How to determine if given OpAmp model supports single supply (Ex. OPA167x)

All OPAmps can be used with a single supply, but some are easier to use than others.

A key criterion for single supply use is that the input common mode voltage should include the negative supply, usually connected to ground.

A very useful criterion is that the output should drive to or nearly to the negative supply.

Two parameters affect whether an op amp can support single-supply, low-voltage operation -- minimum total supply voltage, and output voltage swing.

If output voltage max 12V with 15V supply (for example with a classic 741 op amp), then it needs 3V of "headroom". This is not a formal specification, but something that is inferred based on the specified output voltage limits at specified supply voltage test condition (VCC - VOHmin) and the (VSS - VOLmax).

Running a 741 from 5V single supply doesn't work because its output voltage is too constrained, max output voltage would be 2V but min output voltage would be 3V. This forces the output to sit near the center without any ability to drive signal.

Sometimes the output voltage swing is not symmetrical, it may be weaker driving high output and stronger on low output voltage; or there may be "crossover distortion" when it changes from being a current-source to a current-sink. Unfortunately datasheets don't usually call attention to this kind of distortion, except to specify it is guaranteed below some amount.

If you use an op-amp, it really just needs large enough supply voltage between the supply pins. So the op-amp does not care if you have 12V single supply or +/- 6V dual supply, from the op-amp point of view it just has supplies, it does not make a difference.

However, something else in your circuitry might require a certain configuration for the power supply, like ability to input and output negative DC voltages in respect to common ground.