Relativity in atomic and molecular physics / Part I: |
Elementary ideas / 1: |
The one-electron atom / 1.2: |
Classical Kepler orbits / 1.2.1: |
The Bohr atom / 1.2.2: |
X-ray spectra and Moseley's Law / 1.2.3: |
Transition to quantum mechanics / 1.2.4: |
Sommerfeld's relativistic orbits and Dirac's wave equation / 1.2.5: |
Dirac and Schrodinger charge distributions / 1.2.6: |
The Dirac hydrogenic spectrum at high Z / 1.2.7: |
Many-electron atoms / 1.3: |
Central field models of the atom / 1.3.1: |
Closed and open shells / 1.3.2: |
Mean field potentials / 1.3.3: |
Comparison of Hartree-Fock and Dirac-Hartree-Fock models for ground states / 1.3.4: |
The mechanism of shell filling / 1.3.5: |
Other approaches / 1.3.6: |
Applications to atomic physics / 1.4: |
X-ray spectra / 1.4.1: |
Applications to astrophysics and plasma physics / 1.4.2: |
Modelling atomic processes in plasmas / 1.4.3: |
Relativistic molecular structure / 1.5: |
Relativistic interpretations of chemical anomalies / 1.5.1: |
Relativistic effective core potentials and other approximations / 1.5.2: |
Dirac four-component methods for molecules / 1.5.3: |
Parity violation and hyperfine interactions / 1.5.4: |
High-precision spectroscopy of small molecules containing light elements / 1.5.5: |
References |
Foundations / Part II: |
Relativistic wave equations for free particles / 2: |
The special theory of relativity / 2.1: |
The Lorentz group / 2.2: |
* Spinor representation of Lorentz transformations / 2.2.1: |
* Infinitesimal Lorentz transformations and their generators / 2.2.2: |
* Representations of the Lorentz group / 2.2.3: |
The Poincare group / 2.3: |
* Representations of the Poincare group / 2.3.1: |
* Space and time reflections / 2.3.2: |
The Klein-Gordon equation / 2.4: |
The Dirac equation / 2.5: |
[gamma]-Matrices and covariant form of Dirac's equation / 2.5.1: |
* Lagrangian formulation of Dirac's equation / 2.5.2: |
Foldy canonical form and the Foldy-Wouthuysen transformation / 2.5.3: |
* Position operators in Dirac theory / 2.5.4: |
Dirac particles in electromagnetic fields / 2.5.5: |
* Negative energy states / 2.5.6: |
Maxwell's equations / 2.6: |
Covariant form of Maxwell's equations / 2.6.1: |
* Lagrangian formulation / 2.6.2: |
Gauge invariance / 2.6.3: |
* Motion of a test charge / 2.6.4: |
* Symmetries and local conservation laws / 2.7: |
* Global conservation laws / 2.8: |
* Green's functions / 2.9: |
Nonrelativistic Green's functions / 2.9.1: |
Klein-Gordon operator / 2.9.2: |
Maxwell's equations: the zero-mass case / 2.9.3: |
Free-particle Dirac equation / 2.9.4: |
The Dirac Equation / 3: |
Free particles / 3.1: |
Properties of Dirac matrices / 3.1.1: |
Covariance properties / 3.1.2: |
Bilinear covariants / 3.1.3: |
Plane wave solutions / 3.1.4: |
Energy and spin projectors / 3.1.5: |
Charge conjugation / 3.1.6: |
Spherical symmetry / 3.2: |
Angular structure / 3.2.1: |
The operator [sigma subscript r] / 3.2.2: |
The operator c[sigma] . p / 3.2.3: |
Separation of radial and spin-angular parts / 3.2.4: |
Angular density distributions / 3.2.5: |
Radial solutions for the free particle / 3.2.6: |
Partial wave normalization / 3.2.7: |
Hydrogenic atoms / 3.3: |
Solution of the radial equations / 3.3.1: |
The bound state solutions / 3.3.2: |
Charge distributions and energy levels in hydrogenic atoms / 3.3.3: |
* The continuum solutions / 3.3.4: |
Scattering by a centre of force / 3.4: |
