Relativistic Quantum Theory of Atoms and Molecules - Theory and Computation

Preface

Contents

Part I Relativity in atomic and molecular physics

1 Relativity in atomic and molecular physics

1.1 Elementary ideas

1.2 The one-electron atom

1.3 Many-electron atoms

1.4 Applications to atomic physics

1.5 Relativistic molecular structure

References

Part II Foundations

2 Relativistic wave equations for free particles

2.1 The special theory of relativity

2.2 The Lorentz group

2.3 The Poincar ´ e group

2.4 The Klein-Gordon equation

2.5 The Dirac equation

2.6 Maxwell’s equations

2.7 Symmetries and local conservation laws

2.8 Global conservation laws

2.9 Green’s functions

References

3 The Dirac Equation

3.1 Free particles

3.2 Spherical symmetry

3.3 Hydrogenic atoms

3.4 Scattering by a centre of force

3.5 Relativistic quantum defect theory

3.6 Green’s functions

3.7 The nonrelativistic limit: the Pauli approximation

3.8 Other aspects of Dirac theory

References

4 Quantum electrodynamics

4.1 Second quantization

4.2 Quantization of the electron-positron .eld

4.3 Quantization of the Maxwell .eld

4.4 Interaction of photons and electrons

4.5 Wick’s theorems

4.6 Propagators

4.7 The S-matrix

4.8 Bound states

4.9 E.ective interactions

4.10 Off-shell potentials

4.11 Many-body perturbation theory

4.12 MBPT for atoms and molecules

4.13 Relativistic approaches to atomic and molecular structure

4.14 A strategy for atomic and molecular calculations

4.15 Density functional theories

References

Part III Computational atomic and molecular structure

5 Analysis and approximation of Dirac Hamiltonians

5.1 Self-adjointness of free particle Hamiltonians

5.2 Self-adjointness of Hamiltonians with a local potential

5.3 The radial Dirac di.erential operator

5.4 The radial Dirac equation for atoms

5.5 Variational methods in quantum mechanics

5.6 The Rayleigh-Ritz method in relativistic quantum mechanics

5.7 Spinor basis sets

5.8 L-spinors

5.9 S-spinors

5.10 G-spinors

5.11 Finite di.erence methods

5.12 Finite element methods

References

6 Complex atoms

6.1 Dirac-Hartree-Fock theory

6.2 One-electron matrix elements of tensor operators

6.3 Angular reduction of the Dirac Hamiltonian for a central potential

6.4 Matrix elements of 2-body operators

6.5 Interaction strengths for the magnetic interactions

6.6 Closed shells and con.guration averages

6.7 DHF integro-di.erential equations

6.8 Con.gurations with incomplete subshells

6.9 Atoms with complex con.gurations

6.10 CI and MCDHF problems with large CSF sets

References

7 Computation of atomic structures

7.1 Atomic structure calculations with GRASP

7.2 GRASP modules

7.3 MCDHF integro-di.erential equations

7.4 Solving the integro-di.erential equations

7.5 Starting the calculation

7.6 An EAL calculation

7.7 Diagonal and o.-diagonal energy parameters

7.8 Koopmans’ theorem and Brillouin’s theorem

7.9 Control of MCSCF iterations

7.10 Corrections to the Coulomb interaction: Breit and other approximations

7.11 QED corrections

7.12 Towards higher quality atomic models

7.13 X-ray transition energies

References

8 Computation of atomic properties

8.1 Relativistic radiative transition theory

8.2 Emission and absorption by one-electron atoms

8.3 Radiative transitions in many-electron atoms

8.4 Orbital relaxation

8.5 Application to atomic transition calculations

8.6 Relativistic atomic photo-ionization theory

8.7 Hyper.ne interactions

8.8 Isotope shifts

References

9 Continuum processes in many-electron atoms

9.1 Relativistic elastic electron-atom scattering

9.2 Electron-atom scattering: the close-coupling method

9.3 The relativistic R-matrix method

9.4 The Buttle correction

9.5 R-matrix theory of photo-ionization

9.6 The DARC relativistic R-matrix package

9.7 Truncation of the close-coupling expansion. The nonrelativistic CCC method

9.8 The R-matrix method at intermediate energies

9.9 Electron scattering from heavy atoms and ions

9.10 The relativistic random phase approximation

9.11 RRPA rates for photo-excitation and photo- ionization

9.12 Comparison with experiment

References

10 Molecular structure methods

10.1 Molecular and atomic structure methods

10.2 Dirac-Hartree-Fock-Breit equations for closed shell atoms

10.3 One-centre interaction integrals

10.4 Numerical examples

10.5 The DHFB method for closed shell molecules

10.6 G-spinor basis functions

10.7 The charge-current density

10.8 Two-centre overlaps

10.9 Multi-centre interaction integrals

10.10 Fock matrix in terms of G-spinors

10.11 Electromagnetic .eld energy

10.12 Relativistic density functional calculations

10.13 Computational strategies

10.14 Multicon.gurational Dirac-Hartree-Fock theory

References

11 Relativistic calculation of molecular properties

11.1 Molecular symmetry

11.2 Relativistic e.ects in light molecules

11.3 Electromagnetic properties of atoms and molecules

11.4 The Zeeman e.ect

11.5 Hyper.ne interactions

11.6 NMR shielding in small molecules

11.7 Molecules with high-Z constituents

References

A Frequently used formulae and data

A.1 Relativistic notation

A.2 Dirac matrices

A.3 Special functions

A.4 Central .eld Dirac spinors and their interactions

A.5 Open shells in jj-coupling

A.6 Exponents for atomic and molecular G-spinors

A.7 Software for relativistic molecular calculations

References

B Supplementary mathematics

B.1 Linear operators on Hilbert space

B.2 Lie groups and Lie algebras

B.3 Quantum mechanical angular momentum theory

B.4 Relativistic symmetry orbitals for double point groups

B.5 Basis sets in atomic and molecular physics

B.6 Finite di.erence methods for Dirac equations

B.7 Eigenfunction expansions for the radially reduced Dirac equation

B.8 Iterative processes in nonlinear systems of equations

B.9 Lagrangian and Hamiltonian methods

B.10 Construction of E coefficients

References

Index