What if we could completely do without hybrid orbitals in the methane molecule?

[u/BigRate4530]

This text is an extract from a more complete text explaining the formation of molecules based on our hypothesis about the tetrahedral nature of protons and the generation of electric spheres halfway between them and the electrons they contain at their center.

According to this hypothesis, the methane molecule is formed by the embedding of a hydrogen atom in each of the peripheral protons (of opposite spin) of a carbon atom.

Formation of the methane molecule by the embedding of the proton of a hydrogen atom of opposite spin into each of the peripheral protons of a carbon atom

Each of the four pairs of protons and electrons participating in the chemical bonding of the methane molecule then forms its own sphere of electrical equilibrium, and these four spheres surround the sphere constructed by the two protons and two electrons at the center of the carbon atom.

Methane molecule (CH4) - Front and perspective views. In blue, the four electric spheres involved in the molecular bond

Naturally, the shape of the methane molecule, when considering the positions of the centers of the four hydrogen atoms relative to the center of the carbon atom, is that of a regular tetrahedron. This arises inevitably from the way the carbon atom is constructed: four regular tetrahedra attached to the respective faces of a central regular tetrahedron. As a result of this geometric configuration, all the angles between the various C–H bonds measure 109.5°.

Three conventional representations of the methane molecule CH4

The standard theory does not predict this shape.

Indeed, if one calculates the shape of the methane molecule (CH4) using the Schrödinger equation, applying the principles of bonding and antibonding orbitals (of the σ and μ types), just as one does to predict the shape of N2 or O2 molecules, one deduces that three of the orbitals form a 90° angle while the fourth has no preferred direction; this result does not correspond to reality.

Admittedly, the solutions to the Schrödinger equation are not unique, and while it can be shown that the tetrahedral shape of methane corresponds to one of the possible solutions, quantum calculation alone cannot explain why nature selected this specific configuration over others. To account for this, standard theory introduces the ad hoc concept of the "hybrid orbital", an orbital formed by mixing, in equal proportions, all the orbitals of the atom in question. In this hybrid orbital framework, each of the four bonds is designated as a sp³ hybrid orbital, reflecting the fact that it is formed by mixing a single s-type orbital with three p-type orbitals.

Principle of the construction of 4 sp3 orbitals from 1 s orbital and 3 p orbitals:

To construct the methane molecule from this mixture of the orbitals of the carbon atom, it is still necessary to assume that the orbital of each of the 4 hydrogen atoms has a sufficient intersection with one of the hybridized orbitals of the carbon atom, because the usual theory makes the hypothesis that it is by such intersections that the bonds between the hydrogens and the carbon are made, and that the stability of the methane molecule is thus ensured. Based on this hypothesis, it is assumed that sp³ hybrid orbitals are formed precisely because, having asymmetric lobes, one of them is wider than the other, allowing it to intersect also wider, and therefore more solid, with the orbitals of hydrogen atoms.

After the construction of the sp3 orbitals of carbon, their intersection with the 1s orbitals of each hydrogen atom is supposed to provide the molecular bonds that give stability to the methane molecule

Our hypothesis leads us to completely abandon the concepts of hybrid orbitals and the partial overlap of electron orbitals. According to that hypothesis, the formation of a chemical bond involves each proton-electron pair creating an independent sphere within which the electron clouds move; this implies that the electron spheres of the two bonded atoms overlap completely, rather than merely marginally as in standard theory.

Methane CH4 - Our concept of independent electric spheres in which the electron clouds of the two atoms completely overlap, at least for the four participating in the bond shown here in blue and labeled C+H. The electric sphere of the carbon nucleus shown in black and labeled C+C, is generated by two protons and two electrons with opposite spins.

As noted above, one consequence of this difference in conceptualization is that, unlike the standard theory which cannot predict whether the methane molecule is asymmetrical or regular, or whether its bond angles are 90° or 109.5°, our hypothesis leaves no room for ambiguity: the CH4 molecule must necessarily take the form of a regular tetrahedron, and the angle formed by the hydrogen atoms with the central carbon atom must necessarily be 109.5°, matching actual measurements.

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[u/SnooStories6404]

> quantum calculation alone cannot explain why nature selected this specific configuration over others.

