Lucas Visscher

RELATIVISTIC QUANTUM-CHEMISTRY - THE MOLFDIR PROGRAM PACKAGE

In this article the Dirac-Fock-CI method is reviewed. The MOLFDIR program suite that was developed for calculations of this type on molecular systems is described in detail. Computational details of some recent applications are presented to give an impression of the computational resources necessary.

On the origin and contribution of the diamagnetic term in four-component relativistic calculations of magnetic properties

The relativistic Dirac Hamiltonian that describes the motion of electrons in a magnetic field contains only paramagnetic terms (i.e., terms linear in the vector potential A) while the corresponding nonrelativistic Schrodinger Hamiltonian also contains diamagnetic terms (i.e., those from an A2 operator). We demonstrate that all diamagnetic terms relativistically arise from second-order perturbation theory and that they correspond to a “redressing” of the electrons by the magnetic field. If the nonrelativistic limit is taken with a fixed no-pair Hamiltonian (no redressing), the diamagnetic term is missing. The Schrodinger equation is normally obtained by taking the nonrelativistic limit of the Dirac one-electron equation, we show why nonrelativistic use of the A2 operator is also correct in the many-electron case. In nonrelativistic approaches, diamagnetic terms are usually considered in first-order perturbation theory because they can be evaluated as an expectation value over the ground state wave function...

Formulation and implementation of a relativistic unrestricted coupled-cluster method including noniterative connected triples

The formalism for a relativistic open‐shell CCSD(T) method is presented and implemented in a computer program, RELCCSD. The code can be used for calculations with 2‐ or 4‐component relativistic reference wave functions and allows a full inclusion of the spin–orbit coupling. The code is interfaced to the MOLFDIR program system. We illustrate its use with ab initio calculations of the fine structure splittings of Cl, FO, ClO, O+2, and O−2. The triples correction is found to make a large contribution to the Cl atom splitting, which is within 23 cm−1, of the experimental value. The molecular results are within 4 cm−1 of the experimental values where these are available. The value for FO is predicted to be −195±4 cm−1, in good agreement with experiment.

Full four‐component relativistic calculations of NMR shielding and indirect spin–spin coupling tensors in hydrogen halides

Various methods for the inclusion of relativistic effects in the calculation of NMR parameters are discussed. Benchmark values for the NMR shieldings and indirect nuclear spin–spin coupling tensors for the hydrogen halides are calculated using the four‐component relativistic random phase approximation method. Apart from recovering the well‐known trend of increasing hydrogen isotropic shielding going from HF to HI, we also find a large effect on the anisotropy that decreases along this series. Inclusion of spin‐orbit coupling in a nonrelativistic formalism suffices to recover both effects on the hydrogen shieldings but fails to reproduce the much larger effect on the halogen shieldings. This effect can be explained by considering the relativistic mass‐velocity operator that contains correction terms to the nonrelativistic magnetic field operators. We recommend routine inclusion of the one‐electron spin‐orbit correction in calculations of hydrogen shieldings for hydrogens bonded to heavy atoms. For the heavy nucleus shielding one should include an additional mass‐velocity correction. The relativistic effect on the indirect nuclear spin–spin coupling tensor is large and affects mainly the isotropic values; the effect on the anisotropy is small. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1262–1273, 1999

Formulation and implementation of the relativistic Fock-space coupled cluster method for molecules

An implementation of the relativistic multireference Fock-space coupled cluster method is presented which allows simultaneous calculation of potential surfaces for different oxidation states and electronic levels of a molecule, yielding values for spectroscopic constants and transition energies. The method is tested in pilot calculations on the I2 and HgH molecules, and is shown to give a good and balanced description of various electronic states and energies.

Approximate relativistic electron structure methods based on the quaternion modified Dirac

New implementations of the Levy–Leblond, zeroth-order regular approach (ZORA) and spin-free Dirac equation are presented within the framework of the four-component relativistic program system DIRAC. This implementation allows systematic incorporation of relativistic effects at different levels of theory and corresponding computational cost. One of the possibilities of the new code is to neglect the effect of spin–orbit coupling in the orbital optimization process and introduce it in a later stage of the calculation. This method is shown to be unstable despite the boundedness of the spin–orbit operator itself.

Accurate frozen-density embedding potentials as a first step towards a subsystem description of covalent bonds

The frozen-density embedding (FDE) scheme [Wesolowski and Warshel, J. Phys. Chem. 97, 8050 (1993)] relies on the use of approximations for the kinetic-energy component v(T)[rho(1),rho(2)] of the embedding potential. While with approximations derived from generalized-gradient approximation kinetic-energy density functional weak interactions between subsystems such as hydrogen bonds can be described rather accurately, these approximations break down for bonds with a covalent character. Thus, to be able to directly apply the FDE scheme to subsystems connected by covalent bonds, improved approximations to v(T) are needed. As a first step toward this goal, we have implemented a method for the numerical calculation of accurate references for v(T). We present accurate embedding potentials for a selected set of model systems, in which the subsystems are connected by hydrogen bonds of various strength (water dimer and F-H-F(-)), a coordination bond (ammonia borane), and a prototypical covalent bond (ethane). These accurate potentials are analyzed and compared to those obtained from popular kinetic-energy density functionals.

Relativistic and correlation effects on molecular properties. II. The hydrogen halides HF, HCl, HBr, HI, and HAt

A benchmark study of a number of four‐component relativistic correlation methods is presented. Bond lengths, harmonic frequencies, and dissociation energies of the molecules HF, HCl, HBr, HI, and HAt are calculated at various levels of theory, using both the Schrodinger and the Dirac–Coulomb–(Gaunt) Hamiltonian. The inclusion of relativity leads to a weakening of the bond, giving a decrease in the calculated harmonic frequencies and dissociation energies of the hydrogen halides. The effect on the bond length is small. These trends are explained by considering the relativistic change in hybridization induced by the spin–orbit coupling.

The molecular mean-field approach for correlated relativistic calculations

A new approach for relativistic correlated electron structure calculations is proposed by which a transformation to a two-spinor basis is carried out after solving the four-component relativistic Hartree-Fock equations. The method is shown to be more accurate than approaches that apply an a priori transformation to a two-spinor basis. We also demonstrate how the two-component relativistic calculations with properly transformed two-electron interaction can be simulated at the four-component level by projection techniques, thus allowing an assessment of errors introduced by more approximate schemes.

Molecular open shell configuration interaction calculations using the Dirac–Coulomb Hamiltonian : The f 6‐manifold of an embedded EuO9−6 cluster

We present results of all‐electron molecular relativistic (Hartree–Fock–Dirac) and nonrelativistic (Hartree–Fock) calculations followed by a complete open shell configuration interaction (COSCI) calculation on an EuO9−6 cluster in a Ba2GdNbO6 crystal. The results include the calculated energies of a number of states derived from the f6−manifold and 5D–7F luminescence transition wavelengths. The calculations were performed using the molecular Fock–Dirac (molfdir) program package developed in our laboratory. The theory and methods employed in this package are briefly described. The physical models used to analyze the Eu3+ impurity states range from a bare Eu3+ ion to an EuO9−6 cluster embedded in a Madelung potential representing the rest of the crystal. We show that it is necessary to use the embedded cluster model to get a reasonable description of the crystal field splittings of the states arising from the f6‐manifold. Our results indicate that the calculated splittings are very sensitive to the orbitals used. It is therefore essential that relativistic orbitals be used from the outset.