slater_overlap Module Reference
Functions for overlap integrals over Slater orbitals in the local coordinate frame. More...
Functions/Subroutines | |
| real function | atomicslateroverlap (n1, l1, m10, orbitalExponent1, n2, l2, m20, orbitalExponent2, inputDistance) |
| Calculates the overlap integral over Slater orbitals (with spherical harmonics) in diatomic coordinate frame (a prolate spheroidal coordinate system): the z-axis is the strait line connecting atoms. More... | |
| real function | integral_a (n, a) |
| Helper function, calculates the 'A' integral. More... | |
| real function | integral_b (n, a) |
| Helper function, calculates the 'B' integral. More... | |
| real function | coefficient (l, m, j) |
| Calculates coefficients \((C^{l}_{mj})\). More... | |
Detailed Description
Functions for overlap integrals over Slater orbitals in the local coordinate frame.
- Warning
- It looks out strange: in either case of spherical or cubic harmonincs in the diatomic coordinate frame the oberlap IS real and no complex numbers are needed. - ALT 02.03.2020
- Remarks
- Reply to ALT warning. Yes, the function checks, that overlap integral over cubic harmonics is a real number. And it is always real. But I used complex numbers, because coefficients of transformation from spherical to cubic harmonics may be imaginary. - Ilya Popov 02.03.2020 @TODO Actually Slater overlap integral should be equal to the corresponding Slater-Zener overlap integral (I checked it for p and d-harmonics). It means, that 'slaterZenerOverlap' function is excessive and we can just use 'atomicSlaterOverlap' everywhere. If so, we need to change it accordingly. - Ilya Popov 02.03.2020
- I checked and the procedure 'slaterZenerOverlap' is indeed excessive since it produced absolutely same overlaps as 'atomicSlaterOverlap', so I deleted 'slaterZenerOverlap'. We now use 'atomicSlaterOverlap' everywhere in the library. - Ilya Popov 20.01.2022
Function/Subroutine Documentation
◆ atomicslateroverlap()
| real function slater_overlap::atomicslateroverlap | ( | integer, intent(in) | n1, |
| integer, intent(in) | l1, | ||
| integer, intent(in) | m10, | ||
| real, intent(in) | orbitalExponent1, | ||
| integer, intent(in) | n2, | ||
| integer, intent(in) | l2, | ||
| integer, intent(in) | m20, | ||
| real, intent(in) | orbitalExponent2, | ||
| real | inputDistance | ||
| ) |
Calculates the overlap integral over Slater orbitals (with spherical harmonics) in diatomic coordinate frame (a prolate spheroidal coordinate system): the z-axis is the strait line connecting atoms.
- Parameters
-
[in] orbitalexponent2 orbital exponents in a.u. inputdistance inputDistance in Angstrom, distance in Bohr
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◆ coefficient()
| real function slater_overlap::coefficient | ( | integer, intent(in) | l, |
| integer, intent(in) | m, | ||
| integer, intent(in) | j | ||
| ) |
Calculates coefficients \((C^{l}_{mj})\).
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◆ integral_a()
| real function slater_overlap::integral_a | ( | integer, intent(in) | n, |
| real, intent(in) | a | ||
| ) |
Helper function, calculates the 'A' integral.
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◆ integral_b()
| real function slater_overlap::integral_b | ( | integer, intent(in) | n, |
| real, intent(in) | a | ||
| ) |
Helper function, calculates the 'B' integral.
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