. Author manuscript; available in PMC: 2020 Oct 14.

Published in final edited form as: J Comput Aided Mol Des. 2020 Feb 12;34(5):561–573. doi: 10.1007/s10822-020-00280-7

Table 1:

The pK_as and number of protons provide the input information needed to describe a molecule with 4 protonation states separated by 3 pK_as

Molecule		XH₃³⁺		XH₂²⁺		XH⁺	X
microstate		A		B		C	D
Relative charge		i+3		i+2		i+1	i
pH where G_j=G_k	pK_AB	−2.17	pK_BC	5.61	pK_CD	13.77
ΔG_jk	ΔG°_AB	2.17	ΔG°_CB	−5.61	ΔG°_DC	−13.77
Δm_B		1		0		−1	−2
Δm_C		2		1		0	−1

pK_jk=pK_kj is the pH where G_j=G_k; ΔG°_jk is the free energy difference between states j and k at pH 0. The reference state is the second term in the subscript. ΔG°_jk = −ΔG°_kj. Δm_j is the number of protons relative to the reference state, which is B or C here. As there are no tautomeric states in this simplified example, the microstates and macrostates are equivalent. Free energy (ΔG) is given as unitless free energies where a one unit change in ΔG yields a 10-fold population change.