Relativistic calculation of indirect NMR spin-spin couplings using the Douglas-Kroll-Hess approximation

We have employed the Douglas-Kroll-Hess approximation to derive the perturbative Hamiltonians involved in the calculation of NMR spin-spin couplings in molecules containing heavy elements. We have applied this two-component quasirelativistic approach using finite perturbation theory in combination with a generalized Kohn-Sham code that includes the spin-orbit interaction self-consistently and works with Hartree-Fock and both pure and hybrid density functionals. We present numerical results for one-bond spin-spin couplings in the series of tetrahydrides CH(4), SiH(4), GeH(4), and SnH(4). Our two-component Hartree-Fock results are in good agreement with four-component Dirac-Hartree-Fock calculations, although a density-functional treatment better reproduces the available experimental data.     

Gradients for two-component quasirelativistic methods. Application to dihalogenides of element 116

The authors report the implementation of geometry gradients for quasirelativistic two-component Hartree-Fock and density functional methods using either the zero-order regular approximation Hamiltonian or spin-dependent effective core potentials. The computational effort of the resulting program is comparable to that of corresponding nonrelativistic calculations, as it is dominated by the evaluation of derivative two-electron integrals, which is the same for both types of calculations. Besides the implementation of derivatives of matrix elements of the one-particle Hamiltonian with respect to nuclear displacements, the calculation of the derivative exchange-correlation energy for the open shell case involves complicated expressions because of the noncollinear approach chosen to define the spin density. A pilot application to dihalogenides of element 116 shows how spin-orbit coupling strongly affects the chemistry of the superheavy p-block elements. While these molecules are bent at a scalar-relativistic level, spin-orbit coupling is so strong that only the 7p3/2 atomic orbitals of element 116 are involved in bonding, which favors linear molecular geometries for dihalogenides with heavy terminal halogen atoms.     

Coexistence of 1,3-butadiene conformers in ionization energies and Dyson orbitals

The minimum-energy structures on the torsional potential-energy surface of 1,3-butadiene have been studied quantum mechanically using a range of models including ab initio Hartree-Fock and second-order M?ller-Plesset theories, outer valence Green's function, and density-functional theory with a hybrid functional and statistical average orbital potential model in order to understand the binding-energy (ionization energy) spectra and orbital cross sections observed by experiments. The unique full geometry optimization process locates the s-trans-1,3-butadiene as the global minimum structure and the s-gauche-1,3-butadiene as the local minimum structure. The latter possesses the dihedral angle of the central carbon bond of 32.81 degrees in agreement with the range of 30 degrees-41 degrees obtained by other theoretical models. Ionization energies in the outer valence space of the conformer pair have been obtained using Hartree-Fock, outer valence Green's function, and density-functional (statistical average orbital potentials) models, respectively. The Hartree-Fock results indicate that electron correlation (and orbital relaxation) effects become more significant towards the inner shell. The spectroscopic pole strengths calculated in the Green's function model are in the range of 0.85-0.91, suggesting that the independent particle picture is a good approximation in the present study. The binding energies from the density-functional (statisticaly averaged orbital potential) model are in good agreement with photoelectron spectroscopy, and the simulated Dyson orbitals in momentum space approximated by the density-functional orbitals using plane-wave impulse approximation agree well with those from experimental electron momentum spectroscopy. The coexistence of the conformer pair under the experimental conditions is supported by the approximated experimental binding-energy spectra due to the split conformer orbital energies, as well as the orbital momentum distributions of the mixed conformer pair observed in the orbital cross sections of electron momentum spectroscopy.     

