azo-xcite-tools

This code supports the paper

Sergi Vela, Alberto Fabrizio, Ksenia R. Briling, and Clémence Corminboeuf,
“Machine-Learning the Transition Density of the Productive Excited States of Azo-dyes”
J. Phys. Chem. Lett. 2021, 5957–5962.

It consists of two parts: the scripts to run ab initio computations and the scripts to compute the excited states descriptors.

The tensorial kernels were computed using the SOAPfast routines and the regression weights were obtained using an in-house optimized version of the ML framework.

Contents

• Requirements
• 1. Ab initio computations
  • 1.1. Compute transitions
  • 1.2. Extract hole and particle density matrices
  • 1.3. Density fitting
• 2. Decriptors
  • Transition dipole moments
  • Exciton properties
  • Fragment decomposition

Requirements

• python >= 3.6
• numpy >= 1.16
• pyscf >= 1.6

1. Ab initio computations

1.1. Compute transitions

The script 1_compute_transitions.py runs a TDDFT computation withing the TDA approximation of 8 lowest excited states at the ωB97X-D/def2-SVP level (defined in qm_config.py).

Usage:

$ code/1_compute_transitions.py <molecule>.xyz

Example:

$ code/1_compute_transitions.py examples/C1-13-2-3.xyz > examples/C1-13-2-3.xyz.transition.out

Output files:

File	Description
examples/C1-13-2-3.xyz.mo.npy	ground-state molecular orbital vectors
examples/C1-13-2-3.xyz.dm.dat	ground-state density matrix
examples/C1-13-2-3.xyz.coulomb.dat	electrostatic self-repulsion of the ground-state density (a number)
examples/C1-13-2-3.xyz.X.npy	response vectors (nstates×occ×virt) normalized to 1
examples/C1-13-2-3.xyz.transition.out	pyscf output

1.2. Extract hole and particle density matrices

The script 2_make_dms.py saves hole and particle density matrices (atomic orbital basis) of selected states to separate files.

Usage:

$ code/2_make_dms.py <molecule>.xyz <state1> <state2>

Example (for the S₁ and S₂ states):

$ code/2_make_dms.py examples/C1-13-2-3.xyz 1 2

Output files:

File	Description
examples/C1-13-2-3.xyz.st{1,2}_dm_part.dat	particle density matrices
examples/C1-13-2-3.xyz.st{1,2}_dm_hole.dat	hole density matrices
examples/C1-13-2-3.xyz.st{1,2}_coulomb_part.dat	electrostatic self-repulsion of particle densities
examples/C1-13-2-3.xyz.st{1,2}_coulomb_hole.dat	electrostatic self-repulsion of hole densities

1.3. Density fitting

1. The script 3_fitting.py decomposes the ground-state and hole and particle densities saved on the previous steps onto an atom-centered basis (cc-pVQZ/JKFIT, defined in qm_config.py).

Usage:

$ code/3_fitting.py <molecule>.xyz

Example:

$ code/3_fitting.py examples/C1-13-2-3.xyz

Output files:

File	Description
examples/C1-13-2-3.xyz.dm_fit.dat	fitting coefficients for the ground-state density
examples/C1-13-2-3.xyz.st{1,2}_dm_part_fit.dat	fitting coefficients for the particle densities
examples/C1-13-2-3.xyz.st{1,2}_dm_hole_fit.dat	fitting coefficients for the hole densities

Output: absolute and relative fitting errors and the number of particles in the fitted field,

examples/C1-13-2-3.xyz  ground  Error: 4.790e-04 Eh ( 1.0e-05 %)  Electrons: 1.660e+02 (  1.3e-03 )
examples/C1-13-2-3.xyz  hole_1  Error: 8.813e-07 Eh ( 2.0e-04 %)  Electrons: 1.000e+00 (  1.3e-05 )
examples/C1-13-2-3.xyz  part_1  Error: 8.911e-07 Eh ( 2.9e-04 %)  Electrons: 1.000e+00 (  2.5e-05 )
examples/C1-13-2-3.xyz  hole_2  Error: 3.224e-07 Eh ( 1.8e-04 %)  Electrons: 1.000e+00 (  4.4e-05 )
examples/C1-13-2-3.xyz  part_2  Error: 5.648e-07 Eh ( 2.4e-04 %)  Electrons: 1.000e+00 (  3.3e-05 )

2. The script 3_fitting_td.py decomposes the transition density. The sign is determined so that the density on the left Nitrogen is positive.

