Radius, atomic

Atomic radii. The variation in atomic radii in the representative elements. (Adapted From Ebbing, General Chemistry 9th ed.. 

You have probably noticed that many students try to memorize trends such as those we just discussed. As our network develops, relationships such as that between and atomic radii will become clearer. As previously su ested, try constmcting a paragraph explaining how Ze varies horizontally and vertically and how trends in atomic radius follow. Having done that successfully, you will not need to bother with consciously memorizing such things. You wiU know them because you understand them  

Ionization energies. A plot of ionization energies (in kilojoules per mole) versus atomic number. Ionization energies generally increase across a period and decrease down a group. 

The exception between Groups 5A and 6A is readily explained by referring to the orbital diagram for a Group 6A element shown below  

Variation of the electron affinities (in kilojoules per mole) of the representative elements. (Adapted from Kotz, Chemistry Chemical Reactivity, 9th ed.. Table 14, p. A-21. Copyright 2009 Brooks/CoLe, a part of Cengage Learning, Inc. Reproduced by permission. www.cengage.com/permissions.) 

The atomic radii describe the characteristic size of the neutral and isolated atoms that are not involved in any kind of bonds. The radins of the free atom is considered the distance from the nucleus to the point of maximnm electron radial density of the occnpied atomic orbital. 

The atomic radius cannot be determined directly. The electron cloud is diffuse due to the undulatory waveform nature of the electron, making it impossible to assign a well-dehned outer structure to the atom. One indirect method for the determination of the relative atomic radius is the use of the formula derived from Bohr s atomic model. The formula for the hydrogen atom is the following  

The radius of the hydrogen atom, known as the Bohr radius, is used as a unit of atomic radius. For the other atoms, the calculation of the atomic radius of the free atom involves the relationship  

Although with increasing atomic number in period the number of electrons and number of occupied electrons increase, the atomic radius decreases. This results from the increase in the effective nuclear charge that produces a contraction in periods of the orbitals toward the nucleus. In those cases where the outer electron layer is the same valence layer, the increasing attraction of electrons by the nucleus leads to a decrease in atomic radius. In groups, the atomic radius increases due to the increasing number of electronic layers. 

A special case is that of lanthanides where the 4f subshell is occupied progressively before the filling of the 5d orbital from cerium (Z=58) to lutetium (Z=71) (Table 2.9). The f orbitals have weak shielding and penetration properties so that the electrons are 

The table below shows four sets of radii of different types, taken from a few selected sources  

T almost always an element from the transition groups 4, 5, or 6 [3]. Further sets, modifying the original Geller [8] radii, differ from the tabulated one and among each other. They contain, however, consistent Pd radii, r = 1.3783 0]. 1-374 [11]. 

This book is mainly concerned with intermolecular effects, and therefore with atomic radii in connection with intermolecular contacts. These are sometimes called non-bonding radii, because they refer to contacts between atoms that are not joined by ordinary chemical bonds. For historical reasons they are also sometimes called van der Waals radii in honor of the famous pioneer of intermolecular interaction studies. A non-bonding atomic radius is rather vaguely defined as the radius of a sphere representing the usual space occupation by each atom in a molecule, so that the spheres of neighboring non-bonded atoms may not overlap. This refers both to intermolecular overlap in condensed phases, and to overlap between atoms in distant parts of the same molecule. A sensible procedure for the determination of these radii uses a careful analysis of the geometrical conditions of proximity between pairs of 

Now there is no sound theoretical foundation at the basis of the concept of the atomic radius, and it is thus wholly an empirically established fact that the distances between dissimilar atoms calculated with these atomic radii usually agree well with the values found (within i 0.02 A). 

A revision of Pauling s table has been proposed by Stevenson and Schomaker, in which the strict additivity has been abandoned and in which the influence of the polarity has been taken into account, simultaneously with the above alteration in the radii for O, N and F (see footnote to Table 16). 

In most cases, in particular for organic molecules, this improved formula gives results which differ but little from those derived from the original table. 

