Visualization of Nuclear Spin-Spin Coupling Pathways by Real-Space Functions

Paramagnetic Effects in NMR Spectroscopy of Transition-Metal Complexes: Principles and Chemical Concepts

ConspectusMagnetic resonance techniques represent a fundamental class of spectroscopic methods used in physics, chemistry, biology, and medicine. Electron paramagnetic resonance (EPR) is an extremely powerful technique for characterizing systems with an open-shell electronic nature, whereas nuclear magnetic resonance (NMR) has traditionally been used to investigate diamagnetic (closed-shell) systems. However, these two techniques are tightly connected by the electron-nucleus hyperfine interaction operating in paramagnetic (open-shell) systems. Hyperfine interaction of the nuclear spin with unpaired electron(s) induces large temperature-dependent shifts of nuclear resonance frequencies that are designated as hyperfine NMR shifts (δHF).Three fundamental physical mechanisms shape the total hyperfine interaction: Fermi-contact, paramagnetic spin-orbit, and spin-dipolar. The corresponding hyperfine NMR contributions can be interpreted in terms of through-bond and through-space effects. In this Account, we provide an elemental theory behind the hyperfine interaction and NMR shifts and describe recent progress in understanding the structural and electronic principles underlying individual hyperfine terms.The Fermi-contact (FC) mechanism reflects the propagation of electron-spin density throughout the molecule and is proportional to the spin density at the nuclear position. As the imbalance in spin density can be thought of as originating at the paramagnetic metal center and being propagated to the observed nucleus via chemical bonds, FC is an excellent indicator of the bond character. The paramagnetic spin-orbit (PSO) mechanism originates in the orbital current density generated by the spin-orbit coupling interaction at the metal center. The PSO mechanism of the ligand NMR shift then reflects the transmission of the spin polarization through bonds, similar to the FC mechanism, but it also makes a substantial through-space contribution in long-range situations. In contrast, the spin-dipolar (SD) mechanism is relatively unimportant at short-range with significant spin polarization on the spectator atom. The PSO and SD mechanisms combine at long-range to form the so-called pseudocontact shift, traditionally used as a structural and dynamics probe in paramagnetic NMR (pNMR). Note that the PSO and SD terms both contribute to the isotropic NMR shift only at the relativistic spin-orbit level of theory.We demonstrate the advantages of calculating and analyzing the NMR shifts at relativistic two- and four-component levels of theory and present analytical tools and approaches based on perturbation theory. We show that paramagnetic NMR effects can be interpreted by spin-delocalization and spin-polarization mechanisms related to chemical bond concepts of electron conjugation in π-space and hyperconjugation in σ-space in the framework of the molecular orbital (MO) theory. Further, we discuss the effects of environment (supramolecular interactions, solvent, and crystal packing) and demonstrate applications of hyperfine shifts in determining the structure of paramagnetic Ru(III) compounds and their supramolecular host-guest complexes with macrocycles.In conclusion, we provide a short overview of possible pNMR applications in the analysis of spectra and electronic structure and perspectives in this field for a general chemical audience.

Molecular dynamics and NMR reveal the coexistence of H-bond-assisted and through-space JFH coupling in fluorinated amino alcohols

The JFH coupling constants in fluorinated amino alcohols were investigated through experimental and theoretical approaches. The experimental JFH couplings were only reproduced theoretically when explicit solvation through molecular dynamics (MD) simulations was conducted in DMSO as the solvent. The combination of MD conformation sampling and DFT NMR spin-spin coupling calculations for these compounds reveals the simultaneous presence of through-space (TS) and hydrogen bond (H-bond) assisted JFH coupling between fluorine and hydrogen of the NH group. Furthermore, MD simulations indicate that the hydrogen in the amino group participates in both an intermolecular bifurcated H-bond with DMSO and in transmitting the observed JFH coupling. The contribution of TS to the JFH coupling is due to the spatial proximity of the fluorine and the NH group, aided by a combination of the non-bonding transmission pathway and the hydrogen bonding pathway. The experimental JFH coupling observed for the molecules studied should be represented as 4TS/1hJFH coupling.

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.

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 β-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 J_PP and J_PSe 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).

