We present calculations of the continuum ultraviolet radiation field (91.2 nm ＜ λ ＜ 550 nm) penetrating both uniform and clumpy (3D turbulent supersonic magnetohydrodynamic) starless molecular gas layers. We find that despite the self-shielding of clumps, pristine (i.e., unreddened) radiation penetrates deeply both the cloud's volume and its mass, resulting in a brighter and bluer intracloud radiation field compared to that in an equivalent uniform cloud. Motivated by these results, we construct and test a toy model ray-tracing scheme for the radiative transfer that fits the UV-visible spectral range with a three-parameter function. We calculate the photoionization rates, Γ, of the elements C, Na, Mg, Si, S, and Fe as functions of the visual extinction A_V along lines of sight. Typically, the difference in Γ(A_V) between the clumpy and uniform clouds increases to orders of magnitude at even modest extinctions (A_V ～ 2). Photoionization in the clumpy model extends 2-3 times deeper than in the uniform case, and it dominates cosmic-ray ion-ization throughout almost the entire volume. We encapsulate these average results in a parameterized form appropriate for when an approximate treatment of the effects of dumpiness is desired. However, the large point-to-point variance in this behavior suggests that uncertainties may arise when using mean values to model particular lines of sight in detail. Ideally, these new results would be used in conjunction with established results for homogeneous clouds in order to span a range of behavior that arises due to cloud inhomogeneities. We briefly explore the importance of the adopted dust properties, characterized by the selective extinction R_V and the scattering parameter g. We find that the UV field is considerably less sensitive to these dust properties in clumpy clouds, emphasizing the preeminence of geometry.
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