How does one obtain these achievements in Black Mesa: Source?

Quantum Capacitance

Hold the secondary fire button of the Tau Cannon weapon (right-click, by default). The weapon will then overcharge if you hold it for some time (you will know this as your health and shield will take a hit).

Remote Detonation

This is a barnacle

And here is a satchel charge:

Kill one of the former, with the latter.

Unified Coupling Theorum

Lead a headcrab to a barnacle's tentacles and have the barnacle eat/kill the headcrab.

Permeable Infrastructure

There's an alternate route through the vents in the Office Complex chapter. You need to go through that route to get this achievement. See this Youtube video on how to find that route: