part of the square — what is taught wrongly
A blank is not a pass — what is taught wrongly
A cancellation between two separations — bonding models
The same fraction at six times the barrier — where the atoms go
The band that cannot supply what it changes — where the atoms go
The pair that cancels only at zero overlap — orbitals
The steps were a square root of a mass — where the atoms go
A floor no charge transfer explains — orbitals

17 September 2026

19 essays on what symmetry decides, when the molecule does not stop, what a spectrum settles, what the shape is for, what is taught wrongly, bonding models, beyond the octet, where the atoms go and orbitals

Four alkalis the model cannot hold — what symmetry decides
The gap follows the winner late — when the molecule does not stop
The residual was a loop — what a spectrum settles
Purity renames the poles — what the shape is for
The census a bond rule was hiding — what symmetry decides
The share that was read as a line — when the molecule does not stop
Two coefficients are not a potential — what a spectrum settles
Five more clusters break the band — what the shape is for
The rule is not the lever — what is taught wrongly
Two integers made one exponent — what a spectrum settles
The limit of one is a parity — what is taught wrongly
The spin the count does not hold — bonding models
The scatter counts angular rings — bonding models
An angular ring rescales what lies beyond it — beyond the octet
The long bond goes to the crowded site — where the atoms go
The zero belongs to one determinant — orbitals
Folding the ring does not give the orbital back — beyond the octet
The zero is a parity, not a bond — orbitals
Length did not rescue the consecutive triples — orbitals

16 September 2026

19 essays on what is taught wrongly, what symmetry decides, what a spectrum settles, when the molecule does not stop, what the shape is for, bonding models, beyond the octet, orbitals and where the atoms go

Six of fifteen change verdict — what is taught wrongly
The quarter, generalised — what symmetry decides
The second molecule with a blind spot — what a spectrum settles
A net with no two-colouring — when the molecule does not stop
Adding data made it worse — what a spectrum settles
No length separates them — what symmetry decides
The correction that moves three of them backwards — what the shape is for
A size the fit was not made from — what is taught wrongly
The channel that points at the metal — what the shape is for
Four quantities go and one question stays — what is taught wrongly
Three chains and ninety orderings ruled out — bonding models
A denominator needs three currencies — bonding models
A floor on models written in one scale — bonding models
Six disagreements and three calculations — beyond the octet
The nodes in the other variable — orbitals
The two that are not on the line — where the atoms go
Oblate in the picture nobody draws — orbitals
The basis a diagonaliser happened to return — beyond the octet
The ordering a manifold picks — where the atoms go

13 September 2026

9 essays on what symmetry decides, what a spectrum settles, what is taught wrongly, what the shape is for, bonding models, where the atoms go and orbitals

The crossing nothing couples — what symmetry decides
The cubic a Morse curve guesses — what a spectrum settles
No panel of this kind can find an exception — what is taught wrongly
Two levels cannot make a minimum — what symmetry decides
The sign rule holds between two poles — what the shape is for
A level no symmetry was protecting — bonding models
An ordering worth half a per cent — where the atoms go
Deuterium cannot tell the masses apart — where the atoms go
Three contractions for one shell — orbitals

12 September 2026

5 essays on what symmetry decides and orbitals

Five coordinates for six vibrations — what symmetry decides
The overshoot was one arrangement — orbitals
A repair that costs more than the whole — orbitals
The sum of the exponents, not the softer ion — orbitals
One contraction for two conditions — orbitals

11 September 2026

13 essays on what symmetry decides, what the shape is for, where the atoms go and beyond the octet

The variation was the basis — what symmetry decides
Consistently wrong is not a limit — what symmetry decides
The frustrated cluster with an even count — what the shape is for
A blindness that is inherited — what the shape is for
A barrier is not what a splitting measures — where the atoms go
The exponent that runs both ways — where the atoms go
It was never the mass — where the atoms go
The mass nobody chose — where the atoms go
The lever that was supposed to be smaller — where the atoms go
The cage is on both sides — beyond the octet
Two sweeps and one lever — where the atoms go
The leftover changes sides — beyond the octet
The gap found on purpose — beyond the octet

