For my project, I am using an LM324. According to the datasheet, its power supply can either be +/- 16V or 0-32V (max). The output will range from -3V to +3V (or there abouts), so I realise I'm going to need a positive and negative voltage supply. All I think I'll be needing is +5V and -5V to power the op-amp.
Here is the question. I'll be hooking this up to an Arduino UNO, and this can't produce said negative supply. I was thinking of using one of the 4 op-amps within the chip to invert a +5V input to give -5V. I have ran some simulations using Proteus, and according to these simulations, the idea should work, but I know from experience that theory and practice can have very different results. Would using one of the op-amps in the IC to give itself a -5V be effective, or would I have to look into an alternative method of generating -5V?
I'm using an external DC power source (not portable), and I would like to avoid batteries, if possible.
EDIT: Thanks to everyone for your answers. I had a very strong feeling that it wouldn't be possible, but something in my mind was telling me otherwise. My aim was to use as few components as possible, but I guess I was asking for too much.
I have looked at my simulations again. They are currently on a non-network PC and am unable to transfer screenshots. There was indeed a bug somewhere, and it is now telling me that what I've done is wrong, which supports all your answers.