Well this blog might be a little more advanced but let’s just get right into it. Sometimes it is useful to know more electronic information about an interaction between two atoms or molecules. When you perform an energy calculation in Psi4 it will go something like this, we will be using helium dimer and it’s interaction between two atoms.
In Psi4, you can split a molecule with the ‘ — ‘ string and add as many molecules as you would like into the system. If you do this, it is advisable to specify the charge and multiplicity of each molecule as you go through.
import psi4
psi4.set_memory('1000mb')
psi4.core.set_num_threads(1)
helium_dimer = '''\
HE11
0 1
--
HE21 HE11 2.0000
0 1
'''Let’s go ahead and get the total electronic energy between the helium atoms using MP2 to include electron correlation as an evolution of HF. The atoms are the same we don’t have to worry about basis set superposition error (BSSE). Since we only have 2 atoms and they are low orbitals the number of functions to compute is pretty low so it should be able to run on any laptop.
energy = psi4.energy(
'mp2/aug-cc-pvdz',
)What we get in the output is, now from here we can can calculate a multitude of properties everyone is interested in but can we get a little more information in this interaction:
This is where we can use SAPT. SAPT provides a breakdown of the electronic energy into four classifiers and returns the interaction energy of the complex:
- Electrostatics — This is Coulomb's Law and the Force between the helium atom.
- Exchange — The exchange interaction is the overlap of the orbtial when an atom starts to pierce another atom’s van der waals contact radii. The Pauli Exclusion Principle starts to kick in and there is an exchange of the electrons and amount of energy causing that effect to happen.
- Induction — The response of the molecular orbitals in the presence of the electric field of another. This is polarization and is induced by atoms or molecules interacting with each other in the system.
- Dispersion — An attractive force that is how the electric field of all the atoms in a system affect another causes a weak attractive force which diminishes 1 / r^6.
When we run the SAPT2 (equivalent to mp2 for correlation) and the same basis set:
interaction_energy = psi4.energy(
'sapt2/aug-cc-pvdz',
)What we get in the output is:
This allows us to evaluate the interaction of helium in a little more detail. At 2 Angstroms it looks like the exchange of the Helium at 2kcal/mol causing the total interaction energy 1.272kcal/mol to be unfavorable. For a more in depth look at this table please go to this reference where there will be a big table of a physical description of all these terms:
https://pubs.acs.org/doi/abs/10.1021/cr00031a008
I believe SAPT will be useful later on in the future but it can be pricey to run the more you scale with atoms.
