Global Linear approximation of the ISA (gLISA) method
Non-linear optimization problem
Convex optimization method
[1]:
from setup import prepare_argument_dict, prepare_grid_and_dens, print_results
from horton_part.glisa import GlobalLinearISAWPart
mol, grid, rho = prepare_grid_and_dens("data/h2o.fchk")
def convex_optimization_with_non_negative_params():
kwargs = prepare_argument_dict(mol, grid, rho)
kwargs["solver"] = "cvxopt"
kwargs["solver_options"] = {"feastol": kwargs["threshold"]}
part = GlobalLinearISAWPart(**kwargs)
print(len(part._grid.points))
print(len(part.get_grid(0).points))
part.do_all()
# print_results(part)
convex_optimization_with_non_negative_params()
The number of electrons: 10.000003764139395
Coordinates of the atoms
[[ 0. 0. 0.224]
[-0. 1.457 -0.896]
[-0. -1.457 -0.896]]
Atomic numbers of the atom
[8 1 1]
================================================================================
Information of integral grids.
--------------------------------------------------------------------------------
Grid size of molecular grid: 18460
************************************ Atom 0 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18
18 18 18 18 18 18 26 26 26 26 38 38 38 38 38 50 50 50 50 50
86 86 110 110 110 110 170 194 194 434 590 590 434 434 434 302 302 302 194 194
170 110 110 110 110 110 110 110 110 110 110 110 86 50 50 18 18 18 18 18
************************************ Atom 1 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 18 18 18 18 18
18 18 18 18 18 18 18 18 18 26 26 26 38 38 38 38 38 38 38 50
50 50 50 50 50 86 86 86 110 110 110 170 170 170 194 194 194 194 170 170
170 110 110 110 110 110 110 110 110 110 110 86 86 50 50 50 18 18 18 18
************************************ Atom 2 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 18 18 18 18 18
18 18 18 18 18 18 18 18 18 26 26 26 38 38 38 38 38 38 38 50
50 50 50 50 50 86 86 86 110 110 110 170 170 170 194 194 194 194 170 170
170 110 110 110 110 110 110 110 110 110 110 86 86 50 50 50 18 18 18 18
--------------------------------------------------------------------------------
================================================================================
Performing a density-based AIM analysis with a wavefunction as input.
Molecular grid : MolGrid
Using local grids : True
Scheme : Linear Iterative Stockholder
Outer loop convergence threshold : 1.0e-06
Using global ISA : True
Maximum outer iterations : 1000
lmax : 3
Solver : CVXOPT
Basis function type : GAUSS
feastol : 1e-06
18460
8252
Load GAUSS basis functions
pcost dcost gap pres dres
0: 0.0000e+00 -9.7886e+00 2e+01 1e+00 1e+00
1: 4.4445e-01 -2.7882e+00 6e+00 4e-01 4e-01
2: 3.9147e-01 -1.4671e+00 2e+00 4e-02 2e-02
3: 7.7533e-02 -5.1383e-01 7e-01 3e-02 1e-02
4: 9.8506e-03 -7.4918e-02 1e-01 1e-02 1e-02
5: 3.3587e-02 1.2570e-02 3e-02 3e-03 4e-03
6: 3.7859e-02 3.3697e-02 7e-03 7e-04 2e-03
7: 3.9320e-02 3.8812e-02 9e-04 1e-04 7e-04
8: 3.9451e-02 3.9342e-02 2e-04 2e-05 3e-04
9: 3.9492e-02 3.9474e-02 3e-05 3e-06 6e-05
10: 3.9502e-02 3.9501e-02 2e-06 2e-07 4e-06
11: 3.9503e-02 3.9503e-02 3e-08 3e-09 6e-08
Optimal solution found.
Computing atomic populations.
Computing atomic charges.
Computing density decomposition for atom 0
Computing density decomposition for atom 1
Computing density decomposition for atom 2
Computing cartesian and pure AIM multipoles and radial AIM moments.
Storing proatom density spline for atom 0.
Storing proatom density spline for atom 1.
Storing proatom density spline for atom 2.
If negative parameters are allowed, one should set allow_neg_pars to True.
[2]:
def convex_optimization_with_negative_params():
kwargs = prepare_argument_dict(mol, grid, rho)
kwargs["solver"] = "cvxopt"
kwargs["solver_options"] = {"feastol": kwargs["threshold"], "allow_neg_pars": True}
part = GlobalLinearISAWPart(**kwargs)
try:
part.do_all()
print_results(part)
except RuntimeError as e:
print(e)
convex_optimization_with_negative_params()
================================================================================
Information of integral grids.
--------------------------------------------------------------------------------
Grid size of molecular grid: 18460
************************************ Atom 0 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18
18 18 18 18 18 18 26 26 26 26 38 38 38 38 38 50 50 50 50 50
86 86 110 110 110 110 170 194 194 434 590 590 434 434 434 302 302 302 194 194
170 110 110 110 110 110 110 110 110 110 110 110 86 50 50 18 18 18 18 18
************************************ Atom 1 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 18 18 18 18 18
18 18 18 18 18 18 18 18 18 26 26 26 38 38 38 38 38 38 38 50
50 50 50 50 50 86 86 86 110 110 110 170 170 170 194 194 194 194 170 170
170 110 110 110 110 110 110 110 110 110 110 86 86 50 50 50 18 18 18 18
************************************ Atom 2 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 18 18 18 18 18
18 18 18 18 18 18 18 18 18 26 26 26 38 38 38 38 38 38 38 50
50 50 50 50 50 86 86 86 110 110 110 170 170 170 194 194 194 194 170 170
170 110 110 110 110 110 110 110 110 110 110 86 86 50 50 50 18 18 18 18
--------------------------------------------------------------------------------
================================================================================
Performing a density-based AIM analysis with a wavefunction as input.
Molecular grid : MolGrid
Using local grids : True
Scheme : Linear Iterative Stockholder
Outer loop convergence threshold : 1.0e-06
Using global ISA : True
Maximum outer iterations : 1000
lmax : 3
Solver : CVXOPT
Basis function type : GAUSS
feastol : 1e-06
allow_neg_pars : True
Load GAUSS basis functions
pcost dcost gap pres dres
0: 0.0000e+00 2.1140e-01 1e+00 1e+00 1e+00
1: -3.1765e-01 -1.0025e-01 1e-02 2e-01 3e-01
2: -3.0512e-01 -2.3050e-01 1e-04 6e-02 5e-01
3: -3.1042e-01 -2.7868e-01 1e-06 3e-02 5e-01
4: -2.9110e-01 -2.8617e-01 1e-08 4e-03 3e-01
5: -2.9140e-01 -2.8919e-01 1e-10 2e-03 2e-01
6: -2.9095e-01 -2.9037e-01 1e-12 5e-04 8e-02
7: -2.9171e-01 -2.9125e-01 1e-14 4e-04 3e-02
8: -2.9203e-01 -2.8104e-01 1e-16 9e-03 4e-01
9: -2.8304e-01 -2.8235e-01 1e-18 6e-04 2e-01
10: -2.8420e-01 -2.8362e-01 1e-20 5e-04 1e-01
11: -2.8516e-01 -2.8463e-01 1e-22 4e-04 4e-02
12: -2.8542e-01 -2.8511e-01 1e-24 3e-04 1e-02
13: -2.8524e-01 -2.8518e-01 1e-26 5e-05 2e-03
14: -2.8518e-01 -2.8518e-01 1e-28 2e-06 4e-05
15: -2.8518e-01 -2.8518e-01 1e-30 2e-08 4e-07
Optimal solution found.
Negative pro-atom density found!
/Users/runner/work/horton-part/horton-part/src/horton_part/utils.py:489: UserWarning: WARNING: Not all pro-atom parameters are positive!
warnings.warn(warn_info)
Trust-region method
The optimization problem is solved by using trust constraint solver and all parameters are non-negative.
