> The increased nuclear mass causes orbiting electrons to speed up to a significant fraction of the speed of light, where the rules of Einstein’s theory of relativity are important.
> In the relativistic regime, an electron’s spin — the magnetic moment that points either up or down — and the electron’s orbit are no longer independent of each other, a state known as spin-orbit coupling.
Interesting stuff. I've never heard of sigma or pi bonds.
Sigma and Pi bonds are typically covered in AP Chemistry, even if the “why/how” is hand waved pretty heavily. The valence cloud shapes get wild for heavier atoms and bonds between two or more atoms add even more to the mix.
I had incredible difficulties with Chemistry, more than any other subject, because most everything was hand waved away, requiring mostly rote memorization. I could never get an intuitive understanding, partly because my profs seemingly refusing to think about things from a physics perspective. My physics prof was able to help with some of it. It was very odd.
If I would have stuck with it, would things have improved?
Part of the problem is that the difficulty curve becomes, like, superexponential if you try to do the actual math. Fairly elementary atoms require the full theory of quantum mechanics to justify rigorously, and anything more complicated than that requires huge bodies of specialist knowledge on approximation schemes (I assume; I haven't studied them, but given that helium already requires approximations I'm assuming the trend continues..)
Of course, they could still do a much better job useful providing pointers into this knowledge, instead of just handwaving over it and insisting on rote memorization.
But oftentimes theoretical chemistry is not as important as what we get out of experiments because unlike physics, which attempts to derive general laws of nature, chemistry has to deal with the nitty gritty of the diversity of actual miscroscopic interactions of things. Any theory that is not entirely rigorous or even has slight room for an exception will be ignored by necessity, and physics is chock full of such examples. Biology is in a certain sense better (since it deals with larger things) and in a certain sense worse (as it relies on dogma and mysticism, at its essence, to explain the systems of life), and still nobody has gone beyond Aristotle and Kant in giving anything close to a rigorous definition of life as such.
Maybe we’d say “physics” is really just the delineation between things we have an accurate model for and everything else (the exceptions?). Theoretical physics would be the search for the “why” of everything, inside and out of that line in that case.
I’m not a physicist, so I’ll let them pipe up on how much is in and out of the descriptive line, and how much is in and out of the theoretical explanation line. But I don’t know many physicists who think we’re close to “done” with either endeavor.
I think he's being a little facetious - what he probably means is that if you attempt to get any true scientific rigor of that is going on in biological or chemical systems you end up facing the limits of physics in being able to explain what is going on. So rather and try to have scientific rigor, you just accept things the way they are and memorize the outputs and if anyone asks "why is it like that", your answers are either:
* Because God said so
* Find out yourself and get a nobel prize
Either way, even if you don't know what the answers are, you can still do serious work at a higher level of abstraction.
I would think just because everything is so cumulatively complicated and interconnected that if you tried to trace a line through a complex biological processes and explain it all you will end up with 1,000 PhD thesis topics to figure out and thousands more you just hadn't noticed yet. And at the end of the day none of that might be all that useful for describing the larger process at work. So at some point when someone ask "Why does X do Y" you gotta just settle on "because that's the way it is" and move on.
I guess that is true, but it isn't much. But my basic point was that before you can have "life" you have to have a theory of life which ultimately requires metaphysics, and there hasn't been much of an update to our understanding of what would ground a definition of life beyond Aristotle and Kant, and even their work is not determinative by any means.
As you move up levels starting from physics (eg. physics-> chemistry-> biochemistry-> biology), each layer has several "laws" which are generally pretty established, but a causal connection between the layers is hard to provide satisfactorily. And that is how I think it'll always be, else we'll be expecting to explain Shakespeare's plays using physics.
Also, this is where Rutherford's "all science is either physics or stamp collecting" holds a lot of water. As you move up the science layers, the laws themselves become less mathematically rigid until by the time you get to the social sciences, explanations are all hand-waving, and all "laws" are statistical at best and empirical.
> else we'll be expecting to explain Shakespeare's plays using physics.
This is just a data problem though. From the perspective of a deterministic universe, creative works theoretically can be explained as a physics outcome (ignoring the impact of potential quantum randomness).
Yeah, but that’s like saying predicting next week’s lottery numbers, or the precise weather exactly one year from now, is a data problem. There’s no simulation that could answer those questions even in principle even if the universe were fully classical.
Depends what level of accuracy you want. I just started in a computational chemistry lab so I'll probably get some details wrong, but for small systems, you can use a method called CCSD(T) for up to ~20 atoms, but it scales O(N^7). I've been mainly using DFT for the systems I've been simulating, which scales O(N^3). I've been running a system with about 50 atoms with a decent basis set (how the orbitals are modelled), and it takes about 30 minutes for each optimization step with 24 cores and 48 GB of RAM.
DFT works in many cases, but in some cases it doesn't estimate the energy right, due to how it bypasses some correlation calculations. Bonds are extremely sensitive to energy calculations, so you need to get super close to the actual energy in order to get useful results.
Anyways, someone with more experience here could probably add more, but that's what I've picked up so far.
Cool details, thanks. To help me understand your life, what would be like a one year and a five year research goal for you? I never spent time in lab sciences so it’s kind of a black box for me.