8 September 2026

50 essays on where the atoms go, beyond the octet, orbitals, what the shape is for, bonding models, what a spectrum settles, what symmetry decides, what is taught wrongly and when the molecule does not stop

A dispute is a small difference — where the atoms go
One number decides which way it breaks — where the atoms go
Expensive is not the same as unadopted — beyond the octet
The correction that gets harder to assemble — orbitals
A gap that was a choice of bonds — where the atoms go
The ligand the rule was waiting for — what the shape is for
Fifty descriptions of one molecule — beyond the octet
One basis size where it is worth doing — orbitals
The distortion that opens the gap — what the shape is for
The reach is the molecule's — bonding models
A sign change is not always a zero — beyond the octet
The residue is below its own noise — orbitals
The overlap the model is not proportional to — what the shape is for
A ratio of exactly one is a tie — what a spectrum settles
Four angles the shell chooses — what symmetry decides
The error bar that would be needed — bonding models
A count that changes at one point — beyond the octet
The sign a frustrated ring changes — what the shape is for
The distortion the ratio cannot see — what a spectrum settles
None of the six was a crossing — what symmetry decides
The five figures were an identity — bonding models
Counting was right except where it mattered — beyond the octet
The group nobody wrote a table for — beyond the octet
The second number is the error, rearranged — what is taught wrongly
The number the tie got right — what a spectrum settles
The other end of the bracket is not a number — bonding models
A contraction that cannot reach three of them — what the shape is for
The count the table was hiding — beyond the octet
The exponent was the floor — when the molecule does not stop
A correlation is not an account — what is taught wrongly
It was the count, not the frustration — what the shape is for
One number was a direction too — what a spectrum settles
A bend is not an end — bonding models
The count that was never written down — where the atoms go
Five rings that were five different sizes — when the molecule does not stop
Five failures in five different places — what is taught wrongly
The sum was flat all along — what a spectrum settles
The direction the gap cannot see — what the shape is for
The suspect that did not fit — what a spectrum settles
The worst of the six was the one we asked about — what is taught wrongly
The rule of thumb was on the flat part — when the molecule does not stop
The window that was not a plateau — when the molecule does not stop
Three points, and they all go down — when the molecule does not stop
Two numbers caught what one could not — where the atoms go
The other window was a plateau too — when the molecule does not stop
The line was holding the answer up — orbitals
The ranking moved and the headline did not — bonding models
The error was the row, not the charge — orbitals
The criterion that has never said no — bonding models
A second criterion left a gap too — beyond the octet

5 September 2026

10 essays on what a spectrum settles, what symmetry decides, when the molecule does not stop and what is taught wrongly

Two moments about two different lines — what a spectrum settles
An end effect with two signs — what symmetry decides
Seven points that looked like a switch — when the molecule does not stop
The term a harmonic field cannot produce — what a spectrum settles
One integer, and everything it changes — what symmetry decides
The triangles that were never in the bands — when the molecule does not stop
A filled shell is not an empty statement — what is taught wrongly
A count rather than an average — when the molecule does not stop
A symmetry holds or it does not — what is taught wrongly
The composition that is hard is not the full one — when the molecule does not stop

1 September 2026

20 essays on where the atoms go, orbitals, beyond the octet, what a spectrum settles, what symmetry decides, when the molecule does not stop, what the shape is for, what is taught wrongly and bonding models

Four tables and one molecule to disagree about — where the atoms go
A verdict inside its own error bar — where the atoms go
The assembly that counts one share twice — orbitals
The give-back that turned into a saving — beyond the octet
A contrast with a closed form — what a spectrum settles
Neither of the two separations — what symmetry decides
The constant that belonged to one net — when the molecule does not stop
The gap that only a tetrahedron closes — what the shape is for
The residue that is two numbers — orbitals
Three shapes from one search — beyond the octet
A denominator that fails both ways — what the shape is for
The amplitude the collapse left behind — what is taught wrongly
The axis that goes the other way — what a spectrum settles
The floor was in the bookkeeping — bonding models
Three events, and a ratio of two dipoles — what symmetry decides
Twelve basins where there were two — when the molecule does not stop
A band that is a hundred and seventy decades of nothing — when the molecule does not stop
An interior maximum a third orbital allows — bonding models
The half of the square a ring of four cannot show — what is taught wrongly
A bond order between atoms that do not interact — what is taught wrongly

