The inner couple of hundred parsecs of our Galaxy are characterized by a significant amount of synchrotron-emitting gas. Many of the best studied sources in this region exhibit a mixture of 6.4 keV Fe Kα emission, molecular line emission, and nonthermal radio continuum radiation. The spatial correlation between fluorescent Fe Kα line emission at 6.4 keV and molecular line emission from Galactic center molecular clouds has been explained as reflected X-rays from a past outburst of Sgr A*. Here we present a multiwavelength study of this region and find a correlation between the nonthermal radio filaments and the X-ray features. This correlation, when combined with the distribution of molecular gas, suggests against the irradiation model. Instead, we account for this distribution in terms of the impact of the relativistic particles from local (nonthermal filaments) and extended sources with diffuse neutral gas producing both nonthermal bremsstrahlung X-ray continuum emission and diffuse 6.4 keV line emission. The production rate of Fe Kα photons associated with the injection of electrons into a cloud as a function of column density is calculated. The required energy density of low-energy cosmic rays associated with the synchrotron-emitting radio filaments or extended features is estimated to be in the range between 20 and ∼ 103 eV cm -3 for Sgr C, Sgr B1, Sgr B2, and "the 45 and -30 km s -1" clouds. We also generalize this idea to explain the cosmic-ray heating of molecular gas, the interstellar cosmic-ray ionization, the pervasive production of the diffuse Kα line, and TeV emission from the Galactic center molecular clouds. In particular, we suggest that inverse Compton scattering of the submillimeter radiation from dust by relativistic electrons may contribute substantially to the large-scale diffuse TeV emission observed toward the central regions of the Galaxy.