User:Double sharp/Idealised electron configurations

The LSPT, via electron configurations

Of course, there can be multiple ways to represent the periodic law, as that is only about properties of the elements and their compounds exhibiting periodicity with atomic number. Therefore we can choose to emphasise different properties as we see fit. So, one can come up with many periodic charts emphasising different things: one could be a spiral, to emphasise the uninterrupted progression of atomic number; another could emphasise direct physiochemical similarities (which would demand H-F + He-Ne, and some swaps among the superheavies would be needed, and early actinoids would then need a dual place among the transition metals, etc.); and so on and so on. Then one starts piling up big lists of properties to decide B-Al-Sc vs B-Al-Ga; Be-Mg-Ca vs Be-Mg-Zn; Sc-Y-La vs Sc-Y-Lu; C-Si-Ti vs C-Si-Ge. Then it becomes a fairly close fight, and then one notices that criteria that argue well for one placement tend to result in unwanted consequences. Eventually this culminates in noticing that hydrogen has no good congeners and removing it from the periodic law altogether. So much for it being a law. (And strangely nobody notices the same thing is true of carbon, king of organic chemistry.)

"God said: let Newton be! and all was light". And thus Newtonian mechanics which explained every planet's orbit triumphed over Ptolemy's ad hoc different kinds of epicycles for each one. Modern periodicity is about electronics, as seen from textbooks universally agreeing to talk about orbitals. They explain all the properties: ask any computational chemist. That is what I want as a base form and it is what people use (except helium when they suddenly forget about the electronics they wrote about): there is no other explanation for why everybody puts the superheavies in the same place even though nobody has found any of their physiochemical properties by experiment (and speaking purely from how the atoms would likely behave, Ts and Og are much more similar to groups 13 and 14, yet no one places them there). The point is not to give the closest resemblance (if that even exists for elements like H and C): the point is that it must come from some kind of theory that can give us heuristics to predict pretty well how the reality will be like.

Granting at least the arbitrariness of standard conditions, it seems like the only thing preserved about the elements as they engage in every chemical transformation you can think of in standard conditions is their atomic number order and their electronic structure in the sense of valence subshells. These properties allow us to rationalise all others (only in principle completely, but in practice they go far enough for a quick idea), consistent with the quite universal use of quantum mechanical considerations to build up the table and give easy qualitative explanations. Physics and chemistry would thus reach a symbiosis. It also preserves the idea that we consider abstract elements for the periodic system (hence atoms), not elements as simple substances, as Eric Scerri has recently pointed out. Sodium and chlorine as atoms with electronic structures and a valence/core distinction are preserved in salt, but sodium the reactive metal and chlorine the toxic gas are not. The fact that hydrogen is usually placed in group 1 is a clear precedent. (For a nice text using electronic considerations to rationalise a lot of stuff, see Siekierski and Burgess.)

(Outside standard conditions, all bets are off, e.g. potassium filling 3d instead of 4s under high pressure. This sort of thing, with 5d being used through I, Xe, Cs, and Ba, means that the whole point of the standard PT with its period breaks just doesn't make sense at those pressures. Jovians can use their own periodic tables!)

Having thus decided on using electronics as a basis for the first PT to show (maybe a heuristic or spectroscopic or electronic table), things seem pretty much settled. The only major question is whether to use an fdps (Janet) or sfdp (conventional) arrangement.

The Madelung rule has a natural derivation known since Klechkovsky), and per Demkov and Ostrovsky it may be derived from a specially chosen potential. Even if the choice of potential is open to question, this already demonstrates that the Madelung rule is consistent in principle with quantum theory. Its most natural expression, as noted by Thyssen and Binnemans, is the Janet left-step. (Yes, in practice the computations are too hairy, but so what, you cannot integrate the whole Solar System either.)