Synthesis and reactivity of phosphine borohydride compounds

Four lithium phosphine borohydride compounds featuring phenyl and naphthyl linkers have been synthesized. In-depth NMR analysis affords evidence for non-bonded through space P-B coupling. Reactivity towards CO2 leads to LiH transfer and to the quantitative formation of the corresponding ambiphilic phosphine-borane products.

Weak Intermolecular CH···N Hydrogen Bonding: Determination of 13CH-15N Hydrogen-Bond Mediated J Couplings by Solid-State NMR Spectroscopy and First-Principles Calculations

Weak hydrogen bonds are increasingly hypothesized to play key roles in a wide range of chemistry from catalysis to gelation to polymer structure. Here, ¹⁵N/¹³C spin-echo magic-angle spinning (MAS) solid-state nuclear magnetic resonance (NMR) experiments are applied to "view" intermolecular CH···N hydrogen bonding in two selectively labeled organic compounds, 4-[¹⁵N] cyano-4'-[¹³C₂] ethynylbiphenyl (1) and [¹⁵N₃,¹³C₆]-2,4,6-triethynyl-1,3,5-triazine (2). The synthesis of 2-¹⁵N₃,¹³C₆ is reported here for the first time via a multistep procedure, where the key element is the reaction of [¹⁵N₃]-2,4,6-trichloro-1,3,5-triazine (5) with [¹³C₂]-[(trimethylsilyl)ethynyl]zinc chloride (8) to afford its immediate precursor [¹⁵N₃,¹³C₆]-2,4,6-tris[(trimethylsilyl)ethynyl]-1,3,5-triazine (9). Experimentally determined hydrogen-bond-mediated ^2hJ_CN couplings (4.7 ± 0.4 Hz (1) and 4.1 ± 0.3 Hz (2)) are compared with density functional theory (DFT) gauge-including projector augmented wave (GIPAW) calculations, whereby species-independent coupling values ^2hK_CN (29.0 × 10¹⁹ kg m^-2 s^-2 A^-2 (1) and 27.9 × 10¹⁹ kg m^-2 s^-2 A^-2 (2)) quantitatively demonstrate the J couplings for these "weak" CH···N hydrogen bonds to be of a similar magnitude to those for conventionally observed NH···O hydrogen-bonding interactions in uracil (^2hK_NO: 28.1 and 36.8 × 10¹⁹ kg m^-2 s^-2 A^-2). Moreover, the GIPAW calculations show a clear correlation between increasing ^2hJ_CN (and ^3hJ_CN) coupling and reducing C(H)···N and H···N hydrogen-bonding distances, with the Fermi contact term accounting for at least 98% of the isotropic ^2hJ_CN coupling.

Intramolecular H-Bond Is Formed in 2-Fluorophenol and 2-Fluorothiophenol, but It May Not Be the Main Pathway of the JFH Coupling Constant Transmission

The intramolecular CF···HX (X = O or S) H-bond and J_FH spin-spin coupling constants (SSCCs) in 2-fluorophenol and 2-fluorothiophenol were investigated experimentally by ¹H and ¹⁹F NMR and theoretically in the framework of the natural bond orbital analysis. In contrast with recent findings from the literature, the results obtained in this work showed that an intramolecular H-bond is formed in the cis conformers and that it has an electrostatic origin. Such an intramolecular electrostatic H-bond is the interaction that rules the conformational preferences on these compounds. Moreover, the natural J-coupling analysis indicated that the J_HF SSCC in 2-fluorophenol has its origin on LP(F)/σ_OH steric interactions and should be labeled as ^4TSJ_HF. On the other hand, the analogue SSCC for 2-fluorothiophenol has its origin on the intramolecular H-bond LP(F) → σ_SH^* hyperconjugative interaction and should be described as a ^1hJ_FH SSCC.

Bis-[3]Ferrocenophanes with Central >E-E'< Bonds (E, E'=P, SiH): Preparation, Properties, and Thermal Activation

A series of bis-[3]ferrocenophanes of the general type Fe(C5H4E')2E-E(E'C5H4)2Fe (E=P, SiH and E'=PtBu, NneoPentyl, NSi(CH3)3) with an isolobal molecular framework have been prepared and characterized by heteronuclear NMR spectroscopy and X-ray crystallography. The thermal dissociation behavior with respect to homolytic fission of the central bond generating phosphorus centered radicals was investigated using EPR spectroscopy and quantum chemical calculations.

