Charge-exchange processes in low-energy collisions of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">C</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </m

Charge-exchange processes in collisions of ${\mathrm{C}}^{3+}(1{s}^{2}2\mathit{s}^{2}S)$ ions with hydrogen and deuterium atoms are investigated employing the full quantum-mechanical molecular-orbital close-coupling method in the large energy range of ${10}^{\ensuremath{-}5}$--10 keV/u. The required molecular potential curves and coupling matrix elements are calculated by the ab initio multireference single- and double-excitation configuration interaction method, and large basis sets with full active electrons are employed to obtain accurate asymptotic energy differences. Total and state-selective electron capture cross sections and rate coefficients are obtained and show satisfactory agreement with the experimental data. Total cross sections are found to increase as the collision energy decreases with the dominance of $2s3s$ $^{3}S$ and $2{p}^{2}^{1}S$ channels in the energy region below 0.1 keV/u, and then increase as the collision energy increases above 0.1 keV/u due to the contributions of higher states. Meanwhile, the total cross sections exhibit complex oscillatory behaviors in various energy regions. Below 1 eV/u, the dense oscillatory structures arise from quasibound vibrotational states in the entrance channel, and the isotope effect for hydrogen and deuterium targets is noticeable in this energy region. Around 10 eV/u, the oscillatory patterns originate from the interference between the $2{p}^{2}^{1}S$ channel and the entrance channel, while in the 0.5--3.0 keV/u energy range, the oscillatory structures primarily arise from the multichannel interference among the $2s3s$, $2s3p$, $2p3s$, and $2s4s$ states in both the triplet and singlet states of ${\mathrm{C}}^{2+}$ ions. The ratios of cross sections for electron capture to the triplet- and singlet-state manifolds are found to deviate from the spin-statistics rule bacause of the significant differences in electron capture to $2{p}^{2}$ and $2s3s$ electronic configurations between triplet and singlet states.