Microbial production and consumption of methane are widespread in natural and artificial environments, with important economic and climatic implications. Attempts to use the isotopic composition of methane to constrain its sources are complicated by incomplete understanding of the mechanisms of variation in methane's isotopic composition. Knowledge of the equilibrium isotope fractionations among the large organic intracellular intermediates in the microbial pathways of methane production and consumption must form the basis of any exploration of the mechanisms of isotopic variation, but estimates of these equilibrium isotope fractionations are currently unavailable. To address this gap, we calculated the equilibrium isotopic fractionation of carbon (13C/12C) and hydrogen (D/H) isotopes among compounds in anaerobic methane metabolisms, as well as the abundance of multiple isotope substitutions ("clumping," e.g., 13C--D) in these compounds. The Density Functional Theory calculations employed the M06-L/def2-TZVP level of theory and the SMD implicit solvation model, which we have recently optimized for large organic molecules and tested against measured equilibrium isotope fractionations. The computed 13beta and 2beta values decrease with decreasing average oxidation state of the carbon atom in the molecules, resulting in a preference for enrichment of the molecules with more oxidized carbon in 13C and D. Using the computed $\beta$ values, we calculated the equilibrium isotope fractionation factors in the prominent methanogenesis pathways (hydrogenotrophic, methylotrophic and acetoclastic) and in the pathway for anaerobic oxidation of methane (AOM) over a temperature range of 0-700 degrees Celsius. Our calculated equilibrium fractionation factors compare favorably with experimental constrains, where available, and we used them to investigate the relation between the apparent isotope fractionation during methanogenesis and AOM and the thermodynamic drive for these reactions. We show that a detailed map of the equilibrium fractionation factors along these metabolic pathways allows an evaluation of the contribution of equilibrium and kinetic isotope effects to apparent isotope fractionations observed in laboratory, natural and artificial settings. The comprehensive set of equilibrium isotope fractionation factors calculated in this study provides a firm basis for future explorations of isotope effects in methane metabolism.