The Dirac equation in quantum chemistry: Strategies to overcome the current computational problems

A perspective on the use of the relativistic Dirac equation in quantum chemistry is given. It is demonstrated that many of the computational problems that plague the current implementations of the different electronic structure methods can be overcome by utilizing the locality of the small component wave function and density. Possible applications of such new and more efficient formulations are discussed. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 759–766, 2002

[1]  J. Olsen,et al.  The generalized active space concept for the relativistic treatment of electron correlation. I. Kramers-restricted two-component configuration interaction , 2001 .

[2]  I. P. Grant,et al.  RELATIVISTIC CALCULATION OF ELECTROMAGNETIC INTERACTIONS IN MOLECULES , 1997 .

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

[4]  K. Dyall,et al.  Relativistic four‐component multiconfigurational self‐consistent‐field theory for molecules: Formalism , 1996 .

[5]  Y. Ishikawa,et al.  Relativistic coupled cluster method based on Dirac—Coulomb—Breit wavefunctions. Ground state energies of atoms with two to five electrons , 1994 .

[6]  J. Olsen,et al.  Passing the one-billion limit in full configuration-interaction (FCI) calculations , 1990 .

[7]  K. Dyall Second-order Møller-Plesset perturbation theory for molecular Dirac-Hartree-Fock wavefunctions. Theory for up to two open-shell electrons , 1994 .

[8]  Benny G. Johnson,et al.  THE CONTINUOUS FAST MULTIPOLE METHOD , 1994 .

[9]  L. Visscher,et al.  The electronic structure of the PtH molecule: Fully relativistic configuration interaction calculations of the ground and excited states , 1993 .

[10]  P. Schwerdtfeger,et al.  Fully relativistic coupled cluster treatment for parity-violating energy differences in molecules. , 2000, Physical review letters.

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

[12]  M. Quack,et al.  Multiconfiguration linear response approach to the calculation of parity violating potentials in polyatomic molecules , 2000 .

[13]  M. Dolg ACCURACY OF ENERGY-ADJUSTED QUASIRELATIVISTIC PSEUDOPOTENTIALS : A CALIBRATION STUDY OF XH AND X2 (X = F, CL, BR, I, AT) , 1996 .

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

[15]  G. Breit The Effect of Retardation on the Interaction of Two Electrons , 1929 .

[16]  J. G. Snijders,et al.  Towards an order-N DFT method , 1998 .

[17]  Christoph van Wüllen,et al.  Molecular density functional calculations in the regular relativistic approximation: Method, application to coinage metal diatomics, hydrides, fluorides and chlorides, and comparison with first-order relativistic calculations , 1998 .

[18]  Evert Jan Baerends,et al.  Towards an order , 1998 .

[19]  Kimihiko Hirao,et al.  A new computational scheme for the Dirac–Hartree–Fock method employing an efficient integral algorithm , 2001 .

[20]  J. A. Gaunt The Relativistic Theory of an Atom with Many Electrons , 1929 .

[21]  Laerdahl,et al.  Theoretical analysis of parity-violating energy differences between the enantiomers of chiral molecules , 2000, Physical review letters.

[22]  Michael Dolg,et al.  The Beijing four-component density functional program package (BDF) and its application to EuO, EuS, YbO and YbS , 1997 .

[23]  Luis Seijo,et al.  The ab initio model potential method: Lanthanide and actinide elements , 2001 .

[24]  J. G. Snijders,et al.  NONSINGULAR TWO/ONE-COMPONENT RELATIVISTIC HAMILTONIANS ACCURATE THROUGH ARBITRARY HIGH ORDER IN ALPHA 2 , 1997 .

[25]  K. Dyall Interfacing relativistic and nonrelativistic methods. II. Investigation of a low-order approximation , 1998 .

[26]  Lucas Visscher,et al.  Approximate molecular relativistic Dirac-Coulomb calculations using a simple Coulombic correction , 1997 .

[27]  Han,et al.  Supersymmetrization of N=1 ten-dimensional supergravity with Lorentz Chern-Simons term. , 1986, Physical review. D, Particles and fields.

