4.6. Constructing a fermionic Hamiltonian with Qiskit Nature

The Qiskit Nature platform works with spin orbitals [Qiskit_Nat_1]. Each molecular orbital can have a spin-up or a spin-down electron, or spin-paired electrons. A spin orbital is either of those cases. For each molecular orbital, we have two spin orbitals. Let's now illustrate the construction of a fermionic Hamiltonian operator of the hydrogen molecule with Qiskit Nature.

4.6.1. Constructing a fermionic Hamiltonian operator of the hydrogen molecule

First, we define the molecular geometry of the hydrogen molecule with the Qiskit Molecule class, which has the following input parameters:

• geometry, a list of atom names, such as H for hydrogen, followed by Cartesian coordinates of the atom's position in units of angstroms
• charge, an integer, the electric charge of the molecule
• multiplicity, an integer, the multiplicity of the molecule, where is the total spin angular momentum, which is determined...