[Show abstract][Hide abstract] ABSTRACT: We present a formulation of molecular response theory for the description of a quantum mechanical molecular system in the presence of a weak, monochromatic, linearly polarized electromagnetic field without introducing truncated multipolar expansions. The presentation focuses on a description of linear absorption by adopting the energy-loss approach in combination with the complex polarization propagator formulation of response theory. Going beyond the electric-dipole approximation is essential whenever studying electric-dipole-forbidden transitions, and in general, non-dipolar effects become increasingly important when addressing spectroscopies involving higher-energy photons. These two aspects are examined by our study of the near K-edge X-ray absorption fine structure of the alkaline earth metals (Mg, Ca, Sr, Ba, and Ra) as well as the trans-polyenes. In following the series of alkaline earth metals, the sizes of non-dipolar effects are probed with respect to increasing photon energies and a detailed assessment of results is made in terms of studying the pertinent transition electron densities and in particular their spatial extension in comparison with the photon wavelength. Along the series of trans-polyenes, the sizes of non-dipolar effects are probed for X-ray spectroscopies on organic molecules with respect to the spatial extension of the chromophore.
The Journal of Chemical Physics 06/2015; 142(24):244111. DOI:10.1063/1.4922697 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Spectroscopic constants for the homonuclear dimers of the very heavy rare gases radon (Rn) and eka-radon (Uuo) are reported. A computational protocol using the eXact 2-Component molecular-mean field Hamiltonian has been established based on extensive calculations of the xenon dimer. We find that reliable results require CCSD(T) calculations at the extrapolated basis set limit. In this limit counterpoise corrected results are closer to experimentally derived values than uncorrected ones. Furthermore, in an attempt to reduce the computational cost while retaining very high accuracy, we studied the performance of range-separated density functional theory. Although we observe a somewhat more favorable basis set convergence and reduced importance of connected triples with range-separated methods compared to pure wave function theory, in practice we have to employ the same computational protocol for obtaining converged results. At the Dirac-Coulomb level we find an almost fourfold increase of binding energy when going from the radon to the eka-radon dimer, but the inclusion of spin-other-orbit interaction reduces the dissociation energy of the heaviest dimer by about 40 %.
[Show abstract][Hide abstract] ABSTRACT: This chapter provides a critical review of the use of 2- and 4-component relativistic Hamiltonians combined with all-electron methods and appropriate basis sets for the study of lanthanide and actinide chemistry. These approaches provide in principle the more rigorous treatment of the electronic structure but typically demand large computational resources due to the large basis sets that are required for accurate energetics. For density functional theory (DFT) calculations one needs to select the appropriate density functional approximation (DFA) on basis of assessments for lighter elements because little or no high-precision experimental information on isolated molecules is available for the f elements. The chapter discusses the available relativistic Hamiltonians that form a prerequisite for the treatment of electronic structure of heavy elements. It focuses on methods suitable for an all-electron treatment of f elements.
Computational Methods in Lanthanide and Actinide Chemistry, 02/2015: pages 55-87; , ISBN: 9781118688311
[Show abstract][Hide abstract] ABSTRACT: We present a formulation of 4-component relativistic self-consistent field (SCF) theory for a molecular solute described within the framework of the polarizable continuum model (PCM) for solvation. The linear response function for a 4-component PCM-SCF state is also derived. The explicit form of the additional contributions to the first-order response equations is given. The implementation of such a 4-component PCM-SCF model, as carried out in a development version of the DIRAC program package, is documented. In particular, we present the newly developed application programming interface (API) PCMSolver used in the actual implementation with DIRAC. To demonstrate the applicability of the approach we present and analyze calculations of solvation effects on the geometries, electric dipole moments and static electric dipole polarizabilities for the Group 16 Dihydrides H2X (X = O, S, Se, Te, Po).
The Journal of Physical Chemistry A 11/2014; DOI:10.1021/jp507279y · 2.69 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The effects of parity violation (PV) on the vibrational transitions of chiral uranium compounds of the type N[triple bond, length as m-dash]UXYZ and N[triple bond, length as m-dash]UHXY (X, Y, Z = F, Cl, Br, I) are analysed by means of exact two-component relativistic (X2C) Hartree-Fock and density functional calculations using NUFClI and NUHFI as representative examples. The PV contributions to the vibrational transitions were found to be in the Hz range, larger than for any of the earlier proposed chiral molecules. Thus, these systems are very promising candidates for future experimental PV measurements. A detailed comparison of the N[triple bond, length as m-dash]UHFI and the N[triple bond, length as m-dash]WHFI homologues reveals that subtle electronic structure effects, rather than exclusively a simple Z(5) scaling law, are the cause of the strong enhancement in PV contributions of the chiral uranium molecules.
