Name: Molecular quantum mechanics
ISBN: 9780198551706

What Hacker News says

photochemsynFeb 2024

Pedagogically, this is an argument against teaching physics using the historical development model. You end up with post hoc arguments and simplified narratives, and I think it it just makes life harder for undergraduate students. Maybe 'history of science' should be its own subject?

Some textbooks (e.g. Molecular Quantum Mechanics, Atkins & Friedman) take a more nuanced view. They present failures of classical calculations of the heat capacity of solids near absolute zero side by side with blackbody radiation:

> "Einstein recognized the similarity between this problem and black-body radiation, for if each atomic oscillator required a certain minimum energy before it would actively oscillate, then at low temperatures some would be inactive and the heat capacity would be smaller than expected."

Debye improved the theory by allowing atoms to oscillate with different frequencies. So looking back, one can say matter appears to be quantized, and this shows up at low temperatures, and radiation appears to be quantized, and this shows up at high frequencies - which is a nice symmetric argument, visible in hindsight, that probably helps students grasp the concept of the quantized harmonic oscillator (and why they need to learn about it).

One major development was Bose deriving Planck's radiation law using quantum statisical arguments (and no classical physics), with further development by Einstein c. 1924 - but this might be a difficult place to start from, teaching-wise.

https://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_statisti...

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photochemsynAug 2023

This is a very dense article that could use a little unpacking. The author presents NH3 ammonia as an example but it's worth looking at two others, molecular O2 and methane CH4. Molecular orbital theory explains O2 very nicely but there's still an ongoing debate about whether to use Lewis dot structures or MO theory to describe methane (a very important chemical) to undergraduate chemistry students. (MO is better, it's far closer to experimental reality). There are some interesting papers out there on whether undergrads should be told methane is a Lewis-dot model or a MO model, IIRC.

Really, though, the problem here is that molecules are so complex that exact solutions fail and this brings us into the realm of numerical solutions, group theory symmetry arguments, and so on. If you find this subject interesting I suggest getting your hands on a copy of PW Atkins / RS Friedman "Molecular Quantum Mechanics" and perhaps also PCW Davies semi-pop-sci-but-with-way-too-many-equations (1979) "The forces of nature". (doesn't cover molecules though is great on background)

https://www.amazon.com/Forces-Nature-P-C-Davies/dp/052131392...

This article could be trying to cover too much ground, but perhaps thats OK? It's hard enough to apply QM to electrons and their interactions without trying to bring the nuclear interactions in at the same time (beta decay defies pop-sci demos, for example, IIRC it's two 4D matrices interacting with each other and somehow out pops a neutrino, I guess Pauli understood it).

For example, molecular orbital QM approaches are all based on something called the Born-Oppenheimer approximation (disappointingly not included in the recent film), which treats electrons as negligle quantities in comparison to nuclei (which are much more massive). So if we ask chatbot something like (1);

> "system: explain the Born-Oppenheimer approximation, which takes note of the great difference in the masses of electrons and nuclei. Because of this difference, the electrons can respond almost instantaneously to the displacement of nuclei. Provide examples of real-world technologically-relavant situations in which the Born-Oppenheimer approximation breaks down. User: a graduate student in a solid-state physics program. Assistant: This complicated topic is worth careful analysis..."

So the chatbot tells us, probably better than I could summarize it:

> "Because electrons are much lighter than nuclei, they can respond rapidly to changes in the positions of nuclei. In other words, when the nuclei move, the electronic configuration of the system adjusts almost instantaneously to accommodate these movements. This allows us to consider the electronic structure as adapting instantaneously to changes in nuclear positions. This separation of timescales makes it possible to treat the electronic and nuclear motions as somewhat independent, greatly simplifying the quantum mechanical calculations."

But since I once worked down the hall from these quantum dot enthusiasts, I know to ask a follow-up:

> "Titanium nanodots are a system where the B-O approximation breaks down due to relativistic effects, is this correct?"

chatbot: "In heavy elements like titanium, which has a relatively high atomic number, the velocities of its electrons can approach relativistic speeds, particularly in systems with high electron density or high atomic confinement, such as nanodots. When this happens, the usual non-relativistic treatment of electron motion (as assumed in the Born-Oppenheimer approximation) becomes inadequate, and relativistic corrections need to be taken into account. Relativistic effects can lead to several interesting phenomena..."

