00-Nature Tutorial- Electronic structure

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# This code is from:
https://qiskit-community.github.io/qiskit-nature/tutorials/01_electronic_structure.html

[1]:

from qiskit_nature.units import DistanceUnit
from qiskit_nature.second_q.drivers import PySCFDriver

driver = PySCFDriver(
    atom="H 0 0 0; H 0 0 0.735",
    basis="sto3g",
    charge=0,
    spin=0,
    unit=DistanceUnit.ANGSTROM,
)

[2]:

problem = driver.run()
print(problem)

<qiskit_nature.second_q.problems.electronic_structure_problem.ElectronicStructureProblem object at 0x79190596c850>

[3]:

hamiltonian = problem.hamiltonian

coefficients = hamiltonian.electronic_integrals
print(coefficients.alpha)

Polynomial Tensor
 "+-":
array([[-1.25633907e+00,  0.00000000e+00],
       [-4.16333634e-17, -4.71896007e-01]])
 "++--":
array([6.75710155e-01, 1.38777878e-16, 1.80931200e-01, 6.64581730e-01,
       5.55111512e-17, 6.98573723e-01])

[4]:

second_q_op = hamiltonian.second_q_op()
print(second_q_op)

Fermionic Operator
number spin orbitals=4, number terms=36
  0.33785507740175813 * ( +_0 +_0 -_0 -_0 )
+ 0.3322908651276482 * ( +_0 +_1 -_1 -_0 )
+ 0.33785507740175813 * ( +_0 +_2 -_2 -_0 )
+ 0.3322908651276482 * ( +_0 +_3 -_3 -_0 )
+ 0.09046559989211572 * ( +_0 +_0 -_1 -_1 )
+ 0.09046559989211572 * ( +_0 +_1 -_0 -_1 )
+ 0.09046559989211572 * ( +_0 +_2 -_3 -_1 )
+ 0.09046559989211572 * ( +_0 +_3 -_2 -_1 )
+ 0.09046559989211572 * ( +_1 +_0 -_1 -_0 )
+ 0.09046559989211572 * ( +_1 +_1 -_0 -_0 )
+ 0.09046559989211572 * ( +_1 +_2 -_3 -_0 )
+ 0.09046559989211572 * ( +_1 +_3 -_2 -_0 )
+ 0.3322908651276482 * ( +_1 +_0 -_0 -_1 )
+ 0.34928686136600884 * ( +_1 +_1 -_1 -_1 )
+ 0.3322908651276482 * ( +_1 +_2 -_2 -_1 )
+ 0.34928686136600884 * ( +_1 +_3 -_3 -_1 )
+ 0.33785507740175813 * ( +_2 +_0 -_0 -_2 )
+ 0.3322908651276482 * ( +_2 +_1 -_1 -_2 )
+ 0.33785507740175813 * ( +_2 +_2 -_2 -_2 )
+ 0.3322908651276482 * ( +_2 +_3 -_3 -_2 )
+ 0.09046559989211572 * ( +_2 +_0 -_1 -_3 )
+ 0.09046559989211572 * ( +_2 +_1 -_0 -_3 )
+ 0.09046559989211572 * ( +_2 +_2 -_3 -_3 )
+ 0.09046559989211572 * ( +_2 +_3 -_2 -_3 )
+ 0.09046559989211572 * ( +_3 +_0 -_1 -_2 )
+ 0.09046559989211572 * ( +_3 +_1 -_0 -_2 )
+ 0.09046559989211572 * ( +_3 +_2 -_3 -_2 )
+ 0.09046559989211572 * ( +_3 +_3 -_2 -_2 )
+ 0.3322908651276482 * ( +_3 +_0 -_0 -_3 )
+ 0.34928686136600884 * ( +_3 +_1 -_1 -_3 )
+ 0.3322908651276482 * ( +_3 +_2 -_2 -_3 )
+ 0.34928686136600884 * ( +_3 +_3 -_3 -_3 )
+ -1.2563390730032498 * ( +_0 -_0 )
+ -0.4718960072811421 * ( +_1 -_1 )
+ -1.2563390730032498 * ( +_2 -_2 )
+ -0.4718960072811421 * ( +_3 -_3 )

[5]:

hamiltonian.nuclear_repulsion_energy  # NOT included in the second_q_op above

[5]:

0.7199689944489797

[6]:

problem.molecule

[6]:

MoleculeInfo(symbols=['H', 'H'], coords=[(0.0, 0.0, 0.0), (0.0, 0.0, 1.3889487015553204)], multiplicity=1, charge=0, units=<DistanceUnit.BOHR: 'Bohr'>, masses=[1, 1])

[7]:

problem.reference_energy

[7]:

-1.116998996754004

[8]:

problem.num_particles

[8]:

(1, 1)

[9]:

problem.num_spatial_orbitals

[9]:

2

[10]:

problem.basis

[10]:

<ElectronicBasis.MO: 'molecular'>

[11]:

problem.properties

[11]:

<qiskit_nature.second_q.problems.electronic_properties_container.ElectronicPropertiesContainer at 0x791905982f10>

[12]:

problem.properties.particle_number

[12]:

<qiskit_nature.second_q.properties.particle_number.ParticleNumber at 0x791946f3a790>

[13]:

problem.properties.angular_momentum

[13]:

<qiskit_nature.second_q.properties.angular_momentum.AngularMomentum at 0x79194690ac10>

[14]:

problem.properties.magnetization

[14]:

<qiskit_nature.second_q.properties.magnetization.Magnetization at 0x7919059834d0>

[15]:

problem.properties.electronic_dipole_moment

[15]:

<qiskit_nature.second_q.properties.dipole_moment.ElectronicDipoleMoment at 0x79194b9d5710>

[16]:

from qiskit_algorithms import NumPyMinimumEigensolver
from qiskit_nature.second_q.algorithms import GroundStateEigensolver
from qiskit_nature.second_q.mappers import JordanWignerMapper

solver = GroundStateEigensolver(
    JordanWignerMapper(),
    NumPyMinimumEigensolver(),
)

[17]:

result = solver.solve(problem)
print(result)

=== GROUND STATE ENERGY ===

* Electronic ground state energy (Hartree): -1.857275030202
  - computed part:      -1.857275030202
~ Nuclear repulsion energy (Hartree): 0.719968994449
> Total ground state energy (Hartree): -1.137306035753

=== MEASURED OBSERVABLES ===

  0:  # Particles: 2.000 S: 0.000 S^2: 0.000 M: 0.000

=== DIPOLE MOMENTS ===

~ Nuclear dipole moment (a.u.): [0.0  0.0  1.3889487]

  0:
  * Electronic dipole moment (a.u.): [0.0  0.0  1.388948701555]
    - computed part:      [0.0  0.0  1.388948701555]
  > Dipole moment (a.u.): [0.0  0.0  -0.000000001555]  Total: 0.000000001555
                 (debye): [0.0  0.0  -0.000000003953]  Total: 0.000000003953


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