Also I agree that the Gaussian-type basis functions used in calculations are
chosen for the ease of evaluating the necessary integrals, but contractions of a number of such functions are often used in order to better approximate the Slater-type functions as found in the exact hydrogen-like solutions. Pretty sure this is true for the standard Pople sets, n-31G etc, not sure at all for others. Any thoughts?

Thanks for pointing that out.

This is in essence very similar to Geoff’s description (practically identical when you think about it), but I don’t remember anyone ever teaching me this, certainly not at the undergraduate level [although there is the chance I simply wasn't listening (asleep/dead)]. It seems to be assumed knowledge at the university level but I feel some explanation (just like the one-liners we’re discussing here) is probably warranted after the somewhat poor responses I’ve recieved from PhD students.

That’s not quite right.

Here’s my definition, just for kicks. “An orbital is a one-electron solution to a given Schrodinger equation describing a system.” In short, it’s one eigenfunction from the given Schrodinger equation. That’s it. Add interpretation if you wish, but caveat lector.

Molecular orbitals in theory could be derived from one-electron hydrogenic orbitals as you’ve described. Certainly that’s how we teach it in “general chemistry” classes. But in practice, we don’t use exact hydrogenic orbitals for the electronic structure of multi-electron atoms or molecules. We use some arbitrary basis set functions to describe those because it’s more computationally efficient.

An orbital is a exact solution to the Schrodinger equation for the hydrogen atom, from which descriptions of the motion (extracted by operators) and spatial distribution (related to the square of the orbital/wavefunction) of its electron at a particular energy level can be extracted. It is approximated that electronic structure of multi-electron atoms can described by associating each electron to functions of the same type (in terms of symmetry) as found in the hydrogen atom. It is further approximated that the electronic structure of molecules can be described by a linear combination of these approximate atomic orbitals, producing molecular orbitals with spatial distribution localised to one or two of the constituent atoms or delocalised to occupy space in the proximity of a large number of atoms.

BTW, while I like both MPQC and PyQuante, they’re not the only open source first principles codes, particularly if you’re open to DFT-only programs.

Both MPQC and PyQuante are nice examples, but I’d really like to see some of the open source programs add semiempirical theory (v. important for large systems) and start to work together (e.g., common formats for wavefunctions, “cube” files, etc.)

Certainly the cheminformatics open source projects already are. See http://blueobelisk.org/ for example. I’ve also gotten good feedback through Open Babel and the Computational CML projects — but it may take a little while.