espaloma.nn.readout.charge_equilibrium.get_charges

espaloma.nn.readout.charge_equilibrium.get_charges(node)

Solve the function to get the absolute charges of atoms in a

molecule from parameters. Parameters ———- e : tf.Tensor, dtype = tf.float32,

electronegativity.

stf.Tensor, dtype = tf.float32,

hardness.

Qtf.Tensor, dtype = tf.float32, shape=(),

total charge of a molecule.

We use Lagrange multipliers to analytically give the solution. $$ U({f q}) &= sum_{i=1}^N left[ e_i q_i +

rac{1}{2} s_i q_i^2 ight]

• lambda , left( sum_{j=1}^N q_j - Q

ight)

&= sum_{i=1}^N left[

(e_i - lambda) q_i +

rac{1}{2} s_i q_i^2 ight

] + Q

$$ This gives us: $$ q_i^* &= - e_i s_i^{-1} + lambda s_i^{-1} &= - e_i s_i^{-1} + s_i^{-1}

rac{

Q +

sumlimits_{i=1}^N e_i , s_i^{-1}

}{sumlimits_{j=1}^N s_j^{-1}}

$$