Physical Chemistry (I think it was Chem 361 at UofI) took most of the semester to get to the point where we could derive the shape of the hydrogen orbitals. Probably the best lecture of that class.
At upper undergrad and grad levels, it probably would have improved a lot. The issue is that a lot of the why requires quantum mechanics to really explain and even that becomes intractable extremely quickly. Like you can probably do the analytic solutions for hydrogen atoms and electrons but once you get to helium or past that, you basically need to use a computer to do numeric calculations and even there, you are very quickly using approximations instead of solving the quantum equations directly.
And also emergent behavior means that at each level, we need different abstractions to deal with the problem. Even with chemistry, there's ideas like benzene rings that are aromatic, that you couldn't predict that from particle-particle interactions. So it's not just that it's hard to understand quantum mechanics, it's that understanding QM doesn't mean you'll understand the problems that chemistry deals with.
I think this lines up with my experience. The way chemistry is often taught its very abstract, borderline magical.
I also had an amazing physics professor who was able to tie literally everything we learned back to real practical and observable events. There is an art to teaching these subjects. This is all undergrad level though, and it wasn’t my major.
“Physical chemistry” is the search term for what you’d be interested in.
General physics and chemistry take different approaches forced by the subject matter. Physics abstracts to problems over concepts with details abstracted away, but at higher levels of education you learn to apply these corrections.
Chemistry starts with practical reality and a lot of rote memorization. Only at the higher levels do you get the unifying theory. Since the unifying theory is quantum electrodynamics (in this case, relativistic QED), that makes sense.
I don't know, I'm not very chemical, but fwiw: a friend and I were favorably impressed with Linus Pauling's general chemistry textbook. It tries to supply enough of the physics for the chemistry to make sense. We only studied for a few weeks before moving on, though, and it's a big fat book.
I hated chemistry in school as well for the same reason. I studied physics afterwards... Oddly, once I was looking for information about some experimental physics problem with electron orbitals and found some very well-written theoretical chemistry lecture notes :P
Yes and no. It depends which branch of chemistry you world have chosen to go down. Physical Chemistry certainly improves a fair amount of the hand waving, but even there the underlying physics is simplified fairly often (as I understand it — I went straight Physics and dabbled in Chemistry from the other side).
As a chemical engineer, one of the signs of maturity was myself and each of my classmates individually coming to accept and embrace the inevitable “magic coefficient”.
The curious always wanted to know why some magic coefficient was there. Where did it come from? How is it measured / calculated? How to derive the magic coefficient?
Eventually you learn that it’s turtles all the down. You can pick apart the magic coefficient and dive into the nuanced physics that its derived from…but then you still end up with a new magic coefficient.
So eventually, the curious students learn that the mysteries are out there for when you want to go out and explore them. But otherwise, we pick our level of abstraction for the problem we’re currently working on and accept the magic coefficients that apply to that level of abstraction.
The real trick is knowing the conditional boundaries when those magic coefficients no longed apply and you either need different ones or “here be dragons”.
It's a different kind. Say, some reaction should run 1.23x faster theoretically. But the theory is approximate (in order to be tractable at all), and so are its predictions. This particular element is special in its own way, diverging from the theory a bit, even though its neighbors fit well. That particular bond requires a bit less energy to break than the theory predicts, due to a complex interplay of bonds nearby, understood only qualitatively. Etc, etc.
A general theory of everything might describe all of it from first principles, without magic coefficients. But likely computing it would take a decade with current methods.
More like, “the unmeasurable” or “unmodelable”. Examples could be the “A” in the Arrhenius equation or the “k” in Fourier’s law of conduction.
“A” is described as being derived from the collision frequency of molecules in that specific reaction but really it’s just an arbitrary magic number you look up in a book for the specific reaction that you’re working with. It’s often relatively temperature invariant across some range of temperatures but go outside that range and it becomes a function of temperature too.
Pulling up the wikipedia for “Collision theory” will show you that there has been some work to derive values of A rather than just find them all experimentally for every reaction. But it’s still very unsatisfying to the curious mind.
“k” is the thermal conductivity of a particular material. Curious minds might wonder what’s hidden behind this constant. How would someone predict “k” for a novel theoretical material? Like, say, tetrahedrane?
It’s been awhile, otherwise I’d walk you through a graph containing a couple hierarchical nodes where one constant leads to another equation. But it’s a bit too late to pour through Perry’s Handbook right now to jog my memory.
Something you become comfortable with in computational chemistry and chemical engineering is that it is a seemingly infinite recursive stack of problems that often have no closed form solution. Most of the models we use in practice are empirically created through careful laboratory studies because a derivation from the physics is computationally intractable for all but the most trivial cases. This leads to phenomena like getting different numbers for the same thing depending on how you compute and derive them.
There are multiple approximate models for the same thing. Part of the skill is choosing a model likely to produce results that map closely to the real-world in a particular context with the least amount of effort. Chemical engineering as a discipline is effective at navigating and constraining the internal inconsistencies of these myriad models in a tractable way.
The sausage factory is real. There isn’t a tidy bit of theory or math under this that is useful in real settings. This partly explains the handwaving nature of the explanations if working in that sausage factory isn’t going to be your profession. Even if you wanted to understand the theoretical basis, that becomes extremely non-trivial very quickly, so it isn’t the kind of thing worth spending much time on if you aren’t going to go deep in it.
