Feature Tutorials

Elements, Atomic Radii and the Periodic Table

How big is an atom? Why does its size vary? How can we show this in CrystalMaker?

Periodic Table of the Elements

The Periodic Table of the Elements, showing relative atom sizes. Click the image to display a high-resolution version. Previous Table | Next Table (requires JavaScript enabled).

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How big is an atom? A simple question maybe, but the answer is not at all straighforward. To a first approximation we can regard atoms as "hard spheres", with an outer radius defined by the outer electron orbitals. However, even for atoms of the same type, atomic radii can differ, depending on the oxidation state, the type of bonding and - especially important in crystals - the local coordination environment.

Take the humble carbon atom as an example: in most organic molecules a covalently-bonded carbon atom is around 1.5 Ångstroms in diameter (1 Ångstrom unit = 0.1 nanometres = 10-10 metres); but the same atom in an ionic crystal appears much smaller: around 0.6 Ångstroms. In the following article we'll explore a number of different sets of distinct atomic radius sizes, and later we'll see how you can make use of these "preset" values with CrystalMaker.

Atomic Radii

Atomic radii represent the sizes of isolated, electrically-neutral atoms, unaffected by bonding topologies. The general trend is that atomic sizes increase as one moves downwards in the Periodic Table of the Elements, as electrons fill outer electron shells. Atomic radii decrease, however, as one moves from left to right, across the Periodic Table. Although more electrons are being added to atoms, they are at similar distances to the nucleus; and the increasing nuclear charge "pulls" the electron clouds inwards, making the atomic radii smaller.

Atomic radii are generally calculated, using self-consistent field functions. CrystalMaker uses Atomic radii data from two sources:

  1. VFI Atomic Radii:
    Vainshtein BK, Fridkin VM, Indenbom VL (1995) Structure of Crystals (3rd Edition). Springer Verlag, Berlin.

  2. CPK Atomic Radii:
    Clementi E, Raimondi DL, Reinhardt WP (1963). Journal of Chemical Physics 38:2686-

Covalent Radii

The covalent radius of an atom can be determined by measuring bond lengths between pairs of covalently-bonded atoms: if the two atoms are of the same kind, then the covalent radius is simply one half of the bond length.

Whilst this is straightforward for some molecules such as Cl2 and O2, in other cases one has to infer the covalent radius by measuring bond distances to atoms whose radii are already known (e.g., a C--X bond, in which the radius of C is known).

CrystalMaker uses covalent radii listed on CrystalMaker-user Mark Winter's excellent Web Elements website.

Van-der-Waals Radii

Van-der-Waals radii are determined from the contact distances between unbonded atoms in touching molecules or atoms. CrystalMaker uses Van-der-Waals Radii data from:

Bondi A (1964) Journal of Physical Chemistry 68:441-

Atomic-Ionic Radii

These are the "realistic" radii of atoms, measured from bond lengths in real crystals and molecules, and taking into account the fact that some atoms will be electrically charged. For example, the atomic-ionic radius of chlorine (Cl-) is larger than its atomic radius.

The bond length between atoms A and B is the sum of the atomic radii,

dAB = rA + rB

CrystalMaker uses Atomic-Ionic radii data from:

Slater JC (1964) Journal of Chemical Physics 39:3199-

Crystal Radii

Perhaps the most authoritative and highly-respected set of atomic radii are the "Crystal" Radii published by Shannon and Prewitt (1969) - one of the most cited papers in all crystallography - with values later revised by Shannon (1976). These data, originally derived from studies of alkali halides, are appropriate for most inorganic structures, and provide the basis for CrystalMaker's default Element Table. The data are published in:

Shannon RD Prewitt CT (1969) Acta Crystallographica B25:925-946

Shannon RD (1976) Acta Crystallographica A23:751-761

The Colours of Atoms

Colour-coding atoms by element type is an important way of representing structural information. Of course, atoms don't have "colour" in the conventional sense, but various conventions have been established in different disciplines.

