What is a "formal" dimer?

Question

I was researching for this question and I noticed the term "formal dimer":

Hyponitrous acid is a chemical compound with formula $\ce{H2N2O2}$ or $\ce{HON=NOH}$. It is an isomer of nitramide, $\ce{H2N−NO2}$; and a formal dimer of azanone, $\ce{HNO}$.

Google didn't gave any meaning of this term, rather it gave me bunch of examples:

Carbene dimerization is a type of organic reaction in which two carbene or carbenoid precursors react in a formal dimerization to an alkene.

Specifically, when simple aromatic 6n-electron systems, which are extremely sluggish in Diels-Alder additions, are incorporated into a [2n]cyclophane system, e.g. [2.2]paracyclophane which is a formal dimer of p-xylene, a dramatic increase in the rate of addition is observed in certain cases.

_{ORGANIC REACTIONS AT HIGH PRESSURE. DIELS-ALDER REACTIONS OF [2. 2]PARACYCLOPHANE by Kiyoshi MATSUMOTO, CHEMISTRY LETTERS, pp. 1681-1682, 1985 (link)}

What is the meaning of this term and how is it different from just dimer? Are they referring to "formal charge"?

Answer 1

Glucose $\ce{C6H12O6}$ could be considered as a formal hexamer of methanal $\ce{CH2O}$.

A formal dimer of methanal is acetic acid $\ce{CH3COOH}$ as the very contrasting example, compared to e.g. $\ce{O2N-NO2}$.

A formal trimer of methanal is lactic acid $\ce{CH3CH(OH)COOH}$.

To close the cycle, glucose can be considered also as a formal dimer of lactic acid or a formal trimer of acetic acid.

There is equilibrium $\ce{2 monomer <=> dimer}$ for "true" dimers. Formal dimers have either just atom count multiplicity, or reversible reactions are not observed and structure of the dimer is very different. That said, the boundary between true and formal dimers/oligomers is not sharp, but little fuzzy.

In some way, dimerization could be seen as reversible glueing 2 monomers together by a chemical bond(s). The more the reaction differs from this model, the more the dimer leaves the status of a true dimer toward formal dimers. At the opposite end of the scale, there stand very formal dimers/oligomers, with no way how to get them from monomers, unless by a sophisticated synthetic path.

$\ce{H-O-N=N-O-H}$ could be a true dimer of $\ce{H-N=O}$ if the latter had structure $\ce{H-O-N}$, with the equilibrium reaction $\ce{2 H-O-N <=> HON=NOH}$.

As nitrous acid is $\ce{H-O-N=O}$, hypothetical monomeric hyponitrous acid is supposed to be $\ce{H-O-N}$ like $\ce{H-O-Cl}$, and not $\ce{H-N=O}$.

Interesting fact is that dissociation of $\ce{HNO}$ is spin-forbidden quantum event and the rate of the dissociation is very slow.