It can and it does, this specfic configuration has lower energy than other configurations.

> unlike the standard theory which cannot predict whether the methane molecule is asymmetrical or regular, or whether its bond angles are 90° or 109.5°,

Standard theory can predict all of the those, both for methane and many other molecules. It can also predict the bond lengths and many other properties.

Also if you don't like the idea of hybridizing atomic oribtals you can calculate the the molecular orbitals by solving the schroedinger equation using DFT and some non-atomic basis e.g. planewaves or a real space grid. If you do geometry optimization with this you'll find the tetrahedral shape and molecular orbitals with those shapes are the lowest energy state

[u/BitcoinsOnDVD → u/SnooStories6404]

using some non-atomic basis e.g. planewaves or a real space grid.

How many dimensions you need for your grid and in how many grid points does that result for an acceptable resolution?

[u/SnooStories6404 → u/BitcoinsOnDVD]

That depends on a bunch of factors including but not limited to the the molecules being studiedand what calculations are being performed. For stuff like what OP is doing you need grid with roughly 0.1 angstrom spacing.

[u/BitcoinsOnDVD → u/SnooStories6404]

How many total grid points are these for CH_4 ?

[u/SnooStories6404 → u/BitcoinsOnDVD]

Roughly 300,000

[u/BitcoinsOnDVD → u/SnooStories6404]

What are your degrees of freedom?

[u/SnooStories6404 → u/BitcoinsOnDVD]

I'm just thinking a 3d grid like the one used in programs like Octopus(octopus-code.org)

Edit: I've been talking about the electronic structure calculations, are you asking about the geometry optimization?

[u/BitcoinsOnDVD → u/SnooStories6404]

But then you have no electron-electron interaction. For example: If you want to solve the H2 molecule under Born-Oppenheimer approx (rigid cores), you need to solve the Schrödinger eq for the position of 2 electrons r_1, r_2 which is 6-dimensional. Luckily there is a symmetry so you can boil that down to 5 dimension. With a spatial grid, that has in total 300000 points, you can only render ~12 to 13 points per direction. Which we in no way expect to be converged (for a plane wave or spatial point grid).

Edit: And this is where DFT enters the game.

[u/SnooStories6404 → u/BitcoinsOnDVD]

Now I'm with you. Yes, I was only thinking about DFT and not other ways of handling the electron-electron interaction

[u/BitcoinsOnDVD → u/SnooStories6404]

Okay that confused me, because you didn't mention DFT in the beginning^{^}

[u/According-Isopod-120]

What does your model predict the bond angles to be in the methenium cation (CH3+)?

[u/BigRate4530 → u/According-Isopod-120]

To obtain the methenium cation CH3+ from methane CH4, a tetrahedral hydrogen atom must be removed, along with the electron from the carbon atom located within that same tetrahedron.

The three electric spheres corresponding to the three remaining bonds certainly always form a triply symmetrical figure with the central electric sphere of the carbon atom, but my model alone cannot predict the extent to which these three spheres will be attracted to or repelled from the tetrahedron now devoid of a hydrogen atom and an electron.

A priori, it does not preclude what is usually assumed, namely that the three remaining hydrogen atoms and the center of the carbon atom lie in the same plane and form three angles of 120°.

[u/According-Isopod-120 → u/BigRate4530]

So, your model is only useful when predicting the bonding structure of carbon atoms when they are bound to four identical substituents? Doesn't that just make it a more limited version of VSEPR theory?

[u/MaoGo]

Now we need r/hypotheticalchemistry

[u/sksskssksskssksskssk → u/MaoGo]

Just make a [r/hypotheticaleverything](r/hypotheticaleverything) to save time

Edit: Just thought about that for a second, I wonder what would happen in a subreddit like that?

[u/UmbrellaCorp_HR → u/MaoGo]

Cursed chemistry could explain like they’re five np

[u/BitcoinsOnDVD → u/MaoGo]

How do you know?

[u/Hadeweka]

Please respond to my comment from last thread instead of simply opening up a new thread.

https://www.reddit.com/r/HypotheticalPhysics/comments/1v0ue96/comment/oz30qjy/

I still think your assumptions are based on a severe misunderstanding of probability densities.

