Ab initio relativistic quantum chemistry: four-components good, two-components bad!*

In view of the debate which resulted from the introductory lecture at this meeting, this article has been submitted to address the issues raised concerning the validity and implementation of relativistic theories of many-electron systems. We present the formulation and construction of BERTHA, our relativistic molecular structure program, and illustrate features of relativistic electronic structure theory with examples. These include magnetic and hyperfine interactions in small molecules, the use of spinor basis functions which include a dependence on a magnetic field strength, NMR shielding constants, P-odd interactions in chiral molecules, and computational details of a relativistic ab initio treatment of germanocene.

[1]  Hess,et al.  Applicability of the no-pair equation with free-particle projection operators to atomic and molecular structure calculations. , 1985, Physical review. A, General physics.

[2]  P. Mohr Self-energy of the n = 2 states in a strong Coulomb field , 1982 .

[3]  Lucas Visscher,et al.  RELATIVISTIC QUANTUM-CHEMISTRY - THE MOLFDIR PROGRAM PACKAGE , 1994 .

[4]  W. Kutzelnigg,et al.  Direct perturbation theory of relativistic effects for explicitly correlated wave functions: The He isoelectronic series , 1997 .

[5]  A. Mohanty A Dirac–Fock self‐consistent field method for closed‐shell molecules including Breit interaction , 1992 .

[6]  Trygve Helgaker,et al.  Principles of direct 4-component relativistic SCF: application to caesium auride , 1997 .

[7]  Z. Maksić,et al.  Theoretical Models of Chemical Bonding , 1991 .

[8]  I. P. Grant,et al.  Relativistic many-body perturbation theory using analytic basis functions , 1990 .

[9]  K. Dyall An exact separation of the spin‐free and spin‐dependent terms of the Dirac–Coulomb–Breit Hamiltonian , 1994 .

[10]  R. Feynman Relativistic Cut-Off for Quantum Electrodynamics , 1948 .

[11]  Eric Schwegler,et al.  Linear scaling computation of the Fock matrix. II. Rigorous bounds on exchange integrals and incremental Fock build , 1997 .

[12]  E. A. Uehling Polarization effects in the positron theory , 1935 .

[13]  Bertha Swirles,et al.  The Relativistic Self-Consistent Field , 1935 .

[14]  P. Dirac The quantum theory of the electron , 1928 .

[15]  J. Gauss Calculation of NMR chemical shifts at second-order many-body perturbation theory using gauge-including atomic orbitals , 1992 .

[16]  W. Johnson,et al.  Atomic structure calculations associated with PNC experiments in atomic cesium , 1993 .

[17]  Evert Jan Baerends,et al.  Relativistic regular two‐component Hamiltonians , 1993 .

[18]  G. E. Brown,et al.  On the interaction of two electrons , 1951, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[19]  Wojciech Cencek,et al.  Accurate relativistic energies of one‐ and two‐electron systems using Gaussian wave functions , 1996 .

[20]  Pekka Pyykkö,et al.  On the relativistic theory of NMR chemical shifts , 1983 .

[21]  H. Quiney,et al.  Foundations of the Relativistic Theory of Atomic and Molecular Structure , 1988 .

[22]  E. Davidson,et al.  One- and two-electron integrals over cartesian gaussian functions , 1978 .

[23]  A. Rutkowski Relativistic perturbation theory. I. A new perturbation approach to the Dirac equation , 1986 .

[24]  W. H. Furry ON BOUND STATES AND SCATTERING IN POSITRON THEORY , 1951 .

[25]  R. Feynman,et al.  Space-Time Approach to Non-Relativistic Quantum Mechanics , 1948 .

[26]  J. Almlöf,et al.  Principles for a direct SCF approach to LICAO–MOab‐initio calculations , 1982 .

[27]  D. Rein,et al.  Calculation of the parity nonconserving energy difference between mirror‐image molecules , 1980 .

[28]  Martin Head-Gordon,et al.  Rotating around the quartic angular momentum barrier in fast multipole method calculations , 1996 .

[29]  E. Arimondo,et al.  Observation of inverted infrared lamb dips in separated optical isomers , 1977 .

[30]  Jonathan Sapirstein,et al.  Quantum electrodynamics of many-electron atoms , 1987 .

[31]  Talman Minimax principle for the Dirac equation. , 1986, Physical review letters.

[32]  P. Mohr,et al.  Relativistic, quantum electrodynamic, and weak interaction effects in atoms, Santa Barbara, CA 1988 , 1989 .

[33]  E. Hinds,et al.  Electron dipole moments , 1997 .

[34]  B. Fricke,et al.  A new version of the program TSYM generating relativistic molecular symmetry orbitals for finite double point groups , 1996 .

[35]  Richard E. Stanton,et al.  Kinetic balance: A partial solution to the problem of variational safety in Dirac calculations , 1984 .

[36]  C. E. Wieman,et al.  Measurement of Parity Nonconservation and an Anapole Moment in Cesium , 1997, Science.

[37]  W. Kutzelnigg Perturbation theory of relativistic corrections , 1989 .

[38]  D. Luckhaus,et al.  Fermi resonance structure and femtosecond quantum dynamics of a chiral molecule from the analysis of vibrational overtone spectra of CHBrClF , 1996 .

[39]  K. Fægri,et al.  Optimization of Gaussian basis sets for Dirac-Hartree-Fock calculations , 1996 .

[40]  B. A. Hess,et al.  Relativistic effects on electric properties of many‐electron systems in spin‐averaged Douglas–Kroll and Pauli approximations , 1996 .

[41]  Johnson,et al.  Relativistic all-order many-body calculations of the n=1 and n=2 states of heliumlike ions. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[42]  F. Rosicky On interelectronic magnetic and retardation effects within relativistic hartree-fock theory , 1982 .

[43]  N. Pyper The relativistic theory of the chemical shift , 1983 .

[44]  C. A. Coulson,et al.  Present State of Molecular Structure Calculations , 1960 .

[45]  H. Quiney,et al.  Atomic self-energy calculations using partial-wave mass renormalization , 1994 .