What is an orbital?

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I thought of this interesting question today – “what is an orbital?”

I asked it to the various PhD students that I share an office with and it made some of them squirm, the answers ranged from the (hopefully) humorous – “they’re a bit like a donut”, to the not bad – “area of space within which there is a certain probability that an electron can be found”. I should probably state that none of these match what my answer would be.

The responses made me wonder if some of the frankly bizarre posts on CCL about how nothing meaningful can be obtained from orbitals (a purely mathematical construct) and only the electron density should be used stem from not properly grasping what an orbital (in ab initio theories) is?? Is this a deficiency in how QC is taught / what’s written in texts?

It would be interesting to get a few comments about how readers would answer “what is an orbital?”

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4 Responses to “What is an orbital?”

  1. Gareth Says:

    The concept of an orbital seems to be one of those things that we have an intuitive grasp of; we have a feeling for what they represent, we can use them to predict the nature of reaction mechanisms; but when it comes to an accurate description of what one is, we stumble. (I find myself in a similar situation when trying to explain logarithms tothe uninitiated). Here is my attempt, hopefully, if I stumble, I won’t fall flat on my face:

    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.

  2. Geoff Says:

    I disagree somewhat with Gareth. You first describe an atomic orbital, based on a hydrogen atom.

    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.

  3. qchem Says:

    The answer I thought up to the question as I was asking it was something along the lines of “a wavefunction that describes a single particle, namely an electron”.

    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.

  4. Gareth Says:

    I agree with the definition that an orbital is a function which describes the properties of a single electron. I think that what I was trying to get at by starting with hydrogen (and hydrogen-like systems, I suppose), was that; because hydrogen-like atoms are the only systems with exact analytic solutions, then only they have orbitals which can be exactly defined. It is orbitals of this type that are used when attempting to qualitatively describe electronic structure or reaction mechanisms, involving multi-electron atoms, to a more general audience. The approximation arises due to the lack of exact solutions in such cases. I hope that clarifies my position a bit.

    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?

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