Using a VFD with a single phase motor is in general a bad idea. Starting torque suffers, speed range is very limited. If the motor uses capacitors (start or run caps) they may not be happy with VFD power and the VFD may not be happy with them. If there is a centrifugal start switch the motor won't run right below the speed at which the switch trips. The electrical transient when the switch opens might make the VFD unhappy. You are paying for three phases worth of expensive transistors but only using two (in other words, to run a 2HP single phase motor you would need at LEAST a 3HP VFD).
Basically, three-phase motors are the ideal electro-mechanical machine. Single phase motors make a lot of compromises in order to run on single-phase power. Why would you want to accept those compromises when you have a VFD that is making perfectly good three-phase power? Put a three phase motor on the machine and never look back.