[Kate]

Hello.

Is hybridisation just a model to explain the bond angles between atoms and the planarity of a bond? For instance, take ammonia. The 2 unpaired electrons could be in a p orbital but, instead, hybridisation on nitrogen is sp³.

Thanks.

[Corribus]

It is "just a model", like anything involving molecular orbitals, developed from quantum mechanical theory using approximations to explain molecular structures.

[Kate]

I know it's just a model, for the reasons you explained. My point is, how do you determine the hybridisation of any atom other than carbon?

For instance, in the example I gave, at first glance you could say that nitrogen is sp² or sp³. But what is taught is that it is sp³. And my question is why? It is to conform to the empirical geometry of ammonia and the bond angles between the atoms? An sp² hybridisation for nitrogen here would mean that the bond angles would be 120º and not 107º (which I think is the actual value, would have to check though).

I always thought hybridisation was a model to explain the same bond lengths between carbon and hydrogen in, say, methane. But in atoms other than carbon, the determination of hybridisation only seems to be related to geometry and the directionality of orbitals. This is ultimately my confusion here.

[Babcock_Hall]

At the risk sounding as if I am quibbling, hybridization can be invoked to explain other properties besides bond angles.  I wonder whether or not it would be helpful as part of this discussion to contrast the bond angles in ammonia (about 107° IIRC) with those in phosphine, PH₃, which are about 94°.

[Kate]

At the risk sounding as if I am quibbling, hybridization can be invoked to explain other properties besides bond angles.I wonder whether or not it would be helpful as part of this discussion to contrast the bond angles in ammonia (about 107° IIRC) with those in phosphine, PH₃, which are about 94°.

I wasn't saying that hybridisation is invoked to explain bond angles. What I was trying to say is that the determination of an atom's hybridisation seems more reliant on bond angles and planarity (at least for elements in the second period since, like you mentioned, phosphine has bond angles of 94º and is sp³ hybridised and obviously not planar).

[Irlanur]

In Principle, the hybridization is determined by the geometry, and not the other way around. Nevertheless, chemistry professors tend to ask things like "explain the bond angles with the hybridization". Much of this comes from hand waving arguments. more like mnemonics rather than explanations.

Fact is, if you actually calculate the energy of a molecule, you have to postulate a structure (which you can later optimize, ok). If you then let the computer fiddle around, he will come up with some coefficients for the orbitals, doesn't matter whether you started with sp2 or sp3 or whatever.

Qualitatively (and sometimes also computationally, if you employ symmetry) it's just easier to work with the "correct" hybridization.

In the end, it turns out that there is some chemistry associated with the hybridization. This is what organic chemists use, doesn't make the usual explanations any more correct....

[Kate]

In Principle, the hybridization is determined by the geometry, and not the other way around. Nevertheless, chemistry professors tend to ask things like "explain the bond angles with the hybridization". Much of this comes from hand waving arguments. more like mnemonics rather than explanations.

Fact is, if you actually calculate the energy of a molecule, you have to postulate a structure (which you can later optimize, ok). If you then let the computer fiddle around, he will come up with some coefficients for the orbitals, doesn't matter whether you started with sp2 or sp3 or whatever.

Qualitatively (and sometimes also computationally, if you employ symmetry) it's just easier to work with the "correct" hybridization.

In the end, it turns out that there is some chemistry associated with the hybridization. This is what organic chemists use, doesn't make the usual explanations any more correct....

Nice to know. Like I said, I was always told hybridisation is invoked to explain the same C-H bond length in, for instance, methane. So determining the hybridisation of atoms other than carbon always seemed strange to me. And in inorganic chemistry, my teachers never talked about hybridisation, so this topic only ever came up in my general and organic chemistry classes. My organic chemistry teachers never really cared about orbitals when explaining reactions, but now I have a physical organic chemistry class and I'm reading Clayden's Organic Chemistry, and suddenly hybridisation is important to understand reactivity!

[Corribus]

And in inorganic chemistry, my teachers never talked about hybridisation, so this topic only ever came up in my general and organic chemistry classes.