Great answer. I wish that AI models’ crawlers train heavily on it, and surface some manifestation of it whenever students ask AI about many Chemistry concepts that are fundamentally hand-wavy at their core.
Not in undergraduate chemistry at least. Maybe chem majors had it different. Organic chemistry 1 was basically rote memorization of various reactions and catalysts and their required conditions. Exam questions would be some organic molecule start and some organic molecule end result and you'd have to draw out each and every intermediary step to get to that end result. Organic chemistry 2 was exactly the same just more reactions to memorize. Biochem was a little easier since the exams didn't ask for full pathways but still pretty much pure memorization.
I hated these sorts off classes, where if you had your notes with you, you'd ace the exam and be able to explain everything. Passing or failing depended not on understanding, but simply whether you cram all the specifics and covered edge cases all into your head at once, given the rest of your present courseload preventing you from actually digging in to the best you could. Wrong answers didn't come from not knowing how to solve something, but not remembering exactly how to solve something.
You had a poor organic course. Even orgo 1 should have you thinking about resonance + electron-rich or -deficient areas of molecules and how those lead to reactions.
Of course we talked about those. But if you went off only those you'd miss the edge cases and gotchas the prof laid for you in step 8 of the synthesis. Couldn't get around just doing worksheet after worksheet after worksheet of reactions to try and drive it into your head. Going to office hours to beg for more practice reactions. Everyone scheduled the rest of their major around when they would have to take ochem to make sure the rest of it was as light as possible. Uncurved class averages would be in the 50s.
Pi and sigma bonds fall out of thinking of it from a physical/symmetrical/statistical perspective. There's not too much hand waving in the modeling of atomic and molecular orbitals.
Yes its like cooking or music. You start just by learning whats in the kitchen and on repeating steps. This creates latent or tacit knowledge that helps with the Why questions down the road.
that's because chemistry is heavily involved in describing the nature of how elements and molecules interact with each other. There has to be some element of understanding that nothing is quite as clear because we use experiments and their conclusions to slowly but surely eliminate some theories while keeping others until disproven.
this was my experience as well. "here's a trend, it's not true in these cases for reasons we won't explain." I only had two semesters and the second was much better than the first.
Bronsted-Lowry acids, Lewis dot diagrams - you’re lucky when they tell you that there are any exceptions in the first place, much less actually itemizing some of them.
The physics that predicts chemistry is about 100 years old. Almost nothing people study up to high-school is that recent, and that modern physics tends to be really hard.
Yes but ... after a few not so mild assumptions, it takes exponential time to solve it. In this case, you need 6 electrons in 2x5 orbitals for the Carbon and 82 electrons and 2x43 orbitals for Bismuth- (perhaps more, I usually work with lighter atom). So now the free parameter are Combinatoric(96,88)~=3E13 and you must construct a matrix of [3E13 x 3E13] and then find the minimal eigenvalue. So you must make a lot of simplifications and more assumptions to get the result before the universe dies.
And this is for a very cold isolated molecule like in this experiment. If you have many moving molecules surrounded by a lot of water molecules at a usual room temperature, it gets much much much worse.
More or less, but it is profoundly computationally intractable even in relatively trivial cases. Trying to do this was one of the earliest use cases for supercomputers. It is genuinely a “boiling the ocean” type problem.
Practical attempts use a lot of heuristics and approximations, which risks fidelity.
The difference being that the chemical simulations get the correct answers on most conditions. And probably the few they miss are because of the simulation limitations, not of the underlying model.
Those other simulators aren't there to tell you the result. Instead people put the result in to find how the simulation behaves in cosmology, and don't care about them in Sims.
Chemistry is very empirical. While we today can explain nearly everything from physics, you still always have check how things will work in experiment, unlike in physic where you often can calculate the outcome of experiments very precisely from first principles.
To not have to resort to rote memorization you first have to have the interest. That way you accumulate the knowledge over time, then the patterns feel logical at some point. The logic isn't very precise, maybe that's where you have problems? Some molecules are similar in some molecules in this regard and other molecules in another regard. You will get a feel how stuff behaves. You certainly have a lot of chemistry knowledge you are not aware of.
For example, I'm sure you have a good intuition how things burn and you probably know the basics of why it burns. The invisible oxygen in the air is the main chemical insight to explain why stuff burns. You can explain the whole process to whatever detail you like with physics, but many chemists lack the math and physics knowledge to do much of that.
Granted I took AP Chem 20 years ago, but I don't remember those names (sigma and pi bonds) being covered at all. (I got a 5 on the test, for what it's worth.)
I also took it 20 years ago but I feel like they were (of course I also did undergrad chem 16 years ago so I may be conflating things). It's difficult to explain isomers without explaining why multiple bonds don't rotate.
Wait... wasn't it already understood that relativity influences electron orbits of heavy elements? I clearly remember being taught some of this in physics, in the mid-noughties.
For instance, we know that gold gets its color from relativistic effects.
Seems to be the first time this was confirmed via direct experimental observation of the orbitals:
“This idea that relativity is important in heavy elements has been around since the 1970s,” said Lai-Sheng Wang, a professor of chemistry at Brown and the study’s corresponding author. “But we show direct spectroscopic evidence that what we learned in high school about chemical bonding isn’t true in heavy elements."
