If the Homo-Lumo energy gap of the Liquid Crystalline compound is small , than what does it mean? Is that compound is stable or not? The gap that I found in my case was near about 0.15ev.
The HOMO-LUMO gap of a molecule is the difference in the energy between the highest occupied orbital and the next higher unoccupied orbital. Molecules having small HOMO-LUMO gaps can be stable and tend to be excited by low energy and thus resulting in a very interesting optical properties.
HOMO–LUMO gaps less than 0.5 eV have been recently engineered in small organic molecules through extended conjugation and donor–acceptor covalent coupling approaches. Such compounds reveal a number of unusual electronic properties such as thermo-excited intramolecular electron transfer (in solution) and metallic conductivity (in the solid state).
Regarding your compound, it seems that it has a very low HOMO LUMO gap and if this value is correct, the compound can be stable and should have a unique properties as the ones indicated in the above link.