Phosphine and Selenoether peri-Substituted Acenaphthenes and Their Transition-Metal Complexes: Structural and NMR Investigations.

A series of peri-substituted acenaphthene-based phosphine selenoether bidentate ligands Acenap(iPr2P)(SeAr) (L1-L4, Acenap = acenaphthene-5,6-diyl, Ar = Ph, mesityl, 2,4,6-trisopropylphenyl and supermesityl) were prepared. The rigid acenaphthene framework induces a forced overlap of the phosphine and selenoether lone pairs, resulting in a large magnitude of through-space 4JPSe coupling, ranging from 452 to 545 Hz. These rigid ligands L1-L4 were used to prepare a series of selected late d-block metals, mercury, and borane complexes, which were characterized, including by multinuclear NMR and single-crystal X-ray diffraction. The Lewis acidic motifs (BH3, Mo(CO)4, Ag+, PdCl2, PtCl2, and HgCl2) bridge the two donor atoms (P and Se) in all but one case in the solid-state structures. Where the bridging motif contained NMR-active nuclei (11B, 107Ag, 109Ag, 195Pt, and 199Hg), JPM and JSeM couplings are observed directly, in addition to the altered JPSe in the respective NMR spectra. The solution NMR data are correlated with single-crystal diffraction data, and in the case of mercury(II) complexes, they are also correlated with the solid-state NMR data and coupling deformation density calculations. The latter indicate that the through-space interaction dominates in free L1, while in the L1HgCl2 complex, the main coupling pathway is via the metal atom and not through the carbon framework of the acenaphthene ring system.

The four-component DFT method for the calculation of the EPR g-tensor using a restricted magnetically balanced basis and London atomic orbitals.

Four-component relativistic treatments of the electron paramagnetic resonance g-tensor have so far been based on a common gauge origin and a restricted kinetically balanced basis. The results of such calculations are prone to exhibit a dependence on the choice of the gauge origin for the vector potential associated with uniform magnetic field and a related dependence on the basis set quality. In this work, this gauge problem is addressed by a distributed-origin scheme based on the London atomic orbitals, also called gauge-including atomic orbitals (GIAOs), which have proven to be a practical approach for calculations of other magnetic properties. Furthermore, in the four-component relativistic domain, it has previously been shown that a restricted magnetically balanced (RMB) basis for the small component of the four-component wavefunctions is necessary for achieving robust convergence with regard to the basis set size. We present the implementation of a four-component density functional theory (DFT) method for calculating the g-tensor, incorporating both the GIAOs and RMB basis and based on the Dirac-Coulomb Hamiltonian. The approach utilizes the state-of-the-art noncollinear Kramers-unrestricted DFT methodology to achieve rotationally invariant results and inclusion of spin-polarization effects in the calculation. We also show that the gauge dependence of the results obtained is connected to the nonvanishing integral of the current density in a finite basis, explain why the results of cluster calculations exhibit surprisingly low gauge dependence, and demonstrate that the gauge problem disappears for systems with certain point-group symmetries.

Transmission of spin-polarization by π-orbitals: an approach to assessing its effect on NMR spin-spin coupling and EPR hyperfine structure.

A new approach to assessing the effect of the transmission of spin-polarization by π-orbitals (π-TSP) is presented. In order to switch off the π-TSP effect, we artificially average the α- and ß-densities of the valence π-orbitals when calculating the exchange-correlation contribution to the Fock matrix in the unrestricted Kohn-Sham framework. The π-TSP effect is then evaluated as the difference between the results obtained with switched-on and switched-off options. This approach is applied to estimate the π-TSP effect on the Fermi-contact contribution to spin-spin couplings and EPR hyperfine structure coupling constants. The π-TSP effect on the distribution of spin-density, spin-spin coupling pathways and pathways of EPR hyperfine couplings is demonstrated for benzene, naphthalene, 1,3,5,7,9-decapentaene and the 1,3,5,7,9-decapentaen-1-yl radical. The sign alternation of the spin-polarization transmitted by π-orbitals is explained in a theoretical framework based on perturbation theory. However, the delocalized nature of the π-system can interfere with the sign alternation in certain cases, two of which - the cyclobutadiene dication and the cyclooctatetraene dication - are examined, and an explanation for which is provided.

Distinguishing "Through-Space" from "Through-Bonds" Contribution in Indirect Nuclear Spin-Spin Coupling: General Approaches Applied to Complex JPP and JPSe Scalar Couplings.

