[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.
Physical Chemistry Chemical Physics 07/2014; · 4.20 Impact Factor
[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.
Physical Chemistry Chemical Physics 01/2014; · 4.20 Impact Factor
[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.
Physical Chemistry Chemical Physics 05/2013; · 4.20 Impact Factor
[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; 395:54–62. · 1.96 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. · 3.12 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. · 3.12 Impact Factor
[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: 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). · 3.04 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: 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.
Physical Chemistry Chemical Physics 11/2011; 13(46):20682-9. · 4.20 Impact Factor
[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. · 3.12 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The electrostatic contribution to the Mössbauer isomer shift of mercury for the series HgF
(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 HgF
(n=1,2,4), relevant for the isomer shift, is on the order of 50ppm 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 HgF
(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
= 2.007 Å and ω
KeywordMössbauer spectroscopy–Relativistic quantum chemistry–Density functional theory–Coupled cluster–Contact density–Mercury compounds–Picture change effects
[Show abstract][Hide abstract] ABSTRACT: We report a 4-component relativistic benchmark study of the isotopic field shift in the rotational spectrum of three diatomic molecules: TlI, PbTe and PtSi. A central quantity in the theory is the derivative with respect to internuclear distance of an effective electron density associated with a given nucleus, calculated at the equilibrium distance. The effective density, which is related to the mean electron density within the nuclear volume, is usually replaced with the contact density, that is, the electron density at the origin of the nucleus. Our computational study shows that for the chosen systems this induces errors on the order of 10%, which is not acceptable for high-precision work. On the other hand, the systematic nature of the error suggests that it can be handled by an atom-specific correction factor. Our calibration study reveals that relativistic effects increase the contact density gradient by about an order of magnitude, and that the proper transformation of the associated property operator is mandatory in 1- and 2-component relativistic calculations. Our results show very good agreement with the experimental data presented by Schlembach and Tiemann [Chem. Phys. 68 (1982) 21], but disagree completely with the revised results given by the same group in a later paper [Chem. Phys., 93 (1985) 349]. We have carefully re-derived the relevant formulas and can not see that the rescaling of results is justified. Curiously previous DFT calculations agree quite well with the revised results for TlI and PbTe, but we demonstrate that this is because the authors inadvertently employed a non-relativistic Hamiltonian, which by chance induces an error of the same magnitude as the suggested scaling. For the PtSi molecule our results for the correction term due to nuclear volume disagree with experiment by a factor five, and we recommend a re-examination of the experimental data.
Chemical Physics 01/2011; 401:103-112. · 1.96 Impact Factor
[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.
Physical Chemistry Chemical Physics 01/2011; 13(3):864-76. · 4.20 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Parity violation (PV) effects in chiral molecules have so far never been experimentally observed. To take up this challenge, a consortium of physicists, chemists, theoreticians, and spectroscopists has been established and aims at measuring PV energy differences between two enantiomers by using high-resolution laser spectroscopy. In this article, we present our common strategy to reach this goal, the progress accomplished in the diverse areas, and point out directions for future PV observations. The work of André Collet on bromochlorofluoromethane (1) enantiomers, their synthesis, and their chiral recognition by cryptophanes made feasible the first generation of experiments presented in this article.
[Show abstract][Hide abstract] ABSTRACT: We report the synthesis and resolution of a series of new chiral "3 + 1" oxorhenium(V) complexes, designed for high-resolution laser spectroscopy experiments probing molecular parity-violation (PV) effects in the Re=O stretching mode frequency. These complexes display a particularly simple chemical structure, with the rhenium atom as the stereogenic center, and show large PV energy differences according to our calculations. They were obtained in the racemic and enantioenriched forms, in the latter case by using either semi-preparative chiral HPLC resolution or enantioselective synthesis. The vibrational transition frequency differences between the enantiomeric pairs due to PV have been calculated with two- and four-component relativistic Hamiltonians using Hartree-Fock (HF) and density functional theory (DFT). For three complexes, including one synthesized in enantioenriched form, our HF calculations predict frequency differences above the present resolution limit of 1 Hz. These results confirm the order of magnitude for the calculated HF PV vibrational frequency differences reported earlier for this class of compounds [P. Schwerdtfeger and R. Bast, J. Am. Chem. Soc., 2004, 126, 1652]. However, at the DFT level the PV vibrational frequency differences are in some cases reduced by an order of magnitude, but are still within the sensitivity of 0.01 Hz, which is the anticipated sensitivity in a new proposed experiment. We therefore believe that the present study represents an important step towards the experimental observation of PV in molecular systems, and emphasizes the extreme sensitivity of the PV vibrational frequency difference to the chemical environment around the rhenium center.
Physical Chemistry Chemical Physics 08/2010; 12(31):8792-803. · 4.20 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The triiodide ion I(3)(-) exhibits a complex photodissociation behavior, the dynamics of which are not yet fully understood. As a first step toward determining the full potential energy surfaces of this species for subsequent simulations of its dissociation processes, we investigate the performance of different electronic structure methods [time-dependent density functional theory, complete active space perturbation theory to second order (CASPT2), Fock-space coupled cluster and multireference configuration interaction] in describing the ground and excited states of the triiodide ion along the symmetrical dissociation path. All methods apart from CASPT2 include scalar relativity and spin-orbit coupling in the orbital optimization, providing useful benchmark data for the more common two-step approaches in which spin-orbit coupling is introduced in the configuration interaction. Time-dependent density functional theory with the statistical averaging of model orbital potential functional is off the mark for this system. Another choice of functional may improve performance with respect to vertical excitation energies and spectroscopic constants, but all functionals are likely to face instability problems away from the equilibrium region. The Fock-space coupled cluster method was shown to perform clearly best in regions not too far from equilibrium but is plagued by convergence problems toward the dissociation limit due to intruder states. CASPT2 shows good performance at significantly lower computational cost, but is quite sensitive to symmetry breaking. We furthermore observe spikes in the CASPT2 potential curves away from equilibrium, signaling intruder state problems that we were unable to curb through the use of level shifts. Multireference configuration interaction is, in principle, a viable option, but its computational cost in the present case prohibits use other than for benchmarking purposes.
The Journal of Chemical Physics 08/2010; 133(6):064305. · 3.12 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: An algorithm for the solution of the linear response equation in the random phase approximation is presented. All entities including frequency arguments, matrices, and vectors, are assumed to be complex, and it represents the core equation solver needed in complex polarization propagator approaches where nonstimulated relaxation channels are taken into account. Stability and robustness of the algorithm are demonstrated in applications regarding visible, ultraviolet, and x-ray spectroscopies. An implementation of the algorithm at the level of four-component relativistic, noncollinear, density functional theory for imaginary (but not complex) frequency arguments has been achieved and is used to determine the electric dipole dispersion interaction coefficients for the rubidium and cesium dimers. Our best estimates for the C(6) coefficients of Rb(2) and Cs(2) are equal to 14.0x10(3) and 21.9x10(3) a.u., respectively.
The Journal of Chemical Physics 08/2010; 133(6):064105. · 3.12 Impact Factor