Accessing the First nido-Carborane-Substituted Diphosphetane: A Ligand and Synthon for nido-Carboranylphosphanes

Deboronation of a carborane-substituted diphosphetane 2 in toluene yielded the first nido-carboranyldiphosphetane 1. The P-P bond in 1 can be broken via dismutation reactions with diaryl dichalcogenides yielding nido-carboranyl bis-phosphanes that were not accessible via established synthetic protocols. Additionally, transition metal complexes of 1 could be isolated including one coordination polymer. Notably, when the deboronation of 2 is carried out in ethanol, unprecedented nido-carborane-substituted secondary bis-phosphane monoxides (3, 4) are obtained. These compounds are interesting starting materials for further reactivity studies due to their P-H bonds. Experimental findings are supported by DFT calculations including the calculation of reaction mechanisms and NMR spectroscopic parameters.

"Through-Space" Relativistic Effects on NMR Chemical Shifts of Pyridinium Halide Ionic Liquids

We have investigated, using two-component relativistic density functional theory (DFT) at ZORA-SO-BP86 and ZORA-SO-PBE0 level, the occurrence of relativistic effects on the ¹ H, ¹³ C, and ¹⁵ N NMR chemical shifts of 1-methylpyridinium halides [MP][X] and 1-butyl-3-methylpyridinium trihalides [BMP][X₃ ] ionic liquids (ILs) (X=Cl, Br, I) as a result of a non-covalent interaction with the heavy anions. Our results indicate a sizeable deshielding effect in ion pairs when the anion is I^- and I₃ ^- . A smaller, though nonzero, effect is observed also with bromine while chlorine based anions do not produce an appreciable relativistic shift. The chemical shift of the carbon atoms of the aromatic ring shows an inverse halogen dependence that has been rationalized based on the little C-2s orbital contribution to the σ-type interaction between the cation and anion. This is the first detailed account and systematic theoretical investigation of a relativistic heavy atom effect on the NMR chemical shifts of light atoms in the absence of covalent bonds. Our work paves the way and suggests the direction for an experimental investigation of such elusive signatures of ion pairing in ILs.

A sterically congested 1,2-diphosphino-1′-boryl-ferrocene: synthesis, characterization and coordination to platinum

A unique tritopic (P, P, B)-ferrocene ambiphile with antagonist functions directly attached to a metallocene backbone is described.

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 J_PP couplings in the ³¹P{¹H} NMR spectra. Magnitudes of J_PP 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 J_PP 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 J_PP. For tetrahedral d¹⁰ complexes ([LMCl₂], M = Zn, Cd, Hg), the J_PP 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 J_PP 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.

Gold(I) Complexes of Ferrocenyl Polyphosphines: Aurophilic Gold Chloride Formation and Phosphine-Concerted Shuttling of a Dinuclear [ClAu···AuCl] Fragment

