Motors change a lot of what you though you knew about how load current relates to OCPD, and thus relates to wire size. So expect a lot of sizing results that wouldn't match what you'd do for any other load on a 40A breaker. And for A/C systems, the dominant load is the motor that drives the compressor, usually part of the outdoor unit. For feeders and branch circuits in general, it is the case that you need as much wire size as is necessary to "round up" to the OCPD you use. But for A/C units, this isn't the case. The reason the NEC treats motor loads and HVAC units this way, is that motors tend to spike the load current upon startup, but settle during the steady state on a much lower full load current. A resistive heating unit in an HVAC system will likely have the same sizing strategy that you would use for loads in general, but a motor load HVAC unit will not.
The way to work with AC units is to observe the MCA (minimum circuit amps) and maximum overcurrent device (MOC) values. Minimum circuit amps selects the wire at (usually) 75C, and maximum overcurrent device tells you what branch circuit breaker to use. If applicable, you would also follow (usually) the 90C column for your temperature and bundling derate calculations, to verify this is also above the MCA. You select as high of amps on your maximum circuit breaker as you can, to avoid the outcome of nuisance tripping. There is internal protection in the unit that will protect against overload current, and that internal protection will be selected with a slow time-current curve to avoid nuisance tripping. The branch circuit breaker is mostly there to trip when protecting against short circuits.