Many organic chemists use the so-called CPK colour scheme These colours are derived from those of plastic spacefilling models developed by Corey, Pauling and (later improved on by) Kultun ("CPK").

Whilst the standard CPK colours are limited to the elements found in organic compounds, CrystalMaker's VFI Atomic Radii, CSD Default Radii and Shannon & Prewitt Crystal Radii Element Tables provide a more diverse range of contrasting colours.

Editing Colours & Radii in CrystalMaker

You can easily change the colour and/or radius of a crystal site, or group of sites, using CrystalMaker's Site Browser (to make this visible, choose: Window > Sidebar > Site Browser). The pane shows an hierarchical listing of element types and sites. Each element row has a colour button, which you can use to change the colours for all atoms with that element type. You can edit the radius of atoms of that element type using the radius field "r [Å]".

Site Browser pane

Editing the radii for all oxygen atoms in a structure, using CrystalMaker's Site Browser.

You can edit the colours and/or radii for specific crystal sites, by using the colour/radius fields on a site row. You can also change the colours of individually-selected atoms in your structure, using the Selection > Atoms > Colour command.

Element Tables

Whilst CrystalMaker lets you edit individual atomic radii (and colours), for greater convenience you'll probably want to specify a default set of atomic radii and colours. CrystalMaker includes a number of different "Element Tables", and you can edit these or create your own, using the Element Editor (Edit > Elements).

Edit Elements Window

Editing the default radius of hydrogen, using CrystalMaker's Element Editor.

This floating window displays the currently-active Element Table: a list of element symbols, atomic radii and colours. At the top of the window is a popup menu, which lists the different Element Tables that are included with the program; you can switch between any of these by choosing them from the popup menu.

Once you've loaded an Element Table (e.g., by choosing its name from the popup menu), you can make this your default set by clicking the Save button. The default set is saved in your CrystalMaker Preferences file, ready for use the next time you use the program.

You can apply the current colours and radii to a currently-displayed structure, by clicking the Apply button.

You can also import or export tables of element data (see the CrystalMaker User's Guide for more information on the format required).

More than Just Pretty Colours

It is important to choose the correct, default, Element Table for more than just aesthetic reasons. When auto-generating bonds, CrystalMaker uses the sum of atomic radii (plus 15%) to estimate the maximum search distances. If your default set isn't right, then you may find that not all bonds are generated in the way you'd expect.

Organic Structures Alert! CrystalMaker's default Element Table is the Shannon & Prewitt "Crystal" radii, which is appropriate for most inorganic structures. When working with organic structures, one of the covalent or Van-der-Waals sets will be more appropriate.

Related Link

Table of Atomic Radii

The following table contains some of the atomic radius data used by CrystalMaker. This is a brief summary of a far more extensive body of work - please see the notes at the end of this page for more information.

