QMC studies of the propargyl radical, C₃H₃, peroxynitrite ion, ONOO-, nitrogen atom excited state transition energy, and chromium dimer, each of which proved difficult in other electronic structure methods, are presented here. Two generalized gradient approximation density functionals, B3LYP and B3PW91, are also applied for comparison in the case of propargyl radical. The atomization energy determined by these methods is 2536.0 kJ/mol (B3LYP), 2553.2 kJ/mol (B3PW91), and 2542.2(2.5) kJ/mol (DMC). The latter compares favorably with separate measurements of 2543.9(12.5) and 2546.0(5.0) kJ/mol. The atomization energy of peroxynitrite is estimated by QMC, and three other methods, Hartree-Fock, MP2, and B3LYP, for comparison. Additional studies of basis set effects in the ab initio and generalized gradient approximation density functional approaches were also performed. The atomization energy determined by these methods is 378.89 kJ/mol (RHF), 1227.1 kJ/mol (MP2), 1159.1 kJ/mol, (B3LYP), and 1311.7(10.5) kJ/mol (DMC). The DMC value for the atomization energy compares favorably with an experimental value of 1309.6(4.2) kJ/mol. The transition energy of the nitrogen atom from its spin quartet ground state to the spin doublet excited state is estimated in several methods: B3LYP, 263.6 kJ/mol; PMP2, 307.5 kJ/mol; CCSD, 272.4 kJ/mol; CCSD(T), 257.7 kJ/mol; CASSCF, 237.2 kJ/mol; and QMC, 244.8(3.8) kJ/mol. These results are compared to an experimental value of 230.1 kJ/mol. The dissociation energy of the chromium dimer, a quantity historically noted for being difficult to estimate, is also included. Recent experiments give values of 1.44, 1.42, and 1.53 eV, a billion-determinant MRCI/MRACPF calculation estimates 1.09 eV, various non-B3 density functionals estimate from 1.01 to 2.99 eV, and DMC estimates 1.85(27) eV. Both VMC and B3 exchange functional DFT predict an unbounded molecule.