Equation Icon  1- 2 m1m2-- E = 2 m1v 1 − 2r [ 12 2 ( ) ] + ε2 3-m1v4 + m-1m2-+ m1m2-- 3v2− 7(⃗v1 ⋅⃗v2) − 1(⃗n12 ⋅⃗v1)(⃗n12 ⋅⃗v2) 8 1 2r212 2r12 1 2 2 [ 5 m3 m 19m2 m2 + ε4 ---m1v61 − --13-2− ----13--2 16 ( 2r12 8r12 ) m21m2 2 7 2 29 2 13 2 + ---2-- − 3v1 + -v2 + ---(⃗n12 ⋅⃗v1) − ---(⃗n12 ⋅⃗v1)(⃗n12 ⋅⃗v2) + (⃗n12 ⋅⃗v2) 2r12 ( 2 2 2 m1m2-- 3- 3 3- 2 2 9- 2 + 4r12 2(⃗n12 ⋅⃗v1) (⃗n12 ⋅⃗v2) + 4 (⃗n12 ⋅⃗v1) (⃗n12 ⋅⃗v2) − 2 (⃗n12 ⋅⃗v1)(⃗n12 ⋅ ⃗v2)v 1 13 21 13 − ---(⃗n12 ⋅⃗v2)2v21 +---v41 + --(⃗n12 ⋅⃗v1)2(⃗v1 ⋅⃗v2) 2 2 2 )] 55- 2 17- 2 31- 2 2 + 3(⃗n12 ⋅⃗v1)(⃗n12 ⋅⃗v2)(⃗v1 ⋅⃗v2) − 2 v1(⃗v1 ⋅⃗v2) + 2 (⃗v1 ⋅⃗v2) + 4 v1v 2 [ 4 3 2 + ε6 -35-m v8+ 3m-1m2- + 469m-1m-2- 128 1 1 8r412 18r412 m2 m2 ( 547 3115 123π2 + --13-2 ----(⃗n12 ⋅⃗v1)2 −-----(⃗n12 ⋅⃗v1)(⃗n12 ⋅⃗v2) −------(⃗n12 ⋅⃗v1)(⃗n12 ⋅ ⃗V) 2r12 6 24 ) 32 575 2 41π2 4429 − ----v1 + -----(V⃗ ⋅⃗v2) + ----(⃗v1 ⋅⃗v2) ( 9 32 72 m31m2- 437- 2 317- 2 301- 2 + 2r3 − 4 (⃗n12 ⋅⃗v1) + 4 (⃗n12 ⋅⃗v1)(⃗n12 ⋅⃗v2) + 3(⃗n12 ⋅⃗v2) + 12 v1 12 ) − 337-(⃗v ⋅⃗v ) + 5-v2 12 1 2 2 2 m m ( 5 5 5 + --1--2 − --(⃗n12 ⋅⃗v1)5(⃗n12 ⋅⃗v2) −---(⃗n12 ⋅⃗v1)4(⃗n12 ⋅⃗v2)2 −--(⃗n12 ⋅⃗v1)3(⃗n12 ⋅⃗v2)3 r12 16 16 32 19- 3 2 15- 2 2 2 + 16 (⃗n12 ⋅⃗v1) (⃗n12 ⋅⃗v2)v 1 + 16 (⃗n12 ⋅⃗v1)(⃗n12 ⋅⃗v2) v1 3 19 21 + --(⃗n12 ⋅⃗v1)(⃗n12 ⋅⃗v2)3v21 +---(⃗n12 ⋅⃗v2)4v21 −---(⃗n12 ⋅⃗v1)(⃗n12 ⋅⃗v2)v41 4 16 16 − 2(⃗n ⋅⃗v )2v4 + 55v6 − 19-(⃗n ⋅⃗v )4(⃗v ⋅⃗v ) − (⃗n ⋅ ⃗v )3(⃗n ⋅⃗v )(⃗v ⋅⃗v ) 12 2 1 16 1 16 12 1 1 2 12 1 12 2 1 2 15- 2 2 45- 2 2 − 32 (⃗n12 ⋅⃗v1) (⃗n12 ⋅ ⃗v2)(⃗v1 ⋅⃗v2) + 16(⃗n12 ⋅⃗v1) v1(⃗v1 ⋅⃗v2) 5 11 139 + --(⃗n12 ⋅⃗v1)(⃗n12 ⋅⃗v2)v21(⃗v1 ⋅⃗v2) +--(⃗n12 ⋅⃗v2)2v21(⃗v1 ⋅⃗v2) −----v41(⃗v1 ⋅⃗v2) 4 4 16 − 3-(⃗n ⋅⃗v )2(⃗v ⋅⃗v )2 + -5-(⃗n ⋅⃗v )(⃗n ⋅ ⃗v )(⃗v ⋅⃗v )2 + 41v2(⃗v ⋅⃗v )2 4 12 1 1 2 16 12 1 12 2 1 2 8 1 1 2 -1- 3 45- 2 2 2 23- 2 2 79- 4 2 + 16 (⃗v1 ⋅⃗v2) − 16(⃗n12 ⋅⃗v1) v1v2 − 32(⃗n12 ⋅⃗v1)(⃗n12 ⋅⃗v2)v1v2 + 16 v1v2 ) − 161-v21v22(⃗v1 ⋅⃗v2) 32 m2 m2 ( 49 75 187 11 + --12--- − --(⃗n12 ⋅⃗v1)4 + --(⃗n12 ⋅⃗v1)3(⃗n12 ⋅⃗v2) − ----(⃗n12 ⋅⃗v1)2(⃗n12 ⋅⃗v2)2 +---v41 r12 8 8 8 2 247- 3 49- 2 2 81- 2 + 24 (⃗n12 ⋅⃗v1)(⃗n12 ⋅⃗v2) + 8 (⃗n12 ⋅⃗v1)v1 + 8 (⃗n12 ⋅⃗v1)(⃗n12 ⋅⃗v2)v1 21 15 3 − ---(⃗n12 ⋅⃗v2)2v21 −---(⃗n12 ⋅⃗v1)2(⃗v1 ⋅⃗v2) −--(⃗n12 ⋅⃗v1)(⃗n12 ⋅⃗v2)(⃗v1 ⋅⃗v2) 4 2 2 + 21-(⃗n12 ⋅⃗v2)2(⃗v1 ⋅⃗v2) − 27v2(⃗v1 ⋅⃗v2) + 55(⃗v1 ⋅⃗v2)2 + 49(⃗n12 ⋅⃗v1)2v2 4 1 2 4 2 27- 2 3- 2 2 55- 2 2 2 − 2 (⃗n12 ⋅⃗v1)(⃗n12 ⋅⃗v2)v2 + 4(⃗n12 ⋅⃗v2)v2 + 4 v1v2 − 28(⃗v1 ⋅⃗v2)v2 135 ) ] + ----v42 16 + (1 ↔ 2) + 𝒪 (ε7). (183 )