Solvent effects on heavy atom nuclear spin-spin coupling constants: a theoretical study of Hg-C and Pt-P couplings.

The computation of indirect nuclear spin-spin coupling constants, based on the relativistic two-component zeroth order regular approximate Hamiltonian, has been recently implemented by us into the Amsterdam Density Functional program. Applications of the code for the calculation of one-bond metal-ligand couplings of coordinatively unsaturated compounds containing (195)Pt and (199)Hg, including spin-orbit coupling or coordination effects by solvent molecules, show that relativistic density functional calculations are able to reproduce the experimental findings with good accuracy for the systems under investigation. Spin-orbit effects are rather small for these cases, while coordination of the heavy atoms by solvent molecules has a great impact on the calculated couplings. Experimental trends for different solvents are reproduced. An orbital-based analysis of the solvent effect is presented. The scalar relativistic increase of the coupling constants is of the same order of magnitude as the nonrelativistically obtained values, making a relativistic treatment essential for obtaining quantitatively correct results. Solvent effects can be of similar importance.     

A comparison of two-component and four-component approaches for calculations of spin-spin coupling constants and NMR shielding constants of transition metal cyanides

Relativistic density functional theory (DFT) calculations of nuclear spin-spin coupling constants and shielding constants have been performed for selected transition metal (11th and 12th group of periodic table) and thallium cyanides. The calculations have been carried out using zeroth-order regular approximation (ZORA) Hamiltonian and four-component Dirac-Kohn-Sham (DKS) theory with different nonrelativistic exchange-correlation functionals. Two recent approaches for representing the magnetic balance (MB) between the large and small components of four-component spinors, namely, mDKS-RMB and sMB, have been employed for shielding tensor calculations and their results have been compared. Relativistic effects have also been analysed in terms of scalar and spin-orbit contributions at the two-component level of theory, including discussion of heavy-atom-on-light-atom effects for (1)J(CN), σ(C), and σ(N). The results for molecules containing metals from 4th row of periodic table show that relativistic effects for them are small (especially for spin-spin coupling constants). The biggest effects are observed for the 6th row where nonrelativistic theory reproduces only about 50%-70% of the two-component ZORA results for (1)J(MeC) and about 75% for heavy metal shielding constants. It is important to employ a full Dirac picture for calculations of heavy metal shielding constants, since ZORA reproduces only 75%-90% of the DKS results. Smaller discrepancies between ZORA-DFT and DKS are observed for nuclear spin-spin coupling constants. No significant differences are observed between the results obtained using mDKS-RMB and sMB approaches for magnetic balance in four-component calculations of the shielding constants.     

Relativistic two-component formulation of time-dependent current-density functional theory: application to the linear response of solids

In this paper we derive the relativistic two-component formulation of time-dependent current-density-functional theory. To arrive at a two-component current-density formulation we apply a Foldy-Wouthuysen-type transformation to the time-dependent four-component Dirac-Kohn-Sham equations of relativistic density-functional theory. The two-component Hamiltonian is obtained as a regular expansion which is gauge invariant at each order of approximation, and to zeroth order it represents the time-dependent version of the relativistic zeroth order regular Hamiltonian obtained by van Lenthe et al., for the ground state [J. Chem. Phys.99, 4597 (1993)]. The corresponding zeroth order regular expression for the density is unchanged, whereas the current-density operator now comprises a paramagnetic, a diamagnetic, and a spin contribution, similar to the Gordon decomposition of the Dirac four current. The zeroth order current density is directly related to the mean velocity corresponding to the zeroth order Hamiltonian. These density and current density operators satisfy the continuity equation. This zeroth order approximation is therefore consistent and physically realistic. By combining this formalism with the formulation of the linear response of solids within time-dependent current-density functional theory [Romaniello and de Boeij, Phys. Rev. B71, 155108 (2005)], we derive a method that can treat orbital and spin contributions to the response in a unified way. The effect of spin-orbit coupling can now be taken into account. As first test we apply the method to calculate the relativistic effects in the linear response of several metals and nonmetals to a macroscopic electric field. Treatment of spin-orbit coupling yields visible changes in the spectra: a smooth onset of the interband transitions in the absorption spectrum of Au, a sharp onset with peak at about 0.46 eV in the absorption spectrum of W, and a low-frequency doublet structure in the absorption spectra of ZnTe, CdTe, and HgTe in agreement with experimental results.     

