Bond angles

December 14, 2008 10:03 AM

According to Wikipedia, the bond angle for water is precisely 104.45 degrees. How do they get that number? And how would one experimentally verify it?

Is it just the result of some really long quantum mechanics calculation? Or is there an easier way to see it? And how do you design an experiment to measure it?

posted by metastability to science & nature (16 comments total)

This site has quite a bit of cool info about water...
posted by schyler523 at 10:11 AM on December 14, 2008

You can do an ab into calculation, but you can also determine molecular geometry (which includes bond angle) with various spectroscopic and diffraction methods. Spectroscopy analysis looks at vibrational and rotational absorbency and would be what you would use on water (diffraction methods are more utilized for crystal structures).

Also keep in mind that geometry calculations are usually done at low temperatures to reduce the averaging effects of more accessible geometries.
posted by stevechemist at 10:13 AM on December 14, 2008

Bond angles are determined by electron configuration, specifically, the arrangement of electrons that minimizes the separation between the shared electrons and the nuclei while maximizing the separation between the electrons.
posted by martinX's bellbottoms at 10:20 AM on December 14, 2008

matrinX is correct, that is how the ab into calculations work.
posted by stevechemist at 10:23 AM on December 14, 2008

Spectroscopy analysis looks at vibrational and rotational absorbency

I realize it's complicated, but how does that give you the angle?
posted by metastability at 10:45 AM on December 14, 2008

...the arrangement of electrons that minimizes the separation between the shared electrons and the nuclei while maximizing the separation between the electrons.

matrinX is correct, that is how the ab into calculations work.

Are those really the same? I thought in QM you minimize the total energy. It's possible minimizing the distances would be a lot simpler. Would it lead to the same answer though?
posted by metastability at 10:56 AM on December 14, 2008

I mean, the whole point of QM is that you can't treat atoms like points. So shouldn't we expect the thing with the distances to give the wrong answer?
posted by metastability at 11:01 AM on December 14, 2008

I mean, the whole point of QM is that you can't treat atoms like points.

Not quite.

Sometimes it is a good approximation to treat atoms like points (just like, sometimes, it is a good approximation to treat the Earth as a point). You have to realize that all physical calculations are done with some approximations being used; to take an extreme example, the calculations made to compare with one of the most precise measurements are done with some approximations (for example, that effects of gravity can be ignored - which they can at the level of precision the calculation is done).

So, to calculate the bond angles, it make sense to think of atoms as points (and bonds as line segments connecting these points).
posted by aroberge at 11:17 AM on December 14, 2008

Treating atoms as fixed points is called the Born Oppenheimer (also called adiabatic) Approximation, in that any change in nuclei displacement will occur over a much longer time scale than it takes to an electron to react to this change.
posted by Large Marge at 12:26 PM on December 14, 2008

Ok the message I'm getting is that, once we make all the standard approximations chemists make, then the problem boils down to minimizing the distances between four points and the origin, while simultaneously maximizing their distances from each other, or something like that. It's not at all clear how to actually go about that, but alright. Now the other question is how to measure the bond angle with spectroscopy. I still have no idea how that works.
posted by metastability at 2:29 PM on December 14, 2008

It's also possible to figure out bond angles by X-ray crystallography.

This would be sort of like taking a photograph of water molecules, but with a bunch of complicating factors. Like: because what you're "photographing" is on atomic scale, you need to use "light" (or, more formally, radiation) with a smaller wavelength than the visible light we can detect with our eyes, sufficiently small to be deflected by the subject of the photograph; X rays are small enough to distinguish shapes as tiny as atoms. Also: molecules and atoms are so tiny that in order to have enough of them present in an orderly enough way to gather enough information to detect, they need to be "photographed" in a crystalline sample.

Long story short is that the X-rays get bounced off the orderly crystalline array, the scattering pattern is detected, and a lot of back-calculation is required to interpret the arrangement of electrons and so atoms that make up the repeating unit of the crystal.

Hydrogen atoms are of course the smallest on the Periodic Table, and so you'd need to have really great resolution on your crystallography results to be able to visualize them, but I think that shouldn't be too difficult for a small molecule like water. Maybe a decade ago when I was following this stuff more closely it was sometimes possible for protein structure crystallographers to get sufficient resolution to see H atoms on huge floppy protein molecules in fragile crystals. For something as small and easily ordered as water, I'm sure it's no problem.
posted by Sublimity at 6:59 PM on December 14, 2008

Neutron diffraction. It detects protons, x-ray does not. Ab initio calculations do not constitute proof of anything, unless you're talking about the hydrogen atom. They are approximations only.

The exact structure of H2O ice (as oppoised to D2O, which is easier to detect) was experimentally determined using neutron diffraction in 1973.
posted by overhauser at 10:05 PM on December 14, 2008

[How does one] measure the bond angle with spectroscopy?

