R-DEPENDENT W_PI BOND MODEL
======================================================================
Started: 2026-03-25 20:01:54

W_PI(R) = 0.286 × exp(0.411 × R)

  R(A)  W_PI(R)    GWT const
------------------------------
   0.74    0.3877  10/27 = 0.3704
   0.92    0.4174  10/27 = 0.3704
   1.00    0.4314  10/27 = 0.3704
   1.10    0.4495  cos(pi/d) = 0.5000
   1.20    0.4683  cos(pi/d) = 0.5000
   1.34    0.4961  cos(pi/d) = 0.5000
   1.54    0.5386  cos(pi/d) = 0.5000
   1.89    0.6219  (d-1)/d = 0.6667
   2.00    0.6507  (d-1)/d = 0.6667
   2.36    0.7544  5/6 = 0.8333
   2.67    0.8569  5/6 = 0.8333

MODEL A: coupling = 1 + (bo-1) × W(R)
-------------------------------------------------------
W(R) only matters for double/triple bonds (bo > 1).
Single bonds get coupling = 1 regardless of R.

    Name  bo     R   W(R)    cpl    D_e    D_0    obs     err
-------------------------------------------------------------
      H2   1 0.741  0.388  1.000  4.747  4.481  4.478    +0.1%
     Li2   1 2.673  0.858  1.000  1.882  1.819  1.046   +73.9%
      N2   3 1.098  0.449  1.898  9.630  9.529  9.759    -2.4%
      O2   2 1.208  0.470  1.470  6.987  6.906  5.116   +35.0%
      F2   1 1.412  0.511  1.000  6.082  6.013  1.602  +275.3%
      HF   1 0.917  0.417  1.000  5.332  5.128  5.869   -12.6%
     HCl   1 1.275  0.483  1.000  4.634  4.446  4.434    +0.3%
    NaCl   1 2.361  0.755  1.000  2.569  2.532  4.230   -40.1%
     LiH   1 1.596  0.551  1.000  2.695  2.544  2.429    +4.7%
      OH   1 0.970  0.426  1.000  4.750  4.557  4.392    +3.8%
      CO   3 1.128  0.455  1.909  8.216  8.121 11.090   -26.8%
      NO   2 1.151  0.459  1.459  7.161  7.077  6.497    +8.9%
      NH   1 1.036  0.438  1.000  4.905  4.707  3.910   +20.4%
      CH   1 1.120  0.453  1.000  4.300  4.114  4.290    -4.1%
     C-C   1 1.540  0.539  1.000  3.930  3.861  3.600    +7.2%
      CN   3 1.172  0.463  1.926  8.531  8.432  7.760    +8.7%
     C=C   2 1.339  0.496  1.496  5.880  5.794  6.360    -8.9%
     C=O   2 1.200  0.468  1.468  6.318  6.235  7.710   -19.1%
     CC3   3 1.203  0.469  1.938  7.617  7.519  8.700   -13.6%
 NH(NH3)   1 1.012  0.434  1.000  4.905  4.707  4.513    +4.3%
 OH(H2O)   1 0.958  0.424  1.000  4.750  4.557  4.790    -4.9%
     Cl2   1 1.988  0.647  1.000  4.527  4.483  2.514   +78.3%
      SH   1 1.340  0.496  1.000  4.105  3.928  3.780    +3.9%
      S2   2 1.889  0.622  1.622  5.864  5.812  4.370   +33.0%
      PH   1 1.422  0.513  1.000  4.133  3.956  3.440   +15.0%

