Exact bond angle calculations

Oh - so what did you do to supplement it?

I'm just trying to get my hands on all the resources I can up to that level

Lectures, tutorials and a vast library.

Ah I see ... well Atkins will have to do, not to mention I do have a few other books on top.

Yeah, looking at the table of contents (and being able to "search" through the book online), my impression is that Physical Chemistry by Atkins plus Quantitative Chemical Analysis by Harris will be more than enough for the majority of physical topics (I'll probably need a bit of kinetics on the side, electrolysis, a little solutions chemistry and a lot of surface chemistry which I can't find covered anywhere at all ).

Looks like all the standard Gibbs' equations are covered, including the dependence on Q (concentration of products/reactants); Clapeyron and Clausius-Clapeyron equations are covered (this is my first textbook which covers both!); only electrochemistry is missing but that should be ok, I think I can fill that in from elsewhere. Electrolysis is absent as usual but it's not that big a topic anyway. By the way is it right to say that electrochemistry (e.g. Nernst equation etc.) is found under the field of "electrode potentials", whereas electrolysis is found under "electrode dynamics"?

Is this the inorganic book you mean: http://www.amazon.co.uk/Shriver-Atkins-Inorganic-Chemistry-Peter/dp/0199236178/ref=sr_1_1?s=books&ie=UTF8&qid=1365883363&sr=1-1&keywords=Atkins%27+Inorganic+Chemistry+%5BPaperback%5D#_? I have to say, just looking down the list, it seems to cover my main worries (transition metals and coordination chemistry). There's nothing obvious I can find which I need to know which isn't in there.

Why did you think these books were bad? They look very good to me, I haven't actually done the entirety of any of your prelim papers yet but it doesn't seem like these two books would leave you short ...

Difference I imagine between the physical chem is that we have to derive the thermodynamic equations, not just state them. Atkins doesn't explain the derivations well.

How do we calculate the exact bond angles and bond lengths in a molecule? i.e. are there any online guides, or introductions to whatever field this is?

I'm happy to look at computational methods.

As has been alluded to in this thread, calculation of bond angles is quite a tricky thing. The details will certainly be beyond you at this stage (I covered this stuff at 3rd year undergrad) but I will try and provide a brief overview.

As charco mentioned, bond angles and lengths for very simple molecules can be calculated very accurately from IR spectroscopy, and those for more complex ones may be obtainable (angles fairly accurately, lengths not so accurately) from X-ray diffraction.

However it is possible to calculate these outright using quantum mechanics. There are two approaches, one which is to tackle the schrodinger equation head on, to calculate the orbital energies, and then minimise these adjusting the bond lengths and angles via gradient methods to find the shape of the molecule.

There are various levels of this approach (in increasing accuracy), including Hartree-Fock (HF), Moller Plessat (MP2, MP3 etc), Coupled Cluster (CC) and Full Configuration Interaction (Full CI) which is completely accurate. As we increase accuracy the computational power required drastically increases, I can't remember the exact scalings but I think HF scales as N^3 (N is the number of electrons) whilst full CI as N^N. To put it into perperective I think a water molecule might be the largest molecule done with full CI.

The other method is one called density function theory, which instead of tackling the schrodinger equation head on we look at the electron density. Underpinning this method is a theory which shows that the density uniquely defines the wavefunction, and so we can get the wavefunction (and all other properties) from the density (in theory at least). This method is generally less computationally demanding, but perhaps less rigorous when appled to new systems.

I see.

What do you mean by full CI is completely accurate? I was under the impression that the Schrodinger equation cannot be solved exactly.

Density functional theory looks like the one to take a look at. I'll have a look If you know of any Internet courses, please let me know.

I see.

What do you mean by full CI is completely accurate? I was under the impression that the Schrodinger equation cannot be solved exactly.

Density functional theory looks like the one to take a look at. I'll have a look If you know of any Internet courses, please let me know.