f¹

f²

f³

f⁴

f⁵

f⁶

f⁷

f⁸

f⁹

f¹⁰

f¹¹

f¹²

f¹³

f¹⁴

d¹

d²

d³

d⁴

d⁵

d⁶

d⁷

d⁸

d⁹

d¹⁰

p¹

p²

p³

p⁴

p⁵

p⁶

s¹

s²

1s

H

He

2s

Li

Be

2p 3s

B

C

N

O

F

Ne

Na

Mg

3p 4s

Al

Si

P

S

Cl

Ar

K

Ca

3d 4p 5s

Sc

Ti

V

Cr

Mn

Fe

Co

Ni

Cu

Zn

Ga

Ge

As

Se

Br

Kr

Rb

Sr

4d 5p 6s

Y

Zr

Nb

Mo

Tc

Ru

Rh

Pd

Ag

Cd

In

Sn

Sb

Te

I

Xe

Cs

Ba

4f 5d 6p 7s

La

Ce

Pr

Nd

Pm

Sm

Eu

Gd

Tb

Dy

Ho

Er

Tm

Yb

Lu

Hf

Ta

W

Re

Os

Ir

Pt

Au

Hg

Tl

Pb

Bi

Po

At

Rn

Fr

Ra

5f 6d 7p 8s

Ac

Th

Pa

U

Np

Pu

Am

Cm

Bk

Cf

Es

Fm

Md

No

Lr

Rf

Db

Sg

Bh

Hs

Mt

Ds

Rg

Cn

Nh

Fl

Mc

Lv

Ts

Og

Uue

Ubn

This form of periodic table is congruent with the order in which electron shells are ideally filled according to the Madelung rule, as shown in the accompanying sequence in the left margin (read from top to bottom, left to right). The experimentally determined ground-state electron configurations of the elements differ from the configurations predicted by the Madelung rule in twenty instances, but the Madelung-predicted configurations are always at least close to the ground state. The last two elements shown, elements 119 and 120, have not yet been synthesized.

The blocks then come in the natural order spdf, reading right to left, of their quantum numbers. This also naturally displays the secondary periodicity as the difference between odd and even values of n + ℓ. (It exists in the s-block too: compare atomic radii down H-Li-Na-K. K is much larger than Na.)

However, per Ostrovsky 1981, quantum effects shift the energies of the ns orbitals so that they join rather the next group of n + ℓ values.

Therefore, the available electrons in each element naturally give a form of table that is identical to Janet's, but with the s-block moved to the far left instead:

Is	IIs	IIId	IVd	Vd	VId	VIId	VIIId	IXd	Xd	XId	XIId	IIIp	IVp	Vp	VIp	VIIp	VIIIp
(s++)¹	(s++)²	(dsp)³	(dsp)⁴	(dsp)⁵	(dsp)⁶	(dsp)⁷	(dsp)⁸	(dsp)⁹	(dsp)¹⁰	(dsp)¹¹	(dsp)¹²	(sp)³	(sp)⁴	(sp)⁵	(sp)⁶	(sp)⁷	(sp)⁸
H	He																	1s
Li	Be											B	C	N	O	F	Ne	2s2p
Na	Mg											Al	Si	P	S	Cl	Ar	3s3p
K	Ca	Sc	Ti	V	Cr	Mn	Fe	Co	Ni	Cu	Zn	Ga	Ge	As	Se	Br	Kr	3d4s4p
Rb	Sr	Y	Zr	Nb	Mo	Tc	Ru	Rh	Pd	Ag	Cd	In	Sn	Sb	Te	I	Xe	4d5s5p
Cs	Ba	Lu	Hf	Ta	W	Re	Os	Ir	Pt	Au	Hg	Tl	Pb	Bi	Po	At	Rn	5d6s6p
Fr	Ra	Lr	Rf	Db	Sg	Bh	Hs	Mt	Ds	Rg	Cn	Nh	Fl	Mc	Lv	Ts	Og	6d7s7p
119	120																	8s
		(fdsp)³	(fdsp)⁴	(fdsp)⁵	(fdsp)⁶	(fdsp)⁷	(fdsp)⁸	(fdsp)⁹	(fdsp)¹⁰	(fdsp)¹¹	(fdsp)¹²	(fdsp)¹³	(fdsp)¹⁴	(fdsp)¹⁵	(fdsp)¹⁶
		IIIf	IVf	Vf	VIf	VIIf	VIIIf	IXf	Xf	XIf	XIIf	XIIIf	XIVf	XVf	XVIf
		La	Ce	Pr	Nd	Pm	Sm	Eu	Gd	Tb	Dy	Ho	Er	Tm	Yb			4f5d6s6p
		Ac	Th	Pa	U	Np	Pu	Am	Cm	Bk	Cf	Es	Fm	Md	No			5f6d7s7p

Tossell showed Zn 3d activity, Keeler and Wothers accept it for the Zn group and call it 12 valence electrons. La f-involvement has been known since some early superconductivity research, eloquently argued for by Gschneidner and Wittig, and is the most obvious and parsimonious explanation; it has also been confirmed by later computational chemists. Lu doesn't have any such thing, so this is basically Wittig's argument. Same story for Ac having f-involvement and Lr lacking it.

