102
3 Fundamentals of the Analysis Tools
Glossaries 1: Some notations
Φ I wavefunction of the Ith state (I = 0 represents the ground state)
E I
electronic energy of the Ith state
Z A magnitude of the positive charge (e
+ ) of nucleus A
r μA distance between electron μ and nucleus A
r μν distance between electrons μ and ν
r
coordinate of an arbitrary electron
r A distance between an arbitrary electron and nucleus A
R AB distance between nuclei A and B
It is well known that the Schrödinger equation constitutes an eigenvalue problem
whose eigenfunction and eigenvalue correspond to wavefunction and energy, respectively. It is noted that the atomic unit listed in the Glossaries 2 is employed throughout
this chapter for simplicity unless specially noted.
Glossaries 2: Atomic unit
Mass of a free electron
m e = 1 9.1094 × 10
−31 kg
Bohr radius
a 0 =
2
m e e 2 = 1 5.2918 × 10
−11 m
Energy
E h =
m e e
4
2 = 1 4.3597 × 10
−18 J
Time
τ 0 =
E h
=
3
m e e 4 = 1 2.4189 × 10
−17 s
Elementary charge
+e = 1 1.6022 × 10
−19 C
Planck’s constant
≡
h
2π
= 1 1.0546 × 10
−34 J s
Dielectric constant in vacuum