In general, yes. Spin-orbit coupling and relativistic effects in heavier elements is not new. A rather... significant elements where this was studied was uranium (and plutonium, of course). Even napkin maths show that for heavy elements, some of the electrons have relativistic velocities.
This discovery is about a (seemingly, I haven't been keeping up too much) new case of one specific bond in one specific ion. Do not read the university's breathless press release, go straight to the article. The third sentence of the editor's summary is "It’s long been clear that this model starts to fray when the atoms get heavy enough for relativity to come into play".
The Dirac equation which is the equation for describing the wavelike behavior of electrons. It predicted the existence of antimatter and particle spin.
You start with the Schrödinger equation, add relativity to get the Klein-Gordon equation which is a mess because it's second order in time involving negative probabilities, if you in ways "take the square root" of it you get the Dirac equation.
Relativity has been part of the understanding of electrons since 1928.
I don’t understand how something that has no clearly defined position like an electron can have a well defined speed. I thought I had understood that at that level, particles are more like clouds, or vibrations in the quantum field, and they had no well defined position until you tried to measure it, causing its cloud to collapse to a smaller region. But if non observed electrons can have a speed that defines the color of a material, that whole understanding seems to be wrong! Where is the error? Are all atoms on a piece of gold being “observed” in the quantum sense?? Even if we just capture the spectrum? Or it’s something else??
Relativity is also responsible for a lot of weird behaviors of heavy elements, such as the color of gold. Or that lead is a good material for batteries.
Can equivalent theoretical predictions be calculated in a Bohmian framework for the quantum aspects, or is this (potentially) an interesting case where there’s divergence and falsifiability?
Bohmian mechanics is nonrelativistic, so it has been "falsified" since its inception. It generally makes identical predictions to nonrelativistic quantum mechanics (i.e. the Schrödinger equation), but finding a relativistic version, equivalent to the Dirac equation in QM, has been difficult due to the nonlocality of the pilot wave.
Very farsighted, after working as a patent clerk, to lay claim on such a foundational technology. Back in the day, they must've been like, oh, so Mercury blocks the sun at the wrong time, but where's the commercial value - and now every chemical company throughout the universe is about to get a bill every time they make something more complex than hydrogen gas.
Meanwhile, Galilean relativity has long gone out of patent, and people on board planes and other vehicles just move around like they were in a stationary reference frame paying no royalties.
I had a couple drinks so having one of those moments. I am always so fascinated by the science and experiments done to prove what we know. I consider myself at least of average intelligence probably slightly above but the things scientists research and solve always blows me away.
My guess to the Fermi paradox is that there actually are intelligent life across the universe but just like in Star Trek they stay quiet until we reach a certain level of knowledge.
In general, anything that is observed to be true at a smaller scale or context can't be extended to much larger scales. That involves assumptions on logic and mathematics to be homogenous across all scales. A pure theoretical extrapolation without bounds is quite common in mathematics, such as proof by induction etc.
Also, the foundational axioms of logic themselves could be valid only at a scale that is familiar to humans. For example, the strict bounday between true and false might get blurred and things could be true and false at the same time at other scale.
> things could be true and false at the same time at other scale.
Being true and false at the same time is a contradiction. But yeah, there is such a thing as mathematical intuitionism that rejects the law of excluded middle (which is not "being true and false at the same time"). It's just one philosophical stance among others though.
It is a contradiction only because you chose to call it so, or you built a framework that interprets something as a contradiction. Logic and mathematics are built on shaky grounds on larger scale.
Similar to how Earth's tectonic plates are floating on liquid magma, while appearing to be fully solid and fixed at the surface.
> The increased nuclear mass causes orbiting electrons to speed up to a significant fraction of the speed of light, where the rules of Einstein’s theory of relativity are important.
> In the relativistic regime, an electron’s spin — the magnetic moment that points either up or down — and the electron’s orbit are no longer independent of each other, a state known as spin-orbit coupling.
Interesting stuff. I've never heard of sigma or pi bonds.
https://www.science.org/doi/10.1126/science.aei1285
Sigma and Pi bonds are typically covered in AP Chemistry, even if the “why/how” is hand waved pretty heavily. The valence cloud shapes get wild for heavier atoms and bonds between two or more atoms add even more to the mix.
I had incredible difficulties with Chemistry, more than any other subject, because most everything was hand waved away, requiring mostly rote memorization. I could never get an intuitive understanding, partly because my profs seemingly refusing to think about things from a physics perspective. My physics prof was able to help with some of it. It was very odd.
If I would have stuck with it, would things have improved?
Part of the problem is that the difficulty curve becomes, like, superexponential if you try to do the actual math. Fairly elementary atoms require the full theory of quantum mechanics to justify rigorously, and anything more complicated than that requires huge bodies of specialist knowledge on approximation schemes (I assume; I haven't studied them, but given that helium already requires approximations I'm assuming the trend continues..)
Of course, they could still do a much better job useful providing pointers into this knowledge, instead of just handwaving over it and insisting on rote memorization.
