A geometry optimization and force constant calculation code using analytic gradient has been implemented to a two-component Kramers' restricted Hartree-Fock(KRHF) method for the polyatomic molecules with closed-shell configurations. The KRHF method utilizes the relativistic effective core potentials(RECPs) with effective one-electron spin-orbit operators at the Hartree-Fock level in a variational manner and produces molecular spinors obeying the double group symmetry. Electron correlations are treated at the coupled-cluster level of theory with and without spin-orbit interactions. Spin-orbit effects on many molecules containing sixth-row p-block elements(Tl-Rn), transactinide d-block elements(Rf, Db, and Sg), and p-block elements(Element 113, 117, and 118) are evaluated and discussed. In the present work, the spin-orbit effect is defined by the difference between the results of one- and two-component RECPs. Particular attention is paid to molecular geometries, harmonic vibrational frequencies, and dissociation energies for the ground states of the molecules. Comparisons with available all-electron Dirac-Fock results indicate that the two-component approaches are very promising tools in the calculations for the heavy atom systems. In particular, the straightforward two-component coupled-cluster calculations are useful when the size-extensive property is necessary to determine accurate molecular properties as in the case like $Rn_2$ and when the spin-orbit effects become very large as in the cases like (113)H and (117)H. In the calculations for the molecules containing sixth-row p-block and transactinide d-block elements, spin-orbit effects on the geometries and harmonic vibrational frequencies are very small. Only the dissociation energies are significantly changed by incorporating spin-orbit interactions. However, for the molecules containing transactinide p-block elements, considering spin-orbit interactions in the calculations is necessary to obtain reliable molecular properties. For the (118)$F_4$ molecule, spin-orbit contributions make a spin-orbit induced isomer, which is a local minimum. The one-component RECP, which is derived by potential average scheme, is found to be useful for describing spin-free molecular properties even for the transactinide molecules. The potential average scheme is proposed as the consistent definition of spin-orbit effects in any RECP scheme when spin-orbit effects are compared among various methods.