[3]:
def trust_region_explicitly():
"""Global LISA by solving constraint optimization problem (using trust constraint solver."""
kwargs = prepare_argument_dict(mol, grid, rho)
kwargs["solver"] = "trust-region"
kwargs["solver_options"] = {"allow_neg_pars": False}
part = GlobalLinearISAWPart(**kwargs)
part.do_all()
print_results(part)
trust_region_explicitly()
================================================================================
Information of integral grids.
--------------------------------------------------------------------------------
Grid size of molecular grid: 18460
************************************ Atom 0 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18
18 18 18 18 18 18 26 26 26 26 38 38 38 38 38 50 50 50 50 50
86 86 110 110 110 110 170 194 194 434 590 590 434 434 434 302 302 302 194 194
170 110 110 110 110 110 110 110 110 110 110 110 86 50 50 18 18 18 18 18
************************************ Atom 1 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 18 18 18 18 18
18 18 18 18 18 18 18 18 18 26 26 26 38 38 38 38 38 38 38 50
50 50 50 50 50 86 86 86 110 110 110 170 170 170 194 194 194 194 170 170
170 110 110 110 110 110 110 110 110 110 110 86 86 50 50 50 18 18 18 18
************************************ Atom 2 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 18 18 18 18 18
18 18 18 18 18 18 18 18 18 26 26 26 38 38 38 38 38 38 38 50
50 50 50 50 50 86 86 86 110 110 110 170 170 170 194 194 194 194 170 170
170 110 110 110 110 110 110 110 110 110 110 86 86 50 50 50 18 18 18 18
--------------------------------------------------------------------------------
================================================================================
Performing a density-based AIM analysis with a wavefunction as input.
Molecular grid : MolGrid
Using local grids : True
Scheme : Linear Iterative Stockholder
Outer loop convergence threshold : 1.0e-06
Using global ISA : True
Maximum outer iterations : 1000
lmax : 3
Solver : TRUST-REGION
Basis function type : GAUSS
allow_neg_pars : False
Load GAUSS basis functions
Integral of density: {pop}
| niter |f evals|CG iter| obj func |tr radius | opt | c viol | penalty |barrier param|CG stop|
|-------|-------|-------|-------------|----------|----------|----------|----------|-------------|-------|
| 1 | 1 | 0 | +2.1141e-01 | 1.00e+00 | 1.20e-01 | 0.00e+00 | 1.00e+00 | 1.00e-01 | 0 |
| 2 | 2 | 1 | +1.9929e-01 | 7.00e+00 | 1.67e-01 | 0.00e+00 | 1.00e+00 | 1.00e-01 | 2 |
| 3 | 3 | 3 | +4.7679e-01 | 1.60e+01 | 8.33e-02 | 0.00e+00 | 1.00e+00 | 1.00e-01 | 4 |
| 4 | 3 | 3 | +4.7679e-01 | 8.01e+01 | 6.94e-02 | 0.00e+00 | 1.00e+00 | 2.00e-02 | 0 |
| 5 | 4 | 6 | +1.6137e-01 | 8.01e+01 | 4.16e-02 | 0.00e+00 | 1.00e+00 | 2.00e-02 | 4 |
| 6 | 5 | 11 | +9.5478e-02 | 8.01e+01 | 4.04e-02 | 0.00e+00 | 1.00e+00 | 2.00e-02 | 4 |
| 7 | 6 | 14 | +9.2717e-02 | 8.01e+01 | 3.63e-02 | 0.00e+00 | 1.00e+00 | 2.00e-02 | 4 |
| 8 | 7 | 18 | +8.1314e-02 | 8.01e+01 | 1.59e-02 | 0.00e+00 | 1.00e+00 | 2.00e-02 | 4 |
| 9 | 7 | 18 | +8.1314e-02 | 4.01e+02 | 2.38e-02 | 0.00e+00 | 1.00e+00 | 4.00e-03 | 0 |
| 10 | 8 | 23 | +6.2201e-02 | 4.01e+02 | 2.80e-02 | 0.00e+00 | 1.00e+00 | 4.00e-03 | 4 |
| 11 | 9 | 27 | +5.6830e-02 | 4.01e+02 | 1.98e-02 | 0.00e+00 | 1.00e+00 | 4.00e-03 | 4 |
| 12 | 10 | 34 | +4.9801e-02 | 4.01e+02 | 1.61e-02 | 0.00e+00 | 1.00e+00 | 4.00e-03 | 4 |
| 13 | 11 | 36 | +4.9485e-02 | 4.01e+02 | 1.66e-02 | 0.00e+00 | 1.00e+00 | 4.00e-03 | 4 |
| 14 | 12 | 40 | +4.8207e-02 | 4.01e+02 | 1.11e-02 | 0.00e+00 | 1.00e+00 | 4.00e-03 | 4 |
| 15 | 13 | 46 | +4.6276e-02 | 4.01e+02 | 1.29e-02 | 0.00e+00 | 1.00e+00 | 4.00e-03 | 4 |
| 16 | 14 | 50 | +4.5436e-02 | 4.01e+02 | 9.98e-03 | 0.00e+00 | 1.00e+00 | 4.00e-03 | 4 |
| 17 | 15 | 54 | +4.4941e-02 | 4.01e+02 | 4.90e-03 | 0.00e+00 | 1.00e+00 | 4.00e-03 | 4 |
/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/scipy/optimize/_differentiable_functions.py:317: UserWarning: delta_grad == 0.0. Check if the approximated function is linear. If the function is linear better results can be obtained by defining the Hessian as zero instead of using quasi-Newton approximations.
