Chemistry Reference
In-Depth Information
Electron Density in Quantum Theory
Samuel Fux and Markus Reiher
Abstract In this work, we review the theory of the electron density in quantum
chemistry and discuss to which extent relativistic effects are recovered by approxi-
mate relativistic Hamiltonians. For this purpose, we give an overview on different
approximations to the fully relativistic many-electron Hamiltonian. In addition, we
present new results, considering correlation effects on the electron density of a
transition metal complex.
Keywords Continuity equation
Contact density
Conceptual theories
Dirac-
Coulomb-Breit
Density functional
theory
Douglas-Kroll-Hess
Electron
density
Electron correlation effects
Frozen-density embedding
Picture change
error
Relativistic effects
ZORA
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
2 Definition of the Electron Density Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3 Dependence on Wave Function and Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
3.1 The Wave Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
3.2 The Hamiltonian Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.3 Electron Density Distribution for Different Choices of
Hamiltonian and Wave Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
3.4 Methodological Aspects: Density Functional Theory
and Current-Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4 Analysis of Approximate Electron Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.1 Effect of the Approximate Hamiltonians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.2 Significance of Electron Correlation: Fe(NO)
2+
as an Example . . . . . . . . . . . . . . . . . . . . 120
5 The Most Difficult Case: Contact Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6 Electron Density in Conceptual Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.1 Conceptual Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
