smaerd
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Bonding, what do I need to know?
Okay so from the title, you might be saying "I can't possibly explain bonding in a post go f*$& yourself", which would be entirely valid, if that
was what I was asking. Read through the post.
I'm a chem 1 student(in two weeks chem 2) and I truly want to learn whats going on inside of atoms as well as what they do when bonds are formed.
First it was the octet rule and all that garbage in intro to chem. "just ignore the d-block transition elements until chem 1" lol. Which was useful no
doubt in figuring out the basic concepts of what was going on, but pretty worthless overall.
Then came the electronegativity, lewis structures, VSEPR, and bare-bones hybridization. Yet, pretty much each class my prof says "once you get further
into chem you learn that this isn't the way things are". Which I know to be true to a degree, but I can't find any other information. Is hybridization
theory actually used or is it kind of a visual 'because we told you so' model until people get into the actual quantum mechanics(if that's the right
subject) of it? It's not hard to use or memorize, if you think this is complaining your reading this wrong. I wanna know why!
I learn by taking things apart and seeing how they work(even if it's piles of complex equations). Learning things this way for me, is kind of like
using a nail to understand a hammer. I know it hits really hard and that it puts the nail through the wood, but I'm not seeing the tool.(probably a
shit analogy sorry)
I want to get to the heart of it and don't really know where to go. So what topics/theories/books that are useful should I be reading about and taking
to heart? Or should I stick with my instructors pace(probably)? Any tips for a newb chem major would be highly appreciated(whats important, whats
tricky, etc).
Thanks again scimad!
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DDTea
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Through my chemistry program, they basically taught us as much about bonding as we needed to know for a particular course. That is, they filled in
blanks as we went along and gradually introduced more and more complex models.
What they taught us in O. Chem. was not pure Valence Bond Theory--it was a sort of hybrid of MO/VBT. When you start talking about things like "pi
bonds" or "antibonding orbitals," those are ideas from MO theory. However, we did not even start looking at MO theory in any quantitative way until
Inorganic Chemistry (i.e., our 3rd year). There, the approach we took was: Lewis dot structures are the basis of VSEPR which, in turn, is the basis
for assigning point groups and using a Group Theoretical approach. It became painfully abstract. In fact, many *physicists* shun group theory
because they say it's too abstract! Call it what you will, though, that shit works pretty well for cutting down a LOT of the work in MO calculations.
However, when you're talking about things like molecular structure, orbitals, etc., you're really talking about quantum mechanics--albeit at a much
"coarser" level. All of those ideas come from the behavior of wavefunctions. To truly begin understanding bonding, you need to understand the
implications of the "classic" problems in QM: Particle in a Box, Particle in a 3D Box, Particle in a Ring, Rigid Rotor, etc. etc. That's where
notions of constructive and destructive interference (with extensions to ideas like bonding and antibonding molecular orbitals) arise from as well as
ideas like resonance (i.e., quantum superposition).
Ideas like hybridization are not wrong, per se--they're just not the complete picture. Valence Bond Theory is perfectly acceptable for first-order
calculations, but bear in mind that it has definite limits and some things (e.g., 3-electron bonds) simply cannot be rationalized by a pure VBT
approach. If you pick up Anslyn & Dougherty's "Modern Physical Organic Chemistry," which is an extremely thorough discussion of that subject,
they use mostly a hybrid MO/VBT approach. In-depth discussions, though, are steeped heavily in MO theory and quantum mechanics.
Now if you want some books... Definitely definitely definitely check out the Anslyn & Dougherty book I just recommended. If you want to get a
very thorough description of bonding in inorganic molecules, check out: "Group Theory and Chemistry" by David M. Bishop. It's one of those Dover
science books that only costs $10. For me, it has been invaluable. However, the first half is almost pure abstract algebra. Really, what's relevant
to chemical problems is not *all* of group theory, just representation theory--but there's enough new terminology and linear algebra in there to
really throw you off if you're uninitiated.
If you want to eventually get a truly strong grasp of bonding, there's no substitute for studying some serious math: multivariable calculus, linear
algebra (more than one semester, ideally), abstract algebra (group theory, ring theory, that nonsense), differential equations, and fourier analysis
if you can get it.
But hey, you're a chem major (i.e. hard science), did you think you could shy away from math? 
"In the end the proud scientist or philosopher who cannot be bothered to make his thought accessible has no choice but to retire to the heights in
which dwell the Great Misunderstood and the Great Ignored, there to rail in Olympic superiority at the folly of mankind." - Reginald Kapp.
