LiH dissociation curve using ExactEigensolver

This notebook demonstrates using Qiskit Aqua Chemistry to plot graphs of the ground state energy and dipole moments of a Lithium Hydride (LiH) molecule over a range of inter-atomic distances.

This notebook populates a dictionary, which is a progammatic representation of an input file, in order to drive the qiskit_aqua_chemistry stack. Such a dictionary can be manipulated programmatically and this is indeed the case here where we alter the molecule supplied to the driver in each loop.

This notebook has been written to use the PYSCF chemistry driver. See the PYSCF chemistry driver readme if you need to install the external PySCF library that this driver requires.



In [1]:

    
import numpy as np
import pylab
from qiskit_aqua_chemistry import AquaChemistry



In [2]:

    
# Input dictionary to configure Qiskit Aqua Chemistry for the chemistry problem.
# Note: In order to allow this to run reasonably quickly it takes advantage
#       of the ability to freeze core orbitals and remove unoccupied virtual
#       orbitals to reduce the size of the problem. The result without this
#       will be more accurate but it takes rather longer to run.

# aqua_chemistry_dict_eigen uses classical approach to produce the reference ground state energy.
aqua_chemistry_dict_eigen = {
    'driver': {'name': 'PYSCF'},
    'PYSCF': {'atom': '', 'basis': 'sto3g'},
    'algorithm': {'name': 'ExactEigensolver'},
    'operator': {'name':'hamiltonian','freeze_core': True, 'orbital_reduction': [-3, -2], 'qubit_mapping': 'parity', 'two_qubit_reduction': True},
}

# aqua_chemistry_dict_vqe uses quantum approach to evaluate the ground state energy.
aqua_chemistry_dict_vqe = {
    'driver': {'name': 'PYSCF'},
    'PYSCF': {'atom': '', 'basis': 'sto3g'},
    'algorithm': {'name': 'VQE', 'operator_mode': 'matrix'},
    'operator': {'name':'hamiltonian','freeze_core': True, 'orbital_reduction': [-3, -2], 'qubit_mapping': 'parity', 'two_qubit_reduction': True},
    'optimizer': {'name': 'COBYLA', 'maxiter': 20000},
    'variational_form': {'name': 'RYRZ', 'depth': 10},
    'backend': {'name': 'statevector_simulator'}
}

# tested molecular, LiH
molecule = 'Li .0 .0 -{0}; H .0 .0 {0}'



In [3]:

    
# choose one of configurations above for experiments
aqua_chemistry_dict = aqua_chemistry_dict_eigen



In [4]:

    
# configure distance between two atoms
pts  = [x * 0.1  for x in range(6, 20)]
pts += [x * 0.25 for x in range(8, 16)]
pts += [4.0]
distances   = np.empty(len(pts))
hf_energies = np.empty(len(pts))
energies    = np.empty(len(pts))
dipoles     = np.empty(len(pts))

print('Processing step __', end='')
for i, d in enumerate(pts):
    print('\b\b{:2d}'.format(i), end='', flush=True)
    aqua_chemistry_dict['PYSCF']['atom'] = molecule.format(d/2) 
    solver = AquaChemistry()
    result = solver.run(aqua_chemistry_dict)
    distances[i] = d
    hf_energies[i] = result['hf_energy']
    energies[i] = result['energy']
    dipoles[i]  = result['total_dipole_moment'] / 0.393430307
print(' --- complete')

print('Distances: ', distances)
print('HF Energies:', hf_energies)
print('Energies:', energies)
print('Dipole moments:', dipoles)









    



Processing step 22 --- complete
Distances:  [0.6  0.7  0.8  0.9  1.   1.1  1.2  1.3  1.4  1.5  1.6  1.7  1.8  1.9
 2.   2.25 2.5  2.75 3.   3.25 3.5  3.75 4.  ]
HF Energies: [-7.29954105 -7.48594487 -7.61577016 -7.70575334 -7.76736214 -7.80874318
 -7.83561583 -7.85195386 -7.86053866 -7.86335762 -7.86186477 -7.85714496
 -7.8500187  -7.84111204 -7.83090558 -7.80193896 -7.77087367 -7.74000074
 -7.7108299  -7.68437642 -7.6612016  -7.64145387 -7.62497563]
Energies: [-7.31334583 -7.50092209 -7.63097825 -7.72081241 -7.7822424  -7.82359928
 -7.85069838 -7.86756329 -7.87700149 -7.88101572 -7.88107204 -7.87826817
 -7.87344029 -7.86723396 -7.86015321 -7.84104271 -7.82307664 -7.8086124
 -7.79836343 -7.79175325 -7.78771697 -7.78531972 -7.78391847]
Dipole moments: [5.3479565  5.05436846 4.89154649 4.80824206 4.76423166 4.73775921
 4.71893511 4.70394304 4.69125691 4.67959192 4.66694467 4.65022445
 4.62517401 4.5864183  4.52758314 4.24518851 3.69244462 2.8795465
 1.99991673 1.27228084 0.76878114 0.45190607 0.26134837]



In [5]:

    
pylab.plot(distances, hf_energies, label='HF')
pylab.plot(distances, energies, label='Computed')
pylab.xlabel('Interatomic distance')
pylab.ylabel('Energy')
pylab.title('LiH Ground State Energy')
pylab.legend(loc='upper right')









    Out[5]:





<matplotlib.legend.Legend at 0x108ef4278>



In [6]:

    
pylab.plot(distances, dipoles)
pylab.xlabel('Interatomic distance')
pylab.ylabel('Moment debye')
pylab.title('LiH Dipole Moment')









    Out[6]:





Text(0.5,1,'LiH Dipole Moment')



In [ ]: