NMR parameters of FNNF as a test for coupled-cluster methods: CCSDT shielding and CC3 spin-spin coupling.

NMR shielding and spin-spin coupling constants of cis and trans isomers of FNNF have been determined to near-quantitative accuracy from ab initio calculations. The FNNF system, containing multiple N-F bonds and fluorine atoms, provides a severe test of computational methods. Coupled-cluster methods were used with large basis sets and complete basis set (CBS) extrapolations of the equilibrium geometry results, with vibrational and relativistic corrections. Shielding constants were calculated with basis sets as large as aug-cc-pCV7Z, together with coupled-cluster expansions up to CCSDT, at the all-electron CCSD(T)/aug-cc-pCVQZ optimized geometries. Spin-spin coupling constants have been determined with specialized versions of the correlation consistent basis sets ccJ-pVXZ, further augmented with diffuse functions. All-electron coupled-cluster methods up to CC3 were applied in these calculations. The results of this work highlight the application of state-of-the-art theoretical techniques, and provide the most accurate NMR properties of FNNF to date, which can serve to guide and supplement NMR experimentation.

NMR Spin-Spin Coupling Constants Derived from Relativistic Four-Component DFT Theory-Analysis and Visualization.

An unambiguous assignment of coupling pathways plays an important role in the description and rationalization of NMR indirect spin-spin coupling constants (SSCCs). Unfortunately, the SSCC analysis and visualization tools currently available to quantum chemists are restricted to nonrelativistic theory. Here, we present the theoretical foundation for novel relativistic SSCC visualization techniques based on analysis of the SSCC densities and the first-order current densities induced by the nuclear magnetic dipole moments. Details of the implementation of these techniques in the ReSpect program package are discussed. Numerical assessments are performed on through-space SSCCs, and we choose as our examples the heavy-atom Se-Se, Se-Te, and Te-Te coupling constants in three similar molecules for which experimental data are available. SSCCs were calculated at the nonrelativistic, scalar relativistic, and four-component relativistic density functional levels of theory. Furthermore, with the aid of different visualization methods, we discuss the interpretation of the relativistic effects, which are sizable for Se-Se, very significant for Se-Te, and cannot be neglected for Te-Te couplings. A substantial improvement of the theoretical SSCC values is obtained by also considering the molecular properties of a second conformation.

Interplay of Aromaticity and Antiaromaticity in N-Doped Nanographenes.

The aromaticity of three nonplanar, fully conjugated aza-nanographenes built around a pyrrolo[3,2-b]pyrrole core is assessed through the application of two different computational procedures-GIMIC and NICS. We examine the calculated magnetically induced current densities (GIMIC) and nucleus-independent chemical shifts (NICS). The structural differences between these three apparently similar molecules lead to significantly different aromatic properties. GIMIC analysis indicates that the peripheral diatropic ring current of 3.9 nA/T for the studied bowl-shaped diaza-nanographene is the strongest, followed by the double [6]helicene which lacks seven-membered rings, and is practically nonexistent for the double [5]helicene possessing seven-membered rings. The biggest difference however is that in the two not-fully-fused molecules, the central pyrrole rings possess a significant diatropic current of about 4.1 nA/T, whereas there is no such current in the diaza-nanographene. Moreover, the antiaromaticity of the seven-membered rings is increasing while moving from double [5]helicene to diaza-nanographene (from -2.4 to -6.0 nA/T). The induced currents derived from NICSπ,zz-XY-scan analysis for all of the studied systems are in qualitative agreement with the GIMIC results. Subtle differences may originate from σ-electron currents in GIMIC or inaccuracy of NICSπ,zz values due to the nonplanarity of the systems, but the general picture is similar.

The effect of weak intermolecular interactions on the nuclear magnetic resonance shielding constant in N2.

Ab initio calculations are applied to examine the influence of the intermolecular interactions on the shielding constant in gaseous nitrogen. An accurate literature potential energy surface and the nuclear magnetic resonance shielding surface of the N2 -N2 complex calculated in this work provide results in satisfactory agreement with the available experimental estimates of the effect.

NMR shielding constants in group 15 trifluorides.

By combining large basis and complete basis set (CBS) extrapolations of the coupled-cluster equilibrium geometry results with rovibrational and relativistic corrections, we demonstrate that it is possible to achieve near-quantitative accuracy for the NMR shielding constants in three group 15 trifluorides - NF3, PF3 and AsF3. These systems provide a rich test set for the calculation of dynamic electron correlation effects on NMR shielding constants. Basis sets as large as aug-cc-pCV6Z were employed, together with coupled-cluster expansion up to CCSDT, at the CCSD(T)/aug-cc-pCVTZ optimised geometries. The results of this work serve to highlight the application of state-of-the-art theoretical techniques which can be employed to guide and supplement NMR experimentation. Combining chemical shifts (either from experiment or high-level calculations) has also enabled a revised reference 19F NMR shielding constant for gas phase CFCl3 to be determined.