Nonrelativistic potential scattering / 3.4.1: |
* Relativistic Coulomb scattering / 3.4.2: |
* Polarization effects in Coulomb scattering / 3.4.3: |
Historical note / 3.4.4: |
* Relativistic quantum defect theory / 3.5: |
Green's functions / 3.6: |
* Partial wave Green's functions / 3.6.1: |
The partial wave Green's function for the free Dirac particle / 3.6.2: |
Summation over partial waves in the free electron case / 3.6.3: |
* Green's function for hydrogenic ions / 3.6.4: |
The nonrelativistic limit: the Pauli approximation / 3.7: |
The Pauli approximation / 3.7.1: |
The Foldy-Wouthuysen and related transformations / 3.7.2: |
Other aspects of Dirac theory / 3.8: |
Quantum electrodynamics / 4: |
Second quantization / 4.1: |
Quantization of the Schrodinger equation / 4.1.1: |
Identical particles: the symmetric case / 4.1.2: |
Identical particles: the antisymmetric case / 4.1.3: |
Quantization of the electron-positron field / 4.2: |
The Furry picture / 4.2.1: |
The free electron case / 4.2.2: |
Quantization of the Maxwell field / 4.3: |
Interaction of photons and electrons / 4.4: |
The equations of motion / 4.4.1: |
The interaction picture / 4.4.2: |
Wick's theorems / 4.5: |
Propagators / 4.6: |
Photon propagators / 4.6.1: |
Electron-positron propagators / 4.6.2: |
Feynman diagrams / 4.6.3: |
Second order interaction: U[superscript (2)] (t, t[subscript 0]) / 4.6.4: |
Feynman rules / 4.6.5: |
The S-matrix / 4.7: |
Bound states / 4.8: |
A perturbation expansion / 4.8.1: |
Gell-Mann, Low, Sucher energy shift / 4.8.2: |
Effective interactions / 4.9: |
One-photon exchange: Feynman gauge / 4.9.1: |
One-photon exchange: Coulomb gauge / 4.9.2: |
* Off-shell potentials: heuristic argument / 4.9.3: |
One-photon exchange: the first order energy shift / 4.9.4: |
* Off-shell potentials / 4.10: |
Many-body perturbation theory / 4.11: |
Nonrelativistic many-body theory / 4.11.1: |
MBPT for atoms and molecules / 4.12: |
Particle-hole formalism / 4.12.1: |
Computational methods / 4.12.2: |
Relativistic approaches to atomic and molecular structure / 4.13: |
The no-virtual-pair approximation (NVPA) / 4.13.1: |
The NVPA as an antidote to "continuum dissolution" / 4.13.2: |
The NVPA and "variational collapse" / 4.13.3: |
Semirelativistic approaches / 4.13.4: |
A strategy for atomic and molecular calculations / 4.14: |
Density functional theories / 4.15: |
Basic ideas of RDFT / 4.15.1: |
The relativistic Hohenberg-Kohn theorem / 4.15.2: |
The relativistic Kohn-Sham equations / 4.15.3: |
Exchange and correlation functionals / 4.15.4: |
The optimized potential method / 4.15.5: |
Computational atomic and molecular structure / Part III: |
Analysis and approximation of Dirac Hamiltonians / 5: |
Self-adjointness of free particle Hamiltonians / 5.1: |
Free particles: the Schrodinger case / 5.1.1: |
Free particles: the Dirac case / 5.1.2: |
Self-adjointness of Hamiltonians with a local potential / 5.2: |
The Schrodinger case / 5.2.1: |
The Dirac case / 5.2.2: |
The radial Dirac differential operator / 5.3: |
The boundary condition at a singular endpoint / 5.3.1: |
The Dirac radial operator with one singular endpoint / 5.3.2: |
The radial Dirac equation for atoms / 5.4: |
Power series solutions near r = 0 / 5.4.1: |
Power series solutions in the nonrelativistic limit / 5.4.2: |
The boundary condition at the origin / 5.4.3: |
Variational methods in quantum mechanics / 5.5: |
