Accurate long-range coefficients for two excited like isotope He atoms: He($2^{1}P$)--He($2^{1}P$), He($2^{1}P$)--He($2^{3}P$), and He($2^{3}P$)--He($2^{3}P$)

A general formalism is used to express the long-range potential energies in inverse powers of the separation distance between two like atomic or molecular systems with $P$ symmetries. The long-range molecular interaction coefficients are calculated for the molecular symmetries $\mathrm{\Delta }$, $\mathrm{\Pi }$, and $\mathrm{\Sigma }$, arising from the following interactions: He($2^{1}P$)–He($2^{1}P$), He($2 ^1P$)--He($2 ^3P$),andHe($2 ^3P$)--He($2 ^3P$). The electric quadrupole-quadrupole term, $C_5$, the van der Waals (dispersion) term $C_6$, and higher-order terms, $C_8$, and $C_{10}$, are calculated $\mathit{\text{ab}}\mathit{\text{initio}}$ using accurate variational wave functions in Hylleraas coordinates with finite nuclear mass effects. A comparison is made with previously published results where available.