I have a very rudimentary question on orbitals (I have basic chemistry knowledge, using for a comp chem project)

Lithium, to my understanding, has three electrons allocated to the 1s and 2s orbitals. 2s is not full. How many orbitals are in lithium then? My comp chem package returns 5, which I am assuming has to do with unfilled orbitals in the second shell. Can someone help explain this?

Also, if lithium has one unfilled orbital, it has spin of 1? and charge of 1?

EDIT: A followup question is how many unoccupied orbitals are in LiH? My guess is that it's still the 3 unoccupied orbitals from Li. Is this true?

Thank you for the help!

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    $\begingroup$ This is really an ambiguous question. If you look at the atomic emission spectra of lithium a slew of additional orbitals will be found (theoretically infinite). There is no definite number of orbitals unless the question is restricted such as: How many occupied orbitals are there in a free atom of lithium? // What was the exact wording of the question? $\endgroup$ – MaxW Oct 6 '20 at 3:23
  • $\begingroup$ Basically I am looking at a calculation of the ground state energy of LiH. I would like to construct the hamiltonian describing this molecule. One step of doing so is to retrieve the number of orbitals in this molecule. PYSCF tells me it is 6, and I am trying to understand how it arrived at this conclusion. Furthemore, the example online reduces the calculation by freezing the core and removing the orbitals indexed at 4 and 5. I assume this corresponds to two of the unoccupied orbitals of Li. Based on my basic knowledge, I think there is another unoccupied orbital in Li. I want to confirm. $\endgroup$ – Jason Kang Oct 6 '20 at 3:37
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    $\begingroup$ If an orbital has no electrons in it, does it still exist? $\endgroup$ – Zhe Oct 6 '20 at 13:15
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    $\begingroup$ @Zhe Orbitals do not exist but in our atomic models. $\endgroup$ – Poutnik Oct 6 '20 at 15:38
  • $\begingroup$ @Poutnik I was thinking more metaphysically. Does $f(x)$ exist? $\endgroup$ – Zhe Oct 6 '20 at 19:27

Just to be sure: Note that orbitals(*) themselves have neither spin, neither charge. They are not real objects, but theoretical constructs of quantum atom models, that fit well the observations.

Every atom has theoretically infinite number of orbitals ( 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f etc), all but some unoccupied. For most scenarious, it is practical to consider just few highest occupied and few lowest unoccupied orbitals (like 1s, 2s, 2p, 3s, 3p for Li), what may be the reason your chem package provides just few.

Electrons are fermions, so the unpaired $\mathrm{2s}$ electron has the spin 1/2. The spin of a lithium nucleus depends on the isotope. $^6\ce{Li}$ has the spin 1(**), $^7\ce{Li}$ has spin 1/2. The net charge of lithium atom is zero, the charge of the unpaired 2s electron is obviously $-\mathrm{e}$.

Similarly, $\ce{LiH}$ has unlimited number of atomic or molecular orbitals ( depending on the quantum model ), as they are features of quantum models, not real objects. And again, only highest "valence" occupied and few lowest unoccupied ones are worthy to consider. (For $\ce{LiH}$, s and p for atomic ones, $\sigma, \pi $ for molecular ones. )

The orbitals with very high principal quantum number $n$ converge for $\mathrm{n} \rightarrow \infty$ to energetic continuum with very low ionization energy. If occupied by careful excitation, they have very interesting behaviour like effectively disappearing quantization. Such electrons behave like orbitting classically a point-like central charge. See Rydberg atoms for more. They have also ridiculous values of atomic radius, which increases with $n^2$. E.g. $\ce{H}$ with $n=137$ has radius $\pu{1 \mu m}$ and $\ce{K}$ with $n=600$ would have reportedly size $\pu{0.1 mm}$.

(*) Note that the term orbital has 3 major, related but distinguished meanings:

  • orbital(1) - a wave function as the particular solution of the Schroedinger's quantum wave equation

  • orbital(2) - a quantum state of an electron(energy, orbital angular momentum, spin angular momentum), belonging to orbital(1)

  • orbital(3) - a 3D region (or 3D surface/shape), describing the region of significant probability of electron occurance (or its border threshold value), belonging to orbital(1,2)

(**) The only other stable nuclei with spin 1 are $^2\mathrm{H}$ and $^{14}\mathrm{N}$, as odd-odd nuclei are not generally stable, undergoing beta decay to even-even nuclei. The eventual other stable odd-odd nucleus candidate $\ce{^{10}_{5}B}$ does not count, as its spin is 3, not 1.

  • $\begingroup$ This is very helpful! Thank you for explaining! $\endgroup$ – Jason Kang Oct 8 '20 at 2:57

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