r"""
Rehm-Weller equation: electron-transfer quenching vs. driving force
=====================================================================

Rehm and Weller (1970) measured how fast many donor-acceptor pairs quench
fluorescence by electron transfer in acetonitrile and found that the
quenching rate constant depends on a single quantity, the
electron-transfer free energy
:math:`\Delta G_{ET}=E_{ox}(D)-E_{red}(A)-E_{00}+w`
(:func:`~chemistrykit.photochem.rehm_weller_free_energy`). Their empirical
curve (:func:`~chemistrykit.photochem.rehm_weller_quenching_rate`) is
diffusion-limited for exergonic transfer and falls off exponentially for
endergonic transfer; it does not show the Marcus inverted region at very
negative :math:`\Delta G_{ET}`.
"""

# %%
import matplotlib.pyplot as plt
import numpy as np

from chemistrykit.photochem import rehm_weller_free_energy, rehm_weller_quenching_rate

dG = np.linspace(-2.0, 1.0, 400)
kq = rehm_weller_quenching_rate(dG)

# A series of hypothetical donors quenching an excited acceptor with
# E00 = 2.9 eV and E_red = -1.6 V (vs. SCE).
E_ox = np.array([0.8, 1.0, 1.2, 1.4, 1.6, 1.8])
dG_pairs = np.array([rehm_weller_free_energy(E, -1.6, 2.9, work_term=-0.06) for E in E_ox])
rng = np.random.default_rng(7)
kq_meas = rehm_weller_quenching_rate(dG_pairs) * np.exp(rng.normal(0.0, 0.1, E_ox.size))

fig, ax = plt.subplots()
ax.semilogy(dG, kq, label="Rehm-Weller equation")
ax.semilogy(dG_pairs, kq_meas, "o", label="donor series")
ax.axhline(2.0e10 / 1.25, color="k", ls=":", label="diffusion plateau")
ax.set_xlabel(r"$\Delta G_{ET}$ (eV)")
ax.set_ylabel(r"$k_q$ (M$^{-1}$ s$^{-1}$)")
ax.set_title("Rehm-Weller: quenching rate vs. electron-transfer free energy")
ax.legend()
fig.tight_layout()

for E, g, k in zip(E_ox, dG_pairs, kq_meas):
    print(f"E_ox = {E:.1f} V: dG_ET = {g:+.2f} eV, kq = {k:.2e} 1/(M s)")

plt.show()