ABSTRACT: Young massive stars regulate the physical conditions, ionization, and fate of their natal molecular cloud and surroundings. It is important to find tracers that help quantifying the stellar feedback processes that take place at different spatial scales. We present ~85 arcmin2 (~1.3 pc2) velocity-resolved maps of several submillimeter molecular lines, taken with Herschel/HIFI, toward the closest high-mass star-forming region, the Orion molecular cloud 1 core (OMC-1). The observed rotational lines include probes of warm and dense molecular gas that are difficult, if not impossible, to detect from ground-based telescopes: CH+ (J = 1-0), CO (J = 10-9), HCO+ (J = 6-5) and HCN (J = 6-5), and CH (N, J =1, 3/2-1, 1/2). These lines trace an extended but thin layer (A V ?3-6 mag or ~1016 cm) of molecular gas at high thermal pressure, P th = n H · T k ? 107 - 109 cm-3 K, associated with the far ultraviolet (FUV) irradiated surface of OMC-1. The intense FUV radiation field, emerging from massive stars in the Trapezium cluster, heats, compresses and photoevaporates the cloud edge. It also triggers the formation of specific reactive molecules such as CH+. We find that the CH+ (J = 1-0) emission spatially correlates with the flux of FUV photons impinging the cloud: G 0 from ~103 to ~105. This correlation is supported by constant-pressure photodissociation region (PDR) models in the parameter space P th/G 0 ? [5 · 103 - 8 · 104] cm-3 K where many observed PDRs seem to lie. The CH+ (J = 1-0) emission spatially correlates with the extended infrared emission from vibrationally excited H2 (v ? 1), and with that of [C ii] 158 ?m and CO J = 10-9, all emerging from FUV-irradiated gas. These correlations link the presence of CH+ to the availability of C+ ions and of FUV-pumped H2 (v ? 1) molecules. We conclude that the parsec-scale CH+ emission and narrow-line (?v ? 3 km s-1) mid-J CO emission arises from extended PDR gas and not from fast shocks. PDR line tracers are the smoking gun of the stellar feedback from young massive stars. The PDR cloud surface component in OMC-1, with a mass density of 120-240 M ? pc-2, represents ~5% to ~10% of the total gas mass, however, it dominates the emitted line luminosity; the average CO J = 10-9 surface luminosity in the mapped region being ~35 times brighter than that of CO J = 2-1. These results provide insights into the source of submillimeter CH+ and mid-J CO emission from distant star-forming galaxies.