Macroscopic and Microscopic pK_a

by Corin Wagen · Aug 11, 2025

If you've taken a general or organic chemistry class, you've almost certainly run into the concept of pK_a: the negative logarithm of the acid dissociation constant, K_a. The pK_a of a molecule is a way to quantify how acidic or basic it is, which in turn can be used to predict its stability, reactivity, and ionization state in a variety of downstream environments.

For simple monoprotic acids and bases, a single pK_a value is all you need to fully characterize a molecule's response to changing pH. But almost all complex molecules—like amino acids, nucleotides, peptides, polycarboxylic acids—and drugs, have multiple ionizable sites. This is where the distinction between macroscopic and microscopic pK_a values becomes crucial.

In this post, we'll explore the difference between these two pK_a-prediction paradigms, when they break down, and when to use each method.

Definitions

The "textbook" acid–base equilibrium for a monoprotic acid HA is:

$\text{HA} \rightleftharpoons \text{A}^- + \text{H}^+$

The equilibrium constant is:

$K_a = \frac{[\text{A}^-][\text{H}^+]}{[\text{HA}]}$

and

$pK_a := -\log_{10} K_a$

In this situation, there's only one proton that can be lost, so the pK_a you measure is unambiguous. Each of the above species, HA and A^-, is a "microstate" which corresponds to a given arrangement of protons on the molecule. A molecule with one ionizable site has two protonation microstates, a molecule with two ionizable sites has four protonation microstates, and more generally a molecule with $N$ ionizable sites has $2^N$ protonation microstates.

For molecules with more than one microstate, different forms of pK_a become possible:

• Macroscopic pK_a values connect two protonation states that differ by one total proton. Each protonation state is an ensemble of microstates (different tautomers and conformers with the same total charge).
• Microscopic pK_a connects two specific microstates that differ by moving a named proton at a named site, holding the rest of the bonding pattern fixed. Microscopic constants depend on which other sites are protonated because the local environment shifts.

The two definitions coincide only for a monoprotic solute with a single dominant tautomer at each charge.

Almost all experimental pK_a measurement techniques—like NMR spectroscopy, potentiometric or colorimetric titration, and UV-Vis-spectroscopy-based methods—measure macroscopic pK_a values. This is because these measurements are bulk measurements, averaged over all molecules in solution, and thus record the average protonation state of the molecule and not the specific location of protonation or deprotonation. Measuring microscopic pK_a values experimentally is possible but typically requires unique and well-resolved signals for individual microstates.

Case Study: Glycine

Glycine, the simplest amino acid, has two ionizable sites: a carboxylic acid and an amine. This gives rise to four microstates across three charge states (+1, 0, and -1). There are four microscopic pK_a values for glycine:

These microstates can be combined into three protonation states:

1. Fully protonated: H₂A⁺ (left microstate above)
2. One proton lost: HA(1) and HA(2) (center microstates above)
3. Two protons lost: A^- (right microstate above)

The two macroscopic equilibria, which can be measured experimentally, are:

1. $\text{H}_2\text{A}^+ \rightleftharpoons \text{HA} + \text{H}^+ \quad\quad pK_a^{(1)} \approx 2.4$

2. $\text{HA} \rightleftharpoons \text{A}^- + \text{H}^+ \quad\quad pK_a^{(2)} \approx 9.8$

Notice that the "HA" species in the middle is actually a mixture of two different microstates: one with the acid group deprotonated, and one with the amino group deprotonated. The macroscopic pK_a value treats them as a single "bucket" containing all species with the same net charge.

In this case, the zwitterionic neutral microstate dominates and so the microscopic pK_a values corresponding to proton gain/loss from the zwitterionic microstate become the observed macroscopic pK_a values. Trying to predict the experimental pK_a values from the neutral (canonical) microstate, in contrast, is a fool's errand—the microscopic pK_a values will not only be quantitively wrong (4.3 and 7.6, not 2.4 and 9.8) but also qualitatively incorrect, since the location of the "acidic" and "basic" sites will be backwards.

Case Study: Piperidine

Things become more complex when a molecule doesn't have a single dominant microstate. Piperazine is a symmetric diamine with experimental macroscopic pK_a values of 5.35 and 9.37 (ref). But starting from the neutral microstate, a microscopic pK_a calculation predicts identical pK_a values of approximately 9 for the two amines:

This makes a certain amount of sense: protonation of either amine generates the same symmetric monoprotonated structure. But this calculation does not match the experimental data at all, because it never even considers the diprotonated microstates (which is two seperate protonation steps away from the starting structure). Only by running a second calculation from the output monoprotonated structure can we find a pK_a value that's even close to the experimental value of 5.35:

In contrast, a macroscopic pK_a calculation automatically takes into account all microstates and predicts values of 5.64 and 9.46, in good qualitative agreement with experimental values:

In this case, it's clear that macroscopic pK_a prediction is necessary for sane results.

When To Use Each Method

To summarize, macroscopic and microscopic pK_a calculations are answering different questions:

• Macroscopic pK_a: "At what pH are all molecules in solution evenly split between two protonation states?"
• Microscopic pK_a: "At what pH does this site lose its proton, given the current protonation state of the rest of the molecule?"

If you want to compare computed pK_a values to experimental measurements, you should almost always be using macroscopic pK_a values—for all but the simplest cases, these are significantly more physically accurate and reliable. Particularly for large druglike molecules with dozens or hundreds of potential microstates, it's almost impossible to get meaningful agreement with experimental data when using microscopic pK_a calculations.

However, macroscopic pK_a calculations have their downsides. The predicted pK_a values can no longer be assigned to a single functional group, making them less interpretable and chemically intuitive. For many use cases—like tracking the protonation of specific moieties or residues—microscopic pK_a values may be more useful. Macroscopic pK_a calculations are also more complex and frequently more costly to run, since the number of microstates grows exponentially with the number of ionizable sites. (We've spent a considerable amount of time and energy optimizing our implementation of macroscopic pK_a here at Rowan—smart beam-search-based microstate pruning, ML-based scoring functions, and so on—and it's still quite slow for large molecules.)

Regardless of which paradigm is better for your scientific question, knowing the difference between macroscopic and microscopic pK_a is crucial.

Further Reading

• This paper from Jonathan Zheng and co-workers illustrates how failing to properly disambiguate microscopic and macroscopic pK_a values can lead to bizarre and unphysical predictions.
• This paper from George Bodner illustrates the mathematics behind complex polyprotic pK_a equilibria in more detail.
• This paper on the SAMPL6 challenge compares the performance of a variety of macroscopic and microscopic pK_a-prediction methods on real-world data.