Schomaker-Stevenson equation

The SiF bond in SiF4 has a length of 155.5 pm compared to the value of 169 pm calculated using the Schomaker-Stevenson equation and the value of 177 pm calculated from the sum of the covalent radii (Table 2.6). So Pauling wrote resonance structures such as the following ... 

When the electrons in a covalent bond are shared equally, the length of the bond between the atoms can be approximated as the sum of the covalent radii. However, when the bond is polar, the bond is not only stronger than if it were purely covalent, it is also shorter. As shown earlier, the amount by which a polar bond between two atoms is stronger than if it were purely covalent is related to the difference in electronegativity between the two atoms. It follows that the amount by which the bond is shorter than the sum of the covalent radii should also be related to the difference in electronegativity. An equation that expresses the bond length in terms of atomic radii and the difference in electronegativity is the Schomaker-Stevenson equation. That equation can be written as... 

Peter5 has combined the Schomaker-Stevenson equation with Eq. 6.8. which relates bond length to bond order, and obtained ... 

An updated version of the Schomaker-Stevenson equation, which was generated by fitting more accurate bond distances, is given in Eq. (2) (765) ... 

Calculated from the Schomaker-Stevenson equation. bSum of the covalent radii (Table 2.1). 

The AB bond shortening to less than the sum of the covalent radii is often treated in terms of increasing bond order. According to the Schomaker-Stevenson equation, the polarity of the bond also contributes to the bond shortening. A formal interpretation of the observed PCI bond elongation in aminophosphines would involve bond orders of less than unity this points to the necessity of reconsidering the generally accepted concepts on bond order. 

R is -0.03, 0.02,0.03,0.15,0.27, (0.38) and 0.50 A, respectively. The magnitudes of the differences are relatively constant ( 0.03 A) from Li to B, and increase linearly with group number across the periodic table. The second row elements show a similar trend (Fig. 1 and Table la). These sequences may be accounted for approximately, in terms of the Schomaker-Stevenson equation ... 

XVa<->b) (two similar ionic forms). They therefore proposed an equation known as the Schomaker-Stevenson relationship which takes account of this by making the bond distance depend on the electronegativity difference, which is an index of the ionic character of the bond. The equation they suggested is... 

For calculating the interatomic distance for a single bond, Ri, involving an atom of nitrogen, oxygen, or fluorine (or two such atoms), we use the equation of Schomaker and Stevenson namely... 

Electronegativity values from L. Pauling, Nature of the Chemical Bond, Cornell Univ. Press, Ithaca, New York (1960). Calculated from the Stevenson Schomaker Equation re + tm 0.09 xm — Xo -° For standard deviations, see original articles. 

At first, rte and roc have been calculated only for the elements, for which the corresponding coordination is more typical, i.e. ne for the Group 11-17 elements and Be, roc for the rest. Later, Van Vechten and Phillips [132] have determined ne and roc for the same elements and observed that always ne < roc, and that either radius remains practically constant within the following series of elements, (i) Si, P, S, Cl (ii) Cu, Zn, Ga, Ge, As, Se, Br (iii) Ag, Cd, In, Sn, Te, I, probably because an increase of Z along a period is compensated by an increase of inter-electron repulsion. Note that the systems of ne derived by Pauling and Phillips, differ substantially, as do the r or published by different authors [133-139]. This is so because that additivity of the radii is perfect only for purely covalent (non-polar) bond, while polar bonds are shorter. This tendency, first rationalized by Schomaker and Stevenson [140], can be described by equations... 

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