Section: 9 | Atomic Radii of the Elements |

How to Cite this Reference

ATOMIC RADII OF THE ELEMENTS

Manjeera Mantina, Rosendo Valero, Christopher J. Cramer, and Donald G. Truhlar

Atomic radii are not precisely defined but are nevertheless very widely used parameters in modeling and understanding molecular structure and interactions. Three main classes of radii may be identified: van der Waals radii (which include radii used to characterize steric interactions), covalent radii, and ionic radii. This table is concerned with the first two; ionic radii are covered in a table in Section 12 of the CRC Handbook called “Ionic Radii in Crystals.”

There are many scales of van der Waals radii, but they are not fully consistent with one another. The van der Waals radii determined by Bondi (Ref. 1) from x-ray diffraction data, crystal densities, gas kinetic collision cross sections, critical densities, and liquid-state properties are the most widely used values, but Bondi recommended radius values for only 28 of the 44 main-group elements in the periodic table plus 9 transition metals and one actinide. Rowland and Taylor (Ref. 2) redetermined nine of the main-group radii from crystal structure data and recommended that Bondi’s values be accepted except for H, for which they recommended a new value; we accepted their recommendation for H and adopted Bondi’s 27 other values for main-group elements. Radii for the 16 remaining main-group elements were determined from electronic structure calculations on selected van der Waals molecules by analyzing the results in a way designed to yield radii compatible with Bondi’s scale for main-group elements (Ref. 3). Bondi’s values for the transition metals and actinide are smaller than expected based on ionization potentials and covalent radii, so we do not adopt them, but defer to later recommendations based on analysis of a more extensive set of crystal data. Van der Waals radii for the remaining elements through atomic number Z = 93 were taken from Hu et al. (Ref. 4), who determined them from bond valence parameters (this gives radii usually within 0.1 Å to 0.15 Å of the radii from average atomic volumes in crystals as obtained by statistical analysis of the Cambridge Structural Database (Ref. 5), but the results show a smoother variation with atomic number). Van der Waals radii for the elements with Z = 94 to 103 were based on the work of Guzei and Wendt (Ref. 6), who modeled the zero-potential distance for the interaction potentials involved in nonbonded steric interactions; we increased their values by 6%, which is the value they found is needed to make their steric radii scale most consistent with Bondi’s van der Waals radii.

Covalent radii are more straightforward, especially for elements that tend to form only single bonds, although some researchers distinguish metallic bonds from covalent bonds. The covalent radii tabulated here are recommendations for single covalent bonds, and they are based on a comprehensive evaluation of experimental data by Cordero et al. (Ref. 7), who recommended covalent radii for all elements up to Z = 96, and on an analysis combining experimental data and theoretical calculations by Pyykkö and Atsumi (Ref. 8), who recommended single-bond covalent radii for all elements up to Z = 118. If one is interested in a specific coordination number, oxidation state, or type of ligand, one might find a more appropriate radius in the specialized literature or in the “Characteristic Bond Lengths in Free Molecules” table in this section because the values in the table below are generic average values. In particular, we give the Pyykkö-Atsumi values for carbon and for Z = 97 to 118 and an average of the values from the two sources for all other elements. For Mn, Fe, and Co, Cordero et al. give two values, and we used the lower of these on the average because it corresponds to a smoother periodic trend.

Please note that the van der Waals radii of bromine and lithium have typographical errors in Ref. 3; the correct values (1.85 for Br and 1.82 for Li) in the table below are from Ref. 1.

All values are rounded to the nearest 0.01 Å, but in most cases the uncertainty in the value is of the order of 0.1 Å. Column definitions for the table are as follows.

Column heading	Definition
Name	Element name; elements are listed alphabetically by name
Symbol	Atomic symbol
R_vdw	van der Waals radius, in Å
R_cov	Covalent radius, in Å

References

Bondi, A., J. Phys. Chem. 68, 441, 1964. [https://doi.org/10.1021/j100785a001]
Rowland, R. S., and Taylor, R., J. Phys. Chem. 100, 7384, 1996. [https://doi.org/10.1021/jp953141+]
Mantina, M., Chamberlin, A. C., Valero, R., Cramer, C. J., and Truhlar, D. G., J. Phys. Chem., A 113, 5806, 2009. [https://doi.org/10.1021/jp8111556]
Hu, S.-Z., Zhou, Z.-H., and Robertson, B. E., Z. Kristallogr. 224, 375, 2009. [https://doi.org/10.1524/zkri.2009.1158]
Hu, S.-Z., Zhou, Z-.H., and Tsai, K.-R., Acta Physico-Chimica Sinica 19, 1073, 2003.
Guzei, I. A. and Wendt, M., Dalton Trans., 2006, 3991, 2006. [https://doi.org/10.1039/b605102b]
Cordero, B., Gómez, V., Platero-Prats, A. E., Revés, M., Echeverría, J., Cremades, E., Barragán, F., and Alvarez, S., Dalton Trans. 2008, 2832, 2008. [https://doi.org/10.1039/b801115j]
Pyykkö, P., and Atsumi, M., Chem. Eur. J. 15, 186, 2009. [https://doi.org/10.1002/chem.200800987]

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Van der Waals and Covalent Radii of the Elements

Name	Symbol	R_vdw/Å	R_cov/Å
Continued on next page...
Actinium	Ac	2.47	2.01
Aluminum	Al	1.84	1.24
Americium	Am	2.44	1.73
Antimony	Sb	2.06	1.40
Argon	Ar	1.88	1.01
Arsenic	As	1.85	1.20
Astatine	At	2.02	1.48
Barium	Ba	2.68	2.06
Berkelium	Bk	2.44	1.68
Beryllium	Be	1.53	0.99
Bismuth	Bi	2.07	1.50
Bohrium	Bh		1.41
Boron	B	1.92	0.84
Bromine	Br	1.85	1.17
Cadmium	Cd	2.18	1.40
Calcium	Ca	2.31	1.74
Californium	Cf	2.45	1.68
Carbon	C	1.70	0.75
Cerium	Ce	2.42	1.84

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