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C\ :sub:`2`\ H\ :sup:`+` potentials
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****************
Ab initio points
****************

fit.sci
=======
Information on grid::

    pot = [struct] with 8 fields:
      thetas: [9x1 constant (1)]        # Θ     = [100:10:180] deg
         CCs: [9x1 constant (1)]        # r_CC  = [2.2:0.1:3.2] a₀
         CHs: [11x1 constant (1)]       # r_CH  = [1.6:0.1:2.0 2.05 2.1 2.2  2.3 2.4 2.6] a₀
          zs: [9x1 constant (1)]        # zs(i) = cos(Θᵢ), i=1:nz
          nz: 9
      ntheta: 9
         nCC: 9
         nCH: 11

The MRCI *ab initio* points::

    qmV    = |itheta(9), iCC(10), iCH(12)>A(1080;3)<V(3)|  # All points
    qmPi   = |itheta(9), iCC(9), iCH(11)>A(891;2)<V(2)|    # A'' and A', correlating with ³Π 
    qmSig  = |itheta(9), iCC(9), iCH(11)>A(891;1)<V(1)|    # 2A'', correlating with ³Σ⁻
    qmPi0  = |iCC(9), iCH(11)>A(99;1)<V(1)|                # ³Π, linear geometry
    qmSig0 = |iCC(9), iCH(11)>A(99;1)<V(1)|                # ³Σ⁻, linear geometry


Two-dimensional fits, product of Hermite polynomials

.. math::
   V_\mathrm{2d}(r_\mathrm{CC}, r_\mathrm{CH}) = \sum_{i=0}^{N_x} \sum_{\substack{j=0\\ i+j \leq N_{xy}}}^{N_y} H_i[f_x (r_\mathrm{CC}-r_x)]
    H_j[f_y (r_\mathrm{CC}-r_y)] c_{i,j}

Parameters for ³Π state::

     parPi0 = [struct] with 11 fields:
         fx: 5.30392
         rx: 2.7
         fy: 5.30392
         ry: 2.1
         Nx: 6
         Ny: 6
        Nxy: 6
         c0: |nCC(7), nCH(7)>A(28;1)<V(1)|
        Hxy: |iCC(9), iCH(11)>A(99;28)<nCC(7), nCH(7)|
       namX: CC
       namY: CH

Parameters for ³Σ⁻ state::

    parSig0 = [struct] with 11 fields:
         fx: 5.30392
         rx: 2.7
         fy: 5.30392
         ry: 2.1
         Nx: 6
         Ny: 6
        Nxy: 6
         c0: |nCC(7), nCH(7)>A(28;1)<V(1)|
        Hxy: |iCC(9), iCH(11)>A(99;28)<nCC(7), nCH(7)|
       namX: CC
       namY: CH

Three-dimensional fits:

.. math::
   V_\mathrm{3d}(r_\mathrm{CC}, r_\mathrm{CH}, \theta) = \sum_{i=0}^{N_x}
   \sum_{\substack{j=0\\ i+j \leq N_{xy}}}^{N_y} H_i[f_x (r_\mathrm{CC}-r_x)]
    H_j[f_y (r_\mathrm{CC}-r_y)] 
   \sum_{L=0}^{L_\mathrm{max}} P_L(\cos\theta)c_{ijL}

Parameters for :math:`V_2=V_\mathrm{1A'}` ::

    parV2 = [struct] with 12 fields:
         fx: 5.30392
         rx: 2.7
         fy: 5.30392
         ry: 2.1
         Nx: 6
         Ny: 6
        Nxy: 6
        Hxy: |iCC(9), iCH(11)>A(99;28)<nCC(7), nCH(7)|
       namX: CC
       namY: CH
         LS: |itheta(9)>A(9;5)<L(5)|
          c: |nCC(7), nCH(7), L(5)>A(140;1)<V(1)|