Detailed investigation of the three low-energy resonances seen in electron scattering by the diazabenzene molecule pyrazine reveals that the first two are nearly pure single-channel shape resonances, but the third is, as long suspected, heavily mixed with core-excited resonances built on low-lying triplet states. Such resonant channel coupling is likely to be widespread in -ring molecules, including the nucleobases of DNA and RNA, where it may form a pathway for radiation damage. DOI: 10.1103/PhysRevLett.98.113201 PACS numbers: 34.80.Bm, 34.80.Gs Interactions between slow electrons and conjugated-ring molecules are strongly influenced by resonances. Disruption of DNA by subionization electrons [1][2][3][4], for example, appears to be mediated in part by resonances associated with the ring systems of the pyrimidine and/or purine nucleobases [3,[5][6][7]. These resonances are commonly thought of as shape resonances arising from temporary trapping of the projectile in a vacant molecular orbital. However, as long ago as 1975, Nenner and Schulz hypothesized that the higher-lying shape resonances they observed in benzene and the azabenzenes ''are probably mixed with core-excited shape resonances associated with low-lying excited states of the neutral'' [8]. Subsequent observation [9] of the decay of the 4.8 eV resonance of benzene into electronically excited channels confirmed the reality of such mixing, and it is now routinely invoked in discussions of experimental results (e.g., [10,11]). However, such mixing has not been accounted for in calculations on elastic electron-molecule collisions, which therefore have implicitly assumed its effects on the elastic cross section are negligible. Indeed, many calculations have employed local-potential models of target polarization in which it may be difficult or impossible to account for resonant channel-coupling effects at all.In recent calculations on the pyrimidine nucleobases uracil, thymine, and cytosine [12,13], we observed a consistent pattern: Our resonance positions for the two lowestenergy and narrowest resonances (hereafter R 1 and R 2 ) were in reasonable agreement with measurements [14,15], but our positions for the third and broadest resonance (R 3 ) were too high. This was an unexpected result, because the most critical issue in obtaining good resonance energies is accounting for target polarization, which one might expect to be less important for R 3 than for R 1 and R 2 due to the decreased target-projectile interaction time. The same pattern was found in earlier calculations on benzene [16,17] and the two-ring (purine) nucleobases adenine and guanine [18]; although we noted [17,18] the possible influence of coupling to core-excited resonances, we did not then explore it.Here we investigate the observed trend in -ring resonance energies by studying the diazabenzene molecule pyrazine (Fig. 1). Pyrazine is an ideal subject, because its high symmetry (D 2h ) facilitates calculations and because R 1 , R 2 , and R 3 occur in distinct irreducible representation...