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520 14MOLECULAR INTERACTIONS
atom type number q/e x/Å y/Å z/Å
C 4 0.746 0.469 −0.168 −0.583
O 5 −0.611 1.228 −0.554 −1.430
C 6 −0.288 0.674 −2.216 0.767
N 7 −0.790 0.143 −0.896 0.509
C 8 −0.577 −0.186 1.194 −0.685
H 3 0.231 1.339 −2.475 −0.041
H 1 0.168 1.227 −2.235 1.700
H 2 0.168 −0.122 −2.951 0.819
H 9 0.161 −0.848 1.425 0.141
H 10 0.207 0.591 1.946 −0.738
H 11 0.207 −0.746 1.236 −1.611
H 12 0.380 −0.492 −0.509 1.167
�e dipole moment along x is computed as µx = ∑i q ix i , where i is
the index for the atom, q i is its charge, and x i its coordinate. Using the
data in the table the components of the dipole moment are easily com-
puted in units of the elementary charge times Å, and then these values
are converted to Debye in the usual way. �e total dipole moment is
µ = (µ2x + µ2y + µ2z)1/2.
µx = −0.461 eÅ
= (−0.461 × 10−10 m) × (1.6022 × 10−19 C)/(3.3356 × 10−30 Cm)
= −2.212 D
Similarly µy = 0.607 D and µz = 2.897 D, giving µ = 3.695 D .
�e energy of interaction of two dipoles is given by [14B.3b–595]
V = µ1µ2
4πε0r3
× (1 − 3 cos2 Θ)
With the data given, and converting to molar units
V = [(3.695 D) × (3.3356 × 10−30 Cm)/(1 D)]2)
4π × (8.8542 × 10−12 J−1 C2m−1) × (3.0 × 10−9 nm)3
× (1 − 3 cos2 Θ) × (6.0221 × 1023mol−1)
= (30.4... Jmol−1) × (1 − 3 cos2 Θ)
A plot of this function is shown in Fig. 14.16.
(b) �e maximum of the dipole–dipole interaction is −61 Jmol−1 which is
only 0.3% of the energy of the hydrogen bond.
I14.6 Starting fromG = U −TS− tl , the di�erential is formed and the basic equation
dU = TdS + tdl is introduced to give
dG = dU − d(TS) − d(tl) = dU − TdS − SdT − tdl − ldt
= TdS + tdl − TdS − SdT − tdl − ldt = −SdT − ldt