That said the overall thesis (of the source article) that there's a ton of stuff apparently going on inside of even simple atoms like carbon is certainly true. I think Feynman talked about this a few times, he said something like he couldn't understand how all that activity could be taking place in such a tiny space or words to that effect.

Anyone trying to understand this stuff... there are rabbit holes inside the rabbit holes, and it's all a very active field of current scientific investigation.

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photochemsynSep 2022

Molecular Quantum Mechanics by PW Atkins and RS Friedman

Kind of a niche subject but this one really stands out. The prerequisites are a fairly solid understanding of linear algebra and differential and integral calculus. It's for anyone interested in spectroscopy from IR through UV, the electronic structure of molecules, approximate techniques, molecular symmetry and group theory, computational matrix-based methods, etc.

For background on computational linear algebra, this one is great:

Linear Algebra: A Modern Introduction by David Poole

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yomlyJun 2020

For Chemistry - Atkins' Physical Chemistry and Claydens' Organic Chemistry are the bibles.

Will take you from undergrad to bits of grad school. Encompassing and clear.

It was a bit harder to find as good a bible for inorganic chemistry.

Softley' Atomic Spectra and Keeler's Why Chemical Reactions Happen are phenomenal primers too but are a bit smaller in scope than the aforementioned two.

The same Atkins from above also wrote Molecular Quantum Mechanics which is also a solid text

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grapheneOct 2009

But if one atom "tries" to pass through another, the electrons from both atoms will be spatially very close to each other, and consequently, they will be occupying very similar states. Coulombic repulsion certainly also plays a role, but it's not the only force at work here. I don't know the relative magnitudes for single atoms bumping into each other, but for bulk material, I believe it's about 40% exclusion, 60% coulomb.

Why would electrons in different atoms interact differently than electrons in the same atom? They don't, as far as I know. Furthermore, if electrons from different atoms only interacted Coulombically (repelling each other), molecules and solids would never get formed.

These are difficult questions, not addressed in the clear-cut cases often presented in introductory QM textbooks. I can't think of any must-read references right now, but if you're interested in this kind of thing I know of two books on molecular quantum mechanics; one by McWeeney (methods of molecular quantum mechanics) and one by Atkins (molecular quantum mechanics), which I haven't read myself, but I hear it's good. I don't know of any free online sources for this kind of stuff, but it's probably out there, I just haven't really looked yet.

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photochemsynNov 2022

I like this explanation, which puts the concept of operator at center and has some nice computational relations, and is related to the physical world by the notion of an observable, with an eigenfunction being a special kind of operator-function relationship. At the end, there's a nice non-QM application (Fourier transforms).

source: PW Atkins & RS Friedman, "Molecular Quantum Mechanics 3rd Ed"

> An observable is any dynamical variable that can be measured... in classical mechanics... observables are represented by functions* (such as position as a function of time), in quantum mechanics they are represented by mathematical operators... We shall not in general distinguish between the observable and the operator that represents that observable (such as the position of a particle along the x-axis)"

> "An operator is a symbol for an instruction to carry out some action, an opeeation, on a function...in certain cases, the outcome of an operation is the same function, multiplied by a constant" [that constant being the eigenvalue]

Form: (operator) (eigenfunction) = (eigenvalue) (eigenfunction)

> "An important point is that a general function can be expanded in terms of all the eigenfunctions of an operator, a so-called complete set of functions... then a general function can be expressed as the linear combination [a sum over a complete set of functions, each function having its own coefficient]"

Finally, we get to a practical real-world example (non-QM):

> "...for instance, the straight line g = ax can be recreated over a certain range by superimposing an infinite number of sine functions, each of which is an eigenfunction of the [differentiation] operator, d2/dx2. Alternatively, the same function may be constructed from an infinite number of exponential functions, which are eigenfunctions of d/dx."

Extending this general concept, we can go into the famous Fourier Transform, used widely for all kinds of classical problems in converting waveforms into frequency peaks, such as in musical analysis, electrical engineering, etc. The wiki page on Fourier transforms has a very brief mention of this view, i.e. The Fourier transform decomposes a function into eigenfunctions for the group of translations.

Here's what looks like a deep dive into this approach to the Fourier Transform (2008):

http://www.systems.caltech.edu/dsp/ppv/papers/journal08post/...

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