Quantum Monte Carlo calculations of the dissociation energies of three-electron hemibonded radical cationic dimers

We report variational and diffusion quantum Monte Carlo (VMC and DMC) calculations of the dissociation energies of the three-electron hemibonded radical cationic dimers of He, NH3, H2O, HF, and Ne. These systems are particularly difficult for standard density-functional methods such as the local-density approximation and the generalized gradient approximation. We have performed both all-electron (AE) and pseudopotential (PP) calculations using Slater-Jastrow wave functions with Hartree-Fock single-particle orbitals. Our results are in good agreement with coupled-cluster CCSD(T) calculations. We have also studied the relative stability of the hemibonded and hydrogen-bonded water radical dimer isomers. Our calculations indicate that the latter isomer is more stable, in agreement with post-Hartree-Fock methods. The excellent agreement between our AE and PP results demonstrates the high quality of the PPs used within our VMC and DMC calculations.     

Accurate relativistic energy-consistent pseudopotentials for the superheavy elements 111 to 118 including quantum electrodynamic effects

Energy-consistent two-component semi-local pseudopotentials for the superheavy elements with atomic numbers 111-118 have been adjusted to fully relativistic multi-configuration Dirac-Hartree-Fock calculations based on the Dirac-Coulomb Hamiltonian, including perturbative corrections for the frequency-dependent Breit interaction in the Coulomb gauge and lowest-order quantum electrodynamic effects. The pseudopotential core includes 92 electrons corresponding to the configuration [Xe]4f(14)5d(10)5f(14). The parameters for the elements 111-118 were fitted by two-component multi-configuration Hartree-Fock calculations in the intermediate coupling scheme to the total energies of 267 up to 797 J levels arising from 31 up to 62 nonrelativistic configurations, including also anionic and highly ionized states, with mean absolute errors clearly below 0.02 eV for averages corresponding to nonrelativistic configurations. Primitive basis sets for one- and two-component pseudopotential calculations have been optimized for the ground and excited states and exhibit finite basis set errors with respect to the finite-difference Hartree-Fock limit below 0.01 and 0.02 eV, respectively. General contraction schemes have been applied to obtain valence basis sets of polarized valence double- to quadruple-zeta quality. Results of atomic test calculations in the intermediate coupling scheme at the Fock-space coupled-cluster level are in good agreement with those of corresponding fully relativistic all-electron calculations based on the Dirac-Coulomb-Breit Hamiltonian. The results demonstrate besides the well-known need of a relativistic treatment at the Dirac-Coulomb level also the necessity to include higher-order corrections for the superheavy elements.     

Closed-shell coupled-cluster theory with spin-orbit coupling

A two-component closed-shell coupled-cluster (CC) approach using relativistic effective core potentials with spin-orbit coupling included in the post-Hartree-Fock treatment is proposed and implemented at the CC singles and doubles (CCSD) level as well as at the CCSD level augmented by a perturbative treatment of triple excitations [CCSD(T)]. The latter invokes as an additional approximation the neglect of the occupied-occupied and virtual-virtual blocks of the spin-orbit coupling matrix in order to avoid the iterative N(7) steps in the treatment of triple excitations. The computational effort of the implemented two-component CC methods is about 10-15 times that of its corresponding nonrelativistic counterpart, which needs to be compared to the by a factor of 32 higher cost for fully relativistic schemes and schemes with spin-orbit coupling included already at the Hartree-Fock self-consistent field (HF-SCF) level. This substantial computational saving is due to the use of real molecular orbitals and real two-electron integrals. Results on 5p-, 6p-, and 7p-block element compounds show that the bond lengths and harmonic frequencies obtained with the present two-component CCSD method agree well with those computed with the CCSD approach including spin-orbit coupling at the HF-SCF level even for the 7p-block element compounds. As for the CCSD(T) approach, high accuracy for 5p- and 6p-block element compounds is retained. However, the difference in bond lengths and harmonic frequencies becomes somewhat more pronounced for the 7p-block element compounds.     

