What is the correct connections for a Murray MP215AFC breaker for a Split A/C unit
Use whatever terminals you need.  For instance if you were using this breaker on a 120V circuit, hook up neutral and one hot*, and leave the other hot empty. If using on a 240V only circuit, yes - simply hook up the hots and leave neutral empty.  0 current will flow, and the device will correctly compute differential currents (for its GFCI functionality). 

There's one asterisk. The AFCI needs neutral to power itself.  So you need to hook up the neutral pigtail.  We figured this out when helping a Philippine resident set up GFCI protection for some bathroom circuits; they use North American style equipment but with neutral omitted. In that case we had to add a small transformer to synthesize a 120V center-point (quasi-neutral) to power the AFCIs.  We couldn't use ground because neutral is not ground. 

It is good that you realize not to misuse ground to fill the empty terminal in the breaker.  If you had connected ground to both the ground bar and LOAD neutral, it would have tripped. If you had connected ground to ONLY the breaker, fault current would be misrouted through the AFCI causing too high an impedance for prompt breaker trip, and the GFCI section of this AFCI would see that fault current as normal current, breaking GFCI. So I'm glad you had the horse sense not to do that.  

For reference, neutral is not ground, they have completely different jobs, and entangling/confusing them breaks their safety jobs. The confusion often arises because people see the neutral-ground equipotential bond in the main panel, and this bond is often done informally e.g. with grounds and neutrals going to the same bar. You'll never see that in a panel I do; I prefer bonds I can put a clamp meter around. 





* wait what?  What?  Use this breaker on a 120V circuit!??  Yes, you can use a 240V breaker to power one or two independent 120V circuits.  In fact, when people have a need for a 30A/120V circuit, I recommend they use a 30A/2-pole breaker, because those have many other applications, and a 30A/1-pole has almost no practical use.