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Spin electronic states and optical properties of a circular ruthenium (Ru) terpyridine complex with a triarylamine core (CTTC) are theoretically investigated by first-principles calculations within an all-electron numerical orbital scheme based on spin density functional theory (SDFT), which demonstrate five well-defined redox states for electrochromic functions. Atomic structure of CTTC molecule is obtained by geometric optimization, and its electronic structure with a decreasing semiconductor band-gap exhibits five consecutive single-electron redox states of Ru-coordinated centers. Except for CTTC in (Ru)₃+4 redox state exhibiting a net spin of 2.25 (<i>ћ</i>/2), the other redox states are almost zero in total spin. Density distribution and energy-splitting of spin states indicate that the ferromagnetic coupling of Ru cations coordinating with terpyridine/triarylamine ligands originates dominantly from the spin polarization of Ru 4<i>d</i>-orbitals coordinated by N- and C-2<i>p</i> electrons of triarylamine. CTTC molecule in each redox state represents a well-discriminated absorption in visible region, with the highest characteristic peaks locating at 24.2, 20.2, 21.3, and 19.3/21.7 (10³ cm⁻¹) and a manifold of peaks at 13.4~25.3 (10³ cm⁻¹) for +2~+6 redox states, respectively. Theoretical electronic structure and optics of CTTC complex are used to evaluate the underlying physical mechanism of realizing a multi-color visible electrochromism by four couples of redox pairs, which is suggested to be applied for monitoring electrical information.