The relation between atomic separation and bond type (p. 211) for the C—C bond was originally empirically established by plotting for this separation 1.54 A for a single bond, 1.39 A in benzene and 1.34 A for a double bond against o, x/2 and 1 for the double bond character. A fourth point is formed by the distance 1.42 A at 1/3 double bond character for graphite 

The nature of the relation so found can also be made plausible theoretically and so this curve, deformed proportionally, can certainly also be used for other bonds. 

The effective nuclear charge, Z ff, experienced by an electron in an outer shell is less than the actual nuclear charge, Z. This is because the amucaon of outer-shell electrons by the nucleus is partly counterbalanced by the repulsion of the outer-shell electrons by electrons in inner shells. We say that the electrons in inner shells screen, or shield, electrons in outer shells from the full effect of the nuclear charge. This concept of a screening, or shielding, effect helps us understand many periodic trends in atomic properties. 

Sodium, element number 11, has ten electrons in inner shells, ls 2s 2p, and one electron in an outer shell, 3r. The ten inner-shell electrons of the sodium atom screen (shield) the outer-shell electron from most of the 11 -t- nuclear charge. Recall from Chapter 4 that the third shell n = 3) is farther from the nucleus than the second shell (n = 2). Thus, we see why sodium atoms are larger than lithium atoms. Similar reasoning explains why potassium atoms are larger than sodium atoms and why the sizes of the elements in each column of the periodic table are related in a similar way. 

The radius of an atom, r, is taken as half of the distance between nuclei in homonaclear molecules such as CI2. 

Within a family (vertical group on the periodic table) of representative elements, atomic radii increase from top to bottom as electrons are added to shells farther from the nucleus. 

Unless otheiwise noted, all content on this page Is Cengage Learning. 

A similar trend occurs in the 18-membered periods, but there are slight increases at the end of each group of transition metals (for example, Rh, 1.24 A Pd, 1.28 A Ag, 1.34 A), probably due to increased efficiency of screening as the inner d orbitals are becoming filled. 

Within a given family, the-heavier elements have the larger atomic 

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The wave function T i oo ( = 11 / = 0, w = 0) corresponds to a spherical electronic distribution around the nucleus and is an example of an s orbital. Solutions of other wave functions may be described in terms of p and d orbitals, atomic radii Half the closest distance of approach of atoms in the structure of the elements. This is easily defined for regular structures, e.g. close-packed metals, but is less easy to define in elements with irregular structures, e.g. As. The values may differ between allo-tropes (e.g. C-C 1 -54 A in diamond and 1 -42 A in planes of graphite). Atomic radii are very different from ionic and covalent radii. 

Since taking simply ionic or van der Waals radii is too crude an approximation, one often rises basis-set-dependent ab initio atomic radii and constnicts the cavity from a set of intersecting spheres centred on the atoms [18, 19], An alternative approach, which is comparatively easy to implement, consists of rising an electrical eqnipotential surface to define the solnte-solvent interface shape [20],... 

Tables 2.1, 2.2, 2.3 and 2.4 give data for atomic radii, ionisation energies and electron affinities which allow these rough rules to be justified.

The Universal Force Field, UFF, is one of the so-called whole periodic table force fields. It was developed by A. Rappe, W Goddard III, and others. It is a set of simple functional forms and parameters used to model the structure, movement, and interaction of molecules containing any combination of elements in the periodic table. The parameters are defined empirically or by combining atomic parameters based on certain rules. Force constants and geometry parameters depend on hybridization considerations rather than individual values for every combination of atoms in a bond, angle, or dihedral. The equilibrium bond lengths were derived from a combination of atomic radii. The parameters [22, 23], including metal ions [24], were published in several papers. 

A. rather complex procedure is used to determine the Born radii a values of which. calculated for each atom in the molecule that carries a charge or a partial charge. T Born radius of an afom (more correctly considered to be an effective Born radii corresponds to the radius that would return the electrostatic energy of the system accordi to the Bom equation if all other atoms in the molecule were uncharged (i.e. if the other ato only acted to define the dielectric boundary between the solute and the solvent). In Sti force field implementation, atomic radii from the OPLS force field are assigned to ec... 

Table 4.6 Atom Radii and Effective Ionic Radii of Elements...