Model A: mean=28.2%, median=8.9%, max=275.3%

MODEL B: coupling = W(R) × bo
-------------------------------------------------------
    Name  bo     R   W(R)    cpl    D_e    D_0    obs     err
-------------------------------------------------------------
      H2   1 0.741  0.388  0.388  1.841  1.676  4.478   -62.6%
     Li2   1 2.673  0.858  0.858  1.615  1.556  1.046   +48.8%
      N2   3 1.098  0.449  1.347  6.835  6.750  9.759   -30.8%
      O2   2 1.208  0.470  0.940  4.467  4.403  5.116   -13.9%
      F2   1 1.412  0.511  0.511  3.108  3.058  1.602   +90.9%
      HF   1 0.917  0.417  0.417  2.223  2.091  5.869   -64.4%
     HCl   1 1.275  0.483  0.483  2.238  2.108  4.434   -52.5%
    NaCl   1 2.361  0.755  0.755  1.939  1.907  4.230   -54.9%
     LiH   1 1.596  0.551  0.551  1.486  1.373  2.429   -43.5%
      OH   1 0.970  0.426  0.426  2.024  1.898  4.392   -56.8%
      CO   3 1.128  0.455  1.364  5.870  5.790 11.090   -47.8%
      NO   2 1.151  0.459  0.918  4.506  4.439  6.497   -31.7%
      NH   1 1.036  0.438  0.438  2.147  2.017  3.910   -48.4%
      CH   1 1.120  0.453  0.453  1.949  1.824  4.290   -57.5%
     C-C   1 1.540  0.539  0.539  2.117  2.066  3.600   -42.6%
      CN   3 1.172  0.463  1.389  6.152  6.068  7.760   -21.8%
     C=C   2 1.339  0.496  0.992  3.898  3.828  6.360   -39.8%
     C=O   2 1.200  0.468  0.937  4.031  3.964  7.710   -48.6%
     CC3   3 1.203  0.469  1.407  5.529  5.446  8.700   -37.4%
 NH(NH3)   1 1.012  0.434  0.434  2.126  1.996  4.513   -55.8%
 OH(H2O)   1 0.958  0.424  0.424  2.014  1.888  4.790   -60.6%
     Cl2   1 1.988  0.647  0.647  2.931  2.896  2.514   +15.2%
      SH   1 1.340  0.496  0.496  2.036  1.912  3.780   -49.4%
      S2   2 1.889  0.622  1.243  4.496  4.450  4.370    +1.8%
      PH   1 1.422  0.513  0.513  2.121  1.993  3.440   -42.1%

Model B: mean=44.8%, median=48.4%, max=90.9%

MODEL C: V8 formula but W_PI → W(R)
-------------------------------------------------------
Same 8 corrections as V8, but cos(pi/d) replaced by W(R).

    Name  bo     R   W(R)    cpl    D_e    D_0    obs     err
-------------------------------------------------------------
      H2   1 0.741  0.388  1.000  4.747  4.481  4.478    +0.1%
     Li2   1 2.673  0.858  1.000  1.882  1.819  1.046   +73.9%
      N2   3 1.098  0.449  1.898  9.630  9.529  9.759    -2.4%
      O2   2 1.208  0.470  1.100  5.227  5.157  5.116    +0.8%
      F2   1 1.412  0.511  0.259  1.577  1.542  1.602    -3.8%
      HF   1 0.917  0.417  1.000  5.878  5.664  5.869    -3.5%
     HCl   1 1.275  0.483  1.000  4.634  4.446  4.434    +0.3%
    NaCl   1 2.361  0.755  1.000  3.688  3.643  4.230   -13.9%
     LiH   1 1.596  0.551  1.000  3.868  3.687  2.429   +51.8%
      OH   1 0.970  0.426  0.833  3.958  3.782  4.392   -13.9%
      CO   3 1.128  0.455  1.909  8.553  8.456 11.090   -23.7%
      NO   2 1.151  0.459  1.216  5.968  5.890  6.497    -9.3%
      NH   1 1.036  0.438  0.833  4.087  3.907  3.910    -0.1%
      CH   1 1.120  0.453  0.833  3.917  3.740  4.290   -12.8%
     C-C   1 1.540  0.539  1.000  3.930  3.861  3.600    +7.2%
      CN   3 1.172  0.463  1.605  7.577  7.483  7.760    -3.6%
     C=C   2 1.339  0.496  1.496  5.880  5.794  6.360    -8.9%
     C=O   2 1.200  0.468  1.468  6.655  6.570  7.710   -14.8%
     CC3   3 1.203  0.469  1.938  7.617  7.519  8.700   -13.6%
 NH(NH3)   1 1.012  0.434  1.000  4.905  4.707  4.513    +4.3%
 OH(H2O)   1 0.958  0.424  1.000  4.750  4.557  4.790    -4.9%
     Cl2   1 1.988  0.647  0.671  3.036  3.001  2.514   +19.4%
      SH   1 1.340  0.496  0.833  3.883  3.711  3.780    -1.8%
      S2   2 1.889  0.622  1.457  5.269  5.220  4.370   +19.4%
      PH   1 1.422  0.513  0.833  3.889  3.717  3.440    +8.0%

Model C: mean=12.6%, median=8.0%, max=73.9%

MODEL D: ALL corrections as W(R) at different R-scales
-------------------------------------------------------
Hypothesis: each V8 correction IS W_PI(R) at a different scale.
LP repulsion = W(R - delta_LP) where delta_LP shifts to shorter R.
Radical = W(R + delta_rad) where delta_rad shifts to longer R.

