Slater-type Orbital - Differentials

Differentials

The first radial derivative of the radial part of a Slater-type orbital is

The radial Laplace operator is split in two differential operators

The first differential operator of the Laplace operator yields

The total Laplace operator yields after applying the second differential operator

the result

Angular dependent derivatives of the spherical harmonics don't depend on the radial function and have to be evaluated separately.

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