31 August 2026

20 essays on where the atoms go, orbitals, what a spectrum settles, what the shape is for, beyond the octet, when the molecule does not stop, what symmetry decides, bonding models and what is taught wrongly

The curve between two rows — where the atoms go
A size a confound cannot supply — orbitals
The forty-five that are fixed — what a spectrum settles
The product a curve measures — what the shape is for
The square that wastes an orbital — beyond the octet
A decay that keeps slowing down — when the molecule does not stop
A formula that predicts minus eleven vibrations — what symmetry decides
An expression for what was a warning — what a spectrum settles
The half that cannot be computed — orbitals
The orbital a ligand cannot reach — what the shape is for
The pair that is not a tie — bonding models
Where the count stops being an effort — beyond the octet
A bond with nothing in the middle — bonding models
A capacity that is largest where there is none — what is taught wrongly
One number was one direction — what a spectrum settles
The gap that would have to be smaller — what the shape is for
The length at which levels become a band — when the molecule does not stop
Two events where there was one — what symmetry decides
A satellite that never loses its place — what is taught wrongly
The node that decided a picture — bonding models

30 August 2026

20 essays on orbitals, bonding models, where the atoms go, what the shape is for, what symmetry decides, what a spectrum settles, beyond the octet, what is taught wrongly and when the molecule does not stop

A control that outranked the mechanism — orbitals
An anomaly that is not the first of a series — bonding models
An estimate that can be wrong by two — where the atoms go
How many parameters a curve is worth — what the shape is for
Ten directions no frequency can see — what symmetry decides
The correction that was invented — what a spectrum settles
Two models that disagree about the shape — beyond the octet
A correction that is two functions — orbitals
A label that prices nothing — what symmetry decides
Half of it is given back at one bond — beyond the octet
The boundary belongs to the gap — what a spectrum settles
The count that cannot be broken by strength — what the shape is for
The exponent was the window's — what is taught wrongly
Two systems a model cannot tell apart — bonding models
Two ways of being second order — when the molecule does not stop
A particle in a box the alloy made — when the molecule does not stop
A reach that has no length — what symmetry decides
The angle that does not have to be searched for — bonding models
Where a closed form stops being one — what is taught wrongly
A regime that belongs to the neighbours — what is taught wrongly

28 August 2026

20 essays on where the atoms go, orbitals, what a spectrum settles, what is taught wrongly, bonding models, what the shape is for, beyond the octet, what symmetry decides and when the molecule does not stop

A ceiling that rises where the measurements fall — where the atoms go
A correction computed at one length — orbitals
A hundred lines and no way to sort them — what a spectrum settles
A mean that is low rather than right — what is taught wrongly
A parameter that never finds a value — bonding models
An integer nobody measured — what the shape is for
The answer a search is most likely to give — beyond the octet
The current does not divide — what symmetry decides
Two bands, if the chain is short enough — when the molecule does not stop
A ratio that squares what it measures — what a spectrum settles
How nearly a broken symmetry survives — what symmetry decides
The arrangement a count cannot pick — when the molecule does not stop
The hybrids that point outside the bonds — bonding models
The integral that cannot count electrons — what the shape is for
The surface a neighbour moves — orbitals
The table that could not have mattered — where the atoms go
The warning a cheap calculation gives — what is taught wrongly
Where the electrons are, without subtracting anything — beyond the octet
The carriers a distortion was hiding — what is taught wrongly
The chain distorts hardest where it stops — when the molecule does not stop

27 August 2026

15 essays on beyond the octet, what a spectrum settles, bonding models, what is taught wrongly, orbitals, when the molecule does not stop, what symmetry decides, what the shape is for and where the atoms go

How many descriptions a cage has — beyond the octet
The coordinate an isotope reports — what a spectrum settles
The frame that was allowed to relax — bonding models
The metal a thermometer cannot find — what is taught wrongly
The surface a table draws — orbitals
Two bands, and the shape of each — when the molecule does not stop
A mixture is not the average of its ends — when the molecule does not stop
More bands than there are orbitals — what a spectrum settles
The basis the other atom lent — orbitals
The coordinate it was already soft along — what symmetry decides
The correction that was computed somewhere else — what is taught wrongly
The count is the population — beyond the octet
The distortion the ends decide — what the shape is for
The explanation with the wrong sign — where the atoms go
The value that only exists in the bond — bonding models

26 August 2026

14 essays on where the atoms go, what symmetry decides, when the molecule does not stop, what a spectrum settles, beyond the octet, orbitals, what is taught wrongly, what the shape is for and bonding models

The mode that moves least radiates most — where the atoms go
Two rules that share no arithmetic — what symmetry decides
A band becomes a bell curve — when the molecule does not stop
A band is a filter on the modes — what a spectrum settles
More coordinates than motions — what symmetry decides
One scale, from two centres to a cage — beyond the octet
The radius that was tabulated — orbitals
The same overlap, a different bond — what is taught wrongly
The splitting against something structural — what the shape is for
Three bent bonds, and the same hybrid — where the atoms go
Which numbers carry a frame — bonding models
The model is what is fitted — what the shape is for
The one intensity symmetry does fix — what symmetry decides
Two distortions in one coordinate — where the atoms go

24 August 2026

15 essays on what symmetry decides, when the molecule does not stop, where the atoms go, orbitals, bonding models, beyond the octet, what is taught wrongly, what a spectrum settles and what the shape is for

How far, and along which coordinate — what symmetry decides
One defect is a level, many are a band — when the molecule does not stop
The atoms that meet across a ring — where the atoms go
The property that gets worse — orbitals
The quantity no scale prints — bonding models
The reference decides the correlation — beyond the octet
The third way to be an insulator — what is taught wrongly
The width of a band is a bond length — what a spectrum settles
Four is all that s and p can match — beyond the octet
One spectrum, a line of models — bonding models
The same count, two oxidation states — what the shape is for
The tenth that is not drawn — orbitals
Three numbers is not a structure — what a spectrum settles
Two structures with the same neighbours — when the molecule does not stop
Two wrong numbers and a right difference — what is taught wrongly

23 August 2026

15 essays on where the atoms go, beyond the octet, what a spectrum settles, what the shape is for, orbitals, what symmetry decides, bonding models and what is taught wrongly

A dipole is not what an infrared spectrum sees — where the atoms go
A stabilisation is measured from somewhere — beyond the octet
How much of a band is a bond stretch — what a spectrum settles
The count that is not always eighteen — what the shape is for
The measurement a basis was not fitted to — orbitals
The symmetry that is not a rotation — what symmetry decides
A bond is not two atoms overlapping — orbitals
A distortion needs two states — what the shape is for
A mean field cannot get out of the way — beyond the octet
A weight that depends on how it is weighed — bonding models
How much symmetry is left — what symmetry decides
The bond length that depends on the isotope — what is taught wrongly
The strain that is not in the angles — where the atoms go
The top that reports all three — what a spectrum settles
The moment a fit invents — what the shape is for

21 August 2026

30 essays on orbitals, what the shape is for, what symmetry decides, where the atoms go, beyond the octet, bonding models, what a spectrum settles, what is taught wrongly and when the molecule does not stop

A contraction is a decision made once — orbitals
The bonds are what is left over — what the shape is for
The group of a molecule that will not hold still — what symmetry decides
The sites are not the same size — where the atoms go
Two kinds of correlation, and only one is small — beyond the octet
A slice is not the surface — orbitals
Four centres, and the pair that will not localise — beyond the octet
One table, three groups — what symmetry decides
The double bond a ring cannot hold — where the atoms go
The g-value is the orbital coming back — what the shape is for
Hypervalency does not stop at three centres — beyond the octet
The electrons repel less inside the complex — what the shape is for
The orbital in momentum space — orbitals
The ring's levels are its group's characters — what symmetry decides
Zero dipole is not no interaction — where the atoms go
Closer is not more overlap — bonding models
When a mode becomes a bond stretch — what a spectrum settles
A function that is already there — orbitals
A moment between two integers — what the shape is for
A surface is not a count of broken bonds — what is taught wrongly
A third kind of correlation — beyond the octet
The atoms are not at the points — where the atoms go
The constant a spectrum cannot see — what a spectrum settles
The degeneracy no group predicts — what symmetry decides
Two bent bonds, or a σ and a π — bonding models
Where the states pile up — when the molecule does not stop
A difference does not make a transfer — bonding models
A full band is not an insulator — what is taught wrongly
The distortion the filling chooses — when the molecule does not stop
A vacancy is not an impurity — when the molecule does not stop