[Show abstract][Hide abstract] ABSTRACT: Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree-Fock, Kohn-Sham, multiconfigurational self-consistent-field, Møller-Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.
[Show abstract][Hide abstract] ABSTRACT: Mössbauer spectroscopy is an indispensable spectroscopic technique and analytical tool in iron coordination chemistry. The linear correlation between the electron density at the nucleus ("contact density") and experimental isomer shifts has been used to link calculated contact densities to experimental isomer shifts. Here we have investigated relativistic methods of systematically increasing sophistication, including the eXact 2-Component (X2C) Hamiltonian and a finite-nucleus model, for the calculation of isomer shifts of iron compounds. While being of similar accuracy as the full four-component treatment, X2C calculations are far more efficient. We find that effects of spin-orbit coupling can safely be neglected, leading to further speedup. Linear correlation plots using effective densities rather than contact densities versus experimental isomer shift lead to a correlation constant a = -0.294 a0(-3) mm s(-1) (PBE functional) which is close to an experimentally derived value. Isomer shifts of similar quality can thus be obtained both with and without fitting, which is not the case if one pursues a priori a non-relativistic model approach. As an application for a biologically relevant system, we have studied three recently proposed [Fe]-hydrogenase intermediates. The structures of these intermediates were extracted from QM/MM calculations using large QM regions surrounded by the full enzyme and a solvation shell of water molecules. We show that a comparison between calculated and experimentally observed isomer shifts can be used to discriminate between different intermediates, whereas calculated atomic charges do not necessarily correlate with Mössbauer isomer shifts. Detailed analysis reveals that the difference in isomer shifts between two intermediates is due to an overlap effect.
[Show abstract][Hide abstract] ABSTRACT: The use of magnetic-field dependent London atomic orbitals, also called gauge including atomic orbitals, is known to be an efficient choice for accurate non-relativistic calculations of magnetisabilities. In this work, the appropriate formulas were extended and implemented in the framework of the four-component relativistic linear response method at the self-consistent field single reference level. Benefits of employing the London atomic orbitals in relativistic calculations are illustrated with Hartree–Fock wave functions on the XF3 (X = N, P, As, Sb, Bi) series of molecules. Significantly better convergence of magnetisabilities with respect to the basis set size is observed compared to calculations employing a common gauge origin. In fact, it is mandatory to use London atomic orbitals unless you want to use ridiculously large basis sets. Relativistic effects on magnetisabilities are found to be quite small (g tensors in the relativistic domain and discuss its origin. Finally, we visualise the magnetisability density which shows markedly atomic features evocative of Pascal’s rules.
[Show abstract][Hide abstract] ABSTRACT: With their rich electronic, vibrational, rotational and hyperfine structure, molecular systems have the potential to play a decisive role in precision tests of fundamental physics. For example, electroweak nuclear interactions should cause small energy differences between the two enantiomers of chiral molecules, a signature of parity symmetry breaking. Enantioenriched oxorhenium(vii) complexes S-(-)- and R-(+)- bearing a chiral 2-methyl-1-thio-propanol ligand have been prepared as potential candidates for probing molecular parity violation effects via high resolution laser spectroscopy of the Re[double bond, length as m-dash]O stretching. Although the rhenium atom is not a stereogenic centre in itself, experimental vibrational circular dichroism (VCD) spectra revealed a surrounding chiral environment, evidenced by the Re[double bond, length as m-dash]O bond stretching mode signal. The calculated VCD spectrum of the R enantiomer confirmed the position of the sulfur atom cis to the methyl, as observed in the solid-state X-ray crystallographic structure, and showed the presence of two conformers of comparable stability. Relativistic quantum chemistry calculations indicate that the vibrational shift between enantiomers due to parity violation is above the target sensitivity of an ultra-high resolution infrared spectroscopy experiment under active preparation.
[Show abstract][Hide abstract] ABSTRACT: We present C6 homo- and heteroatomic dispersion coefficients for all closed-shell atoms of the periodic table based on dipole–dipole polarizabilities at imaginary frequencies calculated using our recent extension of the complex polarization propagator approach to the four-component relativistic Kohn–Sham approach. Lack of proper reference data bars definite conclusions as to which density functional shows the overall best performance, and we therefore call for state-of-the-art wave function-based correlated calculations of dispersion coefficients. Scalar relativistic effects are significant already for elements as light as zinc, whereas spin–orbit effects must be taken into account only for very heavy elements.