self.H.update(self.x - self.x_prev, self.g - self.g_prev)
| 18 | 16 | 57 | +4.4293e-02 | 4.01e+02 | 5.40e-03 | 0.00e+00 | 1.00e+00 | 4.00e-03 | 4 |
| 19 | 17 | 61 | +4.3738e-02 | 4.01e+02 | 3.90e-03 | 0.00e+00 | 1.00e+00 | 4.00e-03 | 4 |
| 20 | 17 | 61 | +4.3738e-02 | 2.00e+03 | 4.86e-03 | 0.00e+00 | 1.00e+00 | 8.00e-04 | 0 |
| 21 | 18 | 66 | +4.1343e-02 | 2.00e+03 | 2.45e-03 | 0.00e+00 | 1.00e+00 | 8.00e-04 | 4 |
| 22 | 19 | 74 | +4.1343e-02 | 2.00e+02 | 2.45e-03 | 0.00e+00 | 1.00e+00 | 8.00e-04 | 3 |
| 23 | 20 | 79 | +4.1050e-02 | 2.00e+02 | 3.39e-03 | 0.00e+00 | 1.00e+00 | 8.00e-04 | 4 |
| 24 | 21 | 81 | +4.0956e-02 | 2.00e+02 | 3.81e-03 | 0.00e+00 | 1.00e+00 | 8.00e-04 | 4 |
| 25 | 23 | 85 | +4.0956e-02 | 2.00e+01 | 3.81e-03 | 0.00e+00 | 1.00e+00 | 8.00e-04 | 3 |
| 26 | 24 | 91 | +4.0459e-02 | 2.00e+01 | 1.12e-03 | 0.00e+00 | 1.00e+00 | 8.00e-04 | 4 |
| 27 | 25 | 96 | +4.0351e-02 | 2.00e+01 | 7.43e-04 | 0.00e+00 | 1.00e+00 | 8.00e-04 | 4 |
| 28 | 25 | 96 | +4.0351e-02 | 1.00e+02 | 9.36e-04 | 0.00e+00 | 1.00e+00 | 1.60e-04 | 0 |
| 29 | 26 | 103 | +3.9904e-02 | 1.00e+02 | 1.26e-03 | 0.00e+00 | 1.00e+00 | 1.60e-04 | 4 |
| 30 | 28 | 104 | +3.9904e-02 | 1.00e+01 | 1.26e-03 | 0.00e+00 | 1.00e+00 | 1.60e-04 | 3 |
| 31 | 30 | 109 | +3.9904e-02 | 1.00e+00 | 1.26e-03 | 0.00e+00 | 1.00e+00 | 1.60e-04 | 3 |
| 32 | 32 | 113 | +3.9904e-02 | 1.96e-01 | 1.26e-03 | 0.00e+00 | 1.00e+00 | 1.60e-04 | 3 |
| 33 | 33 | 119 | +3.9812e-02 | 1.37e+00 | 1.21e-03 | 0.00e+00 | 1.00e+00 | 1.60e-04 | 2 |
| 34 | 35 | 128 | +3.9812e-02 | 2.74e-01 | 1.21e-03 | 0.00e+00 | 1.00e+00 | 1.60e-04 | 4 |
| 35 | 37 | 130 | +3.9812e-02 | 6.20e-02 | 1.21e-03 | 0.00e+00 | 1.00e+00 | 1.60e-04 | 3 |
| 36 | 38 | 132 | +3.9812e-02 | 1.50e-02 | 1.21e-03 | 0.00e+00 | 1.00e+00 | 1.60e-04 | 2 |
| 37 | 39 | 134 | +3.9790e-02 | 1.05e-01 | 2.20e-04 | 0.00e+00 | 1.00e+00 | 1.60e-04 | 2 |
| 38 | 40 | 140 | +3.9731e-02 | 7.33e-01 | 3.11e-04 | 0.00e+00 | 1.00e+00 | 1.60e-04 | 2 |
| 39 | 42 | 145 | +3.9731e-02 | 1.11e-01 | 3.11e-04 | 0.00e+00 | 1.00e+00 | 1.60e-04 | 3 |
| 40 | 43 | 151 | +3.9697e-02 | 2.22e-01 | 8.11e-04 | 0.00e+00 | 1.00e+00 | 1.60e-04 | 2 |
| 41 | 44 | 156 | +3.9672e-02 | 3.58e-01 | 3.14e-04 | 0.00e+00 | 1.00e+00 | 1.60e-04 | 4 |
| 42 | 45 | 165 | +3.9594e-02 | 1.55e+00 | 5.50e-04 | 0.00e+00 | 1.00e+00 | 1.60e-04 | 4 |
| 43 | 46 | 167 | +3.9592e-02 | 1.55e+00 | 5.15e-04 | 0.00e+00 | 1.00e+00 | 1.60e-04 | 4 |
| 44 | 47 | 172 | +3.9588e-02 | 1.55e+00 | 7.67e-05 | 0.00e+00 | 1.00e+00 | 1.60e-04 | 4 |
| 45 | 47 | 172 | +3.9588e-02 | 7.75e+00 | 1.15e-04 | 0.00e+00 | 1.00e+00 | 3.20e-05 | 0 |
| 46 | 48 | 183 | +3.9515e-02 | 7.75e+00 | 1.61e-04 | 0.00e+00 | 1.00e+00 | 3.20e-05 | 4 |
| 47 | 49 | 187 | +3.9514e-02 | 7.75e+00 | 1.05e-04 | 0.00e+00 | 1.00e+00 | 3.20e-05 | 4 |
| 48 | 50 | 199 | +3.9505e-02 | 7.75e+00 | 9.39e-05 | 0.00e+00 | 1.00e+00 | 3.20e-05 | 4 |
| 49 | 51 | 200 | +3.9505e-02 | 7.75e+00 | 5.29e-05 | 0.00e+00 | 1.00e+00 | 3.20e-05 | 4 |
| 50 | 52 | 205 | +3.9505e-02 | 7.75e+00 | 1.38e-05 | 0.00e+00 | 1.00e+00 | 3.20e-05 | 4 |
| 51 | 52 | 205 | +3.9505e-02 | 3.88e+01 | 1.51e-05 | 0.00e+00 | 1.00e+00 | 6.40e-06 | 0 |
| 52 | 53 | 216 | +3.9501e-02 | 3.88e+01 | 3.99e-05 | 0.00e+00 | 1.00e+00 | 6.40e-06 | 4 |
| 53 | 54 | 220 | +3.9501e-02 | 3.88e+01 | 1.24e-05 | 0.00e+00 | 1.00e+00 | 6.40e-06 | 4 |
| 54 | 55 | 226 | +3.9501e-02 | 3.88e+01 | 3.03e-06 | 0.00e+00 | 1.00e+00 | 6.40e-06 | 4 |
| 55 | 55 | 226 | +3.9501e-02 | 1.94e+02 | 4.43e-06 | 0.00e+00 | 1.00e+00 | 1.28e-06 | 0 |
| 56 | 56 | 238 | +3.9500e-02 | 1.94e+02 | 6.83e-06 | 0.00e+00 | 1.00e+00 | 1.28e-06 | 4 |
| 57 | 57 | 240 | +3.9500e-02 | 1.94e+02 | 8.25e-06 | 0.00e+00 | 1.00e+00 | 1.28e-06 | 4 |
| 58 | 58 | 241 | +3.9500e-02 | 1.94e+02 | 5.73e-06 | 0.00e+00 | 1.00e+00 | 1.28e-06 | 4 |
| 59 | 59 | 246 | +3.9500e-02 | 1.94e+02 | 7.14e-07 | 0.00e+00 | 1.00e+00 | 1.28e-06 | 4 |
`gtol` termination condition is satisfied.
Number of iterations: 59, function evaluations: 59, CG iterations: 246, optimality: 7.14e-07, constraint violation: 0.00e+00, execution time: 0.19 s.
Optimizer message: "`gtol` termination condition is satisfied."
Constraint: 1.3702170994278617e-05
Optimized parameters:
[0.198 0.633 0.984 2.939 3.294 0.833 0.071 0.35 0.13 0.008 0.071 0.35 0.13 0.008]
Computing atomic populations.
Computing atomic charges.
Computing density decomposition for atom 0
Computing density decomposition for atom 1
Computing density decomposition for atom 2
Computing cartesian and pure AIM multipoles and radial AIM moments.
Storing proatom density spline for atom 0.
Storing proatom density spline for atom 1.
Storing proatom density spline for atom 2.
charges:
[-0.881 0.441 0.441]
cartesian multipoles:
[[-0.881 0. -0. 0.133 -5.381 -0. -0. -4.802 -0. -5.094 -0. 0. 0.034 0. 0. 0. 0. 0.416 0. 0.368]
[ 0.441 0. 0.022 -0.001 -0.275 -0. -0. -0.257 0.002 -0.26 0. 0.008 0.005 0. 0. 0. 0.024 0.009 0.009 0.023]
[ 0.441 0. -0.022 -0.001 -0.275 0. 0. -0.257 -0.002 -0.26 0. -0.008 0.005 0. -0. 0. -0.024 0.009 -0.009 0.023]]
If negative parameters are allowed, one should set allow_neg_pars to True.
[4]:
def trust_region_implicitly():
"""Global LISA by solving constraint optimization problem (using trust constraint solver with negative parameters allowed.)"""
kwargs = prepare_argument_dict(mol, grid, rho)
kwargs["solver"] = "trust-region"
kwargs["solver_options"] = {"allow_neg_pars": True}
part = GlobalLinearISAWPart(**kwargs)
try:
part.do_all()
print_results(part)
except RuntimeError:
print("The program is stoped because proatom density is negative somewhere!")
trust_region_implicitly()
================================================================================
Information of integral grids.
