We present the results of three-dimensional hydrodynamic simulations of evolving isolated low-mass clouds and Bok globules, where the interstellar radiation field plays an important role in the chemical and thermal evolution. We consider two classes of cloud models: (1) clouds that are initially supported against gravitational collapse by thermal pressure alone, and (2) clouds that are initially supported by a mildly supersonic, complex internal velocity field (turbulence). The models are based on our earlier work with a smoothed particle hydrodynamics code, but upgraded to include a larger chemical network, refined chemical and dust properties, and different boundary conditions. The chemical network predicts the abundances of several key tracers of cloud structure and evolution, including C+, C I, and CO. There are two main purposes of this work. The first is to calculate the effective Jeans masses of isolated and externally heated clouds under a range of initial conditions, in order to delineate the physical parameters necessary for gravitational collapse and star formation to occur. The second is to calculate density, temperature, and chemical species profiles for comparison with observations. We consider clouds with masses in the range 8 ≤ M ≤ 70 M☉, radii in the range 0.34 ≤ R ≤ 1.8 pc, and initial number densities in the range 50 ≤ n ≤ 1000 cm-3, corresponding to low-mass Bok globules. We examine the evolution of both uniform-density and centrally condensed clouds, and clouds with and without a turbulent velocity field. The main results of our calculations are: 1. Clouds that proved to be gravitationally unstable collapsed to form cold, dense molecular cores, surrounded by warm, thermally supported, tenuous halos in which the trace species were in ionic or atomic form. 2. The evolution of the thermally supported clouds is driven in the first instance by a pressure gradient through the cloud that arises because of the attenuation of the interstellar radiation field. Subsequent thermal evolution leads to cooling of the gas, which can induce gravitational instability. 3. Initially turbulent clouds evolve through the dissipation of their internal kinetic energy and then follow evolutionary paths similar to those of the thermally supported clouds. The effect of the turbulence is to delay the collapse of the clouds until the turbulence decays, which occurs on a rapid timescale through shock dissipation, and to increase the stability of the cloud models by a small amount. 4. The collapsing dense cores that arise in the simulations have masses in the range 3 M 20 M☉, radii in the range 0.1 R 0.2 pc, and temperatures in the range 8 T 12 K. These align closely with the observationally derived properties of Bok globule cores. 5. The characteristics of the collapsing dense cores are similar to those of collapsing isothermal spheres, since the gas evolves toward a constant temperature of 10 K before collapse ensues, because of gas-dust thermal coupling.