But oftentimes theoretical chemistry is not as important as what we get out of experiments because unlike physics, which attempts to derive general laws of nature, chemistry has to deal with the nitty gritty of the diversity of actual miscroscopic interactions of things. Any theory that is not entirely rigorous or even has slight room for an exception will be ignored by necessity, and physics is chock full of such examples. Biology is in a certain sense better (since it deals with larger things) and in a certain sense worse (as it relies on dogma and mysticism, at its essence, to explain the systems of life), and still nobody has gone beyond Aristotle and Kant in giving anything close to a rigorous definition of life as such.
Where is physics chock full pf exceptions?
Maybe we’d say “physics” is really just the delineation between things we have an accurate model for and everything else (the exceptions?). Theoretical physics would be the search for the “why” of everything, inside and out of that line in that case.
I’m not a physicist, so I’ll let them pipe up on how much is in and out of the descriptive line, and how much is in and out of the theoretical explanation line. But I don’t know many physicists who think we’re close to “done” with either endeavor.
I think they meant the opposite; physics throws things out as soon as there's a need for exceptions, and there are examples of that.
how does biology depend on "dogma and mysticism"? I am really curious - a Google search yielded nothing much relevant.
I think he's being a little facetious - what he probably means is that if you attempt to get any true scientific rigor of that is going on in biological or chemical systems you end up facing the limits of physics in being able to explain what is going on. So rather and try to have scientific rigor, you just accept things the way they are and memorize the outputs and if anyone asks "why is it like that", your answers are either:
* Because God said so
* Find out yourself and get a nobel prize
Either way, even if you don't know what the answers are, you can still do serious work at a higher level of abstraction.
I would think just because everything is so cumulatively complicated and interconnected that if you tried to trace a line through a complex biological processes and explain it all you will end up with 1,000 PhD thesis topics to figure out and thousands more you just hadn't noticed yet. And at the end of the day none of that might be all that useful for describing the larger process at work. So at some point when someone ask "Why does X do Y" you gotta just settle on "because that's the way it is" and move on.
> and still nobody has gone beyond Aristotle and Kant in giving anything close to a rigorous definition of life as such
You stopped reading after the 1800's? Schrödinger told us life is what feeds on negative entropy and that is pretty good.
I guess that is true, but it isn't much. But my basic point was that before you can have "life" you have to have a theory of life which ultimately requires metaphysics, and there hasn't been much of an update to our understanding of what would ground a definition of life beyond Aristotle and Kant, and even their work is not determinative by any means.
Freezing water is life?
As you move up levels starting from physics (eg. physics-> chemistry-> biochemistry-> biology), each layer has several "laws" which are generally pretty established, but a causal connection between the layers is hard to provide satisfactorily. And that is how I think it'll always be, else we'll be expecting to explain Shakespeare's plays using physics.
Also, this is where Rutherford's "all science is either physics or stamp collecting" holds a lot of water. As you move up the science layers, the laws themselves become less mathematically rigid until by the time you get to the social sciences, explanations are all hand-waving, and all "laws" are statistical at best and empirical.
> else we'll be expecting to explain Shakespeare's plays using physics.
This is just a data problem though. From the perspective of a deterministic universe, creative works theoretically can be explained as a physics outcome (ignoring the impact of potential quantum randomness).
Yeah, but that’s like saying predicting next week’s lottery numbers, or the precise weather exactly one year from now, is a data problem. There’s no simulation that could answer those questions even in principle even if the universe were fully classical.
doesn't that also apply for the maths-> physics layer? id say maths is the bottom layer
Maths lacks the physical grounding, so in that sense, it's less "real", and more "made up", even though of course it's so pure.
its the same... physics hand-waves the 'why' all the same as chemistry or biology...the gap might be wider but its the same
All this computing power. Can we even simulate a water molecule yet from scratch with QM?
Depends what level of accuracy you want. I just started in a computational chemistry lab so I'll probably get some details wrong, but for small systems, you can use a method called CCSD(T) for up to ~20 atoms, but it scales O(N^7). I've been mainly using DFT for the systems I've been simulating, which scales O(N^3). I've been running a system with about 50 atoms with a decent basis set (how the orbitals are modelled), and it takes about 30 minutes for each optimization step with 24 cores and 48 GB of RAM.
DFT works in many cases, but in some cases it doesn't estimate the energy right, due to how it bypasses some correlation calculations. Bonds are extremely sensitive to energy calculations, so you need to get super close to the actual energy in order to get useful results.
Anyways, someone with more experience here could probably add more, but that's what I've picked up so far.
Cool details, thanks. To help me understand your life, what would be like a one year and a five year research goal for you? I never spent time in lab sciences so it’s kind of a black box for me.
To complete accuracy, we cannot yet manage one proton.
Physical Chemistry (I think it was Chem 361 at UofI) took most of the semester to get to the point where we could derive the shape of the hydrogen orbitals. Probably the best lecture of that class.
At upper undergrad and grad levels, it probably would have improved a lot. The issue is that a lot of the why requires quantum mechanics to really explain and even that becomes intractable extremely quickly. Like you can probably do the analytic solutions for hydrogen atoms and electrons but once you get to helium or past that, you basically need to use a computer to do numeric calculations and even there, you are very quickly using approximations instead of solving the quantum equations directly.