Energy gradients with respect to atomic positions and cell parameters for the Kohn-Sham density-functional theory at the Gamma point

The application of theoretical methods based on density-functional theory is known to provide atomic and cell parameters in very good agreement with experimental values. Recently, construction of the exact Hartree-Fock exchange gradients with respect to atomic positions and cell parameters within the Gamma-point approximation has been introduced. In this article, the formalism is extended to the evaluation of analytical Gamma-point density-functional atomic and cell gradients. The infinite Coulomb summation is solved with an effective periodic summation of multipole tensors. While the evaluation of Coulomb and exchange-correlation gradients with respect to atomic positions are similar to those in the gas phase limit, the gradients with respect to cell parameters needs to be treated with some care. The derivative of the periodic multipole interaction tensor needs to be carefully handled in both direct and reciprocal space and the exchange-correlation energy derivative leads to a surface term that has its origin in derivatives of the integration limits that depend on the cell. As an illustration, the analytical gradients have been used in conjunction with the QUICCA algorithm to optimize one-dimensional and three-dimensional periodic systems at the density-functional theory and hybrid Hartree-Fock/density-functional theory levels. We also report the full relaxation of forsterite supercells at the B3LYP level of theory.     

Multiconfiguration optimized effective potential method for a density-functional treatment of static correlation

An approach to treat static correlation within a density-functional framework is presented. To that end, a multiconfiguration optimized effective potential (MCOEP) method is derived. In contrast to standard multiconfiguration self-consistent field (MCSCF) methods and previous combinations of MCSCF procedures with density-functional theory, the MCOEP method yields well-defined physically meaningful orbital and eigenvalue spectra. In addition to the electronic ground state also excited electronic states can be described. The MCOEP method is implemented invoking the localized Hartree-Fock approximation, leading to a multiconfiguration localized Hartree-Fock approach. Applications of the new method to the dissociation of the hydrogen molecule and the isomerization of ethene and cyclobutadiene show that it is capable of describing situations that are characterized by strong static correlation.     

A first-principles study of the electronic and structural properties of gamma-TaON

The geometric and electronic structure of the recently found new polymorph of tantalum oxynitride, gamma-TaON, and its structural stability were studied quantum-chemically at the density functional level. Results obtained by complementary quantum-chemical techniques with wavefunctions either expanded in atom-centered functions or in plane waves were compared, having employed pure density-functional functionals within the generalized gradient approximation as well as density-functional/Hartree-Fock hybrid methods. In particular, several plausible anion distributions were investigated and, in accordance with Pauling's second rule, it was found that the configuration in which nitrogen occupies crystallographic sites with highest coordination numbers is the most stable one. Theoretically generated local structural parameters were used to improve the accuracy of the experimentally derived information. The bonding situation in the most stable configuration was investigated by an analysis of the density of states.     

Theoretical study of the electronic spectra of square-planar platinum (II) complexes based on the two-component relativistic time-dependent density-functional theory

In the present work the electronic spectra of [PtCl(4)](2-), [PtBr(4)](2-), and [Pt(CN)(4)](2-) are studied with a recently proposed relativistic time-dependent density-functional theory (TDDFT) based on the two-component zeroth-order regular approximation and a noncollinear exchange-correlation (XC) functional. The contribution to the double group excited states in terms of singlet and triplet single group excited states is estimated through the inner product of the transition density matrix obtained from two-component and scalar relativistic TDDFT calculations to better understand the double group excited states. Spin-orbital coupling effects are found to be very important in order to simulate the electronic spectra of these complexes. The results show that the two-component TDDFT formalism can afford excitation energies with high accuracy for the transition-metal systems studied here when use is made of a proper XC potential.     

Resolution of identity Dirac-Kohn-Sham method using the large component only: Calculations of g-tensor and hyperfine tensor