We present herein two complementary theoretical approaches for analyzing the transmission pathways of indirect nuclear spin-spin couplings in high-resolution nuclear magnetic resonance. This phenomenon is notably conceptually poorly understood in complex experimental situations in which both nonbonded ["through-space" (TS)] and more "classical" bonding ("through-bond") spin-spin coupling pathways are potentially involved. The computational approaches we propose allow the visualization and discussion of individual transmission pathways and estimation of their relative weight from numerical contributions to the spin-spin coupling constant J-value. The first approach is based on the analysis of contributions limited to occupied molecular orbitals [focused on occupied molecular orbitals (FOMO)]. The second approach encompasses the consideration of both occupied and vacant orbitals [global molecular orbital contributions (GMOC)], and, besides the contributions from individual pathways, also considers their cross contributions. Both approaches are applicable to large systems with complex interactions of nuclear magnetic moments. Herein, we have first applied the FOMO and GMOC computational approaches to simple diphosphine models and then extended the analysis to JPP and JPSe experimentally measured in a constrained selenated (diphosphino)naphthalene compound. The new computational tools contributed evidence for the importance of the single lone pair not only from phosphorus but also from selenium in TS spin-spin transmission. It evidenced and modeled for the first time the existence of spin-spin transmission pathways mixing classical covalent bonding parts with a lone pair overlap of proximate heteroatoms (P and Se).

ReSpect: Relativistic spectroscopy DFT program package.

With the increasing interest in compounds containing heavier elements, the experimental and theoretical community requires computationally efficient approaches capable of simultaneous non-perturbative treatment of relativistic, spin-polarization, and electron correlation effects. The ReSpect program has been designed with this goal in mind and developed to perform relativistic density functional theory (DFT) calculations on molecules and solids at the quasirelativistic two-component (X2C Hamiltonian) and fully relativistic four-component (Dirac-Coulomb Hamiltonian) level of theory, including the effects of spin polarization in open-shell systems at the Kramers-unrestricted self-consistent field level. Through efficient algorithms exploiting time-reversal symmetry, biquaternion algebra, and the locality of atom-centered Gaussian-type orbitals, a significant reduction of the methodological complexity and computational cost has been achieved. This article summarizes the essential theoretical and technical advances made in the program, supplemented by example calculations. ReSpect allows molecules with >100 atoms to be efficiently handled at the four-component level of theory on standard central processing unit-based commodity clusters, at computational costs that rarely exceed a factor of 10 when compared to the non-relativistic realm. In addition to the prediction of band structures in solids, ReSpect offers a growing list of molecular spectroscopic parameters that range from electron paramagnetic resonance parameters (g-tensor, A-tensor, and zero-field splitting), via (p)NMR chemical shifts and nuclear spin-spin couplings, to various linear response properties using either conventional or damped-response time-dependent DFT (TDDFT): excitation energies, frequency-dependent polarizabilities, and natural chiroptical properties (electronic circular dichroism and optical rotatory dispersion). In addition, relativistic real-time TDDFT electron dynamics is another unique feature of the program. Documentation, including user manuals and tutorials, is available at the program's website http://www.respectprogram.org.

Dihydrogen contacts observed by through-space indirect NMR coupling.

"Through-space" indirect spin-spin couplings between hydrogen atoms formally separated by up to 18 covalent bonds have been detected by NMR experiments in model helical molecules. It is demonstrated that this coupling can provide crucial structural information on the molecular conformation in solution. The coupling pathways have been visualised and analysed by computational methods. The conformational dependence of the coupling is explained in terms of orbital interactions.

A Study of Through-Space and Through-Bond JPP Coupling in a Rigid Nonsymmetrical Bis(phosphine) and Its Metal Complexes.

A series of representative late d-block metal complexes bearing a rigid bis(phosphine) ligand, iPr2P-Ace-PPh2 (L, Ace = acenaphthene-5,6-diyl), was prepared and fully characterized by various techniques, including multinuclear NMR and single-crystal X-ray diffraction. The heteroleptic nature of the peri-substituted ligand L allows for the direct observation of the JPP couplings in the 31P{1H} NMR spectra. Magnitudes of JPP are correlated with the identity and geometry of the metal and the distortions of the ligand L. The forced overlap of the phosphine lone pairs due to the constraints imposed by the rigid acenaphthene skeleton in L results in a large 4 JPP of 180 Hz. Sequestration of the lone pairs, either via oxidation of the phosphine or via metal chelation, results in distinct changes in the magnitude of JPP. For tetrahedral d10 complexes ([LMCl2], M = Zn, Cd, Hg), the JPP is comparable to or larger than (193-309 Hz) that in free ligand L, although the P···P separation in these complexes is increased by ca. 0.4 Å (compare to free ligand L). The magnitude of JPP diminishes to 26-117 Hz in square planar d8 complexes ([LMX2], M = Ni, Pd, Pt; X = Cl, Br) and the octahedral Mo0 complex ([LMo(CO)4], 33 Hz). Coupling deformation density calculations indicate the through-space interaction dominates in free L, while in metal complexes the main coupling pathway is via the metal atom.