A smart steric control of the metallocene backbone in bis- and poly(phosphino)ferrocene ligands favors intramolecular aurophilic interactions between [AuCl] fragments in polynuclear gold(I) complexes. We synthesized and characterized by multinuclear NMR and X-ray diffraction analysis mono-, di-, and polynuclear gold complexes of constrained ferrocenyl diphosphines, which bear either bulky tert-butyl groups or more flexible siloxane substituents at the cyclopentadienyl rings. The complexes meso-1,1'-bis(diphenylphosphino)-3,3'-di-tert-butylferrocene (4-m), rac-1,1'-bis[bis(5-methyl-2-furyl)phosphino]-3,3'-di-tert-butylferrocene (5-r), and rac-1,1'-bis(diphenylphosphino)-3,3'-bis[(tri-iso-propylsilyl)oxy]ferrocene (6-r) were used to form dinuclear gold complexes. Coordination of tert-butylated ferrocenyl phosphines generated aurophilic interactions in the corresponding dinuclear gold complexes, contrary to gold(I) complexes reported with 1,1'-bis(diphenylphosphino)ferrocene. The structurally related tetraphosphine 1,1',2,2'-tetrakis(diphenylphosphino)-4,4'-di-tert-butylferrocene (11) also gave access to mononuclear, dinuclear, and the original trinuclear gold chloride aurophilic complexes in which 14e^- to 16e^- gold centers coexist. In such complexes, nonbonded ("through-space") ³¹P-³¹P' nuclear spin couplings were evidenced by high-resolution NMR. In these interactions nuclear spin information is transferred between the lone-pair electron of an uncoordinated phosphorus P and a phosphorus P' that is involved in a σ covalent bond Au-P'. The dinuclear aurophilic complex displayed a concerted shuttling of its [ClAu···AuCl] fragment between the four phosphorus donors of the tetraphosphine ligand. Thus, an aurophilic Au···Au bond, which is assumed to be a weak energy interaction, can be conserved within a dynamic shuttling process at high temperature involving an intramolecular coordination-decoordination process of digold(I) at phosphorus atoms.

Conformational analysis of small molecules: NMR and quantum mechanics calculations

This review deals with conformational analysis in small organic molecules, and describes the stereoelectronic interactions responsible for conformational stability. Conformational analysis is usually performed using NMR spectroscopy through measurement of coupling constants at room or low temperature in different solvents to determine the populations of conformers in solution. Quantum mechanical calculations are used to address the interactions responsible for conformer stability. The conformational analysis of a large number of small molecules is described, using coupling constant measurements in different solvents and at low temperature, as well as recent applications of through-space and through-hydrogen bond coupling constants JFH as tools for the conformational analysis of fluorinated molecules. Besides NMR parameters, stereoelectronic interactions such as conjugative, hyperconjugative, steric and intramolecular hydrogen bond interactions involved in conformational preferences are discussed.

Investigation of the resonance-assisted hydrogen bond in model β-diketones through localized molecular orbital analysis of the spin-spin coupling constants related to the O-H···O hydrogen bond

The resonance-assisted hydrogen bond (HB) phenomenon has been studied theoretically by a localized molecular orbital (LMO) decomposition of the spin-spin coupling constants between atoms either involved or close to the O-H···O system of some β-diketones and their saturated counterparts. The analysis, carried out at the level of the second-order polarization propagator approximation, shows that the contributions in terms of LMO to the paramagnetic spin orbital and the spin dipolar Ramsey terms proof the importance of the delocalized π-electron structure supporting the idea of the existence of the resonance-assisted HB phenomenon phenomenon. The LMO contributions to the Fermi contact term indicate mainly the presence of the HB that may or not be linked to the π-electrons.

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.

Modular functionalized polyphosphines for supported materials: previously unobserved31P-NMR «through-space» ABCD spin systems and heterogeneous palladium-catalysed C–C and C–H arylation

Functionalized modular polyphosphines introduce a conceptual novelty in controlling both implantation and conformation of donors in immobilized catalysts.

Observation of scalar nuclear spin–spin coupling in van der Waals complexes

Scalar couplings between covalently bound nuclear spins are a ubiquitous feature in nuclear magnetic resonance (NMR) experiments, imparting valuable information to NMR spectra regarding molecular structure and conformation. Such couplings arise due to a second-order hyperfine interaction, and, in principle, the same mechanism should lead to scalar couplings between nuclear spins in unbound van der Waals complexes. Here, we report the first observation of scalar couplings between nuclei in van der Waals complexes. Our measurements are performed in a solution of hyperpolarized 129Xe and pentane, using superconducting quantum interference devices to detect NMR in 10 mG fields, and are in good agreement with calculations based on density functional theory. van der Waals forces play an important role in many physical phenomena. The techniques presented here may provide a new method for probing such interactions.