Density functional theory study of indirect nuclear spin-spin coupling constants with spin-orbit corrections

This work outlines the calculation of indirect nuclear spin-spin coupling constants with spin-orbit corrections using density functional response theory. The nonrelativistic indirect nuclear spin-spin couplings are evaluated using the linear response method, whereas the relativistic spin-orbit corrections are computed using quadratic response theory. The formalism is applied to the homologous systems H2X (X=O,S,Se,Te) and XH4 (X=C,Si,Ge,Sn,Pb) to calculate the indirect nuclear spin-spin coupling constants between the protons. The results confirm that spin-orbit corrections are important for compounds of the H2X series, for which the electronic structure allows for an efficient coupling between the nuclei mediated by the spin-orbit interaction, whereas in the case of the XH4 series the opposite situation is encountered and the spin-orbit corrections are negligible for all compounds of this series. In addition we analyze the performance of the density functional theory in the calculations of nonrelativistic indirect nuclear spin-spin coupling constants.     

Time-dependent quasirelativistic density-functional theory based on the zeroth-order regular approximation

A time-dependent quasirelativistic density-functional theory for excitation energies of systems containing heavy elements is developed, which is based on the zeroth-order regular approximation (ZORA) for the relativistic Hamiltonian and a noncollinear form for the adiabatic exchange-correlation kernel. To avoid the gauge dependence of the ZORA Hamiltonian a model atomic potential, instead of the full molecular potential, is used to construct the ZORA kinetic operator in ground-state calculations. As such, the ZORA kinetic operator no longer responds to changes in the density in response calculations. In addition, it is shown that, for closed-shell ground states, time-reversal symmetry can be employed to simplify the eigenvalue equation into an approximate form that is similar to that of time-dependent nonrelativistic density-functional theory. This is achieved by invoking an independent-particle approximation for the induced density matrix. The resulting theory is applied to investigate the global potential-energy curves of low-lying LambdaS- and omega omega-coupled electronic states of the AuH molecule. The derived spectroscopic parameters, including the adiabatic and vertical excitation energies, equilibrium bond lengths, harmonic and anharmonic vibrational constants, fundamental frequencies, and dissociation energies, are in good agreement with those of time-dependent four-component relativistic density-functional theory and ab initio multireference second-order perturbation theory. Nonetheless, this two-component relativistic version of time-dependent density-functional theory is only moderately advantageous over the four-component one as far as computational efforts are concerned.     

On convergence of the normalized elimination of the small component (NESC) method

The convergence behavior of the iterative solution of the normalized elimination of the small component (NESC) method is investigated. A simple and efficient computational protocol for obtaining the exact positive-energy eigenvalues of the relativistic Hamiltonian starting from the energies obtained within the regular approximation is suggested. The protocol is based on the analysis of the relationship between the eigenvalues of the quasi-relativistic Hamiltonian in the regular approximation and the positive-energy eigenvalues of the exact relativistic Hamiltonian which was derived in the course of this work. This article is dedicated to Wim Nieuwpoort on the occasion of his 75th birthday.     

Analyzing NMR shielding tensors calculated with two-component relativistic methods using spin-free localized molecular orbitals

A recently developed analysis method [J. Chem. Phys. 127, 124106 (2007)] for NMR spin-spin coupling constants employing two-component (spin-orbit) relativistic density functional theory along with scalar relativistic natural localized molecular orbitals (NLMOs) and natural bond orbitals (NBOs) has been extended for analyzing NMR shielding tensors. Contributions from a field-dependent basis set (gauge-including atomic orbitals) have been included in the formalism. The spin-orbit NLMO/NBO nuclear magnetic shielding analysis has been applied to methane, plumbane, hydrogen iodide, tetracholoplatinate(II), and hexachloroplatinate(IV).     

