Which letters do not appear consecutively in English words?

Are there any letters in the English alphabet that never appear twice consecutively in a word?

For example: the word running has the letter n repeated consecutively in it.

What letters never appear in such way (for example q comes to mind)?

^{For context, this is asked in relation to "breaking" encrypted messages. Knowing about such letters can help rule out some of the options.}

Solution 1:

If I calculate the number of occurrences of double letters in the (about 90 000 words) Mathematica online dictionary (which is not an authoritative dictionary of English because it contains some entries that are proper names), I find the statistics below:

Mathematica online

In this table, the best candidates are qq and xx, which both score zero (xx appears once in Exxon, which is a trade name).

The next is yy with Omayyad, Ayyubid and the proper name Khayyam).

Then we have jj, with various words related to hajj

The subsequent more frequent occurrences are more likely to be found in conventional English dictionaries, where other words may also occur (note doxxing, in Merriam Webster)