COSMO Atomic radii

Following a discussion on the ADF mailing list, where the origin of the atomic radii used within ADF with COSMO was asked for, here is a short description.

It all started with a preliminary report in the SuppInfo of

R.S. Bon, B. van Vliet, N.E. Sprenkels, R.F. Schmitz, F.J.J. de Kanter, C.V. Stevens, M. Swart, F.M. Bickelhaupt, M.B. Groen and R.V.A. Orru
"Multicomponent Synthesis of 2-Imidazolines"
J. Org. Chem. 2005, 70, 3542-3553
http://www.dx.doi.org/10.1021/jo050132g

where we tested an approach towards "non-empirical" choice of atomic radii. This was extended for the whole periodic table in

M. Swart, E. Rösler and F.M. Bickelhaupt
"Proton Affinities in Water of Maingroup-Element Hydrides. Effects of Hydration and Methyl Substitution"
Eur. J. Inorg. Chem. 2007, 3646-3654
http://www.dx.doi.org/10.1002/ejic.200700228 

where we used scaled MM3 radii (Allinger et al. J. Mol. Str. (Theochem) 1994, 312, 69-83). The scaling was necessary because of the form of the repulsion force field used in MM3, leading to a scaling factor 0.8333 (5/6).

Not all elements were included in the MM3 data, which was the origin for the question to the ADF mailing list (Berkelium was one of the elements that was absent). Fortunately, Santiago Alvarez reported in 2013 a new list of van der Waals radii for almost the complete Periodic Table.

S. Alvarez
"A cartography of the van der Waals territories"
Dalton Trans. 2013, 42, 8617-8636
http://www.dx.doi.org/10.1039/c3dt50599e

This was followed one year later by a report on the vdW radii for noble gases.

J. Vogt, S. Alvarez
"van der Waals Radii of Noble Gases"
Inorg. Chem. 2014, 53, 9260-9266

For completeness sake, the full list of scaled MM3 radii for the elements is given below (in Å, angstrom), together with Alvarez's values in brackets []; the Alvarez values are in general larger (except for hydrogen). One should be careful when using the latter values within COSMO calculations in ADF, whose parameters of the solvent radius etc have been obtained with the scaled MM3 radii.

    H   1.350
    He  1.275
    Li  2.125
    Be  1.858
    B   1.792
    C   1.700
    N   1.608
    O   1.517
    F   1.425
    Ne  1.333
    Na  2.250
    Mg  2.025
    Al  1.967
    Si  1.908
    P   1.850
    S   1.792
    Cl  1.725
    Ar  1.658
    K   2.575
    Ca  2.342
    Sc  2.175
    Ti  1.992
    V   1.908
    Cr  1.875
    Mn  1.867
    Fe  1.858
    Co  1.858
    Ni  1.850
    Cu  1.883
    Zn  1.908
    Ga  2.050
    Ge  2.033
    As  1.967
    Se  1.908
    Br  1.850
    Kr  1.792
    Rb  2.708
    Sr  2.500
    Y   2.258
    Zr  2.117
    Nb  2.025
    Mo  1.992
    Tc  1.967
    Ru  1.950
    Rh  1.950
    Pd  1.975
    Ag  2.025
    Cd  2.083
    In  2.200
    Sn  2.158
    Sb  2.100
    Te  2.033
    I   1.967
    Xe  1.900
    Cs  2.867
    Ba  2.558
    La  2.317
    Ce  2.283
    Pr  2.275
    Nd  2.275
    Pm  2.267
    Sm  2.258
    Eu  2.450
    Gd  2.258
    Tb  2.250
    Dy  2.242
    Ho  2.225
    Er  2.225
    Tm  2.225
    Yb  2.325
    Lu  2.208
    Hf  2.108
    Ta  2.025
    W   1.992
    Re  1.975
    Os  1.958
    Ir  1.967
    Pt  1.992
    Au  2.025
    Hg  2.108
    Tl  2.158
    Pb  2.283
    Bi  2.217
    Po  2.158
    At  2.092
    Rn  2.025
    Fr  3.033
    Ra  2.725
    Ac  2.567
    Th  2.283
    Pa  2.200
    U   2.100
    Np  2.100
    Pu  2.100