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Radiation feedback from stellar clusters is expected to play a key role insetting the rate and efficiency of star formation in giant molecular clouds(GMCs). To investigate how radiation forces influence realistic turbulentsystems, we have conducted a series of numerical simulations employing the {\itHyperion} radiation hydrodynamics solver, considering the regime that isoptically thick to ultraviolet (UV) and optically thin to infrared (IR)radiation. Our model clouds cover initial surface densities between$\Sigma_{\rm cl,0} \sim 10-300~M_{\odot}~{\rm pc^{-2}}$, with varying initialturbulence. We follow them through turbulent, self-gravitating collapse,formation of star clusters, and cloud dispersal by stellar radiation. All ourmodels display a lognormal distribution of gas surface density $\Sigma$; for aninitial virial parameter $\alpha_{\rm vir,0} = 2$, the lognormal standarddeviation is $\sigma_{\rm ln \Sigma} = 1-1.5$ and the star formation ratecoefficient $\varepsilon_{\rm ff,\bar\rho} = 0.3-0.5$, both of which aresensitive to turbulence but not radiation feedback. The net star formationefficiency $\varepsilon_\mathrm{final}$ increases with $\Sigma_{\rm cl,0}$ anddecreases with $\alpha_{\rm vir,0}$. We interpret these results via a simpleconceptual framework, whereby steady star formation increases the radiationforce, such that local gas patches at successively higher $\Sigma$ becomeunbound. Based on this formalism (with fixed $\sigma_{\rm ln \Sigma}$), weprovide an analytic upper bound on $\varepsilon_\mathrm{final}$, which is ingood agreement with our numerical results. The final star formation efficiencydepends on the distribution of Eddington ratios in the cloud and is stronglyincreased by turbulent compression of gas.

Numerical Simulations of Turbulent, Molecular Clouds Regulated by Radiation Feedback Forces I: Star Formation Rate and Efficiency