ABSTRACT
Molecular quantum mechanics, as embodied in the time-independent Schrödinger equation ˆ ,H EΨ Ψ= is the physical foundation of chemistry. For systems containing atoms no heavier than Ar, highly accurate results are obtained from the standard nonrelativistic Hamiltonian involving only Coulombic interactions:
Hˆ M m
Z Z e
rii = − ∇ − ∇ +∑ ∑ ∑
02 2 4 α
αα πε πε
∑∑ ∑∑− + >
Z e
r
e
04 4
(1.1)
in which Greek (α and β) indices refer to nuclei with masses Mα and charges Zα, and Latin (i and j) indices refer to electrons with mass me and charge e, while the corresponding interparticle distances are denoted by rαβ, riα, and rij. The Laplacian operator for each particle takes the simple form ∆ ≡ ∇ = ∂ ∂ + ∂ ∂ + ∂ ∂2 2 2 2 2 2 2x y z in rectilinear Cartesian coordinates but generally is considerably more complicated if curvilinear internal coordinates are used.
