# Why Gaussian soft (STO-3G) causes error for Helium anion?

Software: G09.Rev.D.01

=======gjf-file======

%chk=F:\Hanion.chk
# hf/sto-3g geom=connectivity

Title Card Required

-1 2
He                 0.20408162    0.07288005   -0.00095405

1


Causes error message #2070 Log file explanation:

 There are   2 occupied orbitals but only   1 basis functions!


But the same time for the Lithium which is the same electron structure, method STO-3G work fine.

Why Gaussian soft (STO-3G) causes error for Helium anion?

An orbital of a closed-shell Hartree-Fock calculation can only contain two elctrons, one with alpha ("up") and one with beta ("down") spin.

You are calculating the Helium-anion. In a minimal STO-3G basis, it comes with one(!) basis function (or, loosly speaking, "orbital"), as it has two electrons in its neutral form. The anion however has three electrons. So, one closed-shell orbital is certainly not enough to host three electrons. The calculation works for Lithium a.) because gaussian automatically assumes that you want to perform an unrestricted-calculation as the number of electrons is uneven (this is also the case for the helium-anion, but I am not sure if you are aware of this). Furthermore, Lithium has three electrons "by nature" (in its neutral state) and therefore, two basis-functions are enough to host four electrons.

You are using the STO-3G minimal basis, which adds one basis-function per two electrons of the system in the closed-shell case and one per electron in the open-shell case. Of importance is not the actual number of electrons in your system but the number of electrons the neutral atoms composing your system have. For a quick fix, substitute "hf/sto-3g" with "uhf/cc-pVDZ" and your calculation will run without issues.

Your system has an uneven number of electrons, so you cannot run a restricted (closed-shell) HF calculation. Either perform an unrestricted Hartree-Fock (UHF) or a restricted open-shell Hartree-Fock (ROHF) calculation. Both are available in gaussian09. As said, gaussian is already automatically doing this as a restricted HF calculation of a system with an uneven number of electrons is not possible.

Furthermore, as the calculation of the Helium-anion is quite fast, you should considering using a larger basis. You can start with "cc-pVDZ", a Dunning correlation-consistent basis-set, and move on from there.

For a comprehensive introduction to electronic-structure theory I suggest you read the book by Szabo and Ostlund. It assumes no previous mathematical or chemical knowledge above high-school-calculus und explains all the conceptual issues I have just mentioned in a detailed and understandible manner. Also, this book is quite affordable. http://store.doverpublications.com/0486691861.html

If this is too much, I suggest you at least look up the Roothan-Hall and the Pople-Nesbet equations for running an electronic structure calculation in a basis, as Gaussian builds on them.

• For H-atom method STO-3G require three gausians (1s = c1*Gaussian1 + c2*Gaussian2+c3*Gaussian3). For the Helium-atom also three, but for He-anion six or more. Am I right? – Sergio Mar 11 '17 at 17:14
• Ok, I think I understand. STO-3G take 3G per one orbital due to period (in periodic table). For 1st period - 1 STO = 3G, for 2nd - 5STO = 15G and so on. And if I perform STO-3G on He anion, G09 does not know about apeared orbitals, and as a result, crushes. – Sergio Mar 11 '17 at 19:19
• That is sort of right, yes. You have correctly summarized why gaussian crashed in your case. Keep in mind that in a STO-3G basis the coefficients of the three gaussian functions are NOT optimized. They are contracted to one function and the coefficient thereof is optimized. From the view of the Roothan-Hall-Equations, a STO-3G basis has one coefficient. The coefficients of the three gaussians are kept constant. Again, for mroe info, see Szabo & Ostlund – mrnicegyu11 Mar 11 '17 at 20:57