Min-max theorems and the Ritz method / 5.5.1: |
Convergence of the Rayleigh-Ritz eigenvalues in nonrelativistic quantum mechanics / 5.5.2: |
Convergence of the Rayleigh-Ritz method in nonrelativistic quantum mechanics / 5.5.3: |
The Rayleigh-Ritz method in relativistic quantum mechanics / 5.6: |
The finite matrix method for the Dirac equation / 5.6.1: |
Convergence of Rayleigh-Ritz methods for Dirac Hamiltonians / 5.6.2: |
Spinor basis sets / 5.7: |
L-spinors / 5.8: |
Kinetic matching and the nonrelativistic limit / 5.8.1: |
Orthogonality properties / 5.8.2: |
Linear independence of L-spinors / 5.8.3: |
Completeness of L-spinors / 5.8.4: |
Charge conjugation and L-spinors / 5.8.5: |
Construction of [Pi superscript Beta Beta prime], S[superscript Beta Beta prime], and U[superscript Beta Beta prime] matrices for hydrogenic atoms / 5.8.6: |
Numerical study of L-spinor performance in hydrogenic atoms / 5.8.7: |
S-spinors / 5.9: |
Construction of [Pi superscript Beta Beta prime], S[superscript Beta Beta prime], and U[superscript Beta Beta prime] for hydrogenic atoms / 5.9.1: |
G-spinors / 5.10: |
Finite difference methods / 5.11: |
Methods of solution / 5.11.1: |
Acceptable solutions / 5.11.2: |
Finite element methods / 5.12: |
B-splines / 5.12.1: |
Variational formulation of finite element schemes / 5.12.2: |
Schrodinger equations / 5.12.3: |
Dirac equations / 5.12.4: |
Complex atoms / 6: |
Dirac-Hartree-Fock theory / 6.1: |
One-electron matrix elements of tensor operators / 6.2: |
2-spinor matrix elements of even operators / 6.2.1: |
2-spinor matrix elements of odd operators / 6.2.2: |
Angular reduction of the Dirac Hamiltonian for a central potential / 6.3: |
Matrix elements of 2-body operators / 6.4: |
The Coulomb interaction / 6.4.1: |
Relativistic corrections to the Coulomb interaction / 6.4.2: |
The Gaunt interaction / 6.4.3: |
The Moller interaction / 6.4.4: |
The transverse photon interaction in Coulomb gauge / 6.4.5: |
The Breit interaction / 6.4.6: |
Interaction strengths for the magnetic interactions / 6.5: |
The transverse photon interaction / 6.5.1: |
Closed shells and configuration averages / 6.5.2: |
The Dirac-Hartree-Fock model / 6.6.1: |
Inclusion of magnetic interactions / 6.6.2: |
Average of configuration models / 6.6.3: |
DHF integro-differential equations / 6.7: |
Construction of electrostatic potentials / 6.7.1: |
Construction of magnetic potentials / 6.7.2: |
Algorithms for potentials and Slater integrals / 6.7.3: |
Configurations with incomplete subshells / 6.8: |
Atomic states with incomplete subshells / 6.8.1: |
Partially filled subshells in jj-coupling / 6.8.2: |
Creation and annihilation operators as irreducible tensor operators. Quasispin / 6.8.3: |
Double tensor operators / 6.8.4: |
Parentage / 6.8.5: |
Coefficients of fractional parentage in the seniority scheme / 6.8.6: |
Equivalent electrons in LS-coupling / 6.8.7: |
Atoms with complex configurations / 6.9: |
Recoupling coefficients / 6.9.1: |
Matrix elements between open shell states / 6.9.2: |
Matrix elements of two-electron operators of type G / 6.9.3: |
CI and MCDHF problems with large CSF sets / 6.10: |
Decoupling active electrons / 6.10.1: |
One-electron matrix elements / 6.10.2: |
Two-electron matrix elements / 6.10.3: |
Computation of atomic structures / 7: |
Atomic structure calculations with GRASP / 7.1: |
GRASP modules / 7.2: |
MCDHF integro-differential equations / 7.3: |