--------------------------------------------------------------------------------
Grid size of molecular grid: 18460
************************************ Atom 0 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18
18 18 18 18 18 18 26 26 26 26 38 38 38 38 38 50 50 50 50 50
86 86 110 110 110 110 170 194 194 434 590 590 434 434 434 302 302 302 194 194
170 110 110 110 110 110 110 110 110 110 110 110 86 50 50 18 18 18 18 18
************************************ Atom 1 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 18 18 18 18 18
18 18 18 18 18 18 18 18 18 26 26 26 38 38 38 38 38 38 38 50
50 50 50 50 50 86 86 86 110 110 110 170 170 170 194 194 194 194 170 170
170 110 110 110 110 110 110 110 110 110 110 86 86 50 50 50 18 18 18 18
************************************ Atom 2 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 18 18 18 18 18
18 18 18 18 18 18 18 18 18 26 26 26 38 38 38 38 38 38 38 50
50 50 50 50 50 86 86 86 110 110 110 170 170 170 194 194 194 194 170 170
170 110 110 110 110 110 110 110 110 110 110 86 86 50 50 50 18 18 18 18
--------------------------------------------------------------------------------
================================================================================
Performing a density-based AIM analysis with a wavefunction as input.
Molecular grid : MolGrid
Using local grids : True
Scheme : Linear Iterative Stockholder
Outer loop convergence threshold : 1.0e-06
Using global ISA : True
Maximum outer iterations : 1000
lmax : 3
Solver : TRUST-REGION
Basis function type : GAUSS
allow_neg_pars : True
Load GAUSS basis functions
Integral of density: {pop}
| niter |f evals|CG iter| obj func |tr radius | opt | c viol | penalty |CG stop|
|-------|-------|-------|-------------|----------|----------|----------|----------|-------|
| 1 | 1 | 0 | +2.1141e-01 | 1.00e+00 | 2.40e-01 | 1.78e-15 | 1.00e+00 | 0 |
| 2 | 2 | 1 | +1.4008e-01 | 1.00e+00 | 3.76e-01 | 1.78e-15 | 1.00e+00 | 4 |
| 3 | 4 | 3 | +1.4008e-01 | 5.01e-01 | 3.76e-01 | 1.78e-15 | 1.00e+00 | 2 |
| 4 | 5 | 6 | +8.7234e-02 | 6.84e-01 | 1.39e-01 | 0.00e+00 | 1.00e+00 | 4 |
| 5 | 6 | 8 | +6.3406e-02 | 8.78e-01 | 8.59e-02 | 1.78e-15 | 1.00e+00 | 4 |
| 6 | 7 | 11 | +5.0084e-02 | 8.78e-01 | 3.06e-01 | 1.78e-15 | 1.00e+00 | 4 |
| 7 | 8 | 13 | +4.8330e-02 | 8.78e-01 | 6.24e-02 | 1.78e-15 | 1.00e+00 | 4 |
| 8 | 9 | 15 | +4.5952e-02 | 8.78e-01 | 3.49e-02 | 1.78e-15 | 1.00e+00 | 4 |
| 9 | 10 | 18 | +4.4912e-02 | 8.78e-01 | 1.17e+00 | 0.00e+00 | 1.00e+00 | 4 |
| 10 | 11 | 19 | +4.4798e-02 | 8.78e-01 | 1.01e-01 | 0.00e+00 | 1.00e+00 | 4 |
| 11 | 12 | 22 | +4.4103e-02 | 8.78e-01 | 2.88e-02 | 0.00e+00 | 1.00e+00 | 4 |
| 12 | 13 | 25 | +4.3969e-02 | 8.78e-01 | 2.99e-02 | 0.00e+00 | 1.00e+00 | 4 |
| 13 | 14 | 29 | +4.3317e-02 | 8.78e-01 | 2.75e-01 | 1.78e-15 | 1.00e+00 | 4 |
| 14 | 15 | 30 | +4.3190e-02 | 8.78e-01 | 4.41e-02 | 1.78e-15 | 1.00e+00 | 4 |
| 15 | 17 | 32 | +4.3190e-02 | 4.39e-01 | 4.41e-02 | 1.78e-15 | 1.00e+00 | 3 |
| 16 | 19 | 37 | +4.3190e-02 | 1.05e-01 | 4.41e-02 | 1.78e-15 | 1.00e+00 | 4 |
| 17 | 21 | 39 | +4.3190e-02 | 5.24e-02 | 4.41e-02 | 1.78e-15 | 1.00e+00 | 3 |
| 18 | 23 | 42 | +4.3190e-02 | 2.62e-02 | 4.41e-02 | 1.78e-15 | 1.00e+00 | 3 |
| 19 | 24 | 44 | +4.3000e-02 | 3.32e-02 | 2.46e-02 | 0.00e+00 | 1.00e+00 | 4 |
| 20 | 25 | 48 | +4.2510e-02 | 2.32e-01 | 2.14e-02 | 0.00e+00 | 1.00e+00 | 2 |
| 21 | 27 | 49 | +4.2510e-02 | 1.16e-01 | 2.14e-02 | 0.00e+00 | 1.00e+00 | 3 |
| 22 | 28 | 53 | +4.2510e-02 | 5.80e-02 | 2.14e-02 | 0.00e+00 | 1.00e+00 | 2 |
| 23 | 30 | 56 | +4.2510e-02 | 2.90e-02 | 2.14e-02 | 0.00e+00 | 1.00e+00 | 2 |
| 24 | 31 | 60 | +4.2304e-02 | 5.80e-02 | 3.40e-02 | 0.00e+00 | 1.00e+00 | 2 |
| 25 | 33 | 62 | +4.2304e-02 | 2.90e-02 | 3.40e-02 | 0.00e+00 | 1.00e+00 | 3 |
| 26 | 34 | 67 | +4.1707e-02 | 2.03e-01 | 9.61e-03 | 0.00e+00 | 1.00e+00 | 2 |
| 27 | 35 | 74 | +4.1577e-02 | 2.03e-01 | 4.47e-01 | 0.00e+00 | 1.00e+00 | 4 |
| 28 | 36 | 76 | +4.1384e-02 | 2.03e-01 | 2.99e-02 | 0.00e+00 | 1.00e+00 | 4 |
| 29 | 37 | 79 | +4.1226e-02 | 2.03e-01 | 1.77e-02 | 1.78e-15 | 1.00e+00 | 4 |
| 30 | 38 | 83 | +4.0826e-02 | 2.53e-01 | 1.44e-02 | 1.78e-15 | 1.00e+00 | 4 |
| 31 | 40 | 84 | +4.0826e-02 | 1.26e-01 | 1.44e-02 | 1.78e-15 | 1.00e+00 | 3 |
| 32 | 41 | 91 | +4.0519e-02 | 3.15e-01 | 1.49e-02 | 1.78e-15 | 1.00e+00 | 4 |
| 33 | 42 | 94 | +4.0411e-02 | 3.15e-01 | 8.80e-03 | 1.78e-15 | 1.00e+00 | 4 |
| 34 | 43 | 104 | +3.9928e-02 | 3.27e-01 | 6.06e-02 | 0.00e+00 | 1.00e+00 | 4 |
| 35 | 44 | 105 | +3.9793e-02 | 3.27e-01 | 2.13e-02 | 1.78e-15 | 1.00e+00 | 4 |
| 36 | 45 | 108 | +3.9714e-02 | 3.27e-01 | 1.16e-02 | 1.78e-15 | 1.00e+00 | 4 |
| 37 | 46 | 112 | +3.9650e-02 | 3.27e-01 | 5.87e-03 | 0.00e+00 | 1.00e+00 | 4 |
| 38 | 48 | 120 | +3.9650e-02 | 1.05e-01 | 5.87e-03 | 0.00e+00 | 1.00e+00 | 3 |