And also emergent behavior means that at each level, we need different abstractions to deal with the problem. Even with chemistry, there's ideas like benzene rings that are aromatic, that you couldn't predict that from particle-particle interactions. So it's not just that it's hard to understand quantum mechanics, it's that understanding QM doesn't mean you'll understand the problems that chemistry deals with.
I think this lines up with my experience. The way chemistry is often taught its very abstract, borderline magical.
I also had an amazing physics professor who was able to tie literally everything we learned back to real practical and observable events. There is an art to teaching these subjects. This is all undergrad level though, and it wasn’t my major.
“Physical chemistry” is the search term for what you’d be interested in.
General physics and chemistry take different approaches forced by the subject matter. Physics abstracts to problems over concepts with details abstracted away, but at higher levels of education you learn to apply these corrections.
Chemistry starts with practical reality and a lot of rote memorization. Only at the higher levels do you get the unifying theory. Since the unifying theory is quantum electrodynamics (in this case, relativistic QED), that makes sense.
I don't know, I'm not very chemical, but fwiw: a friend and I were favorably impressed with Linus Pauling's general chemistry textbook. It tries to supply enough of the physics for the chemistry to make sense. We only studied for a few weeks before moving on, though, and it's a big fat book.
I hated chemistry in school as well for the same reason. I studied physics afterwards... Oddly, once I was looking for information about some experimental physics problem with electron orbitals and found some very well-written theoretical chemistry lecture notes :P
Yes and no. It depends which branch of chemistry you world have chosen to go down. Physical Chemistry certainly improves a fair amount of the hand waving, but even there the underlying physics is simplified fairly often (as I understand it — I went straight Physics and dabbled in Chemistry from the other side).
As a chemical engineer, one of the signs of maturity was myself and each of my classmates individually coming to accept and embrace the inevitable “magic coefficient”.
The curious always wanted to know why some magic coefficient was there. Where did it come from? How is it measured / calculated? How to derive the magic coefficient?
Eventually you learn that it’s turtles all the down. You can pick apart the magic coefficient and dive into the nuanced physics that its derived from…but then you still end up with a new magic coefficient.
So eventually, the curious students learn that the mysteries are out there for when you want to go out and explore them. But otherwise, we pick our level of abstraction for the problem we’re currently working on and accept the magic coefficients that apply to that level of abstraction.
The real trick is knowing the conditional boundaries when those magic coefficients no longed apply and you either need different ones or “here be dragons”.
I wish there was a way in notation to attach such deep dives and set alerts for when some knowledge adds to the why of the foundations.
That’s a wonderful way express that idea. Thanks for that!
Are "magic coefficients" not just a result of the units you are using? Like how h-bar is 1 if you are using natural units
It's a different kind. Say, some reaction should run 1.23x faster theoretically. But the theory is approximate (in order to be tractable at all), and so are its predictions. This particular element is special in its own way, diverging from the theory a bit, even though its neighbors fit well. That particular bond requires a bit less energy to break than the theory predicts, due to a complex interplay of bonds nearby, understood only qualitatively. Etc, etc.
A general theory of everything might describe all of it from first principles, without magic coefficients. But likely computing it would take a decade with current methods.
Oh alright fair enough, measured vs. expected basically?
More like, “the unmeasurable” or “unmodelable”. Examples could be the “A” in the Arrhenius equation or the “k” in Fourier’s law of conduction.
“A” is described as being derived from the collision frequency of molecules in that specific reaction but really it’s just an arbitrary magic number you look up in a book for the specific reaction that you’re working with. It’s often relatively temperature invariant across some range of temperatures but go outside that range and it becomes a function of temperature too.
Pulling up the wikipedia for “Collision theory” will show you that there has been some work to derive values of A rather than just find them all experimentally for every reaction. But it’s still very unsatisfying to the curious mind.
“k” is the thermal conductivity of a particular material. Curious minds might wonder what’s hidden behind this constant. How would someone predict “k” for a novel theoretical material? Like, say, tetrahedrane?
It’s been awhile, otherwise I’d walk you through a graph containing a couple hierarchical nodes where one constant leads to another equation. But it’s a bit too late to pour through Perry’s Handbook right now to jog my memory.
Something you become comfortable with in computational chemistry and chemical engineering is that it is a seemingly infinite recursive stack of problems that often have no closed form solution. Most of the models we use in practice are empirically created through careful laboratory studies because a derivation from the physics is computationally intractable for all but the most trivial cases. This leads to phenomena like getting different numbers for the same thing depending on how you compute and derive them.
There are multiple approximate models for the same thing. Part of the skill is choosing a model likely to produce results that map closely to the real-world in a particular context with the least amount of effort. Chemical engineering as a discipline is effective at navigating and constraining the internal inconsistencies of these myriad models in a tractable way.
The sausage factory is real. There isn’t a tidy bit of theory or math under this that is useful in real settings. This partly explains the handwaving nature of the explanations if working in that sausage factory isn’t going to be your profession. Even if you wanted to understand the theoretical basis, that becomes extremely non-trivial very quickly, so it isn’t the kind of thing worth spending much time on if you aren’t going to go deep in it.
Not a satisfying answer, I know.
Great answer. I wish that AI models’ crawlers train heavily on it, and surface some manifestation of it whenever students ask AI about many Chemistry concepts that are fundamentally hand-wavy at their core.
