The performance of recently introduced coupled cluster (CC) method exploiting the unitary group approach (UGA) to many-electron systems, truncated at the first order interacting space level [UGA-CCSD(is)] and using the 6-31G* basis set, in computations of equilibrium bond lengths and harmonic vibrational frequencies, is examined for a series of open-shell (OS) states of the first row diatomics and hydrides. Altogether, 48 distinct electronic states are considered for 9 diatomic hydrides (BeH, BH, CH, CH+, NH, NH+, OH, OH+ and FH) and 18 diatomics (BeF, BN, BO, C-2, C-2(+), C-2(-), CN, CO, CO+, CF, N-2(+), NO, NO-, NF, O-2, O-2(+), OF and F-2(+)), involving both high 2 and low spin cases. Very good agreement with the available experimental data is found in all cases, except when the experimental values are marked as "uncertain" or where only the Delta G(1/2) values of harmonic frequencies are available. For the so-called "difficult’ systems, namely NO(X (2) Pi), O-2(X (3) Sigma(g)(-)), O-2(+)(X (2) Pi(g)), OF (X (2) Pi) and F-2(+) (X (2) Pi(g)), the geometries and vibrational frequencies are also calculated using the TZ2P [5s4p2d] basis sets, and the results are compared with both the experiment and existing perturbation theory and CC results. All results indicate that UGA CCSD(is) represents a versatile, reliable and computationally affordable method that can handle a great variety of OS states, including OS singlets.