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Recommendation: You should install Yitzi's patch if you're using SMAX and either kyrub's or scient's if you're using SMAC.
Yitzi's patch breaks backwards compatibility for alphax.txt. If you use old scenarios that require a custom alphax.txt this means that you may need to manually move the changes over. This will not be a concern for most users. Not using Yitzi's patch means that some newer scenarios and custom alphax.txt will not work for you.
To use any patch, extract the zip file into the installation folder and overwrite the existing files.
The patches' AI improvements won't make the AI too hard for new players, and instead aim for a reasonable level of challenge at "Librarian" difficulty. Tweaks mostly involve teaching the AI how to do not-terribly without cheating.
Patches are primarily developed on the Alpha Centauri 2 forum.
Try PRACX, a modified renderer for Alpha Centauri with a number of other improvements. v1.06 is included in version 3.4 of Yitzi's Unofficial Patch, but lacks an essential file and won't work properly unless you've already installed PRACX. You should probably install PRACX separately from its release thread. PRACX Release Thread. PRACX Source Code
PRACX + Official Alien Crossfire doesn't work, you need to install an unofficial patch first. Yitzi's 3.3 patch has been tested to work.
Try the latest copies of Yitzi or kyrub's patches.
Otherwise, might be related to a bug with automated artillery units (though I think Yitzi might have fixed this one sometime). Try turning off automation and see if it helps. More info here.
GOG.com recommends using Catalyst 13.4 or earlier but the game also works with 14.x or earlier.