Visualization of Electron Paramagnetic Resonance Hyperfine Structure Coupling Pathways.

The close relation between the EPR hyperfine coupling constant and NMR indirect spin-spin coupling constant is well-known. For example, the Karplus-type dependence of hyperfine constants on the dihedral angle, originally proposed for NMR spin-spin coupling, is widely used in pNMR studies. In the present work we propose a new tool for visualization of hyperfine coupling pathways based on our experience with visualization of NMR indirect spin-spin couplings. The plotted 3D-function is the difference between the total electron densities when the magnetic moment of the nucleus of interest changes its sign and as such is an observable from the physical point of view. It has been shown that it is proportional to the linear response of the spin density to the nuclear spin (i.e., magnetic moment). In contrast to the widely used visualization of spin density, our new approach depicts only the part of the electron cloud of a molecule that is affected by the interaction of the unpaired electron(s) with the desired nuclear magnetic moment. Because visualization of NMR spin-spin couplings and hyperfine interaction is based on the same ideas and done using similar techniques, it allows a direct comparison of the corresponding pathways for the two phenomena so as to analyze their resemblance and/or dissimilarity.

Energy anisotropy as a function of the direction of spin magnetization for a doublet system.

This manuscript describes new phenomena that currently are not taken into account in both experimental EPR spectra interpretations and quantum chemical calculations of EPR parameters. This article presents an argument, with evidence, against the common belief that in the absence of an external magnetic field the total energy of a doublet system is independent of the spin orientation. Consequences of this phenomenon for interpretation of EPR experimental studies as well as for quantum chemical calculations of EPR parameters are discussed.

Acceleration of Relativistic Electron Dynamics by Means of X2C Transformation: Application to the Calculation of Nonlinear Optical Properties.

The Liouville-von Neumann equation based on the four-component matrix Dirac-Kohn-Sham Hamiltonian is transformed to a quasirelativistic exact two-component (X2C) form and then used to solve the time evolution of the electronic states only. By this means, a significant acceleration by a factor of 7 or more has been achieved. The transformation of the original four-component equation of motion is formulated entirely in matrix algebra, following closely the X2C decoupling procedure of Ilias and Saue [ J. Chem. Phys. 2007 , 126 , 064102 ] proposed earlier for a static (time-independent) case. In a dynamic (time-dependent) regime, however, an adiabatic approximation must in addition be introduced in order to preserve the block-diagonal form of the time-dependent Dirac-Fock operator during the time evolution. The resulting X2C Liouville-von Neumann electron dynamics (X2C-LvNED) is easy to implement as it does not require an explicit form of the picture-change transformed operators responsible for the (higher-order) relativistic corrections and/or interactions with external fields. To illustrate the accuracy and performance of the method, numerical results and computational timings for nonlinear optical properties are presented. All of the time domain X2C-LvNED results show excellent agreement with the reference four-component calculations as well as with the results obtained from frequency domain response theory.

The Relativistic Effects on the Carbon-Carbon Coupling Constants Mediated by a Heavy Atom.

The (2)JCC, (3)JCC, and (4)JCC spin-spin coupling constants in the systems with a heavy atom (Cd, In, Sn, Sb, Te, Hg, Tl, Pb, Bi, and Po) in the coupling path have been calculated by means of density functional theory. The main goal was to estimate the relativistic effects on spin-spin coupling constants and to explore the factors which may influence them, including the nature of the heavy atom and carbon hybridization. The methods applied range, in order of reduced complexity, from the Dirac-Kohn-Sham (DKS) method (density functional theory with four-component Dirac-Coulomb Hamiltonian), through DFT with two- and one-component zeroth-order regular approximation (ZORA) Hamiltonians, to scalar effective core potentials (ECPs) with the nonrelativistic Hamiltonian. The use of DKS and ZORA methods leads to very similar results, and small-core ECPs of the MDF and MWB variety reproduce correctly the scalar relativistic effects. Scalar relativistic effects usually are larger than the spin-orbit coupling effects. The latter tend to influence the most the coupling constants of the sp(3)-hybridized carbon atoms and in compounds of the p-block heavy atoms. Large spin-orbit coupling contributions for the Po compounds are probably connected with the inverse of the lowest triplet excitation energy.