Solving the integro-differential equations / 7.4: |
Starting the calculation / 7.5: |
The radial grid / 7.5.1: |
The nuclear mass / 7.5.2: |
The nuclear size / 7.5.3: |
Initial estimates for radial wavefunctions / 7.5.4: |
An EAL calculation / 7.6: |
Diagonal and off-diagonal energy parameters / 7.7: |
Koopmans' theorem and Brillouin's theorem / 7.8: |
Froese Fischer's analysis / 7.8.1: |
Control of MCSCF iterations / 7.9: |
Corrections to the Coulomb interaction: Breit and other approximations / 7.10: |
QED corrections / 7.11: |
Towards higher quality atomic models / 7.12: |
CSF sets for electron correlation: active space methods / 7.12.1: |
Example: intercombination transitions in Be-like ions / 7.12.2: |
X-ray transition energies / 7.13: |
Computation of atomic properties / 8: |
Relativistic radiative transition theory / 8.1: |
Line transitions / 8.1.1: |
Multipole expansion of the radiation field / 8.1.2: |
Emission and absorption by one-electron atoms / 8.2: |
Evaluation of one-electron transition amplitudes / 8.2.1: |
The nonrelativistic limit: Pauli approximation / 8.2.2: |
Radiative transitions in many-electron atoms / 8.3: |
Transitions in highly ionized atoms: Fe XXIII / 8.3.1: |
Orbital relaxation / 8.4: |
Application to atomic transition calculations / 8.5: |
Large-scale calculations of energies and transition rates / 8.5.1: |
Relativistic atomic photo-ionization theory / 8.6: |
The differential cross-section for photo-ionization / 8.6.1: |
Low energies: the electric dipole case / 8.6.2: |
Angular distributions and polarization parameters for a single channel / 8.6.3: |
Other aspects of photo-ionization / 8.6.4: |
Hyperfine interactions / 8.7: |
Hyperfine interactions in the many-electron atom / 8.7.1: |
Isotope shifts / 8.8: |
Nuclear motion / 8.8.1: |
Nuclear volume effect / 8.8.2: |
Continuum processes in many-electron atoms / 9: |
Relativistic elastic electron-atom scattering / 9.1: |
Model potentials / 9.1.1: |
Computational issues / 9.1.2: |
Determination of phase-shifts / 9.1.3: |
Summation of the partial wave expansion / 9.1.5: |
Electron-atom scattering: the close-coupling method / 9.2: |
Low-energy elastic and inelastic collisions / 9.2.1: |
The distorted wave approximation / 9.2.2: |
The relativistic R-matrix method / 9.3: |
The radial Dirac equation on a finite interval / 9.3.1: |
Bloch operators / 9.3.2: |
The inner region, r [Less than Equal] a / 9.3.3: |
The outer region, r [Greater than] a / 9.3.4: |
Matching inner and outer solutions / 9.3.5: |
The Buttle correction / 9.4: |
R-matrix theory of photo-ionization / 9.5: |
The DARC relativistic R-matrix package / 9.6: |
Truncation of the close-coupling expansion. The nonrelativistic CCC method / 9.7: |
The R-matrix method at intermediate energies / 9.8: |
Electron scattering from heavy atoms and ions / 9.9: |
Early work / 9.9.1: |
Electron scattering from the mercury atom / 9.9.2: |
Scattering of polarized electrons from polarized atoms / 9.9.3: |
The relativistic random phase approximation / 9.10: |
The RRPA equations / 9.10.1: |
Radial equations / 9.10.2: |
Multipole transition amplitudes / 9.10.3: |
RRPA rates for photo-excitation and photo-ionization / 9.11: |
Photo-excitation / 9.11.1: |
Photo-ionization / 9.11.2: |
Comparison with experiment / 9.12: |
Photo-ionization of outer atomic subshells at high Z / 9.12.1: |
Beyond RRPA / 9.12.2: |
Molecular structure methods / 10: |
Molecular and atomic structure methods / 10.1: |