Arguments from the bare-atom configurations are based only on confusion: even if we momentarily forget that chemistry is about interacting atoms, one cannot just look at La and Ac not filling f, and forget that Th also doesn't fill f, and especially forget that f¹⁴ is still where we are at by Yb and No. That is the definition of cherry-picking only the facts one wants to see. Endlessly harping on the delayed appearance of f-electrons in irrelevant lone atoms, while forgetting about Th, Lu, and Lr, is sophomoric, inconsistent, and above all tiresome since Jensen already exploded that in 2015. The simple fact of the matter is that the filling process in gas-phase configurations does not support either Sc-Y-La nor Sc-Y-Lu because 4f fills in only 13, not 14, elements; and 5f fills in only 12, not 14 elements. On them alone there is no basis to pick out 14-element f-blocks. A good thing, therefore, that gas-phase configurations mean zilch for chemistry in real environments, and that actual f-activity in compounds occurs precisely from La-Yb and from Ac-No. This is another way in which support for Sc-Y-La (rather than Sc-Y-Lu, as has been known since at least Bassett 1892) demonstrates a failure to understand the facts of chemistry, and instead substituting them with the rules of a fantasy universe that is not our own.

Modulo the typical scale of bond dissociation energies, the match of the Madelung rule with electron configurations is perfect. Excitation energy La 5d→4f is lower than excitation energy Ag 4d→5s, and lower than excitation energy Be 2s→2p that must be invoked to explain why Be is not an inert gas. Basing things on ground-state anomalies in the gas phase thus does not make any sense, which everybody knows anyway for other elements: nobody moves Cr, nobody moves Cu, nobody moves Nb, etc. Why only do it for two elements, and not even the two with the highest excitation energies (yes, Ac is the first, but La isn't the second)? We are not doing a periodic table just for atoms sitting around doing nothing, but for atoms across all of chemistry (extending a point by Eugen Schwarz). Otherwise the periodic table would have a very limited set of uses.

The column headers express the valence manifold. s++ means "including at least some of the higher-ℓ orbitals in the same row". Not necessarily all of them of course. The numerals represent the number of valence electrons. This is correct up till nihonium (there are some suspicions about francium and radium using 6p, but I am a bit sceptical and it's only one set of authors IIRC). So, what we have is:

Elements get placed in columns according to how many valence electrons they have.
When that doesn't suffice, they are placed according to which valence orbitals they have.

The Madelung rule ensures that this totally follows the Z order.

We admit that this becomes incorrect from flerovium onwards due to relativistic effects drowning 7s. But this is not surprising considering that the derivation of Madelung's rule does not consider relativity. Besides, a weakened version still holds: whatever orbital the Madelung rule says is being filled is always one of the valence orbitals. The idea that an x-block element must have valence x-orbitals still holds true even up to 120; this is an obviously natural requirement. More generally, since relativity messes around with the energy gaps, what happens is that we have the expected configuration but it means something different for the resulting chemistry. Big deal, we see that in kainosymmetric 1s and 2p elements anyway.

Electrons in the ns orbitals don't fall into the core after they finish filling in the neutral atoms, but rather stay on as valence electrons until pretty much the end of the period. It's only after the noble gas that everything rushes into the core and we start again, with one electron outside an inert core (the alkali metals). Therefore, periods now correspond roughly to sets of orbitals at about the same energy, though it's weaker because some drop out before the row ends (the d and f orbitals have become part of the core after we leave those blocks). That said, changes in valence manifold type and participating orbitals generally happen when we cross block boundaries, and trends don't always go perfectly across: just look at what happens to main-group trends in atomic radius, IE, EA, EN, and typical oxidation states once we enter the transition and inner transition elements. (And even s-block and p-block have significant differences in trend type and stereotypical behaviour.)