Usage:

$ code/3_fitting_td.py <molecule>.xyz <state1> <state2> <number_of_left_N> <number_of_right_N>

Example:

$ code/3_fitting_td.py examples/C1-13-2-3.xyz  1 2  9 10

Output files:

File	Description
examples/C1-13-2-3.xyz.st{1,2}_transition_fit.dat	fitting coefficients for the transition densities

Output:

examples/C1-13-2-3.xyz state1 Error:  5.041e-07 Eh ( 4.0e-03 %)  Electrons:  7.6e-07 total, -4.90e-03 left N, -2.11e-03 right N
examples/C1-13-2-3.xyz state2 Error:  2.021e-07 Eh ( 1.6e-03 %)  Electrons:  1.2e-05 total, -1.62e-01 left N,  1.27e-01 right N

For the S₂ state, the sign of the density on the left N is negative thus the fitting coefficients were multiplied by -1 before saving.

2. Decriptors

Transition dipole moments

The scripts transition_dipole_dm.py and transition_dipole.py compute the transition dipole moments. NB: the output values should be multiplied by √2.

• Ab initio transition dipole moments:

$ code/transition_dipole_dm.py <molecule>.xyz <state> <sign_factor>

Example:

$ code/transition_dipole_dm.py examples/C1-13-2-3.xyz 2 -1

examples/C1-13-2-3.xyz [-0.68928  2.10718  1.53424]

• Decomposed / predicted transition dipole moments:

$ code/transition_dipole.py <molecule>.xyz <transition-density-coefficients>

Example:

$ code/transition_dipole.py examples/C1-13-2-3.xyz examples/C1-13-2-3.xyz.st2_transition_fit.dat

examples/C1-13-2-3.xyz [-0.68919  2.10692  1.53400]

Exciton properties

The scripts exciton_properties_dm.py and exciton_properties.py compute the hole–particle distances and hole and particle sizes.

• Ab initio properties:

$ code/exciton_properties_dm.py <molecule>.xyz <hole_density_matrix> <particle_density_matrix>

Example:

$ code/exciton_properties_dm.py examples/C1-13-2-3.xyz examples/C1-13-2-3.xyz.st2_dm_{hole,part}.dat

examples/C1-13-2-3.xyz  dist = 2.598634e+00  hole_size = 7.848500e+00  part_size = 5.676174e+00

• Decomposed / predicted properties:

$ code/exciton_properties.py <molecule>.xyz <hole_coefficients> <particle_coefficients>

Example:

$ code/exciton_properties.py examples/C1-13-2-3.xyz examples/C1-13-2-3.xyz.st2_dm_{hole,part}_fit.dat

examples/C1-13-2-3.xyz  dist = 2.599404e+00  hole_size = 7.847751e+00  part_size = 5.675416e+00

Fragment decomposition

The script fragments.py computes the hole and particle contribution of each fragment:

$ code/fragments.py <molecule>.xyz <fragment_definition> <hole_coefficients> <particle_coefficients>

Example:

$ code/fragments.py examples/C1-13-2-3.{xyz,frag} examples/C1-13-2-3.xyz.st2_dm_{hole,part}_fit.dat

C1-13-2-3.xyz H [ 4.243 25.179  7.802 32.888 29.888] P [ 1.867 20.024 37.237 36.807  4.066]

(The atomic densities were computed with spherical_atoms.py and are stored in spherical_atoms/.)