To answer this, you need to understand a little bit about how the calculations work.

The ab initio or semi-empirical calculations discussed above are iterative (usually some variation of what's called the Hartree-Fock method). These methods uses successive approximation to arrive at the right answer, somewhat like a non-linear least-squares fit or Newton's method for determining zero crossings. To do this each, for each iteration, a quantity, usually total molecular energy is calculated. Various theories (see the Hartree-Fock link above), say that the right answer is the one with the lowest value for total energy. With each iteration certain parameters, nuclei positions, electron density coefficients, are changed to minimize the energy in each calculation. At a certain point, when the energy changes from iteration to iteration are tiny, the calculation is stopped.

The big problem is that experimentalists can't measure total energy directly, so there's no direct way to check if an HF calculation is right or not. Fortunately, the results of the calculation, the electron densities, the nuclear positions, etc... can be used to calculate other quantities. Bond angle is an obvious one, but so are things like spectral excitations and electrical ionization energies.

So, how this works in practice: a calculation is done to minimize energy, starting with a known set of electronic wavefunctions and a best guess at the molecular structure. Bond lengths, bond angles and the combinatorial factors of the electronic wave functions are allowed to vary to minimize energy. When done, the results of this calculation are checked by comparing various measured spectra (IR, UV-Vis, PES, etc...) with synthetic spectra calculated from the results of the HF energy-minimization iterations.

It's indirect, but it works. It's very useful because more direct ways of measuring structures, like X-ray crystallography, need to have crystals of materials or, like NMR, don't give comprehensive structure information. It's very difficult to get precise bond angles out of NMR, for example. Spectroscopic measurements are much more amenable experimentally and require much less material than the more direct structural methods. So for many complicated molecules, like big biochemical structures, ab initio or semi-empirical calculation is the best structural elucidation tool.
posted by bonehead at 7:34 AM on December 15, 2008

Hah, I think I must accuse you of being eponysterical.

First, it is not difficult to form a crystal of water. That would be an ice cube.

Second, there is not one single reported instance of a person using computational methods to accurately predict (in the absence of a similar structure to start with) the structure of a complex biomolecule. This is called the protein folding problem and if you can do this, you get a Nobel prize. It is that hard to do. So the statement that 'many complicated molecules, like big biochemical structures, ab initio or semi-empirical calculation is the best structural elucidation tool' is patently ludicrous.
posted by overhauser at 10:29 AM on December 15, 2008

It's very difficult to get precise bond angles out of NMR, for example. Spectroscopic measurements are much more amenable experimentally and require much less material than the more direct structural methods.

Um. NMR *is* a spectroscopic method.

NMR is generally done in the liquid phase, and that does present challenges for measuring bond angles (free rotation around bonds, relaxation rate effects due to tumbling or to differing dynamics in different parts of the molecule). Generally in practice I think people use established bond distances/angles when making sense of structure and NMR spectra of molecules, both large (protein and DNA) and small.

Getting back to the original question, the precision about the angle (104.45 degrees) really only would apply in the solid phase, i.e., ice. In the liquid phase there's bound to be bond vibration, including scissoring motions, so in any given liquid sample, at any given instant, there's bound to be some range of angles, presumably centered around 104.45.
posted by Sublimity at 5:41 PM on December 15, 2008

Sorry for the late reply, I've been busy with work.

First, it is not difficult to form a crystal of water. That would be an ice cube. Second, there is not one single reported instance of a person using computational methods to accurately predict (in the absence of a similar structure to start with) the structure of a complex biomolecule.

It's true that one wouldn't use this for water, but it's important tool for exploring structure for surprisingly small molecules. I've done confromational analysis using spectroscopic/ab initio techniques for C10 molecules and smaller. It's invaluable for determining how sterically hindered a reaction site is, for example.

It certainly is true that calculation emphatically does not handle large folding problems well. It was sloppy of me to imply that. Large for me means much smaller molecules than a biochemist would be used to.

NMR *is* a spectroscopic method.

Technically yes, in practice (and in theory), it's its own discipline. There's much less crosstalk between NMR and UV-Vis spectroscopy than between Raman and PES, for example. There's a lot of commonality between rotational, vibrational, excitation and ionization spectroscopies, but the nuclear coupling of NMR tends to stand apart from the molecular studies.

In the liquid phase there's bound to be bond vibration, including scissoring motions, so in any given liquid sample, at any given instant, there's bound to be some range of angles, presumably centered around 104.45.

That's true in any phase, not just the liquid. I used to measure bond angles in the gas phase. Vibronic states are very important there also, I assure you. Solid phase vibrations are more complex, one needs to talk about group theory differently, but phonons are very important in condensed matter behaviour.
posted by bonehead at 1:36 PM on December 17, 2008