In other words, this table starts new rows at a new n value rather than a new n + ℓ value.

I first thought of this idea to display chemically active subshells in August 2019; of course, it has been refined since then. :)

(Helium perfectly fits the first-row anomaly trend, because of tiny kainosymmetric 1s and 2p orbitals. So giving it its electronic place has positive chemical consequences as well.)

These are exactly the same form apart from where you put the s-block. Indeed, one should rather consider the table to be a spiral: there are no "gaps" between atomic numbers, the whole thing follows in Z order. So both tables work just as well, something like how mathematicians describe surfaces by using a polygon with side identifications. When you wrap around the right edge, you end up on the left edge, one row lower. The precise choice of where you cut is arbitrary. I therefore agree with Scerri that the LSPT is the most fundamental table, though I don't particularly care where you cut the spiral (to me it is not a real difference) and would probably cut it after the noble gases more often.

Note that this is emphatically not about matching properties of elements. After all, in the first period, properties seem to be more determined by how many vacancies we have in the valence orbitals, rather than occupancies. But it fits in a unified picture that makes for sensible heuristics, and it comes consistently from a not-too-bad model. If it contains the really weird helium over beryllium, then so much the better: it will help teach us that the map is not the territory. That might do a whole lot of good at stopping the myth that elements in the same column of the table must behave similarly. It simply ain't so even for the common elements (boron vs aluminium is pretty obvious; yes, one can scrounge up some similarities, but at that level every element is similar to every other). What is true is that we can heuristically understand what actually happens from the electronic considerations to a surprisingly large degree.

There's a whole bunch of papers by Scerri and others touching on concerns raised here. I don't think much is new; even the group numbers have rough precedents.

Theoretical predictions by Fricke, Pyykko, Nefedov etc. suggest that there may be unforeseen problems past 138, but since calculations there are not complete yet, I prefer to wait and see. It may well be a moot point anyway given how terrible the cross-sections are getting (four years of bombardment at RIKEN for element 119, still no results).

P.S. Stereotypical differences between blocks again don't mean anything. Groups 11 and especially 12 have significant main-group properties, so do groups 3-5 (except Ti and V), and in group 10 Pd and Pt have the typical p-block "oxidation states vary by 2" pattern as explained by Siekierski and Burgess, p. 144.

Metallicity

The easiest way to define metals probably comes from how IUPAC defined "metal-nonmetal transition" (it is about itinerant vs localised valence states). Also note "metal-semiconductor transition" there, since nonmetal is equated with insulator. Of course there is not a clear line separating semiconductors from insulators.

However, this is really a physics definition, and as such it is about substances rather than abstract elements. Hence graphite is a metal, but diamond isn't. Fair enough for physics, but for chemistry we presumably want to classify abstract elements instead.

Nonetheless I note that C and As, while most stable in their metallic forms, have extremely stable nonmetallic forms. Diamond and arsenolamprite are stable enough to be minerals.

So my preferred way to fix it for chemical purposes for chemical purposes would be to take all stable enough allotropes at STP. A metal is an element that has all its stable or metastable allotropes metallic (i.e. no band gap) at standard conditions. A nonmetal is anything else. (One could add a proviso about 3D conductivity to get rid of carbon, but there's actually no need for that because of diamond. But it is true that graphite and grey arsenic have pretty weak delocalisation compared to true metals.)

[Maybe need to deal with single-layer materials...]

Grey tin is sometimes called a zero-gap semiconductor, and sometimes a semimetal. But it is not even metastable above the transition point (13.2°C), so it doesn't matter anyway.

The known metallic elements are thus: lithium through beryllium; sodium through aluminium; potassium through gallium; rubidium through antimony; caesium through polonium; radium through einsteinium. There is some indirect experimental evidence for fermium and mendelevium.

Antimony is a difficult borderline case. Sources differ about the stability of black antimony (a nonmetallic allotrope). The most recent sources say it is stable up to ~100°C in vacuum. On the other hand, it does not seem to have mineral occurrence, even though native antimony is known. So I classify it with metals.