水溶液中碳酸铀酰化合物的电子结构

应用相对论密度泛函理论系统研究了水溶液中非水合化和水合化碳酸铀酰化合物Cn/m(其中n和m分别为结构中碳酸配体和水配体的个数)的结构.溶剂效应采用类导体屏蔽模型(COSMO),并采用零级规整近似(ZORA)方法考虑标量相对论效应和旋-轨耦合相对论效应.电子跃迁采用包含旋-轨耦合相对论效应的含时密度泛函理论并在相关交换势中采用轨道势能统计平均(SAOP)做近似计算.结果表明碳酸配体对配合物结构和电子跃迁有很大的影响.C3/0配合物的稳定性可归于5f轨道参与了高占据轨道的成键作用.增加碳酸盐配体导致最大波长的蓝移,并在近可见光区域出现高强度的吸收.     

Theoretical prediction of the spin-spin coupling constants between an axis and macrocycle of a rotaxane

The indirect nuclear spin-spin coupling constants between nuclei belonging to the axis and to the macrocycle of three structurally related rotaxanes have been calculated by means of density functional theory. It has been shown that the through-space axis-macrocycle proton-proton coupling constants can be as large as 0.4-0.5 Hz and therefore of measurable values. The largest through-space axis-macrocycle carbon-proton and nitrogen-proton coupling constants are 0.2-0.3 Hz. Visualization of coupling pathways by means of the coupling energy density method indicates that the larger proton-proton couplings are indeed transmitted through the space between the coupled nuclei. Thus, it seems that measurement of such couplings should be possible and that indirect spin-spin couplings can be actually transmitted through-space, with no covalent or hydrogen bonds between the coupled nuclei.     

First-principles calculations of zero-field splitting parameters

In this work, an implementation of an approach to calculate the zero-field splitting (ZFS) constants in the framework of ab initio methods such as complete active space self-consistent field, multireference configuration interaction, or spectroscopy oriented configuration interaction is reported. The spin-orbit coupling (SOC) contribution to ZFSs is computed using an accurate multicenter mean-field approximation for the Breit-Pauli Hamiltonian. The SOC parts of ZFS constants are obtained directly after diagonalization of the SOC operator in the basis of a preselected number of roots of the spin-free Hamiltonian. This corresponds to an infinite order treatment of the SOC in terms of perturbation theory. The spin-spin (SS) part is presently estimated in a mean-field fashion and appears to yield results close to the more complete treatments available in the literature. Test calculations for the first- and second-row atoms as well as first-row transition metal atoms and a set of diatomic molecules show accurate results for the SOC part of ZFSs. SS contributions have been found to be relatively small but not negligible (exceeding 1 cm(-1) for oxygen molecule). At least for the systems studied in this work, it is demonstrated that the presented method provides much more accurate estimations for the SOC part of ZFS constants than the emerging density functional theory approaches.     

An NMR and relativistic DFT investigation of one-bond nuclear spin-spin coupling in solid triphenyl group-14 chlorides