Calculation of NMR Spin-Spin Coupling Constants in Strychnine.

We compare the NMR indirect nuclear spin-spin coupling constants in strychnine calculated using density functional theory (DFT) with the semiempirical relativistic force field (RFF) method of Kutateladze and Mukhina (KM) (J. Org. Chem. 2015, 80, 10838-10848). DFT values significantly more accurate than those obtained by KM for their comparison with RFF values can be obtained, at a lower cost, by an appropriate selection of basis set.

NMR absolute shielding scale and nuclear magnetic dipole moment of (207)Pb.

An absolute shielding scale is proposed for (207)Pb nuclear magnetic resonance (NMR) spectroscopy. It is based on ab initio calculations performed on an isolated tetramethyllead Pb(CH3)4 molecule and the assignment of the experimental resonance frequency from the gas-phase NMR spectra of Pb(CH3)4, extrapolated to zero density of the buffer gas to obtain the result for an isolated molecule. The computed (207)Pb shielding constant is 10 790 ppm for the isolated molecule, leading to a shielding of 10799.7 ppm for liquid Pb(CH3)4 which is the accepted reference standard for (207)Pb NMR spectra. The new experimental and theoretical data are used to determine µ((207)Pb), the nuclear magnetic dipole moment of (207)Pb, by applying the standard relationship between NMR frequencies, shielding constants and nuclear moments of two nuclei in the same external magnetic field. Using the gas-phase (207)Pb and (reference) proton results and the theoretical value of the Pb shielding in Pb(CH3)4, we find µ((207)Pb) = 0.59064 µN. The analysis of new experimental and theoretical data obtained for the Pb(2+) ion in water solutions provides similar values of µ((207)Pb), in the range of 0.59000-0.59131 µN.

Indirect Spin-Spin Coupling Constants in the Hydrogen Isotopologues.

The results of experimental and theoretical studies of indirect spin-spin coupling constants for hydrogen deuteride (HD), hydrogen tritide (HT), and deuterium tritide (DT) are described. The reduced coupling constants obtained from the gas-phase NMR (nuclear magnetic resonance) experiment conducted at 300 K are 2.338(1), 2.334(3), and 2.316(1) × 10(20) T(2) J(-1), while the ab initio values computed at the full configuration interaction level of theory equal 2.349(3), 2.343(3), and 2.322(3) × 10(20) T(2) J(-1) for HD, HT, and DT, respectively. The agreement of the experimental and theoretical results is improved when proper treatment of the influence of nuclear relaxation on the NMR spectrum is applied. However, there is a minor discrepancy between experiment and theory, exceeding the estimated error bars; potential sources of this discrepancy are discussed.

Indirect NMR spin-spin coupling constants in diatomic alkali halides.

We report the Nuclear Magnetic Resonance (NMR) spin-spin coupling constants for diatomic alkali halides MX, where M = Li, Na, K, Rb, or Cs and X = F, Cl, Br, or I. The coupling constants are determined by supplementing the non-relativistic coupled-cluster singles-and-doubles (CCSD) values with relativistic corrections evaluated at the four-component density-functional theory (DFT) level. These corrections are calculated as the differences between relativistic and non-relativistic values determined using the PBE0 functional with 50% exact-exchange admixture. The total coupling constants obtained in this approach are in much better agreement with experiment than the standard relativistic DFT values with 25% exact-exchange, and are also noticeably better than the relativistic PBE0 results obtained with 50% exact-exchange. Further improvement is achieved by adding rovibrational corrections, estimated using literature data.

Absolute NMR shielding scales and nuclear spin-rotation constants in (175)LuX and (197)AuX (X = (19)F, (35)Cl, (79)Br and (127)I).