19 August 2026

15 essays on what the shape is for, beyond the octet, orbitals, where the atoms go, what symmetry decides, what a spectrum settles, bonding models and what is taught wrongly

An orbital carries no angular momentum — what the shape is for
Hypervalency is about the ligands — beyond the octet
The isovalue nobody chose — orbitals
The ring that cannot hold still — where the atoms go
The tolerance is a decision — what symmetry decides
A Gaussian is the wrong shape — orbitals
The double hump and what removes it — what the shape is for
The hexagon is the frame's doing — beyond the octet
The lone pair is not the missing term — where the atoms go
The projector is unique, the basis is not — what symmetry decides
Mutual exclusion does not prove a centre — what a spectrum settles
Two pictures, one plane — bonding models
A method that is not additive — bonding models
The rotor that stretches — what a spectrum settles
Koopmans' theorem is exact for nothing — what is taught wrongly

18 August 2026

15 essays on beyond the octet, where the atoms go, orbitals, what symmetry decides, what the shape is for, what a spectrum settles, what is taught wrongly and when the molecule does not stop

The ring with a twist in it — beyond the octet
What a dipole cannot tell apart — where the atoms go
A cage needs one pair more than it has corners — beyond the octet
A filled shell has no shape — orbitals
Every group a molecule can fall to — what symmetry decides
Hybrids that were never orthogonal — where the atoms go
Sixteen is also a count — what the shape is for
Overlap is not interaction — what the shape is for
The angle a ring cannot have — where the atoms go
The atom does not bring its own orbital — orbitals
The hole that is not repulsion — beyond the octet
Why a character table stops where it stops — what symmetry decides
The six motions that are not modes — what a spectrum settles
A better energy is not a better answer — what is taught wrongly
The bond that weakens as neighbours multiply — when the molecule does not stop

16 August 2026

15 essays on beyond the octet, where the atoms go, orbitals, what symmetry decides, what a spectrum settles, bonding models, what is taught wrongly and when the molecule does not stop

Six electrons in a ring that is not all carbon — beyond the octet
The angle does not fix the hybridisation — where the atoms go
One coordinate, three point groups — where the atoms go
One level is not one comparison — orbitals
What one pair can hold together — beyond the octet
Six bonds and four orbitals — what symmetry decides
What the screening model cannot see — orbitals
A spectrum that changes when only a mass does — what a spectrum settles
The moment that is the sum of the other two — what a spectrum settles
Fewer bands than electrons — what a spectrum settles
Where molecular orbital theory dissociates — bonding models
The same ring, three charges — bonding models
A ranking is not a difference — what is taught wrongly
Two defects, and the level between them — when the molecule does not stop
Half filled is as bonded as it gets — when the molecule does not stop

15 August 2026

15 essays on what the shape is for, what a spectrum settles, bonding models, what is taught wrongly and when the molecule does not stop

The splitting is a symmetry statement — what the shape is for
Two models, one ratio — what the shape is for
Where a d–d band falls — what the shape is for
Eighteen is a count — what the shape is for
Back-bonding is two interactions — what the shape is for
The trans influence is an overlap argument — what the shape is for
Copper is never quite octahedral — what the shape is for
A moment counts electrons, not orbitals — what the shape is for
The pairing energy decides the moment — what the shape is for
What couples two spins — what the shape is for
Why a d–d band is weak — what a spectrum settles
The smallest many-electron calculation — bonding models
The spectrochemical series is not electrostatics — what is taught wrongly
The insulator band theory cannot see — when the molecule does not stop
VSEPR does not reach a transition metal — what is taught wrongly