A solid-state nuclear magnetic resonance and zeroth-order regular approximation density functional theory, ZORA-DFT, study of one-bond nuclear spin-spin coupling between group-14 nuclei and quadrupolar 35/37Cl nuclei in triphenyl group-14 chlorides, Ph3XCl (X = C, Si, Ge, Sn and Pb), is presented. This represents the first combined experimental and theoretical systematic study of spin-spin coupling involving spin-pairs containing quadrupolar nuclei. Solid-state NMR spectra have been acquired for all compounds in which X has a spin-1/2 isotope--13C, 29Si, [117/119]Sn and 207Pb-at applied magnetic fields of 4.70, 7.05 and 11.75 T. From simulations of these spectra, values describing the indirect spin-spin coupling tensor-the isotropic indirect spin-spin coupling constant, 1J(X, 35/37Cl)iso and the anisotropy of the J tensor, Delta1J(X, 35/37Cl)--have been determined for all but the lead-chlorine spin-pair. To better compare the indirect spin-spin coupling parameters between spin-pairs, 1J(iso) and Delta1J values were converted to their reduced coupling constants, 1K(iso) and Delta1K. From experiment, the sign of 1K(iso) was found to be negative while the sign of Delta1K is positive for all spin-pairs investigated. The magnitude of both 1K(iso) and Delta1K was found to increase as one moves down group-14. Theoretical values of the magnitude and sign of 1K(iso) and Delta1K were obtained from ZORA-DFT calculations and are in agreement with the available experimental data. From the calculations, the Fermi-contact mechanism was determined to provide the largest contribution to 1K(iso) for all spin-pairs while spin-dipolar and paramagnetic spin-orbit mechanisms make significant contributions to the anisotropy of K. The inclusion of relativistic effects was found to influence K(Sn,Cl) and K(Pb,Cl).     

Analyzing molecular properties calculated with two-component relativistic methods using spin-free natural bond orbitals: NMR spin-spin coupling constants

An analysis method for static linear response properties employing two-component (spin-orbit) relativistic density functional theory along with scalar relativistic "natural localized molecular orbitals" (NLMOs) and "natural bond orbitals" (NBOs) has been developed. The spin-orbit NLMO/NBO analysis has been applied to study the indirect spin-spin coupling (J-coupling) constants in Tl-I, PbH(4), and a dinuclear Pt-Tl bonded complex with a very large Pt-Tl coupling constant (expt.: 146.8 kHz). For Tl-I it is shown that the analysis scheme based on scalar relativistic NLMOs is applicable even if spin-orbit coupling is responsible for most of the coupling's magnitude. For PbH(4) it is shown that electron delocalization plays a much larger role for the Pb-H coupling than it is the case for the C-H coupling in methane. For the Pt-Tl complex the analysis clearly demonstrates the strong influence of the ligands on the Pt-Tl coupling constant and quantifies the effect of the delocalization of the Pt-Tl bond on the Pt-Tl coupling constant.     

Density functional theory calculation of indirect nuclear magnetic resonance spin-spin coupling constants in C(70)

We calculate NMR spin-spin coupling constants in the C70 fullerene by means of density functional theory. We show that using a hybrid density functional (B3LYP) and an adequate basis set (cc-pCVDZ-sd), excellent agreement with experimental values can be achieved for one-bond couplings. These benchmark calculations suggest that theoretical predictions of NMR spin-spin couplings can be extremely valuable for discerning structural information of fullerenes.     

Theoretical investigation of the apparently irregular behavior of pt-pt nuclear spin-spin coupling constants

One-bond Pt-Pt nuclear spin-spin coupling constants J(Pt-Pt) for closely related dinuclear Pt complexes can differ by an order of magnitude without any obvious correlation with Pt-Pt distances. As representative examples, the spin-spin couplings of the dinuclear Pt(I) complexes [Pt(2)(CO)(6)](2+) (1) and [Pt(2)(CO)(2)Cl(4)](2-) (2) have been computationally studied with a recently developed relativistic density functional method. The experimental values are (1)J((195)Pt-(195)Pt) = 5250 Hz for 2 but 551 Hz for 1. Many other examples are known in the literature. The experimental trends are well reproduced by the computations and can be explained based on the nature of the ligands that are coordinated to the Pt-Pt fragment. The difference for J(Pt-Pt) of an order of magnitude is caused by a sensitive interplay between the influence of different ligands on the Pt-Pt bond, and relativistic effects on metal-metal and metal-ligand bonds as well as on "atomic orbital contributions" to the nuclear spin-spin coupling constants. The results can be intuitively rationalized with the help of a simple qualitative molecular orbital diagram.     