| 39 | 49 | 128 | +3.9634e-02 | 1.05e-01 | 1.69e-02 | 0.00e+00 | 1.00e+00 | 4 |
| 40 | 50 | 130 | +3.9589e-02 | 1.05e-01 | 1.35e-02 | 0.00e+00 | 1.00e+00 | 4 |
| 41 | 51 | 133 | +3.9556e-02 | 1.05e-01 | 7.79e-03 | 0.00e+00 | 1.00e+00 | 4 |
| 42 | 52 | 137 | +3.9534e-02 | 1.05e-01 | 3.32e-03 | 1.78e-15 | 1.00e+00 | 4 |
| 43 | 53 | 147 | +3.9508e-02 | 2.67e-01 | 2.66e-03 | 1.78e-15 | 1.00e+00 | 4 |
| 44 | 54 | 150 | +3.9508e-02 | 1.33e-01 | 2.66e-03 | 1.78e-15 | 1.00e+00 | 3 |
| 45 | 55 | 154 | +3.9502e-02 | 1.33e-01 | 1.64e-03 | 1.78e-15 | 1.00e+00 | 4 |
| 46 | 56 | 159 | +3.9501e-02 | 1.33e-01 | 9.66e-04 | 1.78e-15 | 1.00e+00 | 4 |
| 47 | 57 | 162 | +3.9501e-02 | 1.33e-01 | 3.36e-04 | 0.00e+00 | 1.00e+00 | 4 |
| 48 | 58 | 167 | +3.9501e-02 | 1.33e-01 | 1.89e-04 | 1.78e-15 | 1.00e+00 | 4 |
| 49 | 59 | 172 | +3.9500e-02 | 1.33e-01 | 1.62e-04 | 1.78e-15 | 1.00e+00 | 4 |
| 50 | 60 | 174 | +3.9500e-02 | 1.33e-02 | 1.62e-04 | 1.78e-15 | 1.00e+00 | 3 |
| 51 | 62 | 181 | +3.9500e-02 | 1.33e-03 | 1.62e-04 | 1.78e-15 | 1.00e+00 | 4 |
| 52 | 64 | 184 | +3.9500e-02 | 4.27e-04 | 1.62e-04 | 1.78e-15 | 1.00e+00 | 3 |
| 53 | 65 | 189 | +3.9500e-02 | 8.54e-04 | 1.36e-04 | 1.78e-15 | 1.00e+00 | 2 |
| 54 | 66 | 193 | +3.9500e-02 | 2.97e-04 | 1.36e-04 | 1.78e-15 | 1.00e+00 | 3 |
| 55 | 67 | 198 | +3.9500e-02 | 5.93e-04 | 3.53e-05 | 1.78e-15 | 1.00e+00 | 2 |
| 56 | 68 | 205 | +3.9500e-02 | 4.15e-03 | 2.17e-05 | 1.78e-15 | 1.00e+00 | 2 |
| 57 | 69 | 210 | +3.9500e-02 | 4.15e-03 | 2.47e-05 | 1.78e-15 | 1.00e+00 | 4 |
| 58 | 70 | 213 | +3.9500e-02 | 4.15e-03 | 2.14e-05 | 1.78e-15 | 1.00e+00 | 4 |
| 59 | 71 | 218 | +3.9500e-02 | 4.15e-03 | 9.96e-06 | 0.00e+00 | 1.00e+00 | 4 |
| 60 | 72 | 226 | +3.9500e-02 | 4.15e-03 | 1.52e-06 | 0.00e+00 | 1.00e+00 | 4 |
| 61 | 73 | 232 | +3.9500e-02 | 4.15e-03 | 5.84e-07 | 1.78e-15 | 1.00e+00 | 4 |
`gtol` termination condition is satisfied.
Number of iterations: 61, function evaluations: 73, CG iterations: 232, optimality: 5.84e-07, constraint violation: 1.78e-15, execution time: 0.22 s.
Optimizer message: "`gtol` termination condition is satisfied."
Constraint: -2.6298035180616353e-06
Optimized parameters:
[0.198 0.633 0.984 2.939 3.294 0.834 0.071 0.35 0.13 0.008 0.071 0.35 0.13 0.008]
Computing atomic populations.
Computing atomic charges.
Computing density decomposition for atom 0
Computing density decomposition for atom 1
Computing density decomposition for atom 2
Computing cartesian and pure AIM multipoles and radial AIM moments.
Storing proatom density spline for atom 0.
Storing proatom density spline for atom 1.
Storing proatom density spline for atom 2.
charges:
[-0.881 0.441 0.441]
cartesian multipoles:
[[-0.881 0. -0. 0.134 -5.381 -0. -0. -4.802 0. -5.095 -0. 0. 0.034 0. -0. -0. 0. 0.417 0. 0.368]
[ 0.441 0. 0.022 -0.001 -0.275 -0. -0. -0.256 0.002 -0.26 0. 0.008 0.005 0. 0. 0. 0.024 0.009 0.009 0.023]
[ 0.441 0. -0.022 -0.001 -0.275 0. 0. -0.256 -0.002 -0.26 0. -0.008 0.005 0. -0. 0. -0.024 0.009 -0.009 0.023]]
Non-linear equations (fixed-point equations)
Self-consistent method
An equivalent fixed-point problem is addressed by using self-consistent solver and non-negative parameters are guaranteed.
[5]:
def self_consistent_method():
"""Global LISA with self-consistent solver."""
kwargs = prepare_argument_dict(mol, grid, rho)
kwargs["solver"] = "sc"
part = GlobalLinearISAWPart(**kwargs)
part.do_all()
print_results(part)
self_consistent_method()
================================================================================
Information of integral grids.
--------------------------------------------------------------------------------
Grid size of molecular grid: 18460
************************************ Atom 0 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18
18 18 18 18 18 18 26 26 26 26 38 38 38 38 38 50 50 50 50 50
86 86 110 110 110 110 170 194 194 434 590 590 434 434 434 302 302 302 194 194
170 110 110 110 110 110 110 110 110 110 110 110 86 50 50 18 18 18 18 18
************************************ Atom 1 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 18 18 18 18 18
18 18 18 18 18 18 18 18 18 26 26 26 38 38 38 38 38 38 38 50
50 50 50 50 50 86 86 86 110 110 110 170 170 170 194 194 194 194 170 170
170 110 110 110 110 110 110 110 110 110 110 86 86 50 50 50 18 18 18 18
************************************ Atom 2 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 18 18 18 18 18
18 18 18 18 18 18 18 18 18 26 26 26 38 38 38 38 38 38 38 50
50 50 50 50 50 86 86 86 110 110 110 170 170 170 194 194 194 194 170 170
170 110 110 110 110 110 110 110 110 110 110 86 86 50 50 50 18 18 18 18
--------------------------------------------------------------------------------
================================================================================
Performing a density-based AIM analysis with a wavefunction as input.