The analysis of NMR J-couplings of saturated and unsaturated compounds by the localized second order polarization propagator approach method

Calculations of NMR J-coupling with polarization propagators are not invariant under unitary transformations at second order level of approach, second order polarization propagator approach (SOPPA). They are only invariant at first order or random phase level of approach (RPA). We performed "localized" SOPPA (Loc-SOPPA), calculations of J-couplings applying two different schemes for the localization of molecular orbitals(LMO): Foster-Boys and Pipek-Mezey. We show here that results of such Loc-SOPPA calculations are different though not much: they are less than 6% different in the worst case. Therefore it is possible to apply them with confidence in the analysis of the transmission of different coupling mechanisms within the molecule. We are able now to get reliable information on what LMOs are the most important (and so which are not important) for a given J-coupling in a molecule. This information can then be used for selecting which are the paths that should be described with the highest possible accuracy for that J-coupling calculation. A few unsaturated compounds are analyzed: ethene, trans-difluoroethene or DiF-ethene, and imine. It is shown that different lone pairs (of p(z) or p(x/y) type) are responsible for the vicinal F-F J-coupling in DiF-ethene; and also the fact that the main LP contributor is not the same for the fermi contact and the spin-dipolar mechanisms. We also studied phosphorous containing compounds such as phosphine and cis-propylene phosphine. In both cases the analysis of the main LMO contributing to one-bond P-H coupling and through-space P-C coupling were performed. The above mentioned unsaturated molecular systems have quasiinstability problems that arise at RPA level of approach. We show here that they are mostly originated in the antibonding π∗ LMO, corresponding to the C=C or C=N double bonds. We performed the analysis of the origin of quasiinstabilities for the SD mechanism. The contribution of each kind of excitation terms to SOPPA calculations were considered, meaning the main contributions by single and double excitations. It is shown that one can get more than 97% of the total electron correlation contribution when including terms that mainly contain single excitations (though double-excitation matrix elements should still be calculated).

Difference between ²JC2H3 and ²JC3H2 spin-spin couplings in heterocyclic five- and six-membered rings as a probe for studying σ-ring currents: a quantum chemical analysis

Adequate analyses of canonical molecular orbitals (CMOs) can provide rather detailed information on the importance of different σ-Fermi contact (FC) coupling pathways (FC term transmitted through the σ-skeleton). Knowledge of the spatial distribution of CMOs is obtained by expanding them in terms of natural bond orbitals (NBOs). Their relative importance for transmitting the σ-FC contribution to a given spin-spin coupling constants (SSCCs) is estimated by resorting to the expression of the FC term given by the polarisation propagator formalism. In this way, it is possible to classify the effects affecting such couplings in two different ways: delocalisation interactions taking place in the neighbourhood of the coupling nuclei and 'round the ring' effects. The latter, associated with σ-ring currents, are observed to yield significant differences between the FC terms of (2)J(C2H3) and (2)J(C3H2) SSCCs which, consequently, are taken as probes to gauge the differences in σ-ring currents for the five-membered rings (furan, thiophene, selenophene and pyrrol) and also for the six-membered rings (benzene, pyridine, protonated pyridine and N-oxide pyridine) used in the present study.

Relative importance of first and second derivatives of nuclear magnetic resonance chemical shifts and spin-spin coupling constants for vibrational averaging

Relative importance of anharmonic corrections to molecular vibrational energies, nuclear magnetic resonance (NMR) chemical shifts, and J-coupling constants was assessed for a model set of methane derivatives, differently charged alanine forms, and sugar models. Molecular quartic force fields and NMR parameter derivatives were obtained quantum mechanically by a numerical differentiation. In most cases the harmonic vibrational function combined with the property second derivatives provided the largest correction of the equilibrium values, while anharmonic corrections (third and fourth energy derivatives) were found less important. The most computationally expensive off-diagonal quartic energy derivatives involving four different coordinates provided a negligible contribution. The vibrational corrections of NMR shifts were small and yielded a convincing improvement only for very accurate wave function calculations. For the indirect spin-spin coupling constants the averaging significantly improved already the equilibrium values obtained at the density functional theory level. Both first and complete second shielding derivatives were found important for the shift corrections, while for the J-coupling constants the vibrational parts were dominated by the diagonal second derivatives. The vibrational corrections were also applied to some isotopic effects, where the corrected values reasonably well reproduced the experiment, but only if a full second-order expansion of the NMR parameters was included. Contributions of individual vibrational modes for the averaging are discussed. Similar behavior was found for the methane derivatives, and for the larger and polar molecules. The vibrational averaging thus facilitates interpretation of previous experimental results and suggests that it can make future molecular structural studies more reliable. Because of the lengthy numerical differentiation required to compute the NMR parameter derivatives their analytical implementation in future quantum chemistry packages is desirable.