[Show abstract][Hide abstract] ABSTRACT: We report the implementation of long-range second-order Møller–Plesset perturbation theory coupled with short-range density functional theory (MP2-srDFT) based on the 4-component relativistic Dirac–Coulomb Hamiltonian. The range separation of the two-electron interaction is based on the error function, such that the long-range interaction, to be handled by wave function theory, corresponds to the potential of finite electrons with a Gaussian charge distribution. We argue that the interelectronic distance associated with the range-separation parameter should accordingly be determined from a Gaussian rather than a hard-sphere model. As a first application of our relativistic MP2-srDFT implementation we calculate spectroscopic constants of the complete series of homoatomic rare gas dimers, from helium to the superheavy element 118 and with bonding dominated by dispersion forces. We find that the MP2-srDFT method is less sensitive to the basis set quality than pure MP2, but for the heavier rare gas dimers the computational cost is approximately the same as for pure MP2 if one seeks convergence with respect to both basis set and number of correlated electrons. The inclusion of a short-range DFT contribution allows to dampen the tendency of pure MP2 to overbind the heavier dimers, but it is difficult to find an optimal range-separation parameter for the whole series of diatomics. Interestingly, MP2-srLDA shows better performance than MP2-srPBE for the selected molecules.
Chemical Physics 02/2012; 395(1):54–62. DOI:10.1016/j.chemphys.2011.06.024 · 1.65 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We report the implementation of nuclear magnetic resonance (NMR) shielding tensors within the four-component relativistic Kohn-Sham density functional theory including non-collinear spin magnetization and employing London atomic orbitals to ensure gauge origin independent results, together with a new and efficient scheme for assuring correct balance between the large and small components of a molecular four-component spinor in the presence of an external magnetic field (simple magnetic balance). To test our formalism we have carried out calculations of NMR shielding tensors for the HX series (X = F, Cl, Br, I, At), the Xe atom, and the Xe dimer. The advantage of simple magnetic balance scheme combined with the use of London atomic orbitals is the fast convergence of results (when compared with restricted kinetic balance) and elimination of linear dependencies in the basis set (when compared to unrestricted kinetic balance). The effect of including spin magnetization in the description of NMR shielding tensor has been found important for hydrogen atoms in heavy HX molecules, causing an increase of isotropic values of 10%, but negligible for heavy atoms.
The Journal of Chemical Physics 01/2012; 136(1):014108. DOI:10.1063/1.3671390 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We report the implementation of nuclear magnetic resonance (NMR) shielding tensors within the four-component relativistic Kohn–Sham density functional theory including non-collinear spin magnetization and employing London atomic orbitals to ensure gauge origin independent results, together with a new and efficient scheme for assuring correct balance between the large and small components of a molecular four-component spinor in the presence of an external magnetic field (simple magnetic balance). To test our formalism we have carried out calculations of NMR shielding tensors for the HX series (X = F, Cl, Br, I, At), the Xe atom, and the Xe dimer. The advantage of simple magnetic balance scheme combined with the use of London atomic orbitals is the fast convergence of results (when compared with restricted kinetic balance) and elimination of linear dependencies in the basis set (when compared to unrestricted kinetic balance). The effect of including spin magnetization in the description of NMR shielding tensor has been found important for hydrogen atoms in heavy HX molecules, causing an increase of isotropic values of 10%, but negligible for heavy atoms.
The Journal of Chemical Physics 01/2012; 136:014108-014120. · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: An overview is given of 2- and 4-component relativistic Hamiltonians for
use in quantum chemistry. The physics of the relativistic corrections
are discussed in terms of the Pauli Hamiltonian.
[Show abstract][Hide abstract] ABSTRACT: Last years witnessed a remarkable interest in application of quantum
computing for solving problems in quantum chemistry more efficiently than
classical computers allow. Very recently, even first proof-of-principle
experimental realizations have been reported. However, so far only the
non-relativistic regime (i.e. Schroedinger equation) has been explored, while
it is well known that relativistic effects can be very important in chemistry.
In this letter we present the first quantum algorithm for relativistic
computations of molecular energies. We show how to efficiently solve the
eigenproblem of the Dirac-Coulomb Hamiltonian on a quantum computer and
demonstrate the functionality of the proposed procedure by numerical
simulations of computations of the spin-orbit splitting in the SbH molecule.
Finally, we propose quantum circuits with 3 qubits and 9 or 10 CNOTs, which
implement a proof-of-principle relativistic quantum chemical calculation for
this molecule and might be suitable for an experimental realization.
Physical Review A 11/2011; 85(3). DOI:10.1103/PhysRevA.85.030304 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present the implementation and application of 4-component relativistic magnetically induced current density using London atomic orbitals for self-consistent field models. We obtain a magnetically balanced basis by a simple scheme where orbitals obtained by imposing restricted kinetic balance are extended by their unrestricted kinetic balance complement. The presented methodology makes it possible to analyze the concept of aromaticity based on the ring current criterion for closed-shell molecules across the periodic table and is independent of the choice of gauge origin. As a first illustration of the methodology we study plots of the magnetically induced current density and its divergence in the series C(5)H(5)E (E = CH, N, P, As, Sb, Bi) at the Kohn-Sham level, as well as integrated ring current susceptibilities, which we compare to previous results (R. Bast et al., Chem. Phys., 2009, 356, 187) obtained using a common gauge origin approach. We find that the current strength decreases monotonically along the series, but that all molecules qualify as aromatic according to the ring current criterion.