[28]  Gulzari Malli,et al.  Relativistic and electron correlation effects in molecules and solids , 1994 .

[29]  Christel M. Marian,et al.  A mean-field spin-orbit method applicable to correlated wavefunctions , 1996 .

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

[31]  J. G. Snijders,et al.  Relativistic calculations on the adsorption of CO on the (111) surfaces of Ni, Pd, and Pt within the zeroth-order regular approximation , 1997 .

[32]  J. G. Snijders,et al.  Construction of the Foldy–Wouthuysen transformation and solution of the Dirac equation using large components only , 1996 .

[33]  L. Curtiss,et al.  Scalar relativistic effects on energies of molecules containing atoms from hydrogen through argon , 2001 .

[34]  Eberhard Engel,et al.  Four-component relativistic density functional calculations of heavy diatomic molecules , 2000 .

[35]  Trygve Helgaker,et al.  Direct optimization of the AO density matrix in Hartree-Fock and Kohn-Sham theories , 2000 .

[36]  L. Visscher,et al.  On the origin and contribution of the diamagnetic term in four-component relativistic calculations of magnetic properties , 1999 .

[37]  Goldman Sp Variational representation of the Dirac-Coulomb Hamiltonian with no spurious roots. , 1985 .

[38]  Trygve Helgaker,et al.  Coupled cluster energy derivatives. Analytic Hessian for the closed‐shell coupled cluster singles and doubles wave function: Theory and applications , 1990 .

[39]  Hess,et al.  Relativistic electronic-structure calculations employing a two-component no-pair formalism with external-field projection operators. , 1986, Physical review. A, General physics.

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

[41]  Ph. Durand,et al.  Regular Two-Component Pauli-Like Effective Hamiltonians in Dirac Theory , 1986 .

[42]  M. Barysz The relativistic scheme for eliminating small components Hamiltonian: Analysis of approximations , 2000 .

[43]  Jean-Marc Lévy-Leblond,et al.  Nonrelativistic particles and wave equations , 1967 .

[44]  I. P. Grant,et al.  Relativistic, quantum electrodynamic and many-body effects in the water molecule , 1998 .

[45]  K. Dyall,et al.  Interfacing relativistic and nonrelativistic methods. III. Atomic 4-spinor expansions and integral approximations , 1999 .

[46]  R. Nalewajski Density Functional Theory II , 1996 .

[47]  Kenneth G. Dyall,et al.  INTERFACING RELATIVISTIC AND NONRELATIVISTIC METHODS. I. NORMALIZED ELIMINATION OF THE SMALL COMPONENT IN THE MODIFIED DIRAC EQUATION , 1997 .

[48]  C. Bauschlicher,et al.  The dissociation energies of AlH2 and AlAr , 1995 .

[49]  W. R. Wadt,et al.  Ab initio effective core potentials for molecular calculations. Potentials for K to Au including the outermost core orbitals , 1985 .

[50]  K. Dyall,et al.  Formulation and implementation of a relativistic unrestricted coupled-cluster method including noniterative connected triples , 1996 .

[51]  L. Visscher,et al.  Approximate relativistic electron structure methods based on the quaternion modified Dirac , 2000 .

[52]  P. Dirac The Quantum Theory of the Electron. Part II , 1928 .

[53]  T. Saue,et al.  Quaternion symmetry in relativistic molecular calculations: The Dirac–Hartree–Fock method , 1999 .

[54]  P. Pyykkö,et al.  Calculated self-energy contributions for an ns valence electron using the multiple-commutator method , 1999 .

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

[56]  T. H. Dunning Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[57]  D. Cromer,et al.  Self-Consistent-Field Dirac-Slater Wave Functions for Atoms and Ions. I. Comparison with Previous Calculations , 1965 .

[58]  Evert Jan Baerends,et al.  Geometry optimizations in the zero order regular approximation for relativistic effects. , 1999 .

[59]  Pekka Pyykkö,et al.  Relativistic effects in structural chemistry , 1988 .

[60]  M. Esser Direct MRCI method for the calculation of relativistic many-electron wavefunctions. I. General formalism , 1984 .

[61]  L. Visscher On the construction of double group molecular symmetry functions , 1996 .