C₂H⁺ potentials

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

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

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:

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

Parameters for \(V_2=V_\mathrm{1A'}\)

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)|

C2H+ potentials

Ab initio points

fit.sci

C₂H⁺ potentials