The atom radius of an element is the shortest distance between like atoms. It is the distance of the centers of the atoms from one another in metallic crystals and for these materials the atom radius is often called the metal radius. Except for the lanthanides (CN = 6), CN = 12 for the elements. The atom radii listed in Table 4.6 are taken mostly from A. Kelly and G. W. Groves, Crystallography and Crystal Defects, Addison-Wesley, Reading, Mass., 1970. 

In some force fields, especially those using the Lennard-Jones form in eq. (2.12), the /fg parameter is defined as the geometrical mean of atomic radii, implicitly via the geometrical mean rale used for the C and C2 constants. 

Second, using the fully relativistic version of the TB-LMTO-CPA method within the atomic sphere approximation (ASA) we have calculated the total energies for random alloys AiBi i at five concentrations, x — 0,0.25,0.5,0.75 and 1, and using the CW method modified for disordered alloys we have determined five interaction parameters Eq, D,V,T, and Q as before (superscript RA). Finally, the electronic structure of random alloys calculated by the TB-LMTO-CPA method served as an input of the GPM from which the pair interactions v(c) (superscript GPM) were determined. In order to eliminate the charge transfer effects in these calculations, the atomic radii were adjusted in such a way that atoms were charge neutral while preserving the total volume of the alloy. The quantity (c) used for comparisons is a sum of properly... 

In order to check the consistency and mutual relations of ECIs calculated by various methods, as well as to compare them with experimental data, we have performed calculations for several alloy systems, as diverse as Cu-Nl, Al-Li, Al-Ni, Ni-Pt and Pt-Rh. Here we present the results for Al-Ni, Pt-Rh and Ni-Pt alloys in some detail, because the pair interactions between the first neighbors are dominant in these alloys which makes the interpretation relatively simple. On the other hand, the pair interactions between more distant neighbors and also triplet interactions are important for Al-Li and Cu-Ni. The equilibrium atomic radii, bulk moduli and electronegativities of A1 and Ni are rather different, while Pt and Rh are quite similar in this respect. The Ni and Pt atoms differ mainly by their size. 

A different approach is adopted here. Within the LMTO-ASA method, it is possible to vary the atomic radii in such a way that the net charges are non-random while preserving the total volume of the system . The basic assumption of a single-site theory of electronic structure of disordered alloys, namely that the potential at any site R depends only on the occupation of this site by atom A or B, and is completely independent of the occupation of other sites, is fulfilled, if the net charges... 

Interstitial diffusion is rarely possible when two metals interdiffuse, since their atomic radii are usually of the same order. Several mechanisms have been proposed, but it is now generally accepted that interdiffusion is due to the motion of vacant sites within the lattice, solvent and solute atoms moving as the vacant sites migrate. The diffusion process is thus dependent upon the state of imperfection of the solvent metal and the alloy being formed. 

Atomic radii. The radii are determined by assuming that atoms in closest contact in an element touch one another. The atomic radius is taken to be one half of the closest internuclear distance, (a) Arrangement of copper atoms in metallic copper, giving an atomic radius of 0.128 nm for copper, (b) Chlorine atoms in a chlorine (Cl2) molecule, giving an atomic radius of 0.099 nm for chlorine. 

The atomic radii of the main-group elements are shown at the top of Figure 6.13 (p. 153). Notice that, in general, atomic radii—... 

The radii of cations and anions derived from atoms of the main-group elements are shown at the bottom of Figure 6.13. The trends referred to previously for atomic radii are dearly visible with ionic radius as well. Notice, for example, that ionic radius increases moving down a group in the periodic table. Moreover the radii of both cations (left) and anions (right) decrease from left to right across a period. 

The small size of the hydrogen atom allows the unshared pair of an F, O, or N atom of one molecule to approach the H atom in another very closely. It is significant that hydrogen bonding occurs only with these three nonmetals, all of which have small atomic radii. 

Metal-metal bonds and covalent atomic radii of transition metals in their n-complexes and polynuclear carbonyls. B. P. Biryukov and Y. T. Struchkov, Russ. Chem. Rev. (Engl. Transl.), 1970, 39,... 

Figure 1.46 shows some atomic radii, and Fig. 1.47 shows the variation in atomic radius with atomic number. Note the periodic, sawtooth pattern in the latter plot. Atomic radius generally decreases from left to right across a period and increases down a group. 

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