Molecular grid : MolGrid
Using local grids : True
Scheme : Linear Iterative Stockholder
Outer loop convergence threshold : 1.0e-06
Using global ISA : True
Maximum outer iterations : 1000
lmax : 3
Solver : SC
Basis function type : GAUSS
Load GAUSS basis functions
Iteration Change Entropy
1 8.86627e-02 2.11396e-01
2 5.02880e-02 1.36337e-01
3 2.65836e-02 1.03249e-01
4 2.18092e-02 8.45035e-02
5 1.89757e-02 7.24856e-02
6 1.50533e-02 6.43163e-02
7 1.12729e-02 5.85644e-02
8 8.31844e-03 5.44071e-02
9 6.29139e-03 5.13377e-02
10 5.01183e-03 4.90303e-02
11 4.21416e-03 4.72682e-02
12 3.67227e-03 4.59035e-02
13 3.24950e-03 4.48326e-02
14 2.88448e-03 4.39819e-02
15 2.55841e-03 4.32984e-02
16 2.27076e-03 4.27431e-02
17 2.02611e-03 4.22876e-02
18 1.82791e-03 4.19103e-02
19 1.67592e-03 4.15951e-02
20 1.56567e-03 4.13296e-02
21 1.48939e-03 4.11045e-02
22 1.43786e-03 4.09123e-02
23 1.40224e-03 4.07473e-02
24 1.37521e-03 4.06048e-02
25 1.35147e-03 4.04812e-02
26 1.32752e-03 4.03736e-02
27 1.30132e-03 4.02795e-02
28 1.27187e-03 4.01969e-02
29 1.23890e-03 4.01242e-02
30 1.20255e-03 4.00601e-02
31 1.16323e-03 4.00033e-02
32 1.12145e-03 3.99530e-02
33 1.07780e-03 3.99083e-02
34 1.03283e-03 3.98685e-02
35 9.87070e-04 3.98331e-02
36 9.41001e-04 3.98014e-02
37 8.95035e-04 3.97730e-02
38 8.49528e-04 3.97477e-02
39 8.04775e-04 3.97249e-02
40 7.61022e-04 3.97045e-02
41 7.18463e-04 3.96861e-02
42 6.77249e-04 3.96696e-02
43 6.37496e-04 3.96547e-02
44 5.99284e-04 3.96413e-02
45 5.62668e-04 3.96292e-02
46 5.27679e-04 3.96183e-02
47 4.94328e-04 3.96085e-02
48 4.62610e-04 3.95995e-02
49 4.32506e-04 3.95915e-02
50 4.03988e-04 3.95841e-02
51 3.77019e-04 3.95775e-02
52 3.51554e-04 3.95715e-02
53 3.27545e-04 3.95660e-02
54 3.04939e-04 3.95610e-02
55 2.83681e-04 3.95565e-02
56 2.63714e-04 3.95524e-02
57 2.44980e-04 3.95487e-02
58 2.27422e-04 3.95452e-02
59 2.10983e-04 3.95421e-02
60 1.95606e-04 3.95393e-02
61 1.81236e-04 3.95367e-02
62 1.67819e-04 3.95343e-02
63 1.55302e-04 3.95321e-02
64 1.43635e-04 3.95301e-02
65 1.32770e-04 3.95283e-02
66 1.22660e-04 3.95266e-02
67 1.13260e-04 3.95250e-02
68 1.04527e-04 3.95236e-02
69 9.64218e-05 3.95223e-02
70 8.89051e-05 3.95211e-02
71 8.19404e-05 3.95200e-02
72 7.54931e-05 3.95189e-02
73 6.95305e-05 3.95180e-02
74 6.40217e-05 3.95171e-02
75 5.89375e-05 3.95163e-02
76 5.42505e-05 3.95155e-02
77 4.99350e-05 3.95148e-02
78 4.59664e-05 3.95142e-02
79 4.23222e-05 3.95136e-02
80 3.89806e-05 3.95130e-02
81 3.59216e-05 3.95125e-02
82 3.31262e-05 3.95120e-02
83 3.05764e-05 3.95115e-02
84 2.82555e-05 3.95111e-02
85 2.61474e-05 3.95107e-02
86 2.42371e-05 3.95103e-02
87 2.25102e-05 3.95100e-02
88 2.09529e-05 3.95096e-02
89 1.95521e-05 3.95093e-02
90 1.82952e-05 3.95090e-02
91 1.71702e-05 3.95088e-02
92 1.61652e-05 3.95085e-02
93 1.52692e-05 3.95083e-02
94 1.44714e-05 3.95080e-02
95 1.37614e-05 3.95078e-02
96 1.31295e-05 3.95076e-02
97 1.25667e-05 3.95074e-02
98 1.20643e-05 3.95072e-02
99 1.16145e-05 3.95070e-02
100 1.12102e-05 3.95069e-02
101 1.08449e-05 3.95067e-02
102 1.05128e-05 3.95066e-02
103 1.02089e-05 3.95064e-02
104 9.92867e-06 3.95063e-02
105 9.66837e-06 3.95062e-02
106 9.42469e-06 3.95060e-02
107 9.19488e-06 3.95059e-02
108 8.97660e-06 3.95058e-02
109 8.76791e-06 3.95057e-02
110 8.56722e-06 3.95056e-02
111 8.37324e-06 3.95055e-02
112 8.18490e-06 3.95054e-02
113 8.00136e-06 3.95053e-02
114 7.82198e-06 3.95052e-02
115 7.64622e-06 3.95052e-02
116 7.47369e-06 3.95051e-02
117 7.30411e-06 3.95050e-02
118 7.13725e-06 3.95049e-02
119 6.97296e-06 3.95049e-02
120 6.81115e-06 3.95048e-02
121 6.65177e-06 3.95047e-02
122 6.49477e-06 3.95047e-02
123 6.34017e-06 3.95046e-02
124 6.18796e-06 3.95046e-02
125 6.03818e-06 3.95045e-02
126 5.89086e-06 3.95045e-02
127 5.74604e-06 3.95044e-02
128 5.60374e-06 3.95044e-02
129 5.46402e-06 3.95043e-02
130 5.32691e-06 3.95043e-02
131 5.19244e-06 3.95042e-02
132 5.06063e-06 3.95042e-02
133 4.93152e-06 3.95041e-02
134 4.80512e-06 3.95041e-02
135 4.68144e-06 3.95041e-02
136 4.56050e-06 3.95040e-02
137 4.44229e-06 3.95040e-02
138 4.32682e-06 3.95040e-02
139 4.21407e-06 3.95039e-02
140 4.10404e-06 3.95039e-02
141 3.99670e-06 3.95039e-02
142 3.89204e-06 3.95038e-02
143 3.79003e-06 3.95038e-02
144 3.69064e-06 3.95038e-02
145 3.59384e-06 3.95038e-02
146 3.49959e-06 3.95037e-02
147 3.40786e-06 3.95037e-02
148 3.31861e-06 3.95037e-02
149 3.23178e-06 3.95037e-02
150 3.14735e-06 3.95037e-02
151 3.06527e-06 3.95036e-02
152 2.98547e-06 3.95036e-02
153 2.90793e-06 3.95036e-02
154 2.83258e-06 3.95036e-02
155 2.75938e-06 3.95036e-02
156 2.68828e-06 3.95035e-02
157 2.61923e-06 3.95035e-02
158 2.55218e-06 3.95035e-02
159 2.48707e-06 3.95035e-02
160 2.42385e-06 3.95035e-02
161 2.36248e-06 3.95035e-02
162 2.30290e-06 3.95035e-02
163 2.24507e-06 3.95034e-02
164 2.18893e-06 3.95034e-02
165 2.13444e-06 3.95034e-02
166 2.08154e-06 3.95034e-02
167 2.03020e-06 3.95034e-02
168 1.98037e-06 3.95034e-02
169 1.93199e-06 3.95034e-02
170 1.88504e-06 3.95034e-02
171 1.83945e-06 3.95034e-02
172 1.79519e-06 3.95033e-02
173 1.75223e-06 3.95033e-02
174 1.71051e-06 3.95033e-02
175 1.66999e-06 3.95033e-02
176 1.63065e-06 3.95033e-02
177 1.59245e-06 3.95033e-02
178 1.55533e-06 3.95033e-02
179 1.51928e-06 3.95033e-02
180 1.48426e-06 3.95033e-02
181 1.45023e-06 3.95033e-02
182 1.41716e-06 3.95033e-02
183 1.38501e-06 3.95033e-02
184 1.35377e-06 3.95033e-02
185 1.32340e-06 3.95032e-02
186 1.29387e-06 3.95032e-02
187 1.26515e-06 3.95032e-02
188 1.23722e-06 3.95032e-02
189 1.21006e-06 3.95032e-02
190 1.18362e-06 3.95032e-02
191 1.15790e-06 3.95032e-02
192 1.13287e-06 3.95032e-02
193 1.10851e-06 3.95032e-02
194 1.08479e-06 3.95032e-02
195 1.06170e-06 3.95032e-02
196 1.03921e-06 3.95032e-02
197 1.01730e-06 3.95032e-02
198 9.95966e-07 3.95032e-02
Computing atomic populations.
