I don't think that it's possible using only xmodmap
tool to accomplish what you wish. This because the mouse button is not a key, so it can't have a keyname.
One way to do what you wish is to use xdotool
. Using the following command line you can simulate a left click of your mouse:
xdotool click 1
Now, all you have to do is to add a custom keyboard shortcut for the above command. You can't use the F1 key for a custom shortcut, but you can use for example F2 key, then use xmodmap
to make F1 key to act as F2 key:
xmodmap -e "keycode 67 = F2"