    Name  bo     R W_base   W_lp  W_rad    D_0    obs     err
-------------------------------------------------------------
      H2   1 0.741  0.388  0.287  0.646  4.481  4.478    +0.1%
     Li2   1 2.673  0.858  0.636  1.428  1.819  1.046   +73.9%
      N2   3 1.098  0.449  0.333  0.748  9.529  9.759    -2.4%
      O2   2 1.208  0.470  0.348  0.782  5.262  5.116    +2.9%
      F2   1 1.412  0.511  0.379  0.851  1.486  1.602    -7.2%
      HF   1 0.917  0.417  0.309  0.694  5.664  5.869    -3.5%
     HCl   1 1.275  0.483  0.358  0.804  4.446  4.434    +0.3%
    NaCl   1 2.361  0.755  0.559  1.256  3.643  4.230   -13.9%
     LiH   1 1.596  0.551  0.408  0.917  3.687  2.429   +51.8%
      OH   1 0.970  0.426  0.316  0.709  3.206  4.392   -27.0%
      CO   3 1.128  0.455  0.337  0.757  8.456 11.090   -23.7%
      NO   2 1.151  0.459  0.340  0.764  5.398  6.497   -16.9%
      NH   1 1.036  0.438  0.324  0.729  3.406  3.910   -12.9%
      CH   1 1.120  0.453  0.336  0.754  3.409  4.290   -20.5%
     C-C   1 1.540  0.539  0.399  0.897  3.861  3.600    +7.2%
      CN   3 1.172  0.463  0.343  0.771  6.952  7.760   -10.4%
     C=C   2 1.339  0.496  0.367  0.825  5.794  6.360    -8.9%
     C=O   2 1.200  0.468  0.347  0.780  6.570  7.710   -14.8%
     CC3   3 1.203  0.469  0.347  0.781  7.519  8.700   -13.6%
 NH(NH3)   1 1.012  0.434  0.321  0.722  4.707  4.513    +4.3%
 OH(H2O)   1 0.958  0.424  0.314  0.706  4.557  4.790    -4.9%
     Cl2   1 1.988  0.647  0.480  1.078  2.564  2.514    +2.0%
      SH   1 1.340  0.496  0.367  0.826  3.681  3.780    -2.6%
      S2   2 1.889  0.622  0.461  1.035  5.075  4.370   +16.1%
      PH   1 1.422  0.513  0.380  0.854  3.801  3.440   +10.5%

Model D: mean=14.1%, median=10.4%, max=73.9%

COMPARISON
======================================================================

     Model   mean%  median%    max%   <5%  <10%
---------------------------------------------
A (simple)    28.2      8.9   275.3   9/25  13/25
  B (W×bo)    44.8     48.4    90.9   1/25   1/25
C (V8+W(R))    12.6      8.0    73.9  11/25  15/25
D (all W(R))    14.1     10.4    73.9   9/25  12/25

V8 reference: mean=1.7%, median=1.5%, max=4.8%, 25/25 under 5%

MOLECULE-BY-MOLECULE COMPARISON (Model C vs V8 target):
-------------------------------------------------------
    Name     R   W(R)    err_C                 note
--------------------------------------------------
      H2 0.741  0.388     +0.1%        W < cos(pi/d)
     Li2 2.673  0.858    +73.9%        W > cos(pi/d)
      N2 1.098  0.449     +2.4% W < cos(pi/d) pi-bond
      O2 1.208  0.470     +0.8%              pi-bond
      F2 1.412  0.511     +3.8%                     
      HF 0.917  0.417     +3.5%        W < cos(pi/d)
     HCl 1.275  0.483     +0.3%                     
    NaCl 2.361  0.755    +13.9%        W > cos(pi/d)
     LiH 1.596  0.551    +51.8%        W > cos(pi/d)
      OH 0.970  0.426    +13.9%        W < cos(pi/d)
      CO 1.128  0.455    +23.7%              pi-bond
      NO 1.151  0.459     +9.3%              pi-bond
      NH 1.036  0.438     +0.1%        W < cos(pi/d)
      CH 1.120  0.453    +12.8%                     
     C-C 1.540  0.539     +7.2%                     
      CN 1.172  0.463     +3.6%              pi-bond
     C=C 1.339  0.496     +8.9%              pi-bond
     C=O 1.200  0.468    +14.8%              pi-bond
     CC3 1.203  0.469    +13.6%              pi-bond
 NH(NH3) 1.012  0.434     +4.3%        W < cos(pi/d)
 OH(H2O) 0.958  0.424     +4.9%        W < cos(pi/d)
     Cl2 1.988  0.647    +19.4%        W > cos(pi/d)
      SH 1.340  0.496     +1.8%                     
      S2 1.889  0.622    +19.4% W > cos(pi/d) pi-bond
      PH 1.422  0.513     +8.0%                     

Completed: 2026-03-25 20:01:54
