N₂⁺: Localized Hole

Sample directory: adf/ModStPot_N2+/

This calculation illustrates:

• a) How to specify the net total charge on a molecule

• b) How to enforce breaking the symmetry that is present in the start-up situation, in this case to localize a hole in the electron density on one of the two equivalent atoms.

• c) How to prevent the scf from oscillating back and forth between the two equivalent situations or from even restoring the unwanted symmetry

$ADFBIN/adf <<eor
title N2+  hole localization

atoms
N 0 0  -2.0
N 0 0   2.0
end

Basis
 Type DZP
 Core Small
End

symmetry C(lin)  ! allow symmetry breaking

unrestricted

Occupations   keeporbitals=3   &
  ! keeporbitals: let the density relax a bit, then fix the MO occups
  sigma 3 // 1 0 1
  pi    2 // 2
end

CHARGE  1  1   ! this duplicates info from "OCCUPATIONS" (check)

modifystartpotential  ! to break the symmetry in the start-up potential
N/1    0.5   0.5
N/2      4   1 
end

end input
eor

The purpose of this run is to compute the N₂⁺ ion, with the hole localized on one of the atoms. In a very small system like N₂⁺ this is a tricky thing to do. The program has a tendency towards the symmetric solution, with the hole delocalized. A few trial runs, just putting a net +1 charge into the system, will reveal that clearly.

To achieve the desired situation we apply the key modifystartpotential to break the symmetry of the initial potential. A potential is generated as if the electronic cloud in the second N fragment is spin-polarized in a ratio 4:1 (this precise value is not very relevant), which achieves that initially a non-symmetric solution is obtained. The symmetry must be specified, lest the program determine and use the higher symmetry from the nuclear frame. This would prevent any symmetry breaking altogether.

Next, in order to prevent that the system relaxes to the symmetric situation, we apply the keeporbitals option of the occupations key. This fixes the occupied orbitals in the sense that in each scf cycle the program will try to keep the electrons in orbitals that resemble the previously occupied orbitals as much as possible.

The key modifystartpotential here demonstrated has a more relevant and less unstable application in larger systems. See the User's Guide for references.