Why do some commands require explicit braces in subscripts?

Question

Most single commands don't require explicit braces if they appear in a subscript or superscript. For example,

a_\text{n}

compiles fine. But a few do require explicit braces: for example,

a_{\tilde{n}}

compiles while

a_\tilde{n}

does not. Is there any rule for which commands must be surrounded by explicit braces in a subscript even when they appear by themselves?

The \text macro happens to be defined in a particularly clever way. As a side-effect, as you've discovered, it can appear without curly braces as the argument of a _ subscript initiator. For most other macros, it's necessary to help TeX parse the material correctly by enclosing the macro and the argument(s) in a pair of curly braces. — Mico, Mar 07 '16 at 20:56
in addition to what Mico says, unless the sub/superscript is a single letter or digit, it's never a bad idea to enclose it in braces. — barbara beeton, Mar 07 '16 at 21:04
Related question on the topic of super/subscript and braces: macros - Is it possible to define a command taking an optional star and working in a subscript? - TeX - LaTeX Stack Exchange — user202729, Jul 23 '22 at 14:23

score 4 · Answer 1 · answered Dec 03 '16 at 22:52

TL;DR

Always use braces. Always use braces. Always use braces.

The LaTeX manual always uses

_{<subscript>}

even if the subscript consists of a single token and it has very good reasons for doing so; for instance, it would propose

a_{1}+b_{11}

Experienced users tend to omit the braces, but this can be very dangerous. For example, the following example

\documentclass{article}
\begin{document}
$A_\in+A_\notin$
\end{document}

will fail with

! Missing { inserted.
<to be read again> 
                   \mathrel 
l.3 $A_\in+A_\notin
                   $

because \notin is not really a single object.

An input such as A_\tilde{x} will similarly fail. On the other hand,

F_\mathrm{eff}

will work, but it's just luck. So, what's the rule?

Sorry, there's none except always using braces.