Ionic Bond electrostatic interaction of oppositely charged ions

Example: NaCl (sodium chloride)

positive and negative ions arrange by:

Coulomb attraction: between ions of opposite sign

Coulomb repulsion: between ions of same sign

Repulsion more than compensated by attraction

Ionic bond

6.1 eV(electrostatic energy)∞

5.1 eV(ionization energy)

3.6 eV(electron affinity)

Closer look to energetic

Na+ +

∞+

Cl + Cl- +

Na+ + Cl- Cl-Na+

r0

+

-0.3 eV (Pauli repulsion)

Click for reference and additionalinformation

Cl+ Cl-Na+

r0

+ 4.3 eV=(6.1-0.3)eV-5.1eV+3.6eV

(dissociation energy)

How to find r0

)/rexp(Br

eEEE repulsCouli

2

041

?

minimum

From a single Na+Cl- bond to the NaCl solid

Neither contact between cations (Na+ ) nor contact between anions (Cl- )

apart from nearest-neighbor interaction only Coulomb terms involved

r0

20r

Na+ has: 6 Cl- nearest neighbors at distance r0

12 Na+ next nearest neighbors at 02 r

r0

02 r

03 r

8 Cl- further neighbors at distance 03 r

Total Coulomb energy per ion pair: Ecoul

Ecoul= E( 6 Cl- nearest neighbors at distance r0 ) + E( 12 Na+ nearest neighbors at distance ) + E( 8 Cl- at distance )+…

02 r

03 r

...

reEcoul 3

82126

4 00

2

00

2

4 reEcoul

where α=1.748 is the Madelung constant

Erwin Rudolf Madelung1881-1972

Series ...38

2126

alternating sign

slow convergence

methods for accurate sumsEwald (1921) and Evjen (1932)

Madelung Constants

Compound Crystal Lattice MNaCl NaCl 1.74756CsCl CsCl 1.76267CaF2 Cubic 2.51939

CdCl2 Hexagonal 2.244

MgF2 Tetragonal 2.381

ZnS (wurtzite) Hexagonal 1.64132TiO2 (rutile) Tetragonal 2.408

bSiO2 Hexagonal 2.2197

Al2O3 Rhombohedral 4.1719

Madelung Constants

(Data from Handbook Menu )

unknown parameters

Total energy per ion pair: Ei=ECoul+ERepulsive

2/

04r

ieE C er

However: conditiondrdEi

r=r0

0

determination of,e.g., C 0

0

2r /i

2r r 0 0

dE e C e 0dr 4 r

02

r /2

0 0

eC e4 r

2r /

i0

eE e4 r

C 0r r2

i 20 0

e rE 1 e4 r r

2

i0 0 0

eE 14 r r

Ei @ r=r0

? Input from experiment

bulk compressibility1 dVV dp

since NaCl cubic xx yy zz

r

corner shared amog 8 adjacent cubes

1/8 (4Na+ +4Cl-)=1/2 NaCl

3V 2 r +

1 NaCl-molecule requires

Click here for response functions in gases. Note that the bulk modulus B is inverse proportional to the bulk compressibility

32d(2r )dV dr 6r dr

dr

work W=pdV related volume change

T 0dE dU

dW p dV

p F / A dV A dx

dE dE drpdV dr dV

21 dE

dr6r

2dr 1dV 6r

1 dVV dp

Let´s remember

1 dV drV dr dp

2

36r dr 3 dr

dp r dp2r

0 0r r

dp 3dr r

2

2 2 2 3dp d 1 dE 1 d E 1 dEdr dr dr dr6r 6r dr 3r

0 0

2

2 2r r 0 r r

dp 1 d Edr dr6r

0

20

2r r

18rd Edr

Click for details. Note special sign convention in thermodynamics

Aim: dpdr

and2

2

dp d Edr dr

2

2

d Edr

0

00

r r2 2 20

2 2 20 0r r

r r

18r d E d e r1 e4 rdr dr r

40 0 0

2

1r 72 r2

e

Cohesive energie

Properties of ionic crystalso

0.345 A 0.0345nm Mott and Gurney 1948for all alkali halides

However: widely varying values of C in the repulsive term ?

(alkali)+ (halogen)-

closed-shell ions behave like incompressible spherestake into account different radii according

a cr r rr

C e C e

universal C´ for all alkali halides

(can be experimentally determined via Born-Haber cycle)Click for detailed information

Ionic Sizes

Completely ionic bond is an ideal case

In general bond neither covalent nore pure ionic Mixed ionic-covalent bonds

cov ion

determined from H dE

d

Min.

Paulings concept of electronegativity

Electronegativity refers to the ability of an atom in a molecule to attract shared electrons.

Semi-quantitative estimation of λ

A B A B

δ+ δ-

+

> E( )A A E( )B B ]1/2

[A B

δ+ δ-

E( )

because there is Coulomb interaction between δ+und δ-

empirical formula

231 )(eV.)BB(E)AA(E)AB(E BA

)BB(E)AA(E 21

better than

Linus Pauling is the only person ever to receive two unshared Nobel Prizes

—for Chemistry (1954) and for Peace (1962).

Find here Pauling’s electronegativityonline

% ionicity of bond 2

2

1100

determined from dipole moment of molecules BA

BA

% ionicity of bond

2

21100BA

e