Finite nucleus, take 2

[stigrj]

Supersedes #439

Rebase on master and cleanup in nuclear models:

• Combined the new finite nucleus models with Peter's collection of point-nucleus models
• No more param_V.json file for nuclear parameters. Visschers's RMS values are now written directly in the python periodic table, and passed to mrchem.x through the JSON input. RMS values can thus only be changed by interrupting the input parser and manually alter the intermediate file.
• Input keyword changed from int to string

Should be properly tested against Exciting before merging.

• [x] Ready to go

[codecov[bot]]

Codecov Report

Patch coverage: 79.52% and project coverage change: +0.05 :tada:

Comparison is base (357554a) 69.53% compared to head (feff12f) 69.58%.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## master #453 +/- ## ========================================== + Coverage 69.53% 69.58% +0.05% ========================================== Files 175 180 +5 Lines 14853 15027 +174 ========================================== + Hits 10328 10457 +129 - Misses 4525 4570 +45 ``` | [Impacted Files](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/453?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft) | Coverage Δ | | |---|---|---| | [src/analyticfunctions/FiniteNucleusGaussian.h](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/453?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-c3JjL2FuYWx5dGljZnVuY3Rpb25zL0Zpbml0ZU51Y2xldXNHYXVzc2lhbi5o) | `0.00% <0.00%> (ø)` | | | [src/analyticfunctions/FiniteNucleusSphere.h](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/453?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-c3JjL2FuYWx5dGljZnVuY3Rpb25zL0Zpbml0ZU51Y2xldXNTcGhlcmUuaA==) | `0.00% <0.00%> (ø)` | | | [src/analyticfunctions/NuclearFunction.cpp](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/453?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-c3JjL2FuYWx5dGljZnVuY3Rpb25zL051Y2xlYXJGdW5jdGlvbi5jcHA=) | `81.81% <75.00%> (-4.61%)` | :arrow_down: | | [src/qmoperators/one\_electron/NuclearOperator.cpp](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/453?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-c3JjL3Ftb3BlcmF0b3JzL29uZV9lbGVjdHJvbi9OdWNsZWFyT3BlcmF0b3IuY3Bw) | `86.17% <81.57%> (-6.24%)` | :arrow_down: | | [src/chemistry/Nucleus.h](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/453?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-c3JjL2NoZW1pc3RyeS9OdWNsZXVzLmg=) | `95.45% <83.33%> (+19.45%)` | :arrow_up: | | [tests/qmoperators/nuclear\_operator.cpp](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/453?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-dGVzdHMvcW1vcGVyYXRvcnMvbnVjbGVhcl9vcGVyYXRvci5jcHA=) | `90.62% <90.76%> (ø)` | | | [src/analyticfunctions/NuclearFunction.h](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/453?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-c3JjL2FuYWx5dGljZnVuY3Rpb25zL051Y2xlYXJGdW5jdGlvbi5o) | `100.00% <100.00%> (ø)` | | | [src/analyticfunctions/PointNucleusHFYGB.h](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/453?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-c3JjL2FuYWx5dGljZnVuY3Rpb25zL1BvaW50TnVjbGV1c0hGWUdCLmg=) | `100.00% <100.00%> (ø)` | | | [src/analyticfunctions/PointNucleusMinimum.h](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/453?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-c3JjL2FuYWx5dGljZnVuY3Rpb25zL1BvaW50TnVjbGV1c01pbmltdW0uaA==) | `100.00% <100.00%> (ø)` | | | [src/analyticfunctions/PointNucleusParabola.h](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/453?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-c3JjL2FuYWx5dGljZnVuY3Rpb25zL1BvaW50TnVjbGV1c1BhcmFib2xhLmg=) | `100.00% <100.00%> (ø)` | | | ... and [2 more](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/453?src=pr&el=tree-more&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft) | |

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[stigrj]

It was actually the finite_sphere that was claimed to be the same as point_parabola, but they are in fact quite different. All the point_* models are different numerical smoothing strategies operating within the numerical precision, while the finite_* models are for physically extended nuclei. So the mathematical form of the potentials are parabolic in both cases, but the extent of the smoothed region is several orders of magnitude different.