A new relativistic two-component density functional approach, based on the Dirac-Kohn-Sham method and an extensive use of the technique of resolution of identity (RI), has been developed and is termed the DKS2-RI method. It has been applied to relativistic calculations of g and hyperfine tensors of coinage-metal atoms and some mercury complexes. The DKS2-RI method solves the Dirac-Kohn-Sham equations in a two-component framework using explicitly a basis for the large component only, but it retains all contributions coming from the small component. The DKS2-RI results converge to those of the four-component Dirac-Kohn-Sham with an increasing basis set since the error associated with the use of RI will approach zero. The RI approximation provides a basis for a very efficient implementation by avoiding problems associated with complicated integrals otherwise arising from the elimination of the small component. The approach has been implemented in an unrestricted noncollinear two-component density functional framework. DKS2-RI is related to Dyall's [J. Chem. Phys. 106, 9618 (1997)] unnormalized elimination of the small component method (which was formulated at the Hartree-Fock level and applied to one-electron systems only), but it takes advantage of the local Kohn-Sham exchange-correlation operators (as, e.g., arising from local or gradient-corrected functionals). The DKS2-RI method provides an attractive alternative to existing approximate two-component methods with transformed Hamiltonians (such as Douglas-Kroll-Hess [Ann. Phys. 82, 89 (1974); Phys. Rev. A 33, 3742 (1986)] method, zero-order regular approximation, or related approaches) for relativistic calculations of the structure and properties of heavy-atom systems. In particular, no picture-change effects arise in the property calculations.     

Toward an accurate and efficient theory of physisorption. I. Development of an augmented density-functional theory model

Currently available density functionals cannot describe the dispersion component of the interaction energy present in weakly bound complexes. Moreover, the exchange energy as obtained from the density-functional theory is often incorrect. Examples of problematic cases include clusters of van der Waals-bound rare-gas atoms and most hydrogen-bonded molecular systems. Thus, accurate ab initio methods to treat intermolecular forces should be used in such systems. These methods are, however, too slow to be applicable to the large systems needed to model adsorption. This is why DFT continues to be used, where, in addition, a quite common compensation of errors sometimes produces some sort of agreement with the corresponding experimental data. In this paper, we analyze in detail the inadequacy of standard DFT for describing the weak binding present in a few rare gas-rare gas, metal atom-rare gas, and metal atom-metal atom dimers.Inspired by the success of the Hartree-Fock plus (damped) dispersion (HFD) method, we test the use of an improved hybrid model in which to a density-functional interaction energy (with corrected exchange and avoidance of double-counting of dispersion), a (damped) dispersion expansion is added in the usual way.Comparisons with accurate theoretical or experimental benchmarks show that our DFdD method using the revPBEx or revPBEx+VWNc functionals and accurate dispersion coefficients is found to recover the interaction energy curves very well for many of the tested systems. The sec and paper in this series will describe the use of the DFdD method for physisorption for the previously well-studied (but not solved) case of Xe/Cu(111).     

Convergence of approximate two-component Hamiltonians: how far is the Dirac limit

A systematic elimination of the off-diagonal parts of the Dirac Hamiltonian is carried out in the spirit of the Douglas-Kroll [Ann. Phys. 82, 87 1974] approach and the recently proposed infinite-order two-component method. The present approach leads to a series of approximate two-component Hamiltonians which are exact through a certain order in the external potential. These Hamiltonians are used to study the convergence pattern of approximate two-component theories. It is shown that to achieve an acceptably high accuracy for low-lying one-electron levels in heavy and superheavy systems one needs to use approximate Hamiltonians of prohibitively high order in the external potential. One can conclude that the finite-order two-component Hamiltonians are of limited usefulness in accurate relativistic calculations for heavy and superheavy systems.     

Relativistic calculation of nuclear magnetic shielding using normalized elimination of the small component

The normalized elimination of the small component (NESC) theory, recently proposed by Filatov and Cremer, is extended to include magnetic interactions and applied to the calculation of the nuclear magnetic shielding in HX (X=F, Cl, Br, I) systems. The NESC calculations are performed at the levels of the zeroth-order regular approximation (ZORA) and the second-order regular approximation (SORA). The calculations show that the NESC-ZORA results are very close to the NESC-SORA results, except for the shielding of the I nucleus. Both the NESC-ZORA and NESC-SORA calculations yield very similar results to the previously reported values obtained using the relativistic infinite-order two-component coupled Hartree-Fock method. The difference between NESC-ZORA and NESC-SORA results is significant for the shieldings of iodine.     