Computing atomic charges.
Computing density decomposition for atom 0
Computing density decomposition for atom 1
Computing density decomposition for atom 2
Computing cartesian and pure AIM multipoles and radial AIM moments.
Storing proatom density spline for atom 0.
Storing proatom density spline for atom 1.
Storing proatom density spline for atom 2.
charges:
[-0.881 0.441 0.441]
cartesian multipoles:
[[-0.881 0. -0. 0.133 -5.381 -0. -0. -4.801 0. -5.094 0. -0. 0.033 0. -0. 0. -0. 0.416 -0. 0.366]
[ 0.441 0. 0.022 -0.001 -0.275 -0. -0. -0.257 0.002 -0.26 0. 0.008 0.005 0. 0. 0. 0.024 0.009 0.009 0.023]
[ 0.441 0. -0.022 -0.001 -0.275 0. 0. -0.257 -0.002 -0.26 0. -0.008 0.005 0. -0. 0. -0.024 0.009 -0.009 0.023]]
Direct Inversion of Iterative Space (DIIS)
An equivalent fixed-point problem is addressed by using self-consistent solver and non-negative parameters are guaranteed.
[6]:
def diis_method():
"""Global LISA with DIIS solver."""
kwargs = prepare_argument_dict(mol, grid, rho)
kwargs["solver"] = "diis"
kwargs["solver_options"] = {"diis_size": 8, "version": "A"}
part = GlobalLinearISAWPart(**kwargs)
part.do_all()
print_results(part)
# not robust
diis_method()
================================================================================
Information of integral grids.
--------------------------------------------------------------------------------
Grid size of molecular grid: 18460
************************************ Atom 0 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18
18 18 18 18 18 18 26 26 26 26 38 38 38 38 38 50 50 50 50 50
86 86 110 110 110 110 170 194 194 434 590 590 434 434 434 302 302 302 194 194
170 110 110 110 110 110 110 110 110 110 110 110 86 50 50 18 18 18 18 18
************************************ Atom 1 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 18 18 18 18 18
18 18 18 18 18 18 18 18 18 26 26 26 38 38 38 38 38 38 38 50
50 50 50 50 50 86 86 86 110 110 110 170 170 170 194 194 194 194 170 170
170 110 110 110 110 110 110 110 110 110 110 86 86 50 50 50 18 18 18 18
************************************ Atom 2 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 18 18 18 18 18
18 18 18 18 18 18 18 18 18 26 26 26 38 38 38 38 38 38 38 50
50 50 50 50 50 86 86 86 110 110 110 170 170 170 194 194 194 194 170 170
170 110 110 110 110 110 110 110 110 110 110 86 86 50 50 50 18 18 18 18
--------------------------------------------------------------------------------
================================================================================
Performing a density-based AIM analysis with a wavefunction as input.
Molecular grid : MolGrid
Using local grids : True
Scheme : Linear Iterative Stockholder
Outer loop convergence threshold : 1.0e-06
Using global ISA : True
Maximum outer iterations : 1000
lmax : 3
Solver : DIIS
Basis function type : GAUSS
diis_size : 8
version : A
Load GAUSS basis functions
Iter. dRMS
----- ------
0 7.836145E-02
1 8.081885E-02
2 1.233679E-01
3 7.717830E-02
4 4.572785E-02
5 5.201493E-02
6 3.223615E-02
7 9.394718E-03
8 6.061731E-02
9 9.025303E-03
10 5.802607E-03
11 1.029386E-02
12 3.350408E-03
13 3.111845E-03
14 3.744714E-03
15 1.318951E-03
16 6.955798E-05
17 6.533931E-05
18 1.075412E-04
19 1.383956E-04
20 1.588891E-04
21 7.253518E-06
22 9.279781E-06
23 7.070573E-06
24 1.423485E-06
25 3.470689E-06
26 1.397696E-05
27 2.355907E-06
28 2.782021E-07
Computing atomic populations.
Computing atomic charges.
Computing density decomposition for atom 0
Computing density decomposition for atom 1
Computing density decomposition for atom 2
Computing cartesian and pure AIM multipoles and radial AIM moments.
Storing proatom density spline for atom 0.
Storing proatom density spline for atom 1.
Storing proatom density spline for atom 2.
charges:
[-0.881 0.441 0.441]
cartesian multipoles:
[[-0.881 0. 0. 0.134 -5.381 -0. -0. -4.802 -0. -5.095 0. -0. 0.034 0. -0. 0. -0. 0.417 -0. 0.368]
[ 0.441 0. 0.022 -0.001 -0.275 -0. -0. -0.256 0.002 -0.26 0. 0.008 0.005 0. 0. 0. 0.024 0.009 0.009 0.023]
[ 0.441 0. -0.022 -0.001 -0.275 0. 0. -0.256 -0.002 -0.26 0. -0.008 0.005 0. -0. 0. -0.024 0.009 -0.009 0.023]]
[7]:
def cdiis_method():
"""Global LISA with DIIS solver."""
kwargs = prepare_argument_dict(mol, grid, rho)
kwargs["solver"] = "cdiis"
kwargs["solver_options"] = {"diis_size": 8, "param": 1e-5, "mode": "AD-CDIIS"}
part = GlobalLinearISAWPart(**kwargs)
part.do_all()
print_results(part)
# not robust
cdiis_method()
================================================================================
Information of integral grids.
--------------------------------------------------------------------------------
Grid size of molecular grid: 18460
************************************ Atom 0 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18
18 18 18 18 18 18 26 26 26 26 38 38 38 38 38 50 50 50 50 50
86 86 110 110 110 110 170 194 194 434 590 590 434 434 434 302 302 302 194 194
170 110 110 110 110 110 110 110 110 110 110 110 86 50 50 18 18 18 18 18
************************************ Atom 1 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 18 18 18 18 18
18 18 18 18 18 18 18 18 18 26 26 26 38 38 38 38 38 38 38 50
50 50 50 50 50 86 86 86 110 110 110 170 170 170 194 194 194 194 170 170
170 110 110 110 110 110 110 110 110 110 110 86 86 50 50 50 18 18 18 18
************************************ Atom 2 ************************************
|-- Radial grid size: 120
|-- Angular grid sizes:
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 18 18 18 18 18
18 18 18 18 18 18 18 18 18 26 26 26 38 38 38 38 38 38 38 50
50 50 50 50 50 86 86 86 110 110 110 170 170 170 194 194 194 194 170 170
170 110 110 110 110 110 110 110 110 110 110 86 86 50 50 50 18 18 18 18
--------------------------------------------------------------------------------
================================================================================
Performing a density-based AIM analysis with a wavefunction as input.
