In any case there is nothing really to gain. The space saved would be around 2 GB or so, which is totally insignificant in the bigger picture.
A large part of the installation will go to your user account anyway, and the user account has to be on the system drive. This is caches, previews and all kinds of settings, and this tends to grow over time. Furthermore, this is true for all your installed applications, not just Photoshop! It is not an unrealistic scenario that the files in the user account take up more space than the program files.
How big is your drive? A "standard" configuration of OS and applications should not take up much more than 90 - 110 GB. If there is more than that, you should do some housecleaning.
Since you have a D drive, make sure your Photoshop scratch disk is directed there. Photoshop scratch files can easily grow to 50 - 100 GB, or even much more if you work with big files. The scratch file contains all history states for all open documents, and will be orders of magnitude bigger than starting nominal file sizes.
Move all application caches away from the system drive. The Bridge cache alone can grow to many tens of GB. Even your web browser will cache a lot of data.
Download the free WinDirStat. It shows you exactly what takes up disk space, and where it is.