Unusual long-range spin-spin coupling in fluorinated polyenes: a mechanistic analysis

Nuclear magnetic resonance (NMR) is a prospective means to realize quantum computers. The performance of a NMR quantum computer depends sensitively on the properties of the NMR-active molecule used, where one requirement is a large indirect spin-spin coupling over large distances. F-F spin-spin coupling constants (SSCCs) for fluorinated polyenes F-(CH==CH)n-F (n=1cdots, three dots, centered5) are >9 Hz across distances of more than 10 A. Analysis of the F,F spin-spin coupling mechanism with our recently developed decomposition of J into Orbital Contributions with the help of Orbital Currents and Partial Spin Polarization (J-OCOC-PSP=J-OC-PSP) method reveals that coupling is dominated by the spin-dipole (SD) term due to an interplay between the pi lone-pair orbitals at the F atoms and the pi(C2n) electron system. From our investigations we conclude that SD-dominated SSCCs should occur commonly in molecules with a contiguous pi-electron system between the two coupling nuclei and that a large SD coupling generally is the most prospective way to provide large long-range spin-spin coupling. Our results give guidelines for the design of suitable active molecules for NMR quantum computers.

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.

Calculation and analysis of NMR spin-spin coupling constants

The analysis of NMR spin-spin coupling leads to a unique insight into the electronic structure of closed-shell molecules, provided one is able to decode the different features of the spin-spin coupling mechanism. For this purpose, the physics of spin-spin coupling is described and the way how spin-spin coupling constants (SSCCs) can be quantum mechanically determined. Based on this insight, a set of requirements is derived that guide the development of a quantum mechanical analysis of spin-spin coupling. It is demonstrated that the J-OC-PSP (=J-OC-OC-PSP: Decomposition of J into orbital contributions using orbital currents and partial spin polarization) analysis method fulfills all requirements. J-OC-PSP makes it possible to partition the isotropic indirect SSCC J or its reduced analogue K as well as the four Ramsey terms (Fermi contact (FC), spin dipole (SD), diamagnetic spin orbit (DSO), paramagnetic spin orbit (PSO)) leading to J (or K) into Cartesian components (for the anisotropic Ramsey terms SD, DSO, PSO), orbital contributions or electron interaction terms. For the purpose of decoding the spin-spin coupling mechanism, FC, SD, DSO, and PSO coupling is discussed in detail and related to electronic and bonding features of the molecules in question. The myth of empirical and semiempirical relationships between SSCCs and bonding features is unveiled. It is found that most relationships are only of limited, partly dubious value, often arising from a fortuitous cancellation of terms that cannot be expected in general. These relationships are replaced by quantum chemical relations and descriptions that directly reflect the complex electronic processes leading to spin-spin coupling.

Study of static and dynamic first hyperpolarizabilities using time-dependent density functional quadratic response theory with local contribution and natural bond orbital analysis

We apply time-dependent density-functional quadratic response theory to investigate the static and dynamic second-order polarizabilities (first hyperpolarizability) beta. A new implementation using Slater-type basis functions, numerical integration, and density fitting techniques is reported. The second order coupled perturbed Kohn-Sham equations are solved and the second-order perturbed charge density is obtained. It is useful to highlight atomic and bond contributions to understand the relation between molecular structure and properties. Four moderately sized molecules (para-nitroaniline and derivatives thereof) are investigated to assess the accuracy of the time-dependent density-functional theory computations and to investigate the distribution of the second-order charge density as well as the "beta density." Our results highlight the contributions from atoms and bonds on different functional groups to the total value of beta with Mulliken-type and natural bond orbital (NBO) analyses, and demonstrate in some cases how contributions from a particular bond may be identified easily by visual inspection of the beta density. In addition, the position of side group substitution on carbon-carbon bonds significantly affects the hyperpolarizability. A contribution analysis as performed here might be helpful for the design of new materials with desired properties.