Characterization of the molecular parameters determining charge transport in anthradithiophene

The molecular parameters that govern charge transport in anthradithiophene (ADT) are studied by a joint experimental/theoretical approach involving high-resolution gas-phase photoelectron spectroscopy and quantum-mechanical methods. The hole reorganization energy of ADT has been determined by an analysis of the vibrational structure of the lowest ionization band in the gas-phase photoelectron spectrum as well as by density-functional theory calculations. In addition, various dimers and clusters of ADT molecules have been considered in order to understand the effect of molecular packing on the hole and electron intermolecular transfer integrals. The results indicate that the intrinsic electronic structure, the relevant intramolecular vibrational modes, and the intermolecular interactions in ADT are very similar to those in pentacene.     

The calculation of excitation energies based on the relativistic two-component zeroth-order regular approximation and time-dependent density-functional with full use of symmetry

In the present work, we propose a relativistic time-dependent density-functional theory (TDDFT) based on the two-component zeroth-order regular approximation and a noncollinear exchange-correlation (XC) functional. This two-component TDDFT formalism has the correct nonrelativistic limit and affords the correct threefold degeneracy of triplet excitations. The relativistic TDDFT formalism is implemented into the AMSTERDAM DENSITY FUNCTIONAL program package for closed-shell systems with full use of double-group symmetry to reduce the computational effort and facilitate the assignments. The performance of the formalism is tested on some closed-shell atoms, ions, and a few diatomic molecules containing heavy elements. The results show that the fine structure of the excited states for most atoms and ions studied here can be accurately accounted for with a proper XC potential. For the excitation energies of the molecules studied here, the present formalism shows promise and the error encountered is comparable to that of nonrelativistic TDDFT calculations on light elements.     

Ab initio study of optical properties of rhodamine 6G molecular dimers

Equilibrium atomic geometries of rhodamine 6G (R6G) dye molecule dimers are studied using density-functional theory. Electron-energy structure and optical properties of R6G H and J dimers are calculated using the generalized gradient approximation method with ab initio pseudopotentials. Our theory predicts substantial redshifts or blueshifts of the optical absorption spectra of R6G dye molecules after aggregation in J or H dimers, respectively. Predicted optical properties of R6G dimers are interpreted in terms of interatomic and intermolecular interactions. Results of the calculations are discussed in comparison with experimental data.     

A closed-shell coupled-cluster treatment of the Breit-Pauli first-order relativistic energy correction

First-order relativistic corrections to the energy of closed-shell molecular systems are calculated, using all terms in the two-component Breit-Pauli Hamiltonian. In particular, we present the first implementation of the two-electron Breit orbit-orbit integrals, thus completing the first-order relativistic corrections within the two-component Pauli approximation. Calculations of these corrections are presented for a series of small and light molecules, at the Hartree-Fock and coupled-cluster levels of theory. Comparisons with four-component Dirac-Coulomb-Breit calculations demonstrate that the full Breit-Pauli energy corrections represent an accurate approximation to a fully relativistic treatment of such systems. The Breit interaction is dominated by the spin-spin interaction, the orbit-orbit interaction contributing only about 10% to the total two-electron relativistic correction in molecules consisting of light atoms. However, the relative importance of the orbit-orbit interaction increases with increasing nuclear charge, contributing more than 20% in H(2)S.     

Calculations of two-photon charge-transfer excitations using Coulomb-attenuated density-functional theory

In this work, we show that an implementation of Coulomb-attenuated density-functional theory leads to considerably better prospects than hitherto for modeling two-photon absorption cross sections for charge-transfer species. This functional, which corrects for the effect of poor asymptotic dependence of commonly used functionals, essentially brings down the widely different results for larger charge-transfer species between Hartree-Fock and density-functional theory (DFT)-B3LYP into a closer range. The Coulomb-attenuated functional, which retains the best aspects of the Hartree-Fock and DFT-B3LYP methods, proves to be very promising for further modeling design of multiphoton materials with technical applications.