Basically the schrodinger equation is solvable for one electron systems (the hydrogen atom) but unsolvable for many electron systems as the interactions between electrons complicate things a lot.

Hartree Fock makes essentially no allowance for correlation between electrons. Moller Plessat is more accurate for example as it treats the dominant effects of correlation with something called perturbation theory.

Coupled Cluster and Full CI uses something called determinants, but to be completely accurate then all determinants must be included. Thus full CI could be considered in the same way as a series solution, which you might have come across in maths.

E.g. In A level you should be familiar with a Taylor series representation of a function, which is completely accurate as long as you include all (the infinite) terms.

I can't really remember, the series may converge in which case you will get to the exact answer, or they may use some sort of mathematical tricks to calculate the infinite terms.

It doesn't really matter anyway, as at these accuracy levels other effects come into play which I didn't mention before:

- Born-Oppenheimer approximation
- we have assumed no relativity ( ie we should be using the Dirac equation)

This means that you don't gain anything by a more accurate solving of the schrodinger equation past a certain point as these approximations will be larger.

If we can solve the schrodinger equation directly then in principle we know everything. However we can think of two instances:

1) we are able to determine the exact energies, without the wavefunctions. This lets us determine moleculer shapes and also lets us predict the outcome of reactions.

2) we are able to determine the wavefunction exactly. This means in theory we can learn everything about the system, which is more powerful.

We can then tale it one step furhter, in that if we can determine the wavefunction for a single molecule, can we determine the wavefunction for a reaction. If so, we know the exact outcomes of this reaction. Taken even further we might get to a 'universal wavefunction' which will tell us everything that will happen in the universe. So much for free choice!

Of course this is rather fanciful. In fact we try and use these energies to predict reaction outcomes. In these cases we are looking at accuracies of around 1 kj/mol, which is sometimes doable.

Heisenberg's uncertainty principle isn't derived from quantum mechanics (I don't think) so even if we could solve the Schrodinger equation completely, the best we can do is have exact probabilities not exact locations (for particle positions etc.).

In any case, is the Schrodinger equation necessarily complete? Perhaps even if we could solve it exactly it would not always predict perfectly what we observe. In fact I'd guess this is pretty likely?

Heisenberg is definitely from QM, it was derived in one of my lectures. It doesn't just apply to momentum and position but also to energy and time (and many others I believe) which is very important to spectroscopy as it explains line broadening in fast spectroscopic processes.

Well you would know better than me, but from what I looked up briefly (http://www.tjhsst.edu/~2011akessler/notes/hup.pdf) no QM seems to be involved? The wavefunction starting the page is classical mechanical.

If Heisenberg was to be derived from QM rather than pure maths that means it need not hold true throughout our humanity (i.e. when we finally supercede QM we may also not have to abide by predicting probabilities but might be able to track exact motion and position, Einstein after all distrust anything which could not be calculated precisely), as QM has its limits. I'm still not sure though that we could predict the future, e.g. restrain free choice, with this

The quantum mechanics in that derivation comes in the last step, where you link momentum and wave number with h bar. Generally speaking, if you see anything with h bar in it, in comes from QM!

Of course heisenberg means we can't know everything exactly. As Jmaydom said it doesn't just apply to position and momentum, indeed to any two properties who's operators don't commute.

Well you would know better than me, but from what I looked up briefly (http://www.tjhsst.edu/~2011akessler/notes/hup.pdf) no QM seems to be involved? The wavefunction starting the page is classical mechanical.

If Heisenberg was to be derived from QM rather than pure maths that means it need not hold true throughout our humanity (i.e. when we finally supercede QM we may also not have to abide by predicting probabilities but might be able to track exact motion and position, Einstein after all distrusted anything which could not be calculated precisely), as QM has its limits. I'm still not sure though that we could predict the future, e.g. restrain free choice, with this

Ah I see. But is there are a clear link between the impossibility of solving the Schrodinger equation exactly and the Heisenberg uncertainty principle?