Computers in Chemistry
Quantum Chemistry (Part I)

Lecture Overview

Schrödinger equation

wave function (psi), hamiltonian operator (H), eigenvalue (E)

Units used in quantum mechanics

e = -1
m = 1
h/(2 pi) = 1

Hydrogen atom

• Schrödinger equation,wave function [[psi]],

  exp [-zeta r], the best value of zeta is zeta = Z = 1.0)

• hamiltonian operator (H)

  potential energy operator (V) and kinetic energy operator (T)

  expectation value of kinetic energy (+Z^2 / 2)
  expectation value of potential energy (-Z^2)

• eigenvalue (E = -Z^2 / 2), eigenvector (psi)

• the virial ratio (total potential energy/total kinetic energy)

• probability distribution

• calculation of ionization energy, exact agreement with experiment

Two-electron atoms, He, Be+2, etc.

• choice of the wave function, exp [-zeta r]

• treat zeta as a variable and apply the variation principle

• the meaning of effective nuclear charge, zeta

• calculation of ionization energy and compare to experiment, 6% error

• the source of the error in the Hartree method

Introduction to self consistent field theory (SCF) for two-electron atoms

Roger DeKock
deko@calvin.edu

Last Modified on January 16, 1995