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.
If I would have stuck with it, would things have improved?
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.
* 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.
so there is no way to extrapolate/interpolate, anything which was not directly measured is basically unknown since it could be yet another exception
or in programming language, the worse spaghetti code you could imagine, full of feature flags randomly enabled inconsistently
We know that mass of matter does not explain even half of the mass observed in the Universe; we haven't thrown out the explanations of mass and inertial gravity, but have a placeholder called "dark matter" to refer to the missing explanation.
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.
Dark matter is a great example.
Our understanding of gravitation didn't cleanly apply at ultra-large scales so we had to add a massive fudge factor.
You can't "go faster" than the speed of light, but space in between things can expand faster than the speed of light.
It seems like things that are "settled" regularly get an "ope, but except for this special case..." treatment.
Physics education sometimes aligns with historical evolution of the theories, mostly because that builds intuition and because the mathematical founsations of the improved theories need to be taught first. That leads to the "but in this case..." moments, but you need to realize that what you get taught as a "fix" is practically always a careful evolution that also reproduces all predictions from the less complete earlier theory.
You stopped reading after the 1800's? Schrödinger told us life is what feeds on negative entropy and that is pretty good.
Physics, whether at atomic level, or on a much larger scale, is simple enough that reductionism usually works and you can calculate behavior from first principles using a few memorized "laws"
Biology is well past the point of complexity where you can do this most of the time, unless perhaps you are at the level of aspects of cellular behavior that can be analyzed in terms of chemistry.
Chemistry is in-between physics and biology in terms of complexity. In simple cases chemistry can be explained in terms of physics, but as AlphaFold has shown when you get to a certain level of complexity (in this case protein folding) empiricism takes over and you need to perform experiments and memorize results.
I think modern science and philosophy has a reasonable understanding of what life is, even if you disagree. This is certainly more a matter of philosophy than science, but it seems the best definition of life is based on the ability of a system to actively maintain a boundary between itself and the external world, thereby combating the 2nd "law" (statistical tendency) of thermodynamics. Maybe an interesting/useful definition (which is somewhat arbitrary) also needs to involve something like consuming energy/resources from the environment.
Only in the most hand-wavey sense. Actual simulation of the cell interior with even comically coarse grained models is prohibitively expensive. It comes up a lot in neuroscience where it sure would be nice to be able to credibly simulate even a single neuron at the molecular level. (I'm several years out of date on the state of that field so it's possible someone managed to pull it off in the meantime but even if so the broader point still stands.)
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.
Math isn't attempting to describe a physical universe. It provides the substrate upon which such a description can be expressed and validated - found to be consistent with itself - but many valid descriptions do not describe our universe. Physics is the empirical search for the correct mathematical description of our universe.
thats just at the current state of the art...doesnt mean a complete maths cannot...its arguably debatable why physics follow some maths and why the specific constrains
Are there any papers where this possibility is explored? What does it mean to have a complete understanding of mathematics?
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).
In other words, physics can explain Shakespeare's plays when you hand-wave away the biggest reason it cannot.
> theoretically
... meaning not in reality, but in an abstraction of reality that conveniently leaves out the hard part.
> This is just a data problem though.
The word "just" makes it sound like that data problem is a minor inconvenience, and not a fundamental obstacle.
Becoming a billionaire is simple, after all it's just a money problem.
I mean, you're right in that (leaving out quantum randomness), you could predict macroscopic outcomes based on a physics simulation that includes all elementary particles explicitly, if you assume that such a simulation can be scaled from <10 particles to macroscopic numbers. But there is no evidence that this assumption is true, so it remains an interesting thought experiment that gets confused with reality because people like to slap the "in theory" label on it.
Edit: and less universal. Physics underlies biology, chemistry, nuclear tech & more. Biology (so far) only applies to carbon-based life as we know it on Earth.
Yes, this is key in my mind. It's not really that the laws and definitions become less strict of themselves, it's that the subjects under study become less uniform. It's fine to study a few atoms in isolation and describe their features, but if you put a lot of them together they'd better be in a uniform lattice or your calculations will take more than a lifetime to complete. If you want to describe the interaction in a drop of water, you don't use the Standard Model to integrate over 3e22 baryon fields.
Yes, physics underlies all other fields. But fundamental physics is also completely untractable to solve problems in those other fields, even if Heisenberg would allow it.
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.
Right now the lab is having me get comfortable using software like Gaussian and ORCA by simulating a bifurcating reaction. This is a reaction that, depending on the catalyst's momentum, will change what site it bonds to (it makes either a 6-membered or 7-membered ring). I'm finding the intermediate states (where the molecule is most stable) and transition states (the tipping point), and then running trajectories to see which output is more likely.
