# Electronegativities¶

Since electronegativity is useful concept rather than a physical observable, several scales of electronegativity exist and some of them are available in mendeleev. Depending on the definition of a particular scale the values are either stored directly or recomputed on demand with appropriate formulas. The following scales are stored:

Moreover there are electronegativity scales that can be computed from their respective definition and the atomic properties available in mendeleev:

For a short overview on electronegativity see this presentation.

All the examples shown below are for Silicon:

>>> from mendeleev import element
>>> Si = element('Si')


## Allen¶

The electronegativity scale proposed by Allen in ref [2] is defined as:

$\chi_{A} = \frac{\sum_{x} n_{x}\varepsilon_{x}}{\sum_{x}n_{x}}$

where: $$\varepsilon_{x}$$ is the multiplet-averaged one-electron energy of the subshell $$x$$ and $$n_{x}$$ is the number of electrons in subshell $$x$$ and the summation runs over the valence shell.

The values that are tabulated were obtained from refs. [31] and [32].

Example:

>>> Si.en_allen
11.33
>>> Si.electronegativity('allen')
11.33


## Allred and Rochow¶

The scale of Allred and Rochow [4] introduces the electronegativity as the electrostatic force exerted on the electron by the nuclear charge:

$\chi_{AR} = \frac{e^{2}Z_{\text{eff}}}{r^{2}} \notag$

where: $$Z_{\text{eff}}$$ is the effective nuclear charge and $$r$$ is the covalent radius.

Example:

>>> Si.electronegativity('allred-rochow')
0.00028240190249702736


## Cottrell and Sutton¶

The scale proposed by Cottrell and Sutton [17] is derived from the equation:

$\chi_{CS} = \sqrt{\frac{Z_{\text{eff}}}{r}}$

where: $$Z_{\text{eff}}$$ is the effective nuclear charge and $$r$$ is the covalent radius.

Example:

>>> Si.electronegativity('cottrell-sutton')
0.18099342720014772


## Ghosh¶

Ghosh [18] presented a scale of electronegativity based on the absolute radii of atoms computed as

$\chi_{GH} = a \cdot (1/R) + b$

where: $$R$$ is the absolute atomic radius and $$a$$ and $$b$$ are empirical parameters.

Example:

>>> Si.en_ghosh
0.178503


## Gordy¶

Gordy’s scale [20] is based on the potential that measures the work necessary to achieve the charge separation, according to:

$\chi_{G} = \frac{eZ_{\text{eff}}}{r}$

where: $$Z_{\text{eff}}$$ is the effective nuclear charge and $$r$$ is the covalent radius.

Example:

>>> Si.electronegativity('gordy')
0.03275862068965517


## Li and Xue¶

Li and Xue [27, 28] proposed a scale that takes into account different valence states and coordination environment of atoms and is calculated according to the following formula:

$\chi_{LX} = \frac{n^{*}\sqrt{I_{j}/Ry}}{r}$

where: $$n^{*}$$ is the effective principal quantum number, $$I_{j}$$ is the j’th ionization energy in eV, $$Ry$$ is the Rydberg constant in eV and $$r$$ is either the crystal radius or ionic radius.

Example:

>>> Si.en_li_xue(charge=4)
{u'IV': 13.16033405547733, u'VI': 9.748395596649873}
>>> Si.electronegativity('li-xue', charge=4)
{u'IV': 13.16033405547733, u'VI': 9.748395596649873}


## Martynov and Batsanov¶

Martynov and Batsanov [7] used the square root of the averaged valence ionization energy as a measure of electronegativity:

$\chi_{MB} = \sqrt{\frac{1}{n_{v}}\sum^{n_{v}}_{k=1} I_{k}}$

where: $$n_{v}$$ is the number of valence electrons and $$I_{k}$$ is the $$k$$ th ionization potential.

Example:

>>> Si.en_martynov_batsanov()
5.0777041564076963
>>> Si.electronegativity(scale='martynov-batsanov')
5.0777041564076963


## Mulliken¶

Mulliken scale [36] is defined as the arithmetic average of the ionization potential ($$IP$$) and the electron affinity ($$EA$$):

$\chi_{M} = \frac{IP + EA}{2}$

Example:

>>> Si.en_mulliken()
4.0758415
>>> Si.electronegativity('mulliken')
4.0758415


## Nagle¶

Nagle [37] derived his scale from the atomic dipole polarizability:

$\chi_{N} = \sqrt[3]{\frac{n}{\alpha}} \notag$

Example:

>>> Si.electronegativity('nagle')
0.47505611644667534


## Pauling¶

Pauling’s thermochemical scale was introduced in [40] as a relative scale based on electronegativity differences:

$\chi_{A} - \chi_{B} = \sqrt{E_{d}(AB) - \frac{1}{2}\left[E_{d}(AA) + E_{d}(BB)\right] }$

where: $$E_{d}(XY)$$ is the bond dissociation energy of a diatomic $$XY$$. The values available in mendeleev are taken from ref. [23].

Example:

>>> Si.en_pauling
1.9
>>> Si.electronegativity('pauling')
1.9


## Sanderson¶

Sanderson [49, 50] established his scale of electronegativity based on the stability ratio:

$\chi_{S} = \frac{\rho}{\rho_{\text{ng}}}$

where: $$\rho$$ is the average electron density $$\rho=\frac{Z}{4\pi r^{3}/3}$$, and $$\rho_{\text{ng}}$$ is the average electron density of a hypothetical noble gas atom with charge $$Z$$.

Example:

>>> Si.en_sanderson()
0.3468157872145231
>>> Si.electronegativity()
0.3468157872145231


## Fetching all electronegativities¶

If you want to fetch all the available scales for all elements you can use the fetch_electronegativities function, that collect all the values into a DataFrame.