Molecular grid : MolGrid
Using local grids : True
Scheme : Linear Iterative Stockholder
Outer loop convergence threshold : 1.0e-06
Using global ISA : True
Maximum outer iterations : 1000
lmax : 3
Solver : CDIIS
Basis function type : GAUSS
diis_size : 8
param : 1e-05
mode : AD-CDIIS
Load GAUSS basis functions
-----------------------------------------
CDIIS like program
---- Mode: AD-CDIIS
---- param value: 1e-05
======================
iteration: 1
mk value: 0
||r(k)|| = 0.27176733420328947
||r_{k+1}|| = 0.1534880585967473
======================
iteration: 2
mk value: 1
||r(k)|| = 0.1534880585967473
size of Cs: (14, 1)
size of c: 2, size of gamma: (1,)
||r_{k+1}|| = 0.09696370317435703
======================
iteration: 3
mk value: 2
||r(k)|| = 0.09696370317435703
size of Cs: (14, 2)
size of c: 3, size of gamma: (2,)
||r_{k+1}|| = 0.042761510697246465
======================
iteration: 4
mk value: 3
||r(k)|| = 0.042761510697246465
size of Cs: (14, 3)
size of c: 4, size of gamma: (3,)
||r_{k+1}|| = 0.017709062241212693
======================
iteration: 5
mk value: 4
||r(k)|| = 0.017709062241212693
size of Cs: (14, 4)
size of c: 5, size of gamma: (4,)
||r_{k+1}|| = 0.011598638963534582
======================
iteration: 6
mk value: 5
||r(k)|| = 0.011598638963534582
size of Cs: (14, 5)
size of c: 6, size of gamma: (5,)
||r_{k+1}|| = 0.007432425429477454
======================
iteration: 7
mk value: 6
||r(k)|| = 0.007432425429477454
size of Cs: (14, 6)
size of c: 7, size of gamma: (6,)
||r_{k+1}|| = 0.006205314556220946
======================
iteration: 8
mk value: 7
||r(k)|| = 0.006205314556220946
size of Cs: (14, 7)
size of c: 8, size of gamma: (7,)
||r_{k+1}|| = 0.009267245784599308
======================
iteration: 9
mk value: 8
||r(k)|| = 0.009267245784599308
size of Cs: (14, 8)
size of c: 9, size of gamma: (8,)
||r_{k+1}|| = 0.0022213144932380223
======================
iteration: 10
mk value: 9
||r(k)|| = 0.0022213144932380223
size of Cs: (14, 9)
size of c: 10, size of gamma: (9,)
||r_{k+1}|| = 0.004576059062162698
======================
iteration: 11
mk value: 10
||r(k)|| = 0.004576059062162698
size of Cs: (14, 10)
size of c: 11, size of gamma: (10,)
||r_{k+1}|| = 0.0025100330052178197
======================
iteration: 12
mk value: 11
||r(k)|| = 0.0025100330052178197
size of Cs: (14, 11)
size of c: 12, size of gamma: (11,)
||r_{k+1}|| = 0.002038574124953236
======================
iteration: 13
mk value: 12
||r(k)|| = 0.002038574124953236
size of Cs: (14, 12)
size of c: 13, size of gamma: (12,)
||r_{k+1}|| = 0.0020057459953213086
======================
iteration: 14
mk value: 13
||r(k)|| = 0.0020057459953213086
size of Cs: (14, 13)
size of c: 14, size of gamma: (13,)
||r_{k+1}|| = 0.00044180371535251653
======================
iteration: 15
mk value: 14
||r(k)|| = 0.00044180371535251653
size of Cs: (14, 14)
size of c: 15, size of gamma: (14,)
||r_{k+1}|| = 0.0005248687021228399
(14, 15)
(14, 14)
======================
iteration: 16
mk value: 14
||r(k)|| = 0.0005248687021228399
size of Cs: (14, 14)
size of c: 15, size of gamma: (14,)
||r_{k+1}|| = 0.00021227029426046162
(14, 15)
(14, 14)
======================
iteration: 17
mk value: 14
||r(k)|| = 0.00021227029426046162
size of Cs: (14, 14)
size of c: 15, size of gamma: (14,)
||r_{k+1}|| = 0.00020203714015741073
(14, 15)
(14, 14)
======================
iteration: 18
mk value: 14
||r(k)|| = 0.00020203714015741073
size of Cs: (14, 14)
size of c: 15, size of gamma: (14,)
||r_{k+1}|| = 0.00026801476958648206
(14, 15)
(14, 14)
======================
iteration: 19
mk value: 14
||r(k)|| = 0.00026801476958648206
size of Cs: (14, 14)
size of c: 15, size of gamma: (14,)
||r_{k+1}|| = 0.00016812144862644716
(14, 15)
(14, 14)
======================
iteration: 20
mk value: 14
||r(k)|| = 0.00016812144862644716
size of Cs: (14, 14)
size of c: 15, size of gamma: (14,)
||r_{k+1}|| = 1.2040071682057495e-05
(14, 15)
(14, 14)
======================
iteration: 21
mk value: 14
||r(k)|| = 1.2040071682057495e-05
size of Cs: (14, 14)
size of c: 15, size of gamma: (14,)
||r_{k+1}|| = 7.267198500880972e-05
(14, 15)
(14, 14)
======================
iteration: 22
mk value: 14
||r(k)|| = 7.267198500880972e-05
size of Cs: (14, 14)
size of c: 15, size of gamma: (14,)
||r_{k+1}|| = 9.463815824216794e-05
(14, 15)
(14, 14)
======================
iteration: 23
mk value: 14
||r(k)|| = 9.463815824216794e-05
size of Cs: (14, 14)
size of c: 15, size of gamma: (14,)
||r_{k+1}|| = 2.391592794755819e-06
(14, 15)
(14, 14)
======================
iteration: 24
mk value: 14
||r(k)|| = 2.391592794755819e-06
size of Cs: (14, 14)
size of c: 15, size of gamma: (14,)
||r_{k+1}|| = 3.650598421207163e-05
(14, 15)
(14, 14)
======================
iteration: 25
mk value: 14
||r(k)|| = 3.650598421207163e-05
size of Cs: (14, 14)
size of c: 15, size of gamma: (14,)
||r_{k+1}|| = 1.0845937548568449e-05
(14, 15)
(14, 14)
======================
iteration: 26
mk value: 14
||r(k)|| = 1.0845937548568449e-05
size of Cs: (14, 14)
size of c: 15, size of gamma: (14,)
||r_{k+1}|| = 3.553173939271454e-06
(14, 15)
(14, 14)
======================
iteration: 27
mk value: 14
||r(k)|| = 3.553173939271454e-06
size of Cs: (14, 14)
size of c: 15, size of gamma: (14,)
||r_{k+1}|| = 2.7610649331446384e-06
(14, 15)
(14, 14)
======================
iteration: 28
mk value: 14
||r(k)|| = 2.7610649331446384e-06
size of Cs: (14, 14)
size of c: 15, size of gamma: (14,)
||r_{k+1}|| = 1.7104876974778915e-06
(14, 15)
(14, 14)
======================
iteration: 29
mk value: 14
||r(k)|| = 1.7104876974778915e-06
size of Cs: (14, 14)
size of c: 15, size of gamma: (14,)
||r_{k+1}|| = 1.5547486826932455e-06
(14, 15)
(14, 14)
======================
iteration: 30
mk value: 14
||r(k)|| = 1.5547486826932455e-06
size of Cs: (14, 14)
size of c: 15, size of gamma: (14,)
||r_{k+1}|| = 8.068156005548003e-07
(14, 15)
(14, 14)
Computing atomic populations.
Computing atomic charges.
Computing density decomposition for atom 0
Computing density decomposition for atom 1
Computing density decomposition for atom 2
Computing cartesian and pure AIM multipoles and radial AIM moments.
Storing proatom density spline for atom 0.
Storing proatom density spline for atom 1.
Storing proatom density spline for atom 2.
charges:
[-0.881 0.441 0.441]
cartesian multipoles:
[[-0.881 0. -0. 0.134 -5.381 -0. -0. -4.802 0. -5.095 -0. 0. 0.034 0. -0. 0. -0. 0.417 -0. 0.368]
[ 0.441 0. 0.022 -0.001 -0.275 -0. -0. -0.256 0.002 -0.26 0. 0.008 0.005 0. 0. 0. 0.024 0.009 0.009 0.023]
[ 0.441 0. -0.022 -0.001 -0.275 0. 0. -0.256 -0.002 -0.26 0. -0.008 0.005 0. -0. 0. -0.024 0.009 -0.009 0.023]]
[ ]: