Approaching Sixfold Chemical Bonding: Metal Dimers MM' Involving Group 4–8 Transition Metals and the Actinides Th–Np. Additive Covalent Radii r6

A set of additive covalent radii is fitted to a combination of experimental data, accurate ab initio computations, and more approximate DFT MM' bond lengths, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:semantics><mml:mi>R</mml:mi> <mml:annotation>$R$</mml:annotation></mml:semantics> </mml:math> , with 12 valence electrons in approximately <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msup><mml:mrow><mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mi>σ</mml:mi> <mml:mo>)</mml:mo></mml:mrow> <mml:mn>2</mml:mn></mml:msup> <mml:msup><mml:mrow><mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mi>σ</mml:mi> <mml:mo>)</mml:mo></mml:mrow> <mml:mn>2</mml:mn></mml:msup> <mml:msup><mml:mi>π</mml:mi> <mml:mn>4</mml:mn></mml:msup> <mml:msup><mml:mi>δ</mml:mi> <mml:mn>4</mml:mn></mml:msup> </mml:mrow> <mml:annotation>$(1\sigma)^2 (2\sigma)^2 \pi ^4 \delta ^4$</mml:annotation></mml:semantics> </mml:math> molecular orbitals. These <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msub><mml:mi>r</mml:mi> <mml:mn>6</mml:mn></mml:msub> <mml:annotation>$r_6$</mml:annotation></mml:semantics> </mml:math> are typically 10-20 pm shorter than the previous triple-bond radii <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:msub><mml:mi>r</mml:mi> <mml:mn>3</mml:mn></mml:msub> <mml:annotation>$r_3$</mml:annotation></mml:semantics> </mml:math> . Values for the elements Ti-Fe, Zr-Ru, Hf-Os, and Th-Np are fitted. Extrapolated values for suitable cases in Group 3 (including rare earths) and Group 9 plus Pu are also proposed.