HÜXEL = JAX + HÜCKEL

Optimization of the Hückel model à la machine learning

Using JAX, we created a fully differentiable Hückel model where all parameters are optimized with respect to some reference data.

Beta functions (atom-atom interaction)

We implemented various atom-atom interaction functions.

constant (--beta c)
exponential (--beta exp)
linear (--beta linear)
absolute exponential (--beta exp_abs)
absolute linear (--beta linear_abs)
absolute exponential with no gradient for (--beta exp_abs_freezeR)
absolute linear with no gradient for (--beta linear_abs_freezeR)

Quick start

python main.py *args

--N, number of training data points
--l, integer (for random number start jax.random.PRNGKey(l))
--lr, initial learning rate
--batch_size, batch size
--job, type of job (options ['opt','pred','pred_def'])
1. opt -> training
2. pred -> prediction of test set
3. pred_def -> prediction using default parameters (from literature)
--obs, objective to optimize, options [homo_lumo,pol]
--beta, beta function (['c','linear','exp','linear_abs','exp_freezeR','exp_abs_freezeR','linear_freezeR','linear_abs_freezeR'])

examples

python main.py --N 101 --obs pol --lr 2E-2 --l 0 --batch_size 32 --job opt --beta c -Wdecay h_x h_xy 

python main.py --N 50 --job pred --beta exp_abs

Reference data

The data set is a subset of GDB-13, all molecules encompass cyclic $\pi$-systems to increase representation of the relevant structural space that is appropriate for simulation via the Hückel method.

Total data:

training: 100,000 (file name:/huxel/data/data_gdb13_training.npy)
test: 40,000 (file name:/huxel/data/data_gdb13_test.npy)

HOMO-LUMO gap

Reference data was computed at the TDA-SCS-PBEPP86/def2-SVP level of theory using Orca (version 5.0.1).

Polarizability