This is probably because hybridization models have some problems when it comes to d-block elements. My take on hybridization has always been (well, since becoming a physical chemist) that molecular orbital theory can do just about anything hybridization models can, but it is generally more complicated. Especially for organic chemists, who are mainly fixated on the chemistry of carbon, hybridization models offer satisfactory results for a minimum of computational effort. One can derive the chemical structure of methane using molecular orbital theory, and in some cases MO theory is far superior, but on the other hand it takes a lot more effort to get there. Maybe it is no surprise that organic chemistry books dedicate far more space to hybridization models than MO models, even though the latter is far more broadly useful to chemists. (Actually, density functionals do most of the theoretical structure work in chemistry nowadays, but it's practically useless toward helping students understand bonding.)

You might find this thread interesting/relevant:
http://www.chemicalforums.com/index.php?topic=75353.0

[Kate]

Thank you for the link. I appreciate it.

My teachers, when talking about MO theory, usually present diagrams for really simply molecules and the students are required to memorize certain things about them. When they present the diagram for CO it's a mess because of all the s-p mixing and, thankfully, we're not required to memorize it. So my question is, how are these diagrams arrived at? My teachers never got into this. Can you point me to some references?

[Corribus]

Pretty much any physical chemistry textbook will have a very detailed analysis of MO diagrams and how they are derived. General chemistry textbooks will provide a more superficial treatment, the quality of which can very substantially, but most of them should be sufficient for the beginner. One must of course first understand what molecular orbitals are before using them in diagrams, but such an open ended treatment would be difficult to manage. Can you frame your question in more specific terms? (Also, it helps to know what your educational level is - are you taking general chemistry currently?)

Some resources available on the web:

http://chemwiki.ucdavis.edu/Theoretical_Chemistry/Chemical_Bonding/Pictorial_Molecular_Orbital_Theory/How_to_Build_Molecular_Orbitals
https://en.wikipedia.org/wiki/Molecular_orbital_diagram
http://www.ch.ic.ac.uk/vchemlib/course/mo_theory/

[Kate]

Ok, I probably worded that incorrectly. So here it is again. I know how to build MO diagrams for molecules like H₂, N₂ and I know what the difference between MOT and VBT is. My question is how do you get MO diagrams for more complicated molecules starting, for instance, from CO to molecules with 3 different atoms. Is there a software for constructing MO diagrams for any molecule we want? And how do you arrive at the energy levels of each MO in a diagram?

I'm currently doing a masters in organic chemistry and I have a BSc in chemistry as well.

[Corribus]

CO and other heteronuclear diatomics are not too different from the homonuclear diatomics. In general like atomic orbitals mix with like atomic orbitals to form an equal number of molecular orbitals. In some cases it is difficult to determine some of the energetic orderings of the pi and sigma orbitals, but you can memorize them without too much trouble. There are only so many diatomics molecules you can make.

Polyatomic molecules are more difficult to treat. Ultimately it requires symmetry treatments - and you may have noticed that molecular orbitals for such molecules have names like a_1g and so forth. This is basically a way of saying that atomic orbitals can combine to form molecular orbitals only in certain ways. They have to line up with each other correctly for form stable combinations.  E.g., if the line between a hydrogen atom and a carbon atom is the x-axis, an s-orbital on a hydrogen cannot interact/mix/form a molecular orbital with a p-orbital on the carbon oriented in the z direction (the net phase overlap of the two orbitals is zero). Really this kind of stuff is far easier to explain with pictures rather than words.

To determine actual MO energies you usually have to use computational approaches, as they are things that are easy to calculate using a pencil and paper, although often enough they can be determined in a qualitative way using some estimations and simple theoretical strategies. Huckel theory, for example, can be applied to aromatic systems to arrive at reasonably good approximations of the physical properties of conjugated organic molecules. If you are getting a masters in organic chemistry, it is something you should definitely familiarize yourself with. Other helpful tools like Walsh diagrams can help explain a lot of structural and reactivity phenomena in chemistry, such as why some molecules are bent and others are planar, and why some reactions occur.

To calculate more accurate energy values of molecular orbitals - and predict from them accurate molecular structures - you'd have to use ab initio approaches (Hartree-Fock, Moller-Plesset, etc) using sophisticated computational software like Gaussian. However nowadays as mentioned earlier density functionals are used more commonly because they use less computational resources while still giving satisfactory agreement with experimental data.

[Kate]

I know what the idea behind LCAO is, but I've never had to do any quantitative stuff with it apart from Huckel's method for aromatic compounds and pi systems. As for the rest, I'm only having computational chemistry for the first time next semester. Hopefully, after that I'll understand your last paragraph.

Thanks.