Relativistic four-component calculations of indirect nuclear spin-spin couplings with efficient evaluation of the exchange-correlation response kernel.

In this work, we report on the development and implementation of a new scheme for efficient calculation of indirect nuclear spin-spin couplings in the framework of four-component matrix Dirac-Kohn-Sham approach termed matrix Dirac-Kohn-Sham restricted magnetic balance resolution of identity for J and K, which takes advantage of the previous restricted magnetic balance formalism and the density fitting approach for the rapid evaluation of density functional theory exchange-correlation response kernels. The new approach is aimed to speedup the bottleneck in the solution of the coupled perturbed equations: evaluation of the matrix elements of the kernel of the exchange-correlation potential. The performance of the new scheme has been tested on a representative set of indirect nuclear spin-spin couplings. The obtained results have been compared with the corresponding results of the reference method with traditional evaluation of the exchange-correlation kernel, i.e., without employing the fitted electron densities. Overall good agreement between both methods was observed, though the new approach tends to give values by about 4%-5% higher than the reference method. On the average, the solution of the coupled perturbed equations with the new scheme is about 8.5 times faster compared to the reference method.

NMR and DFT analysis of trisaccharide from heparin repeating sequence.

NMR and density functional theory (DFT) have afforded detailed information on the molecular geometry and spin-spin coupling constants of a trisaccharide from the heparin repeating-sequence. The fully optimized molecular structures of two trisaccharide conformations (differing from each other in the form of the central iduronic acid residue) were obtained using the B3LYP/6-311+G(d,p) level of theory in the presence of solvent, the latter included as either explicit water molecules or via a continuum solvent model. NMR spin-spin coupling constants were also computed using various basis sets and functionals and then compared with measured experimental values. Optimized structures for both conformers showed differences in geometry at the glycosidic linkages and in the formation of intramolecular hydrogen bonds. Three-bond proton-proton coupling constants ((3)JH-C-C-H), based on fully optimized geometry computed using the B3LYP/6-311+G(d,p)/UFF level of theory and hydrated with 57 water molecules, showed that the best agreement with experiment was obtained with the 6-311+G(d,p) basis set and a weighted average of 55:45 ((1)C4:(2)S0) of the IdoA2S forms. Other basis sets, DGDZVP and TZVP, also gave acceptable data for most coupling constants, with DGDZVP outperforming the TZVP. Detailed analysis of Fermi-contact contributions to (3)JH-C-C-H showed that important contributions arise from oxygen at both glycosidic linkages, as well as from oxygen atoms on the neighboring monosaccharide units. Their contribution to the Fermi term cannot be neglected and must be taken into account for a correct description of coupling constants. The analysis also showed that the magnitude of paramagnetic (PSO) and diamagnetic (DSO) spin-orbit contributions is comparable to the magnitude of the Fermi-contact contribution in some coupling constants in the IdoA2S residue. Calculations of the localized molecular orbital contributions to the DSO terms from separate conformational residues showed that the contribution from adjacent residues is not negligible and can be important for the spin-spin coupling constants between protons located close to the geometrical center of the molecule. These contributions should be taken into account when interpreting DSO terms in spin-spin coupling constants especially in large molecules.

Implementation of the diagonalization-free algorithm in the self-consistent field procedure within the four-component relativistic scheme.

A recently developed Thouless-expansion-based diagonalization-free approach for improving the efficiency of self-consistent field (SCF) methods (Noga and Simunek, J. Chem. Theory Comput. 2010, 6, 2706) has been adapted to the four-component relativistic scheme and implemented within the program package ReSpect. In addition to the implementation, the method has been thoroughly analyzed, particularly with respect to cases for which it is difficult or computationally expensive to find a good initial guess. Based on this analysis, several modifications of the original algorithm, refining its stability and efficiency, are proposed. To demonstrate the robustness and efficiency of the improved algorithm, we present the results of four-component diagonalization-free SCF calculations on several heavy-metal complexes, the largest of which contains more than 80 atoms (about 6000 4-spinor basis functions). The diagonalization-free procedure is about twice as fast as the corresponding diagonalization.

Four-component relativistic density functional theory calculations of NMR shielding tensors for paramagnetic systems.

A four-component relativistic method for the calculation of NMR shielding constants of paramagnetic doublet systems has been developed and implemented in the ReSpect program package. The method uses a Kramer unrestricted noncollinear formulation of density functional theory (DFT), providing the best DFT framework for property calculations of open-shell species. The evaluation of paramagnetic nuclear magnetic resonance (pNMR) tensors reduces to the calculation of electronic g tensors, hyperfine coupling tensors, and NMR shielding tensors. For all properties, modern four-component formulations were adopted. The use of both restricted kinetically and magnetically balanced basis sets along with gauge-including atomic orbitals ensures rapid basis-set convergence. These approaches are exact in the framework of the Dirac-Coulomb Hamiltonian, thus providing useful reference data for more approximate methods. Benchmark calculations on Ru(III) complexes demonstrate good performance of the method in reproducing experimental data and also its applicability to chemically relevant medium-sized systems. Decomposition of the temperature-dependent part of the pNMR tensor into the traditional contact and pseudocontact terms is proposed.

Indirect nuclear 15N-15N scalar coupling through a hydrogen bond: dependence on structural parameters studied by quantum chemistry tools.

NMR spin-spin couplings through a hydrogen bond in the free-base and protonated forms of the complete series of [(15)N2]-N-methylated 1,8-diaminonaphthalenes have been analyzed using quantum chemistry tools. The dominating role of the overlap of the coupling pathway orbitals has been demonstrated. The correlation of the sum of the (13)C NMR shifts of the naphthalene ring C(1,8) carbons directly attached to the interacting nitrogens with the J(N-N) values and the degree of methylation found earlier by G. C. Lloyd-Jones et al. [Chem.-Eur. J. 2003, 9, 4523] have been reexamined. It has been found that the correlations of J(N-N) and [ΔΣC(1,8)] with the degree of methylation have different reasons. While the former is mostly connected with the structural changes due to the solvent effect, the latter is attributed to the changes in the paramagnetic contributions from the C-N and C-C bonds caused by the replacement of a hydrogen by a methyl group.

Weak Te,Te interactions through the looking glass of NMR spin-spin coupling.

Across the bay: J((125)Te, (125)Te) spin-spin coupling is a highly sensitive probe into the electronic and geometric structure of 1,8-peri-substituted naphthalene tellurium derivatives. The coupling is related to the onset of multicenter bonding in these systems.

Illumination of the effect of the overlap of lone-pairs on indirect nuclear spin-spin coupling constants.

The effect of electron lone-pairs on the Fermi-contact (FC) contribution to indirect nuclear spin-spin coupling constants is analyzed using new tools for their interpretation. In particular, visualization of spin-spin coupling pathways using the coupling deformation density (CDD) has been employed. Furthermore, the recently developed perturbation-stable localization procedure has been applied for decomposition of CDD and the calculated value of couplings into contributions from localized molecular orbitals (LMOs). Correlation between the overlap of densities of LMOs representing lone-pairs and the Fermi-contact contribution to spin-spin coupling constants has been demonstrated. A new way for analyzing spin-spin couplings using the expansion of CDD as a linear combination of the products of molecular orbitals has been suggested. The considered examples include two- and three-bond phosphor-phosphor couplings. Significance of the obtained insight is not restricted to spin-spin couplings of nuclei possessing lone-pairs, as demonstrated in the example of vicinal hydrogen-hydrogen coupling in ethane.

Note: Counterintuitive gauge-dependence of nuclear magnetic resonance shieldings for rare-gas dimers: does a natural gauge-origin for spherical atoms exist?

A counterintuitive gauge-dependence of NMR shieldings for rare-gas dimers is presented and analyzed. It is shown that common belief about the existence of a natural gauge-origin for spherical atoms with respect to NMR shielding calculations is wrong.

Effects of finite size nuclei in relativistic four-component calculations of hyperfine structure.

The effect of a finite size model for both the nuclear charge and magnetic moment distributions on calculated EPR hyperfine structure have been studied using a relativistic four-component method based on density functional theory. This approach employs a restricted kinetically balanced basis (mDKS-RKB) and includes spin-polarization using noncollinear spin-density exchange-correlation functionals in the unrestricted fashion. Benchmark calculations have been carried out for a number of small molecules containing Zn, Cd, Ag, and Hg. The present results are compared with those obtained at the Douglas-Kroll-Hess second order (DKH-2) method. The dependence of the results on the quality of the orbital and auxiliary basis sets has been studied. It was found that some basis sets contain irregularities that deteriorate the results. Especial care has to be taken also on the construction of the auxiliary basis for fitting the total electron and spin-densities.