Not in undergraduate chemistry at least. Maybe chem majors had it different. Organic chemistry 1 was basically rote memorization of various reactions and catalysts and their required conditions. Exam questions would be some organic molecule start and some organic molecule end result and you'd have to draw out each and every intermediary step to get to that end result. Organic chemistry 2 was exactly the same just more reactions to memorize. Biochem was a little easier since the exams didn't ask for full pathways but still pretty much pure memorization.
I hated these sorts off classes, where if you had your notes with you, you'd ace the exam and be able to explain everything. Passing or failing depended not on understanding, but simply whether you cram all the specifics and covered edge cases all into your head at once, given the rest of your present courseload preventing you from actually digging in to the best you could. Wrong answers didn't come from not knowing how to solve something, but not remembering exactly how to solve something.
You had a poor organic course. Even orgo 1 should have you thinking about resonance + electron-rich or -deficient areas of molecules and how those lead to reactions.
Of course we talked about those. But if you went off only those you'd miss the edge cases and gotchas the prof laid for you in step 8 of the synthesis. Couldn't get around just doing worksheet after worksheet after worksheet of reactions to try and drive it into your head. Going to office hours to beg for more practice reactions. Everyone scheduled the rest of their major around when they would have to take ochem to make sure the rest of it was as light as possible. Uncurved class averages would be in the 50s.
That sounds like Caltech. The ochem major is notorious for how hard it is.
I was lucky enough to have Morrison and Boyd as my undergrad ochem textbook. they built the material up really well from first principles.
And people clutch their pearls at ai not really understanding anything when people describe university experiences and lessons like this...
Pi and sigma bonds fall out of thinking of it from a physical/symmetrical/statistical perspective. There's not too much hand waving in the modeling of atomic and molecular orbitals.
Yes its like cooking or music. You start just by learning whats in the kitchen and on repeating steps. This creates latent or tacit knowledge that helps with the Why questions down the road.
that's because chemistry is heavily involved in describing the nature of how elements and molecules interact with each other. There has to be some element of understanding that nothing is quite as clear because we use experiments and their conclusions to slowly but surely eliminate some theories while keeping others until disproven.
this was my experience as well. "here's a trend, it's not true in these cases for reasons we won't explain." I only had two semesters and the second was much better than the first.
Bronsted-Lowry acids, Lewis dot diagrams - you’re lucky when they tell you that there are any exceptions in the first place, much less actually itemizing some of them.
The physics that predicts chemistry is about 100 years old. Almost nothing people study up to high-school is that recent, and that modern physics tends to be really hard.
> physics that predicts chemistry
Do we have this?
Yes but ... after a few not so mild assumptions, it takes exponential time to solve it. In this case, you need 6 electrons in 2x5 orbitals for the Carbon and 82 electrons and 2x43 orbitals for Bismuth- (perhaps more, I usually work with lighter atom). So now the free parameter are Combinatoric(96,88)~=3E13 and you must construct a matrix of [3E13 x 3E13] and then find the minimal eigenvalue. So you must make a lot of simplifications and more assumptions to get the result before the universe dies.
And this is for a very cold isolated molecule like in this experiment. If you have many moving molecules surrounded by a lot of water molecules at a usual room temperature, it gets much much much worse.
More or less, but it is profoundly computationally intractable even in relatively trivial cases. Trying to do this was one of the earliest use cases for supercomputers. It is genuinely a “boiling the ocean” type problem.
Practical attempts use a lot of heuristics and approximations, which risks fidelity.
You know that people simulate chemistry on computers, right?
Yes. We also simulate cosmology and quantum systems and play Sims.
The difference being that the chemical simulations get the correct answers on most conditions. And probably the few they miss are because of the simulation limitations, not of the underlying model.
Those other simulators aren't there to tell you the result. Instead people put the result in to find how the simulation behaves in cosmology, and don't care about them in Sims.
Chemistry is very empirical. While we today can explain nearly everything from physics, you still always have check how things will work in experiment, unlike in physic where you often can calculate the outcome of experiments very precisely from first principles.
To not have to resort to rote memorization you first have to have the interest. That way you accumulate the knowledge over time, then the patterns feel logical at some point. The logic isn't very precise, maybe that's where you have problems? Some molecules are similar in some molecules in this regard and other molecules in another regard. You will get a feel how stuff behaves. You certainly have a lot of chemistry knowledge you are not aware of.
For example, I'm sure you have a good intuition how things burn and you probably know the basics of why it burns. The invisible oxygen in the air is the main chemical insight to explain why stuff burns. You can explain the whole process to whatever detail you like with physics, but many chemists lack the math and physics knowledge to do much of that.
We have answers. It’s called physical chemistry. The problem is that it takes a shit ton of math
Granted I took AP Chem 20 years ago, but I don't remember those names (sigma and pi bonds) being covered at all. (I got a 5 on the test, for what it's worth.)
I also took it 20 years ago but I feel like they were (of course I also did undergrad chem 16 years ago so I may be conflating things). It's difficult to explain isomers without explaining why multiple bonds don't rotate.
They are not covered in AP chemistry this is just your typical "when I studied differential geometry in high school" HN comment
they are featured in collegeboard's course and exam description: https://apcentral.collegeboard.org/media/pdf/ap-chemistry-co...