Atomic
Number
Element
Symbol
Atomic
Radius [Å]
Ionic
Radius [Å]
Covalent
Radius [Å]
Van-der-Waals
Radius [Å]
"Crystal"
Radius [Å]
1H 0.530.250.371.200.10
2He0.310.310.321.40
3Li1.671.451.341.820.90
4Be1.121.050.90 0.41
5B 0.870.850.820.25
6C 0.670.700.771.700.29
7N 0.560.650.751.550.30
8O 0.480.600.731.521.21
9F 0.420.500.711.471.19
10Ne0.380.380.691.54
11Na1.901.801.542.271.16
12Mg1.451.501.301.730.86
13Al1.181.251.180.53
14Si1.111.101.112.100.40
15P 0.981.001.061.800.31
16S 0.881.001.021.800.43
17Cl0.791.000.991.751.67
18Ar0.710.710.971.88
19K 2.432.201.962.751.52
20Ca1.941.801.741.14
21Sc1.841.601.440.89
22Ti1.761.401.360.75
23V 1.711.351.250.68
24Cr1.661.401.270.76
25Mn1.611.401.390.81
26Fe1.561.401.250.69
27Co1.521.351.260.54
28Ni1.491.351.211.630.70
29Cu1.451.351.381.400.71
30Zn1.421.351.311.390.74
31Ga1.361.301.261.870.76
32Ge1.251.251.220.53
33As1.141.151.191.850.72
34Se1.031.151.161.900.56
35Br0.941.151.141.851.82
36Kr0.880.881.102.02
37Rb2.652.352.111.66
38Sr2.192.001.921.32
39Y 2.121.851.621.04
40Zr2.061.551.480.86
41Nb1.981.451.370.78
42Mo1.901.451.450.79
43Tc1.831.351.560.79
44Ru1.781.301.260.82
45Rh1.731.351.350.81
46Pd1.691.401.311.630.78
47Ag1.651.601.531.721.29
48Cd1.611.551.481.580.92
49In1.561.551.441.930.94
50Sn1.451.451.412.170.69
51Sb1.331.451.380.90
52Te1.231.401.352.061.11
53I 1.151.401.331.982.06
54Xe1.081.081.302.160.62
55Cs2.982.602.251.81
56Ba2.532.151.981.49
57La1.951.951.691.36
58Ce1.851.85 1.15
59Pr2.471.85 1.32
60Nd2.061.85 1.30
61Pm2.051.85 1.28
62Sm2.381.85 1.10
63Eu2.311.85 1.31
64Gd2.331.80 1.08
65Tb2.251.75 1.18
66Dy2.281.75 1.05
67Ho2.261.75 1.04
68Er2.261.75 1.03
69Tm2.221.75 1.02
70Yb2.221.75 1.13
71Lu2.171.751.601.00
72Hf2.081.551.500.85
73Ta2.001.451.380.78
74W 1.931.351.460.74
75Re1.881.351.590.77
76Os1.851.301.280.77
77Ir1.801.351.370.77
78Pt1.771.351.281.750.74
79Au1.741.351.441.661.51
80Hg1.711.501.491.550.83
81Tl1.561.901.481.961.03
82Pb1.541.801.472.021.49
83Bi1.431.601.46 1.17
84Po1.351.90 1.08
85At1.271.27 0.76
86Rn1.201.201.45
87Fr 1.94
88Ra 2.15 1.62
89Ac1.951.95 1.26
90Th1.801.80 1.19
91Pa1.801.80 1.09
92U1.751.75 1.860.87
93Np1.751.75
94Pu1.751.75 1.00
95Am1.751.75 1.12
96Cm 1.11

Notes

  1. Atomic Radii: values are calculated from:

    E Clementi, D L Raimondi, W P Reinhardt (1963) J Chem Phys. 38:2686.

  2. Ionic Radii: these data are taken from an empirical system of unified atomic-ionic radii, which is suitable for describing anion-cation contacts in ionic structures. The data were derived by the comparison of bond lengths in over 1200 bond types in ionic, metallic, and covalent crystals and molecules by:

    J C Slater (1964) J Chem Phys 41:3199

    J C Slater (1965) Quantum Theory of Molecules and Solids. Symmetry and Bonds in Crystals. Vol 2. McGraw-Hill, New York.

    Note that calculated data have been used for the following elements: He, Ne, Ar, Kr, Xe, At and Rn. These data were taken from:

    E Clementi, D L Raimondi, W P Reinhardt (1963) J Chem Phys 38:2686

  3. Covalent Radii: Data given here are taken from WebElements, copyright Mark Winter, University of Sheffield, UK.

  4. Van-der-Waals Radii: Van der Waals radii are established from contact distances between non-bonding atoms in touching molecules or atoms. Most data here are from:

    A Bondi (1964) J Phys Chem 68:441

  5. "Crystal" Radii: These data are taken from Shannon & Prewitt's (S∓P) seminal work on "physical" ionic radii, as determined from measurements of real structures.

    Note that in most cases S∓P quote different radii for the same element: the radii vary according to charge and coordination number. We have chosen the most-common charges (oxidation states) and coordination numbers. The details are given in the element text file after each data entry.

    R D Shannon and C T Prewitt (1969) Acta Cryst. B25:925-946

    R D Shannon (1976) Acta Cryst. A23:751-761

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