def test_contracted_gradients():
"""
check gradients of contractions
* dA/dx(U)
* d(diagA)/dx(V)
* dF^(e)/dx(E)
* dF^(n)/dx(N)
* dS/dx(R)
"""
# load QM and MM regions from AMBER files
molecule, polarizable_atoms, point_charges, polarizabilities = amber2psi4('solvated.prmtop', 'solvated.rst7', 'solvated.qmregion')
# basis for QM atoms
wfn = psi4.core.Wavefunction.build(molecule, 'sto-3g')
basis = wfn.basisset()
ribasis = basis
polham_grad = PolarizationHamiltonianGradients(molecule, basis, ribasis,
polarizable_atoms, point_charges,
polarizabilities=polarizabilities,
verbose=0)
# number of polarizable sites
npol = polham_grad.npol
# number of AOs
nbf = polham_grad.nbf
# make random numbers reproducible
np.random.seed(101)
# random tensor V for contracting with the gradients of diag(A)
V = np.random.rand(npol, 3, 3)
# random matrix D for contracting with the gradients of overlap matrix
D = np.random.rand(nbf, nbf)
# random tensor E for contracting with the gradients of F^(elec)_{i,m,n}
E = np.random.rand(3*npol, nbf, nbf)
# random tensor Y for contracting with the gradients of I^(elec)_{k,a,b,m,n}
Y = np.random.rand(npol, 3, 3, nbf, nbf)
# symmetrize matrices in 2nd and 3rd indices
Y = 0.5 * (Y + np.einsum('kabmn->kbamn', Y))
grad_comp = GradientComparison(molecule, basis, ribasis,
polarizable_atoms, point_charges,
polarizabilities=polarizabilities,
verbose=0)
# compute analytical and numerical QM gradients and compare them
assert grad_comp.compare_contracted_gradients_diagA(V)
assert grad_comp.compare_contracted_gradients_overlap(D)
assert grad_comp.compare_contracted_gradients_F(E)
assert grad_comp.compare_contracted_gradients_I(Y)
def test_one_electron_part_gradients():
"""
check gradients of one-electron energy of polarization Hamiltonian
"""
# load QM and MM regions from AMBER files
molecule, polarizable_atoms, point_charges, polarizabilities = amber2psi4('solvated.prmtop', 'solvated.rst7', 'solvated.qmregion')
# basis for QM atoms
wfn = psi4.core.Wavefunction.build(molecule, 'sto-3g')
basis = wfn.basisset()
ribasis = basis
polham_grad = PolarizationHamiltonianGradients(molecule, basis, ribasis,
polarizable_atoms, point_charges,
polarizabilities=polarizabilities,
verbose=0)
# number of polarizable sites
npol = polham_grad.npol
# number of AOs
nbf = polham_grad.nbf
# make random numbers reproducible
np.random.seed(101)
# random density matrix
D = np.random.rand(nbf, nbf)
# # symmetrize matrix
# D = 0.5 * (D + np.einsum('mn->nm', D))
# 1) All integrals are treated with resolution of identity (R.I.)
grad_comp = GradientComparison(molecule, basis, ribasis,
polarizable_atoms, point_charges,
polarizabilities=polarizabilities,
same_site_integrals='R.I.',
verbose=0)
# compute analytical and numerical QM gradients and compare them
assert grad_comp.compare_one_electron_part_gradients(D)
# 2) Same-site integrals are treated exactly.
grad_comp = GradientComparison(molecule, basis, ribasis,
polarizable_atoms, point_charges,
polarizabilities=polarizabilities,
same_site_integrals='exact',
verbose=0)
# compute analytical and numerical QM gradients and compare them
assert grad_comp.compare_one_electron_part_gradients(D)
def test_RHF_QMMM2ePol_energy_gradients():
"""
compare analytical and numerical gradients of the RHF+QM/MM-2e-Pol energy
"""
# load QM and MM regions from AMBER files
molecule, polarizable_atoms, point_charges, polarizabilities = amber2psi4('solvated.prmtop', 'solvated.rst7', 'solvated.qmregion')
# run closed-shell SCF calculation
grad_comp = GradientComparisonRHF(molecule, polarizable_atoms, point_charges, 'sto-3g',
polarizabilities=polarizabilities,
same_site_integrals="exact", #"R.I.",
qmmm=True,
verbose=0)
# compute analytical and numerical QM gradients and compare them
assert grad_comp.compare_energy_gradients()
def test_RHF_energy_gradients():
"""
compare analytical and numerical gradients of the plain RHF energy
"""
# load QM and MM regions from AMBER files
molecule, polarizable_atoms, point_charges, polarizabilities = amber2psi4('solvated.prmtop', 'solvated.rst7', 'solvated.qmregion')
# plain RHF, no polarizable environment of point charges
polarizable_atoms = psi4.geometry("")
point_charges = psi4.geometry("")
# run closed-shell SCF calculation
grad_comp = GradientComparisonRHF(molecule, polarizable_atoms, point_charges, 'sto-3g',
polarizabilities=polarizabilities,
verbose=0)
# compute analytical and numerical QM gradients and compare them
assert grad_comp.compare_energy_gradients()
def test_zero_electron_part_gradients():
"""
compare analytical and numerical gradients for the following terms of the polarization Hamiltonian:
* 0-electron part h^(0)
"""
# load QM and MM regions from AMBER files
molecule, polarizable_atoms, point_charges, polarizabilities = amber2psi4('solvated.prmtop', 'solvated.rst7', 'solvated.qmregion')
# basis for QM atoms
wfn = psi4.core.Wavefunction.build(molecule, 'sto-3g')
basis = wfn.basisset()
ribasis = basis
grad_comp = GradientComparison(molecule, basis, ribasis,
polarizable_atoms, point_charges,
polarizabilities=polarizabilities,
verbose=0)
assert grad_comp.compare_gradients('zero_electron_part')
def test_coulomb_exchange_gradients():
"""
check gradients of Coulomb and exchange energy
"""
# load QM and MM regions from AMBER files
molecule, polarizable_atoms, point_charges, polarizabilities = amber2psi4('solvated.prmtop', 'solvated.rst7', 'solvated.qmregion')
# basis for QM atoms
wfn = psi4.core.Wavefunction.build(molecule, 'sto-3g')
basis = wfn.basisset()
ribasis = basis
polham_grad = PolarizationHamiltonianGradients(molecule, basis, ribasis,
polarizable_atoms, point_charges,
polarizabilities=polarizabilities,
verbose=0)
# number of polarizable sites
npol = polham_grad.npol
# number of AOs
nbf = polham_grad.nbf
# make random numbers reproducible
np.random.seed(101)
# random density matrices
D1 = np.random.rand(nbf, nbf)
D2 = np.random.rand(nbf, nbf)
# # symmetrize matrices
# D1 = 0.5 * (D1 + np.einsum('mn->nm', D1))
# D2 = 0.5 * (D2 + np.einsum('mn->nm', D2))
grad_comp = GradientComparison(molecule, basis, ribasis,
polarizable_atoms, point_charges,
polarizabilities=polarizabilities,
verbose=0)
# compute analytical and numerical gradients and compare them
assert grad_comp.compare_coulomb_J_gradients(D1, D2)
assert grad_comp.compare_exchange_K_gradients(D1, D2)