Spin-orbit relativistic long-range corrected time-dependent density functional theory for investigating spin-forbidden transitions in photochemical reactions

A long-range corrected (LC) time-dependent density functional theory (TDDFT) incorporating relativistic effects with spin-orbit couplings is presented. The relativistic effects are based on the two-component zeroth-order regular approximation Hamiltonian. Before calculating the electronic excitations, we calculated the ionization potentials (IPs) of alkaline metal, alkaline-earth metal, group 12 transition metal, and rare gas atoms as the minus orbital (spinor) energies on the basis of Koopmans' theorem. We found that both long-range exchange and spin-orbit coupling effects are required to obtain Koopmans' IPs, i.e., the orbital (spinor) energies, quantitatively in DFT calculations even for first-row transition metals and systems containing large short-range exchange effects. We then calculated the valence excitations of group 12 transition metal atoms and the Rydberg excitations of rare gas atoms using spin-orbit relativistic LC-TDDFT. We found that the long-range exchange and spin-orbit coupling effects significantly contribute to the electronic spectra of even light atoms if the atoms have low-lying excitations between orbital spinors of quite different electron distributions.     

Relativistic effects on the Fukui function

The extent of relativistic effects on the Fukui function, which describes local reactivity trends within conceptual density functional theory (DFT), and frontier orbital densities has been analysed on the basis of three benchmark molecules containing the heavy elements: Au, Pb, and Bi. Various approximate relativistic approaches have been tested and compared with the four-component fully relativistic reference. Scalar relativistic effects, as described by the scalar zeroth-order regular approximation methodology and effective core potential calculations, already provide a large part of the relativistic corrections. Inclusion of spin–orbit coupling effects improves the results, especially for the heavy p-block compounds. We thus expect that future conceptual DFT-based reactivity studies on heavy-element molecules can rely on one of the approximate relativistic methodologies.     

A fully relativistic method for calculation of nuclear magnetic shielding tensors with a restricted magnetically balanced basis in the framework of the matrix Dirac-Kohn-Sham equation

A new relativistic four-component density functional approach for calculations of NMR shielding tensors has been developed and implemented. It is founded on the matrix formulation of the Dirac-Kohn-Sham (DKS) method. Initially, unperturbed equations are solved with the use of a restricted kinetically balanced basis set for the small component. The second-order coupled perturbed DKS method is then based on the use of restricted magnetically balanced basis sets for the small component. Benchmark relativistic calculations have been carried out for the (1)H and heavy-atom nuclear shielding tensors of the HX series (X=F,Cl,Br,I), where spin-orbit effects are known to be very pronounced. The restricted magnetically balanced basis set allows us to avoid additional approximations and/or strong basis set dependence which arises in some related approaches. The method provides an attractive alternative to existing approximate two-component methods with transformed Hamiltonians for relativistic calculations of chemical shifts and spin-spin coupling constants of heavy-atom systems. In particular, no picture-change effects arise in property calculations.     

Gauge invariance of the nuclear spin/electron orbit interaction and NMR spectral parameters

A gauge transformation of the vector potential A(m(I) ), associated to the magnetic dipole m(I) of nucleus I in a molecule, has been studied. The conditions for gauge invariance of nuclear magnetic shielding, nuclear spin/electron orbit contribution to spin-spin coupling between two nuclei, I and J, and electronic current density induced by m(I), have been expressed via quantum mechanical sum rules that are identically satisfied for exact and optimal variational wavefunctions. It is shown that separate diamagnetic and paramagnetic contributions to the properties transform into one another in the gauge transformation, whereas their sum is invariant. Therefore, only total response properties have a physical meaning. In particular, the disjoint diamagnetic and paramagnetic components of nuclear spin/electron orbit contributions to coupling constants are not uniquely defined. The diamagnetic contribution to the nuclear spin-spin coupling tensor, evaluated as an expectation value in the Ramsey theory, can alternatively be expressed as a sum-over-states formula, by rewriting the second-order Hamiltonian in commutator form a? la Geertsen, as previously reported by Sauer. Other sum-over-states formulae are obtained via a gauge transformation, by a procedure formally allowing for a continuous translation of the origin of the m(I)-induced current density, analogous to those previously proposed for magnetizabilities and nuclear magnetic shielding.