Computational Chemistry

Force and force constant, for a spring or bond, reflect the dependence of energy
on extension:

Force¼F¼#dE=dx (1)

Force constant¼k¼#dF=dx¼d^2 E=dx^2 (2)

(Force is a vector, acting in the opposite direction to the that along which the
spring or bond is extended, hence the minus sign; the force constant is positive).
Energy and charge density are closely connected,Ebeing a functional ofrfor the
ground state:

E 0 ¼F½r 0 Š (3)

We want equations analogous to Eqs. 1 and 2 withrinstead ofE. Equation 3
leads us to

Force¼F¼#dF½rŠ=dx (4)

and

Force constant¼k¼#dF=dx¼d^2 F½r 0 Š=dx^2 (5)

both for the ground electronic state.
Units of electronegativity and hardness in the international system
Electronegativity can be defined as

w¼#m¼#

@E

@N



V

(6)

and hardness can be defined as

¼

@^2 E

@N^2



V

¼

@m

@N



V

¼

@w

@N



V

(7)

Within these definitions, the units of electronegativity must then be

Change in energy/change in pure number¼J (joules)
and the units of hardness must be
Change in electronegativity/change in pure number
¼change in J/change in pure number¼J

Electronegativity is a measure of how fast energy changes as electrons are
added, and hardness is a measure of how fast electronegativity changes as electrons
are added. In the “classical” Pauling definition, electronegativity is commonly said
to be dimensionless, but should really have the units of square root of energy
(arising from bond energy difference to the power of 1/2), and in the Mulliken
definition the units are those of energy (see Chapter 7, Harder Question 6).

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