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smaerd
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I truly appreciate your response. I'm almost done with Calculus 1, couple weeks until the final. Math isn't my biggest fear, but certainly not my
biggest ally either . All the notation really messes me up, I can solve the
problems but my calc. prof won't settle for notation/symbol errors in proofs or work.
I'm seeing how it all pans out a lot better now. Thanks for the recommendations now I know more of what to be studying in my spare time  . I'll try and see if I can find that book somewhere. Ah so this is what Physical
Chemistry is about. Only thing I've heard about it is that it's one of those courses that hurts the whole way through haha.
Again, I really appreciate you pointing me in the right direction.
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DDTea
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To be honest, nothing in your Chemistry studies will be easy. However, people much dumber than you and I have passed with flying colors and so have
people much smarter than you and I. There's no reason why you can't do it either.
I was terrible in physical chemistry but now I'm in love with the field. I really wish I knew more math going in, though. More math never hurts.
Roughly, you can break it down into classical thermodynamics, statistical mechanics, and quantum mechanics. Somewhere in there, kinetics fits in.
Basically though, P. Chem. just reteaches you everything you've already learned in general chemistry but at a much more sophisticated level. There's
a much greater emphasis on derivation, so it becomes easy to get lost in the math. That's why it's best to go into P. Chem already knowing a good bit
of math (at the very least, Calc 3, but Linear Algebra is great to have, and even more math is better).
But basically, physical chem is your gateway into graduate studies. All graduate-level courses are heavily based on ideas from physical chemistry.
So again, it's something that's worth doing well in even if it's hard.
Back to the ideas of bonding... that topic can get as sophisticated as you want to take it and theories are still being developed. Eventually,
though, you will focus on a particular facet of chemistry. In that case, you may only need to understand bonding concepts that are related to that
field. For example, describing a protein with the Schrodinger equation is not going to be very useful. For things like macromolecules, Density
Functional Theory is a much better approach. That's all just detail though.
"In the end the proud scientist or philosopher who cannot be bothered to make his thought accessible has no choice but to retire to the heights in
which dwell the Great Misunderstood and the Great Ignored, there to rail in Olympic superiority at the folly of mankind." - Reginald Kapp.
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watson.fawkes
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Quote: Originally posted by smaerd  | | I want to get to the heart of it and don't really know where to go. So what topics/theories/books that are useful should I be reading about and taking
to heart? |
I'll echo what other have said: learn quantum mechanics. Finishing the second semester of an
undergraduate, upper-division QM course is your first goal here. If your course is anything like mine was (and this kind of QM is old science at this
point), you'll compute the closed-form solutions of an electron in a central electrostatic potential (i.e. near a nucleus). You can identify each and
every one of these solutions by means of four quantum numbers, and these solutions generate the periodic table. The first quantum number, representing
total energy, yields the row in the periodic table. The fourth number, intrinsic spin, structure the column as multiples of two. The second and third
are angular momentum numbers and structure the column in their basic groups of 2, 6, 10 (transition metals), 18 (rare earth and lanthanides). That
expression is 2 (2x + 1) for x = 0, 1, 2, 3, and it comes straight from the form of the solutions. These basic solutions are the basis of all bonding
theory, because the form they provide the overall structure of atomic states.
Once you understand how atomic states are derived, it will be pretty clear how simple two-atom bonding states are derived, namely, from a two-centered
potential. Molecular states have accordingly more complicated potentials. DFT, as mentioned, makes large calculations tractable and makes other
people's work readable, but at heart it's still QM, albeit armed with some nice theorems.
As for the mathematical apparatus of DFT, you'll need to have a grasp of variational calculus. This can be a horribly confusing subject, largely
because of bad pedagogy (and bad notation) but in part because the subject itself has a lot of moving parts. At root, variational calculus is pretty
much like regular calculus except that your basic points are not points in an ordinary geometric space but functions in a function space (with either
a discrete or continuous domain). The most direct way I know of (in curriculum, at least) to get at this is a good course in classical mechanics in
which they treat both Langrangian and Hamiltonian mechanics; these both rely upon variational calculus in a foundational way. Depending on your
institution, this will be either an upper division undergraduate physics course or a first year graduate one.
Welcome to applied mathematics.
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franklyn
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Sit around the campfire with everyone else and drink beer , you'll bond
just fine.
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