[Show abstract][Hide abstract] ABSTRACT: The spectrum arising from the (π*)(2) configuration of the chalcogen dimers, namely, the X(2)1, a2, and b0(+) states, is calculated using wave-function theory based methods. Two-component (2c) and four-component (4c) multireference configuration interaction (MRCI) and Fock-space coupled cluster (FSCC) methods are used as well as two-step methods spin-orbit complete active space perturbation theory at 2nd order (SO-CASPT2) and spin-orbit difference dedicated configuration interaction (SO-DDCI). The energy of the X(2)1 state corresponds to the zero-field splitting of the ground state spin triplet. It is described with high accuracy by the 2- and 4-component methods in comparison with experiment, whereas the two-step methods give about 80% of the experimental values. The b0(+) state is well described by 4c-MRCI, SO-CASPT2, and SO-DDCI, but FSCC fails to describe this state and an intermediate Hamiltonian FSCC ansatz is required. The results are readily rationalized by a two-parameter model; Δε, the π* spinor splitting by spin-orbit coupling and K, the exchange integral between the π(1)* and the π(-1)* spinors with, respectively, angular momenta 1 and -1. This model holds for all systems under study with the exception of Po(2).
The Journal of Chemical Physics 09/2011; 135(11):114106. DOI:10.1063/1.3636084 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The electrostatic contribution to the Mössbauer isomer shift of mercury for the series HgFn
(n = 1, 2, 4) with respect to the neutral atom has been investigated in the framework of four- and two-component relativistic theory. Replacing the integration of the electron density over the nuclear volume by the contact density (that is, the electron density at the nucleus) leads to a 10% overestimation of the isomer shift. The systematic nature of this error suggests that it can be incorporated into a correction factor, thus justifying the use of the contact density for the calculation of the Mössbauer isomer shift. The performance of a large selection of density functionals for the calculation of contact densities has been assessed by comparing with finite-field four-component relativistic coupled-cluster with single and double and perturbative triple excitations [CCSD(T)] calculations. For the absolute contact density of the mercury atom, the Density Functional Theory (DFT) calculations are in error by about 0.5%, a result that must be judged against the observation that the change in contact density along the series HgFn
(n = 1, 2, 4), relevant for the isomer shift, is on the order of 50 ppm with respect to absolute densities. Contrary to previous studies of the 57Fe isomer shift (F Neese, Inorg Chim Acta 332:181, 2002), for mercury, DFT is not able to reproduce the trends in the isomer shift provided by reference data, in our case CCSD(T) calculations, notably the non-monotonous decrease in the contact density along the series HgFn
(n = 1, 2, 4). Projection analysis shows the expected reduction of the 6s
1/2 population at the mercury center with an increasing number of ligands, but also brings into light an opposing effect, namely the increasing polarization of the 6s
1/2 orbital due to increasing effective charge of the mercury atom, which explains the non-monotonous behavior of the contact density along the series. The same analysis shows increasing covalent contributions to bonding along the series with the effective charge of the mercury atom reaching a maximum of around +2 for HgF4 at the DFT level, far from the formal charge +4 suggested by the oxidation state of this recently observed species. Whereas the geometries for the linear HgF2 and square-planar HgF4 molecules were taken from previous computational studies, we optimized the equilibrium distance of HgF at the four-component Fock-space CCSD/aug-cc-pVQZ level, giving spectroscopic constants r
e
= 2.007 Å and ωe
= 513.5 cm−1.
[Show abstract][Hide abstract] ABSTRACT: In order to guide the experimental search for parity violation in molecular systems, in part motivated by the possible link to biomolecular homochirality, we present a detailed analysis in a relativistic framework of the mechanism behind the tiny energy difference between enantiomers induced by the weak force. A decomposition of the molecular expectation value into atomic contributions reveals that the effect can be thought of as arising from a specific mixing of valence s(1/2) and p(1/2) orbitals on a single center induced by a chiral molecular field. The intra-atomic nature of the effect is further illustrated by visualization of the electron chirality density and suggests that a simple model for parity violation in molecules may be constructed by combining pre-calculated atomic quantities with simple bonding models. A 2-component relativistic computational procedure is proposed which bridges the relativistic and non-relativistic approaches to the calculation of parity violation in chiral molecules and allows us to explore the single-center theorem in a variational setting.