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2001•New Journal of ChemistryRequires access

657, a method for estimating tetrahedral bond angles

Edward McNelis, Maureen Blandino

Open publisher page 12 citations

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.

About this research paper

What this paper is about

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.

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OpenAlex reports 12 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Tetrahedron, Chemistry, Group (periodic table), Bond length, Geometry, Crystallography, Mathematics, Crystal structure

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