INO-22

Hard–soft interaction snapshot

E ≈ −(χA − χB)² / (2(ηA + ηB)). Charge-transfer stabilisation.

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AcidityPearson–Parr

Governing equation

E=-\dfrac{(\chi_A-\chi_B)^2}{2(\eta_A+\eta_B)}

$\chi_A \in \left[2, 15\right]$

where

\chi_A: EN of A (eV)
\chi_B: EN of B (eV)
\eta_A: Hardness of A (eV)
\eta_B: Hardness of B (eV)
E: Stabilisation (eV)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

E=-\dfrac{(\chi_A-\chi_B)^2}{2(\eta_A+\eta_B)}

$\chi_A \in \left[2, 15\right]$

$\chi_A = 2$ $E = -2$

Along the curve

②

Domain of the variable — blue

\chi_A_{\min} = 2,\quad \chi_A_{\max} = 15

$\chi_A \in \left[2, 15\right]$

$\chi_A = 2$ $\chi_A = 2$

Along the curve

③

Response curve — green

E=-\dfrac{(\chi_A-\chi_B)^2}{2(\eta_A+\eta_B)}

$\chi_A \in \left[2, 15\right]$

$\chi_A = 2$ $E = -2$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}E}{\mathrm{d}\chi_A}

$\chi_A \in \left[2, 15\right]$

$\chi_A = 2.082$ $E^{\prime} = 0.658$

Along the curve

Lecture brief

Historical brief

Pauling and Allred–Rochow electronegativity, Kapustinskii lattice energy, CFSE and Goldschmidt radii organise the periodic solid. The sheets predict bond character and crystal packing. This sheet (INO-22 — Hard–soft interaction snapshot) is the form associated with Pearson–Parr. Working symbols: $\chi_A$ , $\chi_B$ , $\eta_A$ , $\eta_B$ $\rightarrow$ $E$ . The Klopman–Parr formula: a large EN mismatch on two soft (small-η) partners is strongly stabilising.

Purpose

Purpose: compute

E

from

\chi_A

\chi_B

\eta_A

\eta_B

in Inorganic chemistry via

E=-\dfrac{(\chi_A-\chi_B)^2}{2(\eta_A+\eta_B)}

E ≈ −(χA − χB)² / (2(ηA + ηB)). Charge-transfer stabilisation. Use it when a real inorganic chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\chi_A = 6.000\,\mathrm{eV}

\chi_B = 8.000\,\mathrm{eV}

\eta_A = 5.000\,\mathrm{eV}

\eta_B = 4.000\,\mathrm{eV}

, the governing relation

E=-\dfrac{(\chi_A-\chi_B)^2}{2(\eta_A+\eta_B)}

yields

E = -0.2222\,\mathrm{eV}

. Two partners, Mulliken χ and hardness η in eV. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

EN of A \chi_A6 eVEN of B \chi_B8 eVHardness of A \eta_A5 eVHardness of B \eta_B4 eV

Outputs

Stabilisation E-0.2222 eV

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Narration of this film

Two partners, Mulliken χ and hardness η in eV.

The Klopman–Parr formula: a large EN mismatch on two soft (small-η) partners is strongly stabilising.

Reading speed

Watch on YouTube