Gaussian does use AVX in their most recent builds (Rev E.) Get this distribution if you can. There is no GPU acceleration yet (rumors are that Gaussian might have it in the next version), but your relative might want to look into TeraChem if he's interested. I haven't used it myself, but I have heard good things about it. They use NVIDIA GPUs to get incredible speedups, but the scope of calculations is more limited compared to Gaussian, which is probably the most versatile out there.
Don't use the linda system for multinode computing. There is a minimal performance boost. If you can, build as powerful of a dual socket node as you can afford.
It scales decently well, but clockspeed is also important. Benchmarks on the Internet suggest that it scales very well to 12-20 cores, and good out to 48 cores, so pretty much get the biggest 2P system you can afford (dual E5-2699v4, ideally).
Get as much RAM as you can get your hands on. This is just as important as cores and clockspeed, and you need to have the RAM to match your processors. Frequency calculations on larger systems require enormous amounts of memory, like 5 or more GB of RAM per core to run efficiently. Otherwise, it can't keep all the cores fed and will only use a few. Most computing clusters actually don't have this much memory per node, so your friend will have a significant speed advantage if he can get like 1TB. If you can get enough RAM, you might be able to run your calculation "in core" which means entirely in memory instead of having to recompute the integrals as the processor works through them.
Get a very fast SSD if he's planning on running the "conventional" algorithm.
Here's some links about Gaussian's need for memory and fast I/O.
http://www.lct.jussieu.fr/manuels/Gaussian03/g_ur/m_eff.htm
http://www.cup.uni-muenchen.de/ch/compchem/energy/hf5.html
Also, diasble HyperThreading. Gaussian does not gain from it, and in some cases it will slow it down. Finally, if you are interested in the effects of various configurations on speed, DO NOT bench gaussian and report the times on the Internet. It is not allowed and you could get yourself as well as any institution associated with you banned.
Edit: A note on overclocking - anecdotal experience from the internet and "other sources" seems to suggest that a significant speedup can be obtained by doing so, but do so at your own risk. Recommend checking geometries and energies yourself and maybe running a duplicate calculation on a system at stock speed. Chances are if the program gets an error, it will simply crash rather than proceeding. Take all of this with a grain of salt though and proceed carefully. Either way Intel does not allow overclocking on Xeons post Nehalem so this will only apply if you get the 5960x or 6950x (don't buy the 6950x, get a dual Xeon instead).
Anyways, I'm curious to see what you get. I'd be so jealous if you got a dual 2699v4 system with 1TB of RAM. That would be a beast.