# Allred-Rochow Electronegativity

Allred-Rochow Electronegativity is a measure that determines the values of the electrostatic force exerted by the effective nuclear charge on the valence electrons. The value of the effective nuclear charges is estimated from Slater's rules. The higher charge, the more likely it will attract electrons. Although, Slater's rule are partly empirical. So the Allred-Rochow electronegativity is no more rigid than the Pauling Electronegativity.

### Electronegativity

Pauling established Electronegativity as the "power" of an atom in a molecule to attract electron to itself. It is a measure of the atom's ability to attract electron to itself while the electron is still attached to another atom. The higher the values, the more likely that atom can pull electron from another atom and into itself. Electronegativity correlates with bond polarity, ionization energy, electron affinity, effective nuclear charge, and atomic size.

H2.1 |
||||||||||||||||

Li1.0 |
Be1.6 |
B2.0 |
C2.50 |
N3.0 |
O3.5 |
F4.0 |
||||||||||

Na0.9 |
Mg1.3 |
Al1.6 |
Si1.9 |
P2.2 |
S2.5 |
Cl3.0 |
||||||||||

K0.8 |
Ca1.3 |
Sc1.4 |
Ti1.5 |
V1.6 |
Cr1.7 |
Mn1.6 |
Fe1.8 |
Co1.9 |
Ni1.9 |
Cu1.9 |
Zn1.7 |
Ga1.6 |
Ge2.0 |
As2.2 |
Se2.6 |
Br2.8 |

Rb0.8 |
Sr1.0 |
Y1.2 |
Zr1.3 |
Nb1.6 |
Mo2.2 |
Te2.1 |
Ru2.2 |
Rh2.3 |
Pd2.2 |
Ag1.9 |
Cd1.7 |
In1.8 |
Sn2.0 |
Sb2.1 |
Te2.1 |
I2.7 |

Cs0.8 |
Ba0.9 |
La1.1 |
Hf1.3 |
Ta1.5 |
W1.7 |
Re1.9 |
Os2.2 |
Ir2.2 |
Pt2.2 |
Au2.4 |
Hg1.9 |
Tl2.0 |
Pb2.3 |
Bi2.0 |
Po2.0 |
At2.2 |

The periodic trend for electronegativity generally increases from left to right and decreases as it go down the group. The exception are Hydrogen and the noble gases because the noble gases are content with their filled outermost shells, and hydrogen cannot bear to lose a valence electron unlike the rest of the group 1 metals. The elements in the halogen group usually have the highest electronegativity values because they only need to attract one valence electron to complete the octet in their outer shell. Whereas the group 1 elements except for Hydrogen, are willing to give up their only valence electron so they can fulfill having a complete, filled outer shell.

### Slater's rules

Slater's rules are rules that provides the values for the effective nuclear charge concept, or \(Z_{eff}\). These rules are based on experimental data for electron promotion and ionization energies, and \(Z_{eff}\) is determined from this equation:

\[Z_{eff} = Z - S\]

Where

- \(Z\) is the nuclear charge,
- \(Z_{eff}\) is the effective nuclear charge, and
- \(S\) is the shielding constant

Through this equation, this tells us that electron may get reduced nuclear charge due to high shielding. Allred and Rochow used \(Z_{eff}\) because it is accurate due to the involvement of shielding that prevents electron to reach its true nuclear charge: \(Z\). When an atom with filled s-shell attracts electrons, those electrons will go to the unfilled p-orbital. Since the electrons have the same negative charge, they will not only repel each other, but also repel the electrons from the filled s-shell. This creates a shielding effect where the inner core electrons will shield the outer core electrons from the nucleus. Not only would the outer core electrons experience effective nuclear charge, but it will make them easily removed from the outer shell. Thus, It is easier for outer electrons to penetrate the p shell, which has little likelihood of being near the nuclear, rather than the s shell. Consider this, each of the outer electron in the (ns, np) group contributes S = 0.35, S = 0.85 in the (n - 1) shell, and S = 1.00 in the (n - 2) or lower shells.

Example 1: Slater's Rules

Let's consider this example of finding the \(Z_{eff}\) for 4s electrons in Ca. Since Ca has atomic number of 20, Z = 20.

Then, we find the electron configuration for Ca, which is **1s ^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}**.

Now we got that, we can use Slater's rules:

\[Z_{eff} = Z - S\]

\[= 20 - ((8\times 0.85) + (10 \times 1.00))\]

\[= 3.2\]

So, Ca has a \(Z_{eff}\) of 3.2.

### Allred-Rochow Electronegativity

Allred and Rochow were two chemists who came up with the Allred-Rochow Electronegativity values by taking the electrostatic force exerted by effective nuclear charge, Z_{eff}, on the valence electron. To do so, they came up with an equation:

\[\chi^{AR} = \left(\dfrac{3590 \times Z_{eff}}{r^2_{cov}}\right) + 0.744 \label{1}\]

At the time, the values for the covalent radius, \(r_{cov}\), were inaccurate. Allred and Rochow added certain perimeters so that it would more closely correspond to Pauling's electronegativity scale.

H2.20 |
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Li0.97 |
Be1.47 |
B2.01 |
C2.50 |
N3.07 |
O3.50 |
F4.10 |
||||||||||

Na1.01 |
Mg1.23 |
Al1.47 |
Si1.74 |
P2.06 |
S2.44 |
Cl2.83 |
||||||||||

K0.91 |
Ca1.04 |
Sc1.20 |
Ti1.32 |
V1.45 |
Cr1.56 |
Mn1.60 |
Fe1.64 |
Co1.70 |
Ni1.75 |
Cu1.75 |
Zn1.66 |
Ga1.82 |
Ge2.02 |
As2.20 |
Se2.48 |
Br2.74 |

Rb0.89 |
Sr0.99 |
Y1.11 |
Zr1.22 |
Nb1.23 |
Mo1.30 |
Te1.36 |
Ru1.42 |
Rh1.45 |
Pd1.35 |
Ag1.42 |
Cd1.46 |
In1.49 |
Sn1.72 |
Sb1.82 |
Te2.01 |
I2.21 |

Cs0.86 |
Ba0.97 |
La1.08 |
Hf1.23 |
Ta1.33 |
W1.40 |
Re1.46 |
Os1.52 |
Ir1.55 |
Pt1.44 |
Au1.42 |
Hg1.44 |
Tl1.44 |
Pb1.55 |
Bi1.67 |
Po1.76 |
At1.90 |

In this table, the electronegativities increases from left to right just like Pauling's scale because the \(Z\) is increasing. As we go down the group, it decreases because of the larger atomic size that increases the distance between the electrons and nucleus.

### References

- Gary Wulfsberg.
*Inorganic Chemistry*. University Science Books, February 2000. - Housecroft, Catherine E., and Alan G. Sharpe.
*Inorganic Chemistry*. 3rd ed. Harlow: Pearson Education, 2008. Print. (Pg. 43-44) - Sarah Anderson.
*Intro to Inorganic Chemistry*. University Science Books, September 2004. - Linus Pauling.
*General Chemistry*. University Science Books, March 2002. - Leroy G. Wade.
*Organic Chemistry. 7th ed. Harlow: Pearson Education, 2006.* *John E. McMurry. General Chemistry: Atoms. 1st ed.**Harlow: Pearson Education, 2000.*

### Problems

- From lowest to highest, order the elements in terms of Z
_{eff}: Ni, Cu, Zn, Ga, Ge - Using the equations above, find the Z
_{eff}for the Br by using Slater's rules. - Using the equations above, Find the X
^{ar}for Br.

### Contributors

- Mark Vu