Isomers of C11H8 have been theoretically examined using density functional theory and coupled-cluster methods. The current investigation reveals that 2aH-cyclopenta[cd]indene (2), 7-ethynyl-1H-indene (6), 4-ethynyl-1H-indene (7), 6-ethynyl-1H-indene (8), 5-ethynyl-1H-indene (9), and 7bH-cyclopenta[cd]indene (10) remain elusive till date in the laboratory. The puckered low-lying isomer 2 lies at 9 kJ mol-1 below the experimentally known molecule, cyclobuta[de]naphthalene (3), at the fc-CCSD(T)/cc-pVTZ//fc-CCSD(T)/cc-pVDZ level of theory. 2 lies at 36 kJ mol-1 above the thermodynamically most stable and experimentally known isomer, 1H-cyclopenta[cd]indene (1), at the same level. It is identified that 1,2-H transfer from 1 yields 2H-cyclopenta[cd]indene (14) and subsequent 1,2-H shift from 14 yields 2. Appropriate transition states have been identified, and intrinsic reaction coordinate calculations have been carried out at the B3LYP/6-311+G(d,p) level of theory. Recently, 1-ethynyl-1H-indene (11) has been detected using synchrotron-based vacuum ultraviolet ionization mass spectrometry. 2-Ethynyl-1H-indene (4) and 3-ethynyl-1H-indene (5) have been synthetically characterized in the past. While the derivatives of 7bH-cyclopenta[cd]indene (10) have been isolated elsewhere, the parent compound remains unidentified till date in the laboratory. Although C11H8 is a key elemental composition of astronomical interest for the formation of polycyclic aromatic hydrocarbons in the interstellar medium, none of its low-lying isomers have been characterized by rotational spectroscopy though they are having a permanent dipole moment (μ ≠ 0). Therefore, energetic and spectroscopic properties have been computed, and the present investigation necessitates new synthetic studies on C11H8, in particular 2, 6-10, and also rotational spectroscopic studies on all low-lying isomers.