Dirac-Hartree-Fock-Breit equations for closed shell atoms / 10.2: |
DHFB energy of a closed shell atom / 10.2.1: |
Spinor basis function representation / 10.2.2: |
Matrix of the radial Dirac operator / 10.2.3: |
Coulomb Slater integrals / 10.2.4: |
Breit integrals for closed shells / 10.2.5: |
The DHFB Fock matrix / 10.2.6: |
One-centre interaction integrals / 10.3: |
Numerical examples / 10.4: |
The DHFB method for closed shell molecules / 10.5: |
G-spinor basis functions / 10.6: |
The charge-current density / 10.7: |
Two-centre overlaps / 10.8: |
Relativistic expansion coefficients / 10.8.1: |
Symmetry properties of E[subscript q] coefficients / 10.8.2: |
Multi-centre interaction integrals / 10.9: |
Auxiliary integrals involving HGTFs / 10.9.1: |
Multi-centre one-electron integrals / 10.9.2: |
Multi-centre two-electron integrals / 10.9.3: |
Fock matrix in terms of G-spinors / 10.10: |
The BERTHA integral package / 10.10.1: |
Electromagnetic field energy / 10.11: |
Interaction energy in terms of internal fields / 10.11.1: |
The nonrelativistic Fock matrix / 10.11.2: |
The relativistic Fock matrix / 10.11.3: |
Implementation of the field formulation / 10.11.4: |
Relativistic density functional calculations / 10.12: |
Computational strategies / 10.13: |
The Roothaan bound / 10.13.1: |
Integral-direct Fock matrix evaluation / 10.13.2: |
Symmetry properties of interaction matrix elements / 10.13.3: |
Stepwise refinement / 10.13.4: |
Level-shifting / 10.13.5: |
Multiconfigurational Dirac-Hartree-Fock theory / 10.14: |
Orbital optimization / 10.14.1: |
Relativistic calculation of molecular properties / 11: |
Molecular symmetry / 11.1: |
Diatomic molecules / 11.1.1: |
Polyatomic molecules / 11.1.2: |
Relativistic effects in light molecules / 11.2: |
Nonrelativistic Breit-Pauli model / 11.2.1: |
DHF and DHFB calculations for water using BERTHA / 11.2.2: |
Second-order many-body corrections / 11.2.3: |
Relativistic study of the potential energy surface and vibration-rotation levels of water / 11.2.4: |
Electromagnetic properties of atoms and molecules / 11.3: |
Gauge transformations in electromagnetic processes / 11.3.1: |
B-spinors / 11.3.2: |
The Zeeman effect / 11.4: |
NMR shielding in small molecules / 11.5: |
NMR shielding constants for [superscript 17]O in water / 11.6.1: |
NMR shielding constants for [superscript 15]N in ammonia / 11.6.2: |
Molecules with high-Z constituents / 11.7: |
Electronic structure of TlF / 11.7.1: |
Electronic structure of YbF / 11.7.2: |
DHF+CI study of uranium hexafluoride / 11.7.3: |
Frequently used formulae and data / A: |
Relativistic notation / A.1: |
Dirac matrices / A.2: |
Special functions / A.3: |
Spherical Bessel functions / A.3.1: |
Confluent hypergeometric functions / A.3.2: |
Generalized Laguerre polynomials / A.3.3: |
Hermite polynomials / A.3.4: |
Incomplete gamma functions / A.3.5: |
Incomplete Beta functions / A.3.6: |
Continued fraction evaluation / A.3.7: |
Central field Dirac spinors and their interactions / A.4: |
Central field Dirac spinors / A.4.1: |
Matrix elements of simple ITOs / A.4.2: |
Magnetic interactions / A.4.3: |
Effective interaction strengths for two-body operators / A.4.4: |
Open shells in jj-coupling / A.5: |
Exponents for atomic and molecular G-spinors / A.6: |
Software for relativistic molecular calculations / A.7: |
BERTHA / A.7.1: |
DIRAC / A.7.2: |
MOLFDIR / A.7.3: |