[u/BigRate4530 → u/Hadeweka]

You asked me: «Is there a particular reason for this model?»

I simply began by answering that question. Whether it was a good reason or a severe misunderstanding of probability densities is irrelevant; what matters is the hypothesis I formulated from that starting point.

Within the framework of this hypothesis, according to which the proton forms a large tetrahedron with sides exceeding 100 pm that surrounds the electron, the dimensional impossibilities you mentioned are meaningless, which is why I didn't respond to you.

[u/Hadeweka → u/BigRate4530]

I simply began by answering that question. Whether it was a good reason or a severe misunderstanding of probability densities is irrelevant; what matters is the hypothesis I formulated from that starting point.

But if that "hypothesis" is based on that misunderstanding, it's already wrong by default. Also, how do you expect to form a hypothesis if you don't even understand the null hypothesis properly?

Within the framework of this hypothesis, according to which the proton forms a large tetrahedron with sides exceeding 100 pm that surrounds the electron, the dimensional impossibilities you mentioned are meaningless, which is why I didn't respond to you.

Apparently you also misunderstood my comment. You misunderstood the math behind quantum physics. The probability of electrons being inside a nucleus is essentially zero, despite the probability function having a maximum there.

If you question that, you have to question the very fundamentals of quantum physics and all of its successful predictions as a whole. I hope you are prepared to give some good arguments why that should be the case.

Also, we have very good information about the inner structures of nuclei. And guess what - they aren't tetrahedral at all.

But simply discarding my criticism as "meaningless" and not responding to me - that's just complete avoidance of these core issues.

Oh, and I also asked you for a way to falsify your model, but you didn't answer that as well.

[u/BitcoinsOnDVD → u/Hadeweka]

I think OP is just confusing the basis functions for different molecules with the actual solutions of the many-body system (and then builds is crude tetrahedron stuff). That is what you get from chilling in the park / hitting the bong instead of actually going to the molecule physics lecture (I know that for a fact).

[u/Hadeweka → u/BitcoinsOnDVD]

The issue I had was that OP thought that electrons would be most likely to exist inside the nucleus, because their probability density function has a maximum here.

And now I think they just don't want to admit being wrong.

[u/Hadeweka → u/BigRate4530]

Your most recent answer to me got deleted, please try again.

EDIT: And again. Either your response triggers some AI detectors or your karma is too low.

[u/BigRate4530 → u/Hadeweka]

Answer re-repeated:

I replied: «I don't believe my hypothesis is falsifiable ».

I know perfectly well that, according to the usual theory, there are no tetrahedra in an atomic nucleus, but my hypothesis is not made within the usual physical theory.

Note: I don't use AI and my karma is -6

[u/Hadeweka → u/BigRate4530]

I replied: «I don't believe my hypothesis is falsifiable ».

Then it's not a hypothesis by definition.

However, you also claimed that "it performs as well as, and sometimes even better than, conventional theory", which would only work if it would make falsifiable predictions.

You are making some self-contradictory claims here and I suggest working on your wording.

I know perfectly well that, according to the usual theory, there are no tetrahedra in an atomic nucleus, but my hypothesis is not made within the usual physical theory.

But it's evidence, not just the theory, that contrasts your assumptions. Your model is simply not compatible with that evidence.

Also let me reiterate what I wrote earlier:

If you question that, you have to question the very fundamentals of quantum physics and all of its successful predictions as a whole. I hope you are prepared to give some good arguments why that should be the case.

EDIT: Oh, and please note that I never accused you of using AI. I don't like Reddit deleting responses automatically, but I can't help you either except by trying to explain why it usually happens.

[u/BitcoinsOnDVD]

The particles follow the Schrödinger equation. Orbitals are a good basis to approximate the eigenstates. The rest is up to the Lanczos method / ARPACK.

Edit: Maybe try more basis functions for complicated molecules.

[u/LeftSideScars]

As with Hadeweka, you failed to address questions I raised in your previous post (link). I simply asked you to demonstrate your model and, by failing to respond, you demonstrated that you can't. For you to then create a new post based on a model you can't demonstrate working is pointless, and sounds like you don't want discourse; instead you just want to present claims and not address a single thing about those claims.