Electron-impact excitation of H_2_ triplet states plays an important role in the heating of outer planet upper thermospheres. The d^3^{Pi}u state is the third ungerade triplet state, and the d^3^{Pi}u-a^3^{Sigma}g^+^ emission is the largest cascade channel for the a^3^{Sigma}g^+^ state. Accurate energies of the d^3^{Pi}u^-^(v, J) levels are calculated from an ab initio potential energy curve. Radiative lifetimes of the d^3^{Pi}u(v,J) levels are obtained by an accurate evaluation of the d^3^{Pi}u-a^3^{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^{Pi}u-a^3^{Sigma}g^+^ spectra at 20eV impact energy. Spectral analysis revealed that multipolar components beyond the dipolar term are required to model the X^1^{Sigma}g^+^-d^3^{Pi}u excitation, and significant cascade excitation occurs at the d^3^{Pi}u (v=0,1) levels. Kinetic energy (E_k_) distributions of H atoms produced via predissociation of the ^3^{Pi}u state and the d^3^{Pi}u-a^3^{Sigma}g^+^-b^3^{Sigma}u^+^ cascade dissociative emission are obtained. Predissociation of the d^3^{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^{Pi}u-a^3^{Sigma}g^+^-b^3^{Sigma}u^+^ channel is similar to that of the X^1^{Sigma}g^+^-a^3^{Sigma}g^+^-b^3^{Sigma}u^+^ channel and produces H(1s) atoms with an average E_k_ of 1.15+/-0.05eV/atom. On average, each H_2_ excited to the d^3^{Pi}u state in an H_2_-dominated atmosphere deposits 3.3+/-0.4eV into the atmosphere, while each H_2_directly excited to the a^3^{Sigma}g^+^ state gives 2.2-2.3eV to the atmosphere. The spectral distribution of the calculated a^3^{Sigma}g^+^-b^3^{Sigma}u^+^ continuum emission due to the X^1^{Sigma}g^+^-d^3^{Pi}u excitation is significantly different from that of direct a^3^{Sigma}g^+^ excitation.