A colleague of mine recently used the word "herein" in a research article (of which I am a co-author) to mean essentially "in this paper". To me it makes the paper read more like a legal document than a research article, so I commented that I would I prefer a phrase like "in this research", "in this paper", or "in this work". A quick google search showed that sometimes researchers use such words, but I haven't done a detailed check of how common it is. I can only go from my own experience that I don't often see this type of language used in scientific articles and that it sounds awkward to me. My question for this community is would you use words like "herein", "hereinafter", etc. in a scientific research article, or do they belong rather exclusively to legal literature/documents as my intuition tells me?
Here's a factual and quantifiable answer to your question :)
As you can see in the Google NGram, the word "herein" has been the popular way to convey this idea historically but has since 1920 lost popularity. "in this study" and "in this paper" together outweigh "herein" almost double up at this point.
(end:facts, begin: speculation)
Take the following with a pinch of salt; but if you consider why this is the case, I'd say "herein" is the old way of saying the exact same thing as the other two. Sometimes people associate older phrasing with being finer, more eloquent and indeed sometimes even more intellectual, in a Twain-esque way. Please note that I am not accusing your colleague of thinking in this way, but sometimes people tend to choose the fancier/older word because it "sounds better".
I have to say I really don't buy the argument of "herein" being shorter; you save 2 words or 6 characters (incl. whitespace). I would presume that you don't refer to the article more than 4-5 times throughout the course of the paper, so your saving is approximately 10 words, or 30 characters, which is not that much. I am willing to accept that excuse for an abstract maybe but certainly not for a research article where you typically have 5000 words or more to describe your work.
As a quick attempt at a relatively objective answer to this question, I searched all the PDFs in my "papers" folder for the string "herein". I didn't restrict to whole words, because I think that any word containing "herein" as a substring is also one of the words you're asking about. ("wherein", "therein", "hereinafter").
The data set consisted of 1709 PDF files of scientific articles, most of them in the field of geosciences, the overwhelming majority published after 1950.
Results of the search: 614 hits for "herein" in 286 documents; that is, around 17% of the articles contain this string. The real figure is likely to be a little higher, since not all the PDFs contain text (some are scanned images with no OCR); also, a few of them are in French, German, or Swedish rather than English, and should thus have been excluded from consideration.
Conclusion: "herein" is not particularly unusual or unnatural, at least in my field.
As a side note: personally I'm cautious about using phrases like "in this work", because I've come across many instances of ambiguity with such phrases. Sometimes authors use it to refer to the paper they're writing, and at other times to another paper they've just mentioned. I'd prefer "in the present work" over "in this work" for this reason, even though I consider it a little clunkier.
I would not. I have no data to back this up, but in my experience (and field: physics), these words are uncommon, and I would probably consider such usage bad writing. The last point of course depends somewhat on the context; maybe it is more accurate to say, I would expect to see such usage only in a badly written paper.
As alternatives, I would prefer “in this work” (but not “in this research”, which sounds wrong, nor “in this paper” which sounds too colloquial to me) or something similar (“in this article”; “in this Letter” for some journals); or even just “here”.
"Herein" is fine to use, even today, in English-language writing. It does not relate to "legal" documents only.
Scientific research papers are often read by those whose native language is not English. Thus, in such writing, it is better to use simple English than sophisticated English. So why not use a simpler alternative to "herein"?