[en] Electron-impact excitation of H₂ triplet states plays an important role in the heating of outer planet upper thermospheres. The $d^3{\mathrm{\Pi <!--\; ??\; -->}}_u$ state is the third ungerade triplet state, and the $d^3{\mathrm{\Pi <!--\; ??\; -->}}_u$–$a{}^3{\mathrm{\Sigma <!--\; ??\; -->}}_g^{+}$ emission is the largest cascade channel for the $a{}^3{\mathrm{\Sigma <!--\; ??\; -->}}_g^{+}$ state. Accurate energies of the $d{}^3{\mathrm{\Pi <!--\; ??\; -->}}_u^{-<!--\; ???\; -->}$(v, J) levels are calculated from an ab initio potential energy curve. Radiative lifetimes of the $d^3{\mathrm{\Pi <!--\; ??\; -->}}_u$(v, J) levels are obtained by an accurate evaluation of the $d^3{\mathrm{\Pi <!--\; ??\; -->}}_u$–$a{}^3{\mathrm{\Sigma <!--\; ??\; -->}}_g^{+}$ transition probabilities. The emission yields are determined from experimental lifetimes and calculated radiative lifetimes and are further verified by comparing experimental and synthetic $d^3{\mathrm{\Pi <!--\; ??\; -->}}_u$–$a{}^3{\mathrm{\Sigma <!--\; ??\; -->}}_g^{+}$ spectra at 20 eV impact energy. Spectral analysis revealed that multipolar components beyond the dipolar term are required to model the $X^1{\mathrm{\Sigma <!--\; ??\; -->}}_g^{+}$–$d^3{\mathrm{\Pi <!--\; ??\; -->}}_u$ excitation, and significant cascade excitation occurs at the $d^3{\mathrm{\Pi <!--\; ??\; -->}}_u$(v = 0,1) levels. Kinetic energy (E_k) distributions of H atoms produced via predissociation of the $d^3{\mathrm{\Pi <!--\; ??\; -->}}_u$ state and the $d^3{\mathrm{\Pi <!--\; ??\; -->}}_u$−$a{}^3{\mathrm{\Sigma <!--\; ??\; -->}}_g^{+}$−$b{}^3{\mathrm{\Sigma <!--\; ??\; -->}}_u^{+}$ cascade dissociative emission are obtained. Predissociation of the $d^3{\mathrm{\Pi <!--\; ??\; -->}}_u$ state produces H atoms with an average E_k of 2.3 ± 0.4 eV/atom, while the E_k distribution of the $d^3{\mathrm{\Pi <!--\; ??\; -->}}_u$−$a{}^3{\mathrm{\Sigma <!--\; ??\; -->}}_g^{+}$−$b{}^3{\mathrm{\Sigma <!--\; ??\; -->}}_u^{+}$ channel is similar to that of the $X^1{\mathrm{\Sigma <!--\; ??\; -->}}_g^{+}$–$a{}^3{\mathrm{\Sigma <!--\; ??\; -->}}_g^{+}$−$b{}^3{\mathrm{\Sigma <!--\; ??\; -->}}_u^{+}$ channel and produces H(1s) atoms with an average E_k of 1.15 ± 0.05 eV/atom. On average, each H₂ excited to the $d^3{\mathrm{\Pi <!--\; ??\; -->}}_u$ state in an H₂-dominated atmosphere deposits 3.3 ± 0.4 eV into the atmosphere, while each H₂ directly excited to the $a{}^3{\mathrm{\Sigma <!--\; ??\; -->}}_g^{+}$ state gives 2.2–2.3 eV to the atmosphere. The spectral distribution of the calculated $a{}^3{\mathrm{\Sigma <!--\; ??\; -->}}_g^{+}$ –$b{}^3{\mathrm{\Sigma <!--\; ??\; -->}}_u^{+}$ continuum emission due to the $X^1{\mathrm{\Sigma <!--\; ??\; -->}}_g^{+}$–$d^3{\mathrm{\Pi <!--\; ??\; -->}}_u$ excitation is significantly different from that of direct $a{}^3{\mathrm{\Sigma <!--\; ??\; -->}}_g^{+}$ excitation.