On the negative side, antimonides are far too often nonmetallic. And nonmetal Sb is not always the weakest – As as grey As has better conductivity. Grey antimony does look like a metal, but tellurium is also more reflective than many true metals. But on the positive side, antimony can be worked sort of like a metal (you need to be careful, but the same is true for bismuth). And as a metal Sb is also not always the weakest: astatine has a more nonmetallic chemistry than antimony, and bismuth is a worse conductor than Sb (or even As). To some extent, therefore, the line we draw here will be a little bit arbitrary, like all categories really. Antimony is on the "good" side of the metalloid line, and it is a metal physically; why not give it the benefit of the doubt? (Germanium and arsenic pass one of those but not the other.)

Astatine, francium, and nobelium through oganesson so far are known to live about a day or less, and are truly ephemeral. No one has any knowledge of their bulk properties, so they should be classed as unknown. This differs slightly from Rayner-Canham's definition of ephemerality by including dubnium, which lives only for modestly over a day. The limit of non-mayflies is thus placed at radon, the shortest-lived element for which bulk properties are known by experiment. Fermium and mendelevium would be non-ephemeral if you could only make enough. :(

Latest predictions (including spin-orbit effects) say At should be a metal, Cn should be a dispersion-bound liquid (so a nonmetal), and Fl and Og should be a semiconductor. The rest should presumably be metals. However, I'm not sure I buy this about Cn, Fl, and Og. Metallisation tends to happen with increasing atomic radius, and Og already has a large radius. Predictions have a tendency to underrate the metallicity of Cn and Fl compared with experiment. I would suspect they are all metals, but the jury is still out there.

If one wishes, a metalloid can be a subtype of nonmetal which has all non-metallic allotropes clearly semiconductors (in all three dimensions) instead of insulators. These would be boron, silicon, germanium, arsenic, and tellurium. Carbon out because of diamond; phosphorus because red phosphorus; selenium because black selenium; iodine because it's only a 2D semiconductor. This is more or less the normal list, although often people add antimony.

Physical and chemical versions of metallicity are not entirely in sync, of course, but the synchronisation is close enough.

I have previously considered a criterion based on what happens when the material is amorphised. It gives pretty much the same results; Sb is now almost but not quite a metal. However, carbon and selenium end up as metalloids if you do that, and carbon seems a step too far for the "king of nonmetals" and king of organic chemistry. Besides, amorphous metals are not exactly the phase the metal would like to be in. :(

In the end, though, the precise boundary is not too important. What is rather important instead is that there are some elements that are obviously metals (e.g. sodium) and some that obviously are not (e.g. chlorine). The precise location of the boundary is not the most important thing. After all, consider astronomy. For a dynamicist, obviously the big guys are the eight major planets, Mercury through Neptune. Satellites are just satellites, even if they are so big they have weather (Titan); clearly subordinate. On the other hand, for a planetary geologist, the divide is clearly roundness in order to have geology, so the big satellites like Ganymede, Callisto, and Titan are clearly rather different from "space junk" moons like Hyperion. And there are clearly borderline cases, like the big asteroid Vesta, which once was round and actually developed like a mini-planet, before it got a really big whack and stopped being round. (Some models suggest it might still relax to roundness eventually, showing more borderline-ness. In fact, even Hyperion was probably once part of a larger moon that may have been Tethys-sized!) And both sides just carry on using different definitions of "planet". Unfortunately it would be too much of a stretch to say that everyone's happy, but hey, maybe we can do even better with "metal". Actually we already do, since for astronomers metals are whatever isn't hydrogen and helium (the universe's rounding error)! :D

Subclasses

Nonmetals (including metalloids if one wishes) are not too hard to classify: they can be classified into the weak nonmetals, strong nonmetals, noble gases, and one special case. Such a classification generally matches a bunch of criteria: oxidising power, physical structure, electronegativity, electron affinity, acid-base properties. But of course all but physical structure are showing a smoother trend between metals and nonmetals, and physical structure is slightly clearer (although there is some trend, just look at bromine, iodine, gallium).

