@@ -145,8 +145,7 @@ def _eval_deriv_contractions(coords, orders, center, angmom_comps, alphas, prim_
145145def _eval_first_second_order_deriv_contractions (
146146 coords , orders , center , angmom_comps , alphas , prim_coeffs , norm
147147):
148- r"""Return the evaluation of direct implementation of 1st and 2nd derivative orders
149- of a Cartesian contraction.
148+ """Return the evaluation of direct 1st and 2nd derivative orders of a Cartesian contraction.
150149
151150 Parameters
152151 ----------
@@ -217,15 +216,17 @@ def _eval_first_second_order_deriv_contractions(
217216
218217 # Calling 1st and 2nd derivatives functions for different combination of orders
219218 if indices_first_deriv .any ():
220- first_deriv = _first_derivative (new_coords , gauss , indices_first_deriv , angmom_comps , alphas )
219+ first_deriv = _first_derivative (new_coords , gauss , indices_first_deriv ,
220+ angmom_comps , alphas )
221221 if indices_second_deriv .any ():
222- second_deriv = _second_derivative (new_coords , gauss , indices_second_deriv , angmom_comps ,
223- alphas )
222+ second_deriv = _second_derivative (new_coords , gauss , indices_second_deriv ,
223+ angmom_comps , alphas )
224224 elif indices_second_deriv .any ():
225- second_deriv = _second_derivative (new_coords , gauss , indices_second_deriv , angmom_comps , alphas )
225+ second_deriv = _second_derivative (new_coords , gauss , indices_second_deriv ,
226+ angmom_comps , alphas )
226227 if indices_first_deriv .any ():
227- first_deriv = _first_derivative (new_coords , gauss , indices_first_deriv , angmom_comps ,
228- alphas )
228+ first_deriv = _first_derivative (new_coords , gauss , indices_first_deriv ,
229+ angmom_comps , alphas )
229230 # Combining all the derivatives
230231 norm = norm .T [:, :, np .newaxis ]
231232 output = np .tensordot (prim_coeffs , norm * zeroth_deriv * first_deriv * second_deriv , (0 , 0 ))
@@ -234,7 +235,7 @@ def _eval_first_second_order_deriv_contractions(
234235
235236
236237def _first_derivative (center_coords , gauss , indices_first_deriv , angmom_comps , alphas ):
237- r"""Helper function for calculation of explicit first derivative order for contracted gaussian
238+ r"""Help function for calculation of explicit first derivative order for contracted gaussian.
238239
239240 Parameters
240241 ----------
@@ -296,7 +297,7 @@ def _first_derivative(center_coords, gauss, indices_first_deriv, angmom_comps, a
296297
297298
298299def _second_derivative (center_coords , gauss , indices_second_deriv , angmom_comps , alphas ):
299- r"""Helper function for calculation of explicit second derivative order for contracted gaussian
300+ r"""Help function for calculation of explicit second derivative order for contracted gaussian.
300301
301302 Parameters
302303 ----------
@@ -341,8 +342,8 @@ def _second_derivative(center_coords, gauss, indices_second_deriv, angmom_comps,
341342 n_2_indices = second_ang_comp >= 2
342343
343344 # angular momentum == 0
344- total_n_0 = ((4 * alphas [:, None , None ] ** 2 ) * (second_coords ** 2 )) \
345- - (2 * alphas [:, None , None ])
345+ total_n_0 = ((4 * alphas [:, None , None ] ** 2 ) * (second_coords ** 2 )) - \
346+ (2 * alphas [:, None , None ])
346347 raw_second_deriv = total_n_0 [:, :, None , :] ** array_ones [None , :, :, None ]
347348 # angular momentum == 1
348349 if any (second_ang_comp [0 ] == 1 ):
@@ -360,10 +361,11 @@ def _second_derivative(center_coords, gauss, indices_second_deriv, angmom_comps,
360361 power_part_1 [power_part_1 < 0 ] = 0
361362 part1_n_2 = second_coords [:, None , :] ** (power_part_1 [:, :, None ])
362363 # Calculating
363- # ..math:: 4 \alpha^{2}\left(x-X_{A}\right)^{4}-\alpha(4 n+2)\left(x-X_{A}\right)^{2}+n(n-1)
364+ # ..math:: 4 \alpha^{2}\left(x-X_{A}\right)^{4}-
365+ # \alpha(4 n+2)\left(x-X_{A}\right)^{2}+n(n-1)
364366 part2_1_n_2 = (4 * alphas [:, None , None ] ** 2 ) * (second_coords ** 4 )
365367 part2_2_n_2 = alphas [:, None , None , None ] * (4 * second_ang_comp [:, :, None ] + 2 ) \
366- * second_coords [:, None , :] ** 2
368+ * second_coords [:, None , :] ** 2
367369 part2_3_n_2 = second_ang_comp * (second_ang_comp - 1 )
368370 part2_n_2 = part2_1_n_2 [:, :, None , :] - part2_2_n_2 + part2_3_n_2 [None , :, :, None ]
369371 total_n_2 = part1_n_2 [None , :, :, :] * part2_n_2
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