When you see the capacitive divider C4/C5, it's usually a Colpitts oscillator or similar. In this case, it's also something like the Clapp oscillator variant. The derivations are a bit lengthy and there's not much point in repeating them here- they're basic knowledge and the Wikipedia page and its references are a good start.

Here's a simulation with a different transistor model. Startup is fairly slow (milliseconds) but it does start and produces a waveform that would switch the LS gate. The 20kΩ load is a (very) rough simulation of the gate input loading.

When you see the capacitive divider C4/C5, it's usually a Colpitts oscillator or similar. In this case, it's also something like the Clapp oscillator variant. The derivations are a bit lengthy and there's not much point in repeating them here- they're basic knowledge and the Wikipedia page and its references are a good start.

Here's a simulation with a different transistor model. Startup is fairly slow (milliseconds) but it does start and produces a waveform that would switch the LS gate. The 20kΩ load is a (very) rough simulation of the gate input loading.

You can find design equations in Crystal Oscillator Design and Frequency Compensation by Ferking 1978.