[Jim W N]

...the scope of the functions of the Presidency.

Where is that requirement in the Constitution?

It's a circular argument. If a President commits a crime while in office, he almost certainly is NOT performing his official duties or constitutional "function of the Presidency".

[PTBAA]

“...If a President commits a crime while in office, he almost certainly is NOT performing his official duties or constitutional “function of the Presidency”.

Then you agree, the answer is “yes”.