11 Vibrational motion and infrared spectroscopy
221
Simple harmonic oscillator: classical theory
221
Potential energy for the simple harmonic oscillator
223
Simple harmonic oscillator: quantum theory
223
Derivation box 11.1 Solving Schrödinger’s equation for the simple
harmonic oscillator
224
Properties of the solutions
225
Forbidden region
228
Transitions
229
Vibrational spectra
230
Research direction: hydrogenase
232
References
235
Problems
235
12 Atomic structure: hydrogen atom and multi-electron atoms
238
Schrödinger’s equation for the hydrogen atom
238
Derivation box 12.1 Solving Schrödinger’s equation for the hydrogen atom
239
Separation of variables
239
Angular solution
240
Radial solution
243
Properties of the general solution
244
Angular momentum
246
Orbitals
247
s Orbitals
247
p Orbitals
251
d Orbitals
252
Transitions
253
Research direction: hydrogen economy
254
Spin
257
Derivation box 12.2 Relativistic equations
258
Multi-electron atoms
260
Empirical constants
260
Self-consistent field theory (Hartree–Fock)
261
Helium atom
262
Spin–orbital coupling
264
Periodic table
265
References
267
Problems
267
13 Chemical bonds and protein interactions
270
Schrödinger’s equation for a hydrogen molecule
270
Valence bonds
275
The Hückel model
276
Interactions in proteins
276
CONTENTS
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