Once I've finished simulating that, I should be comfortable enough with the process to jump on the bigger project, which is machine learning interatomic potential (MLIP) model distillation. There's a lot of exciting work around speeding up DFT methods by using machine learning (note this is not generative AI, it's merely predicting the molecule energy based on atomic positions). So my one year goal is to get on that project and start contributing.
My five year goal is to, well, graduate. But then I'll probably do a PhD in computational chemistry, since I'm really interested in ways to speed up and scale existing methods. My big dream is to simulate large biological systems while still having bond formation and breaking, to automatically elucidate biochemical pathways, but there's still a lot of steps in-between.
I assume you are familiar with:
https://matt.might.net/articles/phd-school-in-pictures/
I hope and pray that your research helps to make the world a better place and that the rest of us can use your knowledge to help to make the world a place which merits your research.
I haven't seen that website before, but it sounds pretty accurate from what I've heard. It's insane how high of a mountain needs to be climbed just to catch up to the state-of-the-art, and how much work is needed to push through to figure out something truly new.
Here's to making the world a better place!
To simulate a water molecule you do so with a weakly coupled SU(1) gauge theory (light does not interact with itself at tree order) problem where the masses of all constituents are orders of magnitude above the relevant energy scales (you can think of it as the electrons and nuclei and particles coming in and out of existence are contained in a renormalization scheme).
We have "good simulation models" of both, but the former is extraordinarily complicated compared to the latter for the reasons stated above.
To a useful level of accuracy we can certainly simulate water. And we can do the same for a single proton for some definitions of useful (but not other definitions).
truly ab initio methods involve figuring out electronic properties from scratch like ionization energy or bandstructure. the real issue is that we dont have exact relations for the exchange and correlation terms. we can know the kinetic energy and charge screening, but we dont know how the electrons are interacting with each other. generally the xc term is treated as a function of electron density or its gradient (see: lda, gga, meta-gga) but there are so many different ways to approximate that. different models are good for different applications also, like transition metals vs organics. and then theres the issue of basis sets (most people use gaussian basis sets that have been tuned over many years but theres also plane waves and finite element methods) which can also change results. and even once u have a decent approximation of density you can try perturbative methods (GW family, delta scf i count also) to try and improve the approximation. i am rambling and typing this on my phone. essentially yes, but often calculations are a little inaccurate. but more accuracy has a higher computational cost, which makes it hard to run larger simulations. tradeoffs of engineering. hope this was coherent.
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”.
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.
“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.
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.
Do we have this?
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.
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.
Practical attempts use a lot of heuristics and approximations, which risks fidelity.
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.
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.
I think misconceptions commonly arise because there are so many examples where we know how to simulate each part with arbitrary precision but the scale of the system is where it all falls over. That just doesn't match up with our everyday experiences because systems on the scale of avagadros number or O(n^7) algorithms applied to absurdly small timesteps are anything but typical. It's difficult for people to wrap their minds around the implications of having to consider things on nanosecond timescales.
But yes, nano and even femtosecond level second stuff is pretty mind bending.
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.
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.
Yes.
I have a B.Sc in Chemistry (Honours) from late 1980s and it was not until the final year that things finally began to click. The main catalysts were the books "Concise Inorganic Chemistry by J.D.Lee" and "Mechanism in Organic Chemistry by Peter Sykes". Both beautifully written and try to give a framework within which to think viz. the former based on the periodic table and the latter on carbon valence bond properties. I think i need to revisit these (and other books) to justify my degree in Chemistry :-)
For background and inspiration, consult Linus Pauling's classics; The Nature of the Chemical Bond and General Chemistry - https://archive.org/search?query=creator%3A%22Pauling+Linus%...
Linus Pauling (the only scientist in history to be awarded two undivided, unshared Nobel Prizes) - https://en.wikipedia.org/wiki/Linus_Pauling
> Exclusion Statement: Molecular orbital theory is recommended as a way to provide deeper insight into bonding. However, the AP Exam will neither explicitly assess molecular orbital diagrams, filling of molecular orbitals, nor the distinction between bonding, nonbonding, and antibonding orbitals.
Orbital theory is usually taught in organic chemistry and then inorganic for those who take that in college. AP chem targets "gen chem" which does not, as the above statement says, does not get into orbitals on that level at all. I'm familiar with gen chem as taught at least in 3 universities, none touched molecular orbitals.
If someone were to teach orbital theory in general chemistry, it would be a lot of hand waving and not much actual mathematics which was the point of the original comment. To cover molecular orbital theory is satisfactorily. You need to know quite a bit of the mathematics behind differential equations and statistical mechanics etc. AP chem isn't going to cover this. But maybe your 9th grade differential geometry class covered all this ;))