Supplementary mathematics / B: |
Linear operators on Hilbert space / B.1: |
Hilbert spaces / B.1.1: |
Linear operators / B.1.2: |
Spectrum and resolvent of linear operators / B.1.3: |
Self-adjoint operators / B.1.4: |
Observables and self-adjoint operators / B.1.5: |
Commuting operators / B.1.6: |
Unitary and anti-unitary operators / B.1.7: |
Lie groups and Lie algebras / B.2: |
Lie groups / B.2.1: |
Lie algebras / B.2.2: |
Representations of Lie groups and Lie algebras / B.2.3: |
The Cartan-Weyl classification / B.2.4: |
Casimir operators / B.2.5: |
Kronecker products of group representations / B.2.6: |
Tensor operators and the Wigner-Eckart theorem / B.2.7: |
Quantum mechanical angular momentum theory / B.3: |
The rotation group / B.3.1: |
Abstract angular momentum / B.3.2: |
Orbital angular momentum / B.3.3: |
Representation functions / B.3.4: |
Kronecker products of irreducible representations / B.3.5: |
Coupling of three or more angular momenta / B.3.6: |
The 3j-symbol / B.3.7: |
The 6j-symbol / B.3.8: |
The 9j-symbols / B.3.9: |
Graphical treatment of angular momentum algebra / B.3.10: |
Diagrammatic treatment of Clebsch-Gordan coefficients / B.3.11: |
Diagrammatic treatment of 3jm-symbols / B.3.12: |
Generalized angular momentum couphng schemes / B.3.13: |
GCG and njm coefficients / B.3.14: |
Manipulating angular momentum diagrams / B.3.15: |
Composite tensor operators / B.3.16: |
Diagrammatic representation of tensor operators / B.3.18: |
Relativistic symmetry orbitals for double point groups / B.4: |
Construction of symmetry orbitals / B.4.1: |
Linear independence of molecular symmetry orbitals / B.4.2: |
Reduction of operator matrices / B.4.3: |
Time reversal / B.4.4: |
The TSYM software package / B.4.5: |
Basis sets in atomic and molecular physics / B.5: |
The Coulomb Sturmian functions / B.5.1: |
Completeness and linear independence of Coulomb Sturmians / B.5.2: |
Basis sets of exponential-type functions / B.5.3: |
Finite difference methods for Dirac equations / B.6: |
An existence theorem / B.6.1: |
Initial value methods / B.6.2: |
Linear multistep methods / B.6.3: |
The nodal structure of Dirac radial wavefunctions / B.6.4: |
Discretization of two-point boundary value problems / B.6.5: |
Two-point boundary value problems: the deferred correction method / B.6.6: |
Construction of difference corrections / B.6.7: |
Single stepping algorithms / B.6.8: |
Stepping outwards from the origin / B.6.9: |
Algorithm for the outer region / B.6.10: |
The boundary condition at T = t[subscript N] / B.6.11: |
Improving a trial solution / B.6.12: |
Eigenfunction expansions for the radially reduced Dirac equation / B.7: |
The fundamental lemma / B.7.1: |
Boundary conditions: the two-point boundary value problem / B.7.2: |
Boundary conditions at the nucleus / B.7.3: |
Pauli approximation at R[subscript 2] / B.7.4: |
The MIT bag model at R[subscript 2] / B.7.5: |
The eigenvalue spectrum / B.7.6: |
The inhomogeneous boundary value problem / B.7.7: |
Eigenfunction expansions / B.7.8: |
Iterative processes in nonlinear systems of equations / B.8: |
Lagrangian and Hamiltonian methods / B.9: |
Lagrange's equations / B.9.1: |
Hamilton's equations / B.9.2: |
Symmetries and conservation laws / B.9.3: |
Construction of E coefficients / B.10: |
E-coefficients through Cartesian intermediates / B.10.1: |
Recurrence relations for E-coefficients / B.10.2: |
Implementation issues / B.10.3: |
Index |