Noble gases: He, Ne, Ar, Kr, Xe, Rn. The weirdos: no electron affinity but also high ionisation energy.
Strong nonmetals: N, O, F, S, Cl, Br, I. The ones forming small molecules (except hydrogen and maybe astatine if it's a nonmetal), strong oxidants normally. (Nitrogen is kinetically hindered, but attacks lithium and alkaline earths quite well. Nothing wrong with that; compared with fluorine, oxygen is also – thank goodness – kinetically hindered. That's why magnesium doesn't start reacting till you burn it. Sulfur readily attacks silver with its lower oxygen affinity. If we did not make allowances for the restraints, then halogens and soon fluorine will stand in isolation, which starts to get a bit silly.) If one wishes, we may note that N, S, I are somewhat hobbled.
Weak nonmetals: B, C, Si, P, Ge, Se, Te. The "large-structure" ones, mostly. (Here I'm considering red phosphorus, although for pragmatism's sake it does make sense to consider white phosphorus the standard state.) One could argue to separate C, P, Se from true metalloids.

Absence of arsenic is not a mistake: if we consider standard states, it is a metal! (Needed to put phosphorus in the right place.) It does rather pattern with weak nonmetals though, so it should be an honorary addition. Remember, physical and chemical metallicity correlate, but not 100%!

The special case is hydrogen, which has a small-molecule structure like strong nonmetals, but is a poor oxidising agent like weak nonmetals, acts rather as a reducing agent to displace metals from their salts, and in water prefers to be a cation like metals. (Hydrogen is mostly only an oxidising agent in hydrides, which reduce water.) So it stands alone, as it cannot be incorporated into any of the three categories without some violence. If it must be somewhere, weak nonmetals seems best.

In general, things like antimony, bismuth, polonium, and astatine can be given an "ambiguous" dual citizenship. Strictly speaking they are metals, but their chemistry has significant nonmetallic elements that makes discussing them with nonmetals reasonable for comparison. Similarly, hydrogen and arsenic, maybe even carbon, may be given a dual citizenship into the metals. This is why some of them often appear in the reactivity and electrochemical series. If we consider mostly physics and liquid states as well, then Si, Ge, As, Se, and Te deserve to enter metals too (chemically, the last four even are not totally a stretch). If we think of electronegativity series, gold deserves to be listed with nonmetals!

Metals are harder to classify in such a nice way. There are a lot of "senses" and the orders are often not exactly consistent. Electronegativity (important mostly for intermetallics) vs reduction potential (strength) vs acid-base vs ionisation energy vs physical properties vs reactivity with air (i.e. ignore, passivate, tarnish, flaky rust, or catch fire?) are pretty different orders. For example, aluminium defeats nickel in reduction potential, but it is the other way round for electronegativity! Because there are so many of them, no natural breaks match up across series, unlike for nonmetals. The wisdom of the masses seems to support this, in how most metal categories are exactly or almost exactly blocks possibly intersected with groups or periods; the cool boundaries seem to occur for nonmetals including metalloids.

If liquid drop was correct, then the periodic table would pretty much end after the actinoids, but polonium through actinium would be a whole lot less unstable. I think I prefer having seven complete rows, but I can't deny that stable-ish Po, At, and Rn would get rid of a lot of fuzzy thinking about group trends. ;)

---

Alternate idea: just use the standard state and demand 3D. Arsenic is a metal, carbon isn't. Metalloids then just overlap the line for those with intermediate chemistry and/or physics, an element can be both a metalloid and a metal (As) or a metalloid and a nonmetal (Ge). Well, I guess that makes Re a metalloid though. Oh well.

Standard states

Caesium and gallium are so close to melting (and will melt in your hand), so it seems a shame to not single them out.

Francium is sometimes marked as liquid, but because of relativity, energy of 7s orbital is intermediate between 6s of Cs and 5s of Rb. If you considered a temperature like 35°C, it might well melt: so I guess it would pass the bar of "will it melt in your hand?", ignoring the fact that it would melt your hand and then some. Although at this point one might as well mark rubidium as liquid too (it melts just above body temperature). That gets us to a sweltering 40°C standard state (but not unheard of for summer heat waves already...), at which Sn is not likely to go crazy on us anymore. Cn and Fl are probably liquid metals, basically for the same reason that Hg is one. I'd rather not raise the temperature further than that, because (1) then we get into the allotrope problem for P again, and (2) Cn might soon start to boil. Also (3) it's way too hot.

Energy of 8s orbital for 119 drops below potassium (link), and so that should quite likely be solid again.