657, a method for estimating tetrahedral bond angles

Abstract

A regular tetrahedron has six spatial angles. The sum of these spatial angles for a tetrahedron with all four groups the same (CA₄) is 6 × 109.4712206°. To the nearest degree that value is 657°. For a tetrahedron with one group different (CA₃B), there are two different bond angles. The sum of these two angles can be approximated to be 219°, one third of 657°. For a tetrahedron with disubstitution by the same group (CA₂B₂), the approximate sum involves three different angles: ∠ACA +  ∠BCB + 4 ∠ACB = 657°. For a tetrahedron with disubstitution by two different groups (CA₂BD), the approximate sum uses four different angles: ∠ACA +  ∠BCD + 2 ∠ACB + 2 ∠ACD = 657°. For a tetrahedron with all groups different (CABDE), the approximate sum comes from six angles. Examples of each type are given along with the limitations of the method.