The optimal hardware configuration for running HyperChem will depend on what kind of calculations you wish to do.
As long as your calculations are done completely within RAM, the calculation speed depends strictly upon your processor speed; the faster the computer, the faster the calculations.
The amount of RAM required depends on the calculation. (Please see the Memory FAQ for more information about the memory requirements of the various kinds of calculations.) In general, molecular mechanics calculations on moderate systems, and semi-empirical calculations on small systems, can be done in the RAM of a moderate computer.
If there is not enough space in RAM to hold the calculations, HyperChem must use Windows swap space, resulting in a lot of hard-disk access as data are swapped to and from the disk. This swapping is the rate-limiting step and makes calculations much slower. If you had to make a choice between having not quite enough RAM for your usual calculations, and having to take a slightly slower computer, it would be preferable to have more RAM and a slower processor since the overall computing speed would be better.
If you are doing ab initio calculations, then unless your calculations are very small indeed you will have to store two-electron integrals on disk. In this case, disk access is the limiting factor and having a fast processor won't make much difference in the computing time. If you can get a hard drive with the fastest possible access time, that will let your calculations run as quickly as possible. Alternately, if you are running large ab initio calculations in the "Direct SCF" mode, such that integrals are recomputed at each iteration instead of being stored, there will not be a need to access the drive, and you are back to trying to get as fast a processor as possible.
HyperChem does not explicitly take advantage of parallel processing except in the sense that since its operations involve several modules running at once -- the graphical module and a computational module -- if those modules are being run on different processors, calculations will be faster. That would be under the control of the operating system.
HyperChem does not make direct use of add-on hardware such as graphics accelerators; all of its drawing and printing functions are done through Windows. However, if you do have something like a graphics accelerator installed, then when HyperChem tells Windows to go and draw a picture, then Windows would relay the request to the accelerator. The result is an indirect improvement in performance.
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