How do molecular orbitals differ from atomic orbitals?

[photon79]

ok thankyou malron,,,but what about molecular orbitals? the different shapes given for them are because of sharing of electrons where as the concept of finding a particle remains the same as in atomic arbital..i think i am correct,,.

 

[marlon]

ok thankyou malron,,,but what about molecular orbitals?

Good question. Just use the Wikipedia site and search for this term. It is also in there.

Basically, once you know the atomic orbitals (of the H-atom for example) You can compose more complex orbitals (describing a molecule) by constructing linear combinations of atomic orbitals. I must say that the orbitals are solutions of the Schrödinger equation. Only in the H and H2 case, we are ablt to solve this equation exactly. In the other cases we have to resort to approximative techniques to extract any physical data

marlon

 

[solidspin]

molecular orbitals

photon79 -

I posted an answer to your question in the other thread. Molecular orbitals are, like marlon said, linear combinations of atomic orbitals. While he is correct that we can only solve for H, H2, He exactly, the approximation methods are used extensively for gargantuan molecules like amino acids and organics and such w/ excellent results. Entire software packages are available like Gaussian 03 and others.

 

[Juan R.]

Basically, once you know the atomic orbitals (of the H-atom for example) You can compose more complex orbitals (describing a molecule) by constructing linear combinations of atomic orbitals. I must say that the orbitals are solutions of the Schrödinger equation. Only in the H and H2 case, we are ablt to solve this equation exactly. In the other cases we have to resort to approximative techniques to extract any physical data

marlon

While he is correct that we can only solve for H, H2, He exactly [...]

Hum! i think that you are wrong guys.

Either i am very confounded in this topic or nobody has obtained the exact solutions for H₂ molecules or He atoms. For instance, the Wiki is not computing the exact molecular orbitals for H₂.

The only exact solutions that i know are for H₂⁺ (on prolate spherodial coordinates) and for the He⁺. And the solution for H₂⁺ is only electronically exact!

The idea of that a molecular orbital is a linear combination of atomic orbitals is rather common but misleading by two motives:

1) Strictly speaking, one (e.g. the Gaussian) builds molecular wavefunctions from a linear combination of HF-like functions rather than directly from atomic orbitals (functions).

2) That linear combination is valid only in the MO-CI approach. In other more advanced methods (e.g the MO-CCSD implemented by Pople in the Gaussian) there is not linear combination.

 

[εllipse]

ok thankyou malron,,,but what about molecular orbitals? the different shapes given for them are because of sharing of electrons where as the concept of finding a particle remains the same as in atomic arbital..i think i am correct,,.

I see you keep using the word arbital, and it looks like you picked it up from marlon here:

An arbital is a spatial volume whithin which you can find a particle (eg an electron) with a certain probability.

Just thought I'd let you know, I'm pretty sure marlon accidentally typed orbital wrong.

 

[Neha Sanghvi]

I know sigma and pi bond formation. But what are delta bonds, how and why are they formed? And are there any other types of bonds too? And as you guys keep on saying molecular orbitals, i get that they are the same as bonds, right?

 

[leoant]

I have been thinking on this question during the last few monthes on my spare time. I think molecular orbitals, such as HOMO, LUMO, are the same as those of an atom, if we can consider molecular as a pseudo atom, since there are s, p, d orbitals in atoms. However, the origin of molecular orbitals dues to the interaction of different atoms which construct the molecular. And we can consider those molecular orbitals to be linear combination of atom orbitals or other things--they are solutions of Schrödinger equation, anyway. Maybe we can say, I think, bands of solid are its orbitals, but there are so many that we should deal with them in the band theory's realm.
I think W.A.Harrison's book titled "Electronic Structure and the Properties of Solids" is a good textbook on this question.
btw, is there anyone who are doing calculation using molecular orbitals? May someone tell me how to deal with them in a practical calculation-how can I get the wave functions of molecular orbitals? And is there any physically transparent software/code for me to follow to get the band structure of a kind of organic crystals?

 

[solidspin]

leoant -

While you are numerically correct, for every atomic orbital there can be only one molecular orbital, HOMO actually stands for 'highest occupied molecular orbital and LUMO stands for lowest unoccupied molecular orbital. This threshold is exactly what physicists refer to as the Fermi energy.

In molecular orbital theory, the s, p, d, f, etc. orbitals become sigma, pi delta, phi etc. They take on shapes similar to but distorted from the the original atomic orbitals.

The reason is that the orbitals have phase, can be antibonding and also have symmetry, indicated by u or g (for ungerade or gerade, German for odd or even). The rationale for this 'antibonding' is very sound in the sense that one can very closely predict wavefunctions and coefficients for QM. This concept is foreign to most physicists, but chemists use approximation methods quite extensively to get the wavefunctions and states.

A very good software package is called Gaussian (v. 0.3) which will allow you to see all the calculated orbitals of a certain molecule.

does that help? There are some excellent books out there that can help w/ molecular orbital theory. Let me know and I can recommend several.