# 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:

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. [34] and [35].

Example:

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

### Graph¶

## 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:

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

Example:

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

### Graph¶

## Cottrell and Sutton¶

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

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

Example:

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

### Graph¶

## Ghosh¶

Ghosh [19] presented a scale of electronegativity based on the absolute radii of atoms computed as

where: \(R\) is the absolute atomic radius and \(a\) and \(b\) are empirical parameters.

Example:

```
>>> Si.en_ghosh
0.178503
```

### Graph¶

## Gordy¶

Gordy’s scale [21] is based on the potential that measures the work necessary to achieve the charge separation, according to:

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

Example:

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

### Graph¶

## Li and Xue¶

Li and Xue [30, 31] proposed a scale that takes into account different valence states and coordination environment of atoms and is calculated according to the following formula:

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:

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
```

### Graph¶

## Miedema¶

Miedema et. al. [18, 66] devised a semi-empirical theory that could predict formation enthalpies and other basic properties of various alloys. It is based on estimating quantitatively the enthalpy (energy) effects when bringing dissimilar elements into contact, which will change the electron density at the so-called Wigner-Seitz cell boundary, and would tend to shift their electron densities due to an electronegativity difference.

The enthalpy can be estimated with three critical parameters, i.e. the electronegativity difference \(\Delta\phi\) (defined as \(\phi_A - \phi_B\)), the electron-density discontinuity \(\Delta n^{1/3}_{WS}\), which is the difference in the \(n_{WS}\) - the electron density based on the volume of Wigner-Seitz atomic cells \(V_{m}\).

Atomic electronegativities \(\phi\) are empirical parameters in this model and are tabulated in `mendeleev`

.

Example:

```
>>> Si.en_miedema
4.7
```

### Graph¶

## Mulliken¶

Mulliken scale [39] is defined as the arithmetic average of the ionization potential (\(IP\)) and the electron affinity (\(EA\)):

Example:

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

### Graph¶

## Nagle¶

Nagle [40] derived his scale from the atomic dipole polarizability:

Example:

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

### Graph¶

## Pauling¶

Pauling’s thermochemical scale was introduced in [44] as a relative scale based on electronegativity differences:

where: \(E_{d}(XY)\) is the bond dissociation energy of a diatomic \(XY\). The values available in mendeleev are taken from ref. [24].

Example:

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

### Graph¶

## Sanderson¶

Sanderson [53, 54] established his scale of electronegativity based on the stability ratio:

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
```

### Graph¶

## 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`

.