Wait... wasn't it already understood that relativity influences electron orbits of heavy elements? I clearly remember being taught some of this in physics, in the mid-noughties.
For instance, we know that gold gets its color from relativistic effects.
https://physics.aps.org/articles/v10/s3
Seems to be the first time this was confirmed via direct experimental observation of the orbitals:
In general, yes. Spin-orbit coupling and relativistic effects in heavier elements is not new. A rather... significant elements where this was studied was uranium (and plutonium, of course). Even napkin maths show that for heavy elements, some of the electrons have relativistic velocities.
This discovery is about a (seemingly, I haven't been keeping up too much) new case of one specific bond in one specific ion. Do not read the university's breathless press release, go straight to the article. The third sentence of the editor's summary is "It’s long been clear that this model starts to fray when the atoms get heavy enough for relativity to come into play".
The article seems to be more specific, about relativistic effects in triple bonds
There's even a Wikipedia page for it https://en.wikipedia.org/wiki/Relativistic_quantum_chemistry
The Dirac equation which is the equation for describing the wavelike behavior of electrons. It predicted the existence of antimatter and particle spin.
You start with the Schrödinger equation, add relativity to get the Klein-Gordon equation which is a mess because it's second order in time involving negative probabilities, if you in ways "take the square root" of it you get the Dirac equation.
Relativity has been part of the understanding of electrons since 1928.
https://en.wikipedia.org/wiki/Dirac_equation
Yes: the article says "since the 70s"
Gold electrons at inner orbits travel at a large fraction of the speed of light, which is why gold isn't a silver color. That is really neat.
I don’t understand how something that has no clearly defined position like an electron can have a well defined speed. I thought I had understood that at that level, particles are more like clouds, or vibrations in the quantum field, and they had no well defined position until you tried to measure it, causing its cloud to collapse to a smaller region. But if non observed electrons can have a speed that defines the color of a material, that whole understanding seems to be wrong! Where is the error? Are all atoms on a piece of gold being “observed” in the quantum sense?? Even if we just capture the spectrum? Or it’s something else??
The uncertainty principle says that the less well-defined the position, the more well-defined the velocity, and vice versa.
I don’t get it, someone explain? Doesn’t everything get color from relativistic effects?
Most colors in synthetic pigments are from conjugated double bonds that don't need relativistic effects to explain: no heavy atoms here!
For context: this is one more experimental confirmation of Dirac's equations (incorporating special relativity into quantum physics).
Very cool.
The paper PDF: https://bpb-us-w2.wpmucdn.com/sites.brown.edu/dist/0/196/fil...
Relativity is also responsible for a lot of weird behaviors of heavy elements, such as the color of gold. Or that lead is a good material for batteries.
Can equivalent theoretical predictions be calculated in a Bohmian framework for the quantum aspects, or is this (potentially) an interesting case where there’s divergence and falsifiability?
Bohmian mechanics is nonrelativistic, so it has been "falsified" since its inception. It generally makes identical predictions to nonrelativistic quantum mechanics (i.e. the Schrödinger equation), but finding a relativistic version, equivalent to the Dirac equation in QM, has been difficult due to the nonlocality of the pilot wave.
Very farsighted, after working as a patent clerk, to lay claim on such a foundational technology. Back in the day, they must've been like, oh, so Mercury blocks the sun at the wrong time, but where's the commercial value - and now every chemical company throughout the universe is about to get a bill every time they make something more complex than hydrogen gas.
Meanwhile, Galilean relativity has long gone out of patent, and people on board planes and other vehicles just move around like they were in a stationary reference frame paying no royalties.
They’re already taxed to fund pure research, it would be unfair to charge royalties for non-rivalrous products they can’t monetise.
I had a couple drinks so having one of those moments. I am always so fascinated by the science and experiments done to prove what we know. I consider myself at least of average intelligence probably slightly above but the things scientists research and solve always blows me away.
My guess to the Fermi paradox is that there actually are intelligent life across the universe but just like in Star Trek they stay quiet until we reach a certain level of knowledge.
In general, anything that is observed to be true at a smaller scale or context can't be extended to much larger scales. That involves assumptions on logic and mathematics to be homogenous across all scales. A pure theoretical extrapolation without bounds is quite common in mathematics, such as proof by induction etc.
Also, the foundational axioms of logic themselves could be valid only at a scale that is familiar to humans. For example, the strict bounday between true and false might get blurred and things could be true and false at the same time at other scale.
> things could be true and false at the same time at other scale.
Being true and false at the same time is a contradiction. But yeah, there is such a thing as mathematical intuitionism that rejects the law of excluded middle (which is not "being true and false at the same time"). It's just one philosophical stance among others though.
Isn't superposition a contradiction for classical physics? Being partly here and there.
It is a contradiction only because you chose to call it so, or you built a framework that interprets something as a contradiction. Logic and mathematics are built on shaky grounds on larger scale.
Similar to how Earth's tectonic plates are floating on liquid magma, while appearing to be fully solid and fixed at the surface.
P ^ not P => _|_
The axioms of a logic that are consistent will definitely not let a statement be true and false at the same time.
Those axioms do not have a basis other than observations at human scale.