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Electronegativity Calculator (Mulliken)

Calculate the Mulliken electronegativity of an element from its ionization energy and electron affinity, with automatic conversion to the Pauling scale. Understand how strongly an atom attracts bonding electrons.

eV

The first ionization energy of the element in electron volts (eV). This is the energy required to remove the outermost electron from a neutral atom in the gas phase.

eV

The electron affinity of the element in electron volts (eV). This is the energy change when an electron is added to a neutral atom. Positive values mean energy is released; negative values (for noble gases, alkaline earths) mean energy is required.

What is a Electronegativity Calculator (Mulliken)?

Electronegativity is a measure of the tendency of an atom to attract a shared pair of electrons in a chemical bond. It is one of the most important concepts in chemistry, influencing bond polarity, molecular geometry, and chemical reactivity. While Linus Pauling's thermochemical scale is the most widely used, Robert S. Mulliken proposed an alternative definition based on measurable atomic properties: electronegativity is the average of the ionization energy (IE) and electron affinity (EA). The Mulliken scale has the advantage of being directly calculable from experimental spectroscopic data without needing thermochemical bond energies. This calculator computes the Mulliken electronegativity from IE and EA values and provides approximate conversions to the familiar Pauling scale using both a linear relationship and the Bratsch empirical formula. Electronegativity generally increases across a period (left to right) and decreases down a group in the periodic table, with fluorine (3.98 Pauling) being the most electronegative element.

Formula

χMulliken=IE+EA2\chi_{Mulliken} = \frac{IE + EA}{2}

Where IE is the first ionization energy in eV (energy to remove the outermost electron), EA is the electron affinity in eV (energy released when gaining an electron), and chi_Mulliken is the Mulliken electronegativity in eV. The Pauling scale approximation uses the linear conversion: chi_Pauling = (chi_Mulliken - 1.613) / 3.481, or the Bratsch empirical formula: chi_Pauling = 0.359 * sqrt(chi_Mulliken) + 0.744.

How to Calculate

  1. 1

    Look up or measure the first ionization energy (IE) of the element in electron volts (eV).

  2. 2

    Look up or measure the electron affinity (EA) of the element in electron volts (eV).

  3. 3

    Calculate the Mulliken electronegativity: chi_M = (IE + EA) / 2.

  4. 4

    Optionally convert to the Pauling scale using: chi_P = (chi_M - 1.613) / 3.481 (linear) or chi_P = 0.359 * sqrt(chi_M) + 0.744 (Bratsch).

  5. 5

    Compare the result with tabulated Pauling electronegativity values to verify reasonableness.

Worked Examples

Electronegativity of Hydrogen

Input: IE = 13.598 eV, EA = 0.754 eV

  1. chi_M = (IE + EA) / 2 = (13.598 + 0.754) / 2 = 14.352 / 2 = 7.176 eV
  2. Pauling (linear): chi_P = (7.176 - 1.613) / 3.481 = 5.563 / 3.481 = 1.598
  3. Pauling (Bratsch): chi_P = 0.359 * sqrt(7.176) + 0.744 = 0.359 * 2.679 + 0.744 = 1.706
  4. Tabulated Pauling value for H is 2.20 (the approximations give ballpark estimates)

Result: Mulliken: 7.176 eV; Pauling (linear): ~1.60; Pauling (Bratsch): ~1.71

Electronegativity of Fluorine

Input: IE = 17.422 eV, EA = 3.401 eV

  1. chi_M = (17.422 + 3.401) / 2 = 20.823 / 2 = 10.412 eV
  2. Pauling (linear): chi_P = (10.412 - 1.613) / 3.481 = 8.799 / 3.481 = 2.528
  3. Pauling (Bratsch): chi_P = 0.359 * sqrt(10.412) + 0.744 = 0.359 * 3.227 + 0.744 = 1.902
  4. Tabulated Pauling value for F is 3.98 (Mulliken scale gives 10.41 eV)

Result: Mulliken: 10.412 eV; Pauling (linear): ~2.53; Pauling (Bratsch): ~1.90

Electronegativity of Sodium

Input: IE = 5.139 eV, EA = 0.548 eV

  1. chi_M = (5.139 + 0.548) / 2 = 5.687 / 2 = 2.844 eV
  2. Pauling (linear): chi_P = (2.844 - 1.613) / 3.481 = 1.231 / 3.481 = 0.354
  3. Pauling (Bratsch): chi_P = 0.359 * sqrt(2.844) + 0.744 = 0.359 * 1.686 + 0.744 = 1.349
  4. Tabulated Pauling value for Na is 0.93

Result: Mulliken: 2.844 eV; Pauling (linear): ~0.35; Pauling (Bratsch): ~1.35

Frequently Asked Questions

The Pauling scale, developed in 1932, is based on thermochemical bond dissociation energies and is the most commonly used. Values range from about 0.7 (francium) to 3.98 (fluorine). The Mulliken scale, proposed in 1934, defines electronegativity as the average of ionization energy and electron affinity, making it directly calculable from spectroscopic data. While the two scales correlate, they use different units and numerical ranges.
Electron affinity is negative when energy must be input to force an atom to accept an additional electron. This occurs for elements like noble gases (which have completely filled shells) and some alkaline earth metals. A negative EA means the atom does not naturally attract extra electrons, reflecting very low or effectively zero electronegativity for the Mulliken definition.
The difference in electronegativity between two bonded atoms determines bond polarity. If the difference is zero, the bond is nonpolar covalent. Small differences (0.4-1.7) produce polar covalent bonds where electrons are shared unequally. Large differences (>1.7) typically result in ionic bonds where electrons are essentially transferred from the less electronegative atom to the more electronegative one.
Electronegativity generally increases across a period from left to right (as effective nuclear charge increases) and decreases down a group (as atomic radius increases and valence electrons are farther from the nucleus). Fluorine has the highest electronegativity, while francium and cesium have the lowest among naturally occurring elements.
The conversion formulas are approximations and should be used with caution. The linear conversion (chi_P = (chi_M - 1.613) / 3.481) and the Bratsch formula (chi_P = 0.359 * sqrt(chi_M) + 0.744) both provide rough estimates. For precise Pauling values, consult established reference tables. The conversions are most useful for understanding relative trends rather than obtaining exact Pauling numbers.

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