Laplacian #32
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When n=1, the first component (n-1)/r does not exist
Certain components of the derivatives aren't needed when n=1,2
When r=0, n=1, then the kinetic energy should return infinity
When r=0, n=1, the Laplacian should be infinity
FarnazH
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Jun 7, 2022
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FarnazH
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@Ali-Tehrani, my commit updates the comments to make it more clear how 1st and 2nd derivatives are computed. I also removed the Notes of the second_derivative_radial_slater_type_orbital docstring which stated that When :math:n=1,2 and :math:r=0, then the derivative is infinity. Are you fine with that?
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| norm = np.power(2. * exps, numbers) * np.sqrt((2. * exps) / factorial(2. * numbers)) | ||
| slater_minus_one = SlaterAtoms.radial_slater_orbital( | ||
| exps, numbers - 1, points, normalized=False | ||
| ) | ||
| slater_r = norm.T * slater_minus_one | ||
| # When r=0 and n = 1, then slater/r is infinity. | ||
| i_r_zero = np.where(np.abs(points) == 0.0)[0] | ||
| i_numb_one = np.where(numbers[0] == 1)[0] | ||
| indices = np.array([[x, y] for x in i_r_zero for y in i_numb_one]) | ||
| if len(indices) != 0: # if-statement needed to remove numpy warning using list | ||
| slater_r[indices] = np.inf | ||
| phi_i_r[:, index] += np.ravel(np.dot(slater_r, self.orbitals_coeff[orbital])) |
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@Ali-Tehrani can this be computed using first_derivative_radial_slater_type_orbital function?
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| norm = np.power(2. * exps, numbers) * np.sqrt((2. * exps) / factorial(2. * numbers)) | ||
| # Take unnormalized slater with number n-1, this is needed to remove divide by r^2 | ||
| slater_minus_one = SlaterAtoms.radial_slater_orbital( | ||
| exps, numbers - 1, points, normalized=False | ||
| ) | ||
| deriv_pref = norm.T * slater_minus_one | ||
| # When r=0 and n = 1, then the derivative is undefined and this returns infinity or nan | ||
| i_r_zero = np.where(np.abs(points) == 0.0)[0] | ||
| i_numb_one = np.where(numbers[0] == 1)[0] | ||
| indices = np.array([[x, y] for x in i_r_zero for y in i_numb_one]) | ||
| if len(indices) != 0: # if-statement needed to remove numpy warning using list | ||
| deriv_pref[indices] = np.inf |
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@Ali-Tehrani can this be computed using first_derivative_radial_slater_type_orbital?
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Added the second derivative of Slater orbital, second derivative of molecular orbital and the Laplacian of the atomic density.
The tests that were added are: