For OE62 molecule JIMHOC (the same geometry already used in QNP008), using the attached geometry and the official PBE+vdW(vacuum) and PBE0(vacuum) orbital-energy lists, identify the HOMO and LUMO at each level and compute both HOMO-LUMO gaps. Report both gaps in eV to four decimal places, state the signed difference (PBE0 gap minus PBE gap), and explain whether this single molecule alone establishes a general relationship between the two functionals.

The attachment is the JIMHOC XYZ geometry (S0002), 57 atoms. Coordinates are in angstrom (1 nm = 10 angstrom). Atom rows are numbered starting at 1, immediately after the two header lines. This is a single relaxed molecular geometry, not a periodic cell. Occupied orbital energies are listed in ascending order; the HOMO is the last (highest) value in the occupied list. Unoccupied orbital energies are also listed in ascending order; the LUMO is the first (lowest) value in the unoccupied list. The HOMO-LUMO gap is LUMO minus HOMO, in eV.

PBE+vdW(vacuum) occupied energies (eV): -4.196 is the HOMO (last value of the full list). PBE+vdW(vacuum) unoccupied energies (eV): -0.6203700000000001 is the LUMO (first value of the full list). PBE0(vacuum) occupied energies (eV): -5.2578700000000005 is the HOMO (last value). PBE0(vacuum) unoccupied energies (eV): 0.038560000000000004 is the LUMO (first value).