Fig. 1. Relationship between molecular orbitals in real space and reciprocal space and measured momentum maps (k-maps). (a) Structural formula and calculated HOMO of pentacene; (b) FT of pentacene HOMO, in which hemisphere with radius k=2meEkin/ℏ is shown in gray; (c) absolute value of HOMO’s FT on hemisphere

Fig. 2. Schematic sketch of final state with damped plane wave in z direction. Above z₀ final state is treated as a pure plane wave, and below z₀ it is exponentially damped [reprinted with permission from Ref. [29] (©American Physical Society)]

Fig. 3. Geometry factor and its influence on theoretical HOMO of pentacene with different polarizations of incident light. (a) ARPES geometry with y-z being incidence plane, angle of incidence α=65°, θ(ϕ) being polar (azimuth) angle of photoelectrons, and k_|| being in-plane component of momentum vector k; (b) calculated distribution of geometry factor; (c) product of geometry factor and squared FT of theoretical pentacene HOMO, with kinetic energy being 30 eV

Fig. 4. Different molecular orientations and corresponding theoretical k-maps. (a) Brickwall phase on Ag(110), real-space distribution and k-map of PTCDA LUMO; (b) herringbone phase on Ag(110) and T-phase on Ag(100), k-map constructed by two perpendicular orientations; (c) theoretical HOMO k-map contributed by two pentacene molecules with out-of-plane tilt angles of ±26°

Fig. 5. DFT calculation and POT experiment for pentacene on Cu(110). (a) pDOS for pentacene using PBE-GGA functional and HSE hybrid functional, photoemission spectra of pentacene monolayer along [11¯0] and 45° apart, dashed vertical lines are for comparing HOMO positions; (b) experimental k-maps at two binding energies compared to theoretical k-maps of LUMO/HOMO (1 Å=0.1 nm) [reprinted with permission from Ref. [42] (©American Physical Society)]

Fig. 6. POT deconvolution procedure for PTCDA/Ag(110). (a) Experimental band map and integrated energy distribution curve (reprinted from Ref. [43], under Creative Commons license CC BY 3.0); (b) pDOS for four orbitals deconvoluted by POT, measured k-maps and corresponding calculated orbitals (reprinted from Ref. [48], under Creative Commons license CC BY 4.0)

Fig. 7. Iterative wave function reconstruction for HOMO of PTCDA molecule. (a) Initial step with random phase, FT to real space, confinement box (green rectangle), FT back to k-space and resulted new phase; (b)-(d) results after 2, 50, 250 iterations, including reconstructed orbital in k-space and real space [reprinted with permission from Ref. [50] (©PNAS)]

Fig. 8. Real-space orbital reconstruction of PTCDA LUMO. (a) LUMO illustrated in k-space with two hemispherical cuts (kinetic energies of 29.7 eV and 58.1 eV); (b) simulated and measured k-maps at various photon energies; (c) 3D images of LUMO in top view and side view (reprinted from Ref. [35], under Creative Commons license CC BY 4.0)

Fig. 9. Intermolecular dispersion in PTCDA layer on Cu(100). (a) Experimental and simulated band map, in which dashed line shows band dispersion, and horizontal lines indicate energies where corresponding k-maps in (b) are measured; (b) simulated k-map for LUMO of isolated PTCDA, and comparisons between experimental (left halves) and simulated (right halves) k-maps [reprinted with permission from Ref. [29] (©American Physical Society)]

Fig. 10. Momentum maps of HOMO of coronene on Au(111). (a)-(c) Experimental momentum maps measured at three different binding energies; (d) simulated momentum map of Au(111) as background [reprinted with permission from Ref. [58] (©American Physical Society)]

Fig. 11. Femtosecond time-resolved POT for PTCDA molecules. (a) Experimental scheme; (b) experimental band map; (c) experimental momentum maps of LUMO obtained at selected delay time [reprinted with permission from Ref. [37] (©American Association for the Advancement of Science)]