Quantum

[vegardjervell]

Contains basically all the stuff related to "The limits of the FH corrections"

Short summary:

• Quantum mechanical methods for calculation of second virials and collision integrals
  • Including tabulated values of bound state energies computed using MolCas VibRot
• Several new multiparameter (ab initio) interaction potentials
• Functionality for quasi-symbolic differentiation
• Feynman-Hibbs correction of arbitrary potentials to arbitrary order
• Functionality for tabulating potentials (gives a solid speed-up for the heavy multiparameter potentials)

Basic structure:

• The Quantum class inherits from Spherical and implements all our quantum mechanical calculations
  • If you set_quantum_active(false), calls will forwarded to Spherical, which does the same old classical calculations.
  • The multiparameter classes ( ModTangToennies, Patowski, and HFD_B2) now inherit from Quantum instead of Spherical
• Feynman-Hibbs corrections are implemented as the template class FH_Corrected in extensions.h
  • The template requires that the underlying potential implements potential_dn, which is the n'th derivative of the potential.
  • See multiparam.h for example usage of the FH_Corrected template.
  • See multiparam.cpp for examples on how to implement arbitrary order derivatives.
• In extensions.h we now also have the Tabulated template class, which can be used to quickly create a tabulated version of some other model. For example: Tabulated<Patowski, 1000, 1>, will create a class identical to the Patowski class, which uses 1000 tabulated points for the potential and first and second derivative, with first order (1) interpolation between points.
• The quasi-symbolic differentiation is implemented in Factorials.(h|cpp). I have a more fleshed-out implementation that is more or less completely general (can handle pretty much any analytical function) over in a different repo. That implementation is also ported to Fortran and Python, which is nice.
• The fluid files (fluids/) have been supplemented with fluids/E_bound/*.dat and fluids/E_bound/*.phase_shifts. These are tables of bound-state energies (computed using MolCas) and phase shifts (computed using KineticGas). The former is required in order to calculate second virial coefficients. The latter is just nice to have, since these calculations are expensive.
• Fluids now have the Quantum field in the fluid file, which contains information required for classes inheriting from Quantum. This includes the half_spin(i.e. spin multiplied by two) which determines whether the species is a Boson or a Fermion, and the E_bound (or alternatively, has_E_bound_file: true) which contains the bound state energies in Kelvin.

[vegardjervell]

Just pinging @johanslo since reading the top-level description of this PR might be nice to get a quick overview of some new functionality that could turn out to be useful.