Excited states solver

[Gabrielgerez]

Implementing the Excited states solver. This is a re-make of #395 with better structure and is rebased on the changes introduced in #435, which needs to be merged before this one. I have Created an additional class called ExcitedStatesSolver to solve for the excited states. The functionality of this class is very similar to LinearResponseSolver so we might consider adding the excited states solver in the LinearResponseSolver in the future, or creating an entirely new class to hold different response solvers, or the future, HigherOrderResponseSolver.

TODO:

• [x] Have a working TDA single state implementation.
• [x] Update frequencies through the integral equation, still only TDA.
• [x] Extend to multiple states and consider no coupling between states.
• [x] Have a proper input section for the calculation
• [ ] Extend to RPA.
• [ ] Clean-up and refactoring
• [ ] Form and solve the generalized eigenvalue problem.

First step is almost ready as I create this draft PR.

[Gabrielgerez]

the latest commit introduces a bug, but commit edc857f will compute single excited states given a proper initial guess

[codecov[bot]]

Codecov Report

Patch coverage: 31.04% and project coverage change: -1.34 :warning:

Comparison is base (57b33fb) 70.00% compared to head (0bf26fe) 68.67%.

:exclamation: Current head 0bf26fe differs from pull request most recent head 15b7814. Consider uploading reports for the commit 15b7814 to get more accurate results

Additional details and impacted files

```diff @@ Coverage Diff @@ ## master #437 +/- ## ========================================== - Coverage 70.00% 68.67% -1.34% ========================================== Files 183 185 +2 Lines 15593 15792 +199 ========================================== - Hits 10916 10845 -71 - Misses 4677 4947 +270 ``` | [Impacted Files](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/437?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft) | Coverage Δ | | |---|---|---| | [src/qmoperators/two\_electron/ExchangePotentialD2.h](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/437?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-c3JjL3Ftb3BlcmF0b3JzL3R3b19lbGVjdHJvbi9FeGNoYW5nZVBvdGVudGlhbEQyLmg=) | `50.00% <ø> (ø)` | | | [src/scf\_solver/ExcitedStatesSolver.cpp](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/437?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-c3JjL3NjZl9zb2x2ZXIvRXhjaXRlZFN0YXRlc1NvbHZlci5jcHA=) | `0.00% <0.00%> (ø)` | | | [src/scf\_solver/ExcitedStatesSolver.h](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/437?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-c3JjL3NjZl9zb2x2ZXIvRXhjaXRlZFN0YXRlc1NvbHZlci5o) | `0.00% <0.00%> (ø)` | | | [src/driver.cpp](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/437?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-c3JjL2RyaXZlci5jcHA=) | `67.12% <51.74%> (-5.49%)` | :arrow_down: | | [...c/qmoperators/two\_electron/ExchangePotentialD2.cpp](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/437?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-c3JjL3Ftb3BlcmF0b3JzL3R3b19lbGVjdHJvbi9FeGNoYW5nZVBvdGVudGlhbEQyLmNwcA==) | `44.55% <58.33%> (-1.00%)` | :arrow_down: | | [src/scf\_solver/GroundStateSolver.cpp](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/437?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-c3JjL3NjZl9zb2x2ZXIvR3JvdW5kU3RhdGVTb2x2ZXIuY3Bw) | `88.70% <62.50%> (-0.24%)` | :arrow_down: | | [...rc/qmoperators/two\_electron/CoulombPotentialD2.cpp](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/437?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-c3JjL3Ftb3BlcmF0b3JzL3R3b19lbGVjdHJvbi9Db3Vsb21iUG90ZW50aWFsRDIuY3Bw) | `53.84% <66.66%> (-1.71%)` | :arrow_down: | | [src/qmfunctions/density\_utils.cpp](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/437?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-c3JjL3FtZnVuY3Rpb25zL2RlbnNpdHlfdXRpbHMuY3Bw) | `95.16% <70.00%> (-0.71%)` | :arrow_down: | | [src/chemistry/Molecule.cpp](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/437?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-c3JjL2NoZW1pc3RyeS9Nb2xlY3VsZS5jcHA=) | `71.03% <100.00%> (+3.38%)` | :arrow_up: | | [src/chemistry/Molecule.h](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/437?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft#diff-c3JjL2NoZW1pc3RyeS9Nb2xlY3VsZS5o) | `86.20% <100.00%> (+0.49%)` | :arrow_up: | | ... and [5 more](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/437?src=pr&el=tree-more&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=MRChemSoft) | | ... and [30 files with indirect coverage changes](https://app.codecov.io/gh/MRChemSoft/mrchem/pull/437/indirect-changes?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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