14 August 2026

15 essays on when the molecule does not stop and what is taught wrongly

A solid is a molecule that did not stop — when the molecule does not stop
The width of a band is a count of neighbours — when the molecule does not stop
A density of states is not a spectrum — when the molecule does not stop
A band with no structure in it — when the molecule does not stop
Where a molecule stops being one — when the molecule does not stop
What a metal actually is — when the molecule does not stop
A chain cannot stay even — when the molecule does not stop
The gap is not the band width — when the molecule does not stop
Counting electrons in an extended structure — when the molecule does not stop
A defect is a level in the gap — when the molecule does not stop
A half-filled band is not always a metal — what is taught wrongly
The end is the hardest place to bind — when the molecule does not stop
A band gap is not a bond energy — what is taught wrongly
What holds a solid together — when the molecule does not stop
The lattice sum that depends on the order of adding — when the molecule does not stop

11 August 2026

15 essays on what a spectrum settles, beyond the octet, what is taught wrongly, what symmetry decides and bonding models

Normal modes are not bond stretches — what a spectrum settles
The isotope shift is arithmetic — what a spectrum settles
Group frequencies, and where they stop — what a spectrum settles
How many frequencies, not how many modes — what a spectrum settles
Two structures, two spectra — what a spectrum settles
What an absence proves — what a spectrum settles
A spectrum counts environments, not atoms — what a spectrum settles
The vibration that lowers the symmetry — beyond the octet
The force field is not in the spectrum — what is taught wrongly
The rotational spectrum is a moment of inertia — what a spectrum settles
A bond length out of a spectrum — what a spectrum settles
An infinite group, worked in a finite one — what symmetry decides
The frequency is not the bond strength — what is taught wrongly
What a photoelectron spectrum measures — what is taught wrongly
Water's lone pairs are not a pair — bonding models

10 August 2026

12 essays on beyond the octet, what is taught wrongly, where the atoms go, what symmetry decides, orbitals and bonding models

The band limit — beyond the octet
A double bond is not two single bonds — what is taught wrongly
Three-centre bonding, computed — beyond the octet
What a lone pair is worth — where the atoms go
Degeneracy is a group theorem — what symmetry decides
The aufbau order is not a property of the atom — what is taught wrongly
What an electron actually feels — orbitals
Which angles are symmetry and which are the model — where the atoms go
Descent in symmetry — what symmetry decides
How big is an orbital — orbitals
The antibonding level goes up more — bonding models
Hückel with a heteroatom — bonding models

4–8 August 2026

34 essays on what is taught wrongly, beyond the octet, bonding models, what symmetry decides, where the atoms go and orbitals

Hybridisation does not explain — what is taught wrongly
Hypervalency without d orbitals — beyond the octet
Overlap decides — bonding models
Point groups from coordinates — what symmetry decides
VSEPR, computed — where the atoms go
What an orbital is — orbitals
Delocalisation — beyond the octet
Exactly zero — bonding models
Five sites are not alike — where the atoms go
Orbitals are not where the electron is — what is taught wrongly
Say what it encloses — orbitals
Symmetry forbids a dipole — what symmetry decides
Chirality is a symmetry statement — what symmetry decides
Conjugation, and its limits — beyond the octet
Hybrids are a basis — bonding models
Nodes — orbitals
The dipole is not a sum of bonds — what is taught wrongly
Why water is bent — where the atoms go
The shapes above six coordination — where the atoms go
Character tables and reduction — what symmetry decides
Electronegativity is not one quantity — what is taught wrongly
Molecular orbital and valence bond — bonding models
Where the electron is — orbitals
Where two-centre bonding stops — beyond the octet
Bent's rule, against the substituent series — where the atoms go
Delocalisation is stabilising, and other things that are false in general — what is taught wrongly
Hückel theory and what it gets right — bonding models
Selection rules are one theorem — what symmetry decides
The radial distribution across the periodic table — orbitals
Aromaticity as a computed shell closure — bonding models
Complex harmonics against real ones — orbitals
Site symmetry, and what it constrains — what symmetry decides
Bond order from the eigenvectors — bonding models
The localisation transformation, demonstrated — bonding models

Every essay, by subject · by subject · by thread · search