We present nuclear spin-rotation constants, absolute nuclear magnetic resonance (NMR) shielding constants, and shielding spans of all the nuclei in (175)LuX and (197)AuX (X = (19)F, (35)Cl, (79)Br, (127)I), calculated using coupled-cluster singles-and-doubles with a perturbative triples (CCSD(T)) correction theory, four-component relativistic density functional theory (relativistic DFT), and non-relativistic DFT. The total nuclear spin-rotation constants determined by adding the relativistic corrections obtained from DFT calculations to the CCSD(T) values are in general in agreement with available experimental data, indicating that the computational approach followed in this study allows us to predict reliable results for the unknown spin-rotation constants in these molecules. The total NMR absolute shielding constants are determined for all the nuclei following the same approach as that applied for the nuclear spin-rotation constants. In most of the molecules, relativistic effects significantly change the computed shielding constants, demonstrating that straightforward application of the non-relativistic formula relating the electronic contribution to the nuclear spin-rotation constants and the paramagnetic contribution to the shielding constants does not yield correct results. We also analyze the origin of the unusually large absolute shielding constant and its relativistic correction of gold in AuF compared to the other gold monohalides.

A theoretical study of potentially observable chirality-sensitive NMR effects in molecules.

Two recently predicted nuclear magnetic resonance effects, the chirality-induced rotating electric polarization and the oscillating magnetization, are examined for several experimentally available chiral molecules. We discuss in detail the requirements for experimental detection of chirality-sensitive NMR effects of the studied molecules. These requirements are related to two parameters: the shielding polarizability and the antisymmetric part of the nuclear magnetic shielding tensor. The dominant second contribution has been computed for small molecules at the coupled cluster and density functional theory levels. It was found that DFT calculations using the KT2 functional and the aug-cc-pCVTZ basis set adequately reproduce the CCSD(T) values obtained with the same basis set. The largest values of parameters, thus most promising from the experimental point of view, were obtained for the fluorine nuclei in 1,3-difluorocyclopropene and 1,3-diphenyl-2-fluoro-3-trifluoromethylcyclopropene.

Spin-rotation and NMR shielding constants in XF molecules (X = B, Al, Ga, In, and Tl).

Accurate spin-rotation and absolute shielding constants in a series of XF molecules (X = (11)B, (27)Al, (69)Ga, (115)In, and (205)Tl) determined using high-level ab initio coupled-cluster and four-component relativistic density-functional theory (DFT) calculations are presented. The accuracy of the results is established by comparing the relativistically and vibrationally corrected calculated values with available experimental data; for spin-rotation and shielding constants for which no experimental data exist, we provide new and reliable values. For both properties, our results can be considered as reference values against which more approximate quantum-chemical methods can be benchmarked.

The NMR spin-spin coupling constant ¹J(³¹P,¹H) in an isolated PH3 molecule.

We present new experimental and calculated values of the indirect spin-spin coupling constant (1)J((31)P,(1)H) in the PH3 molecule. The line shape analysis of (1)H and (31)P gas-phase NMR spectra recorded at several densities of PH3, followed by extrapolation of the results to the zero-density limit, gives 176.18(2) Hz as the experimental value at 300 K. The coupled-cluster singles-and-doubles (CCSD) model used in the quantum chemical ab initio calculation gives 187.86 Hz as the nonrelativistic equilibrium geometry value; adding the relativistic and temperature corrections we obtain (1)J((31)P,(1)H) = 177.14 Hz at 300 K. The comparison of this ab initio result with the experimental value shows that proper analysis of nuclear relaxation in the gas phase is essential and leads to very good agreement between theory and experiment.

Ab initio and relativistic DFT study of spin-rotation and NMR shielding constants in XF6 molecules, X = S, Se, Te, Mo, and W.

We present an analysis of the spin-rotation and absolute shielding constants of XF6 molecules (X = S, Se, Te, Mo, W) based on ab initio coupled cluster and four-component relativistic density-functional theory (DFT) calculations. The results show that the relativistic contributions to the spin-rotation and shielding constants are large both for the heavy elements as well as for the fluorine nuclei. In most cases, incorporating the computed relativistic corrections significantly improves the agreement between our results and the well-established experimental values for the isotropic spin-rotation constants and their anisotropic components. This suggests that also for the other molecules, for which accurate and reliable experimental data are not available, reliable values of spin-rotation and absolute shielding constants were determined combining ab initio and relativistic DFT calculations. For the heavy nuclei, the breakdown of the relationship between the spin-rotation constant and the paramagnetic contribution to the shielding constant, due to relativistic effects, causes a significant error in the total absolute shielding constants.

Analytic density functional theory calculations of pure vibrational hyperpolarizabilities: the first dipole hyperpolarizability of retinal and related molecules.

We present a general approach for the analytic calculation of pure vibrational contributions to the molecular (hyper)polarizabilities at the density functional level of theory. The analytic approach allows us to study large molecules, and we apply the new code to the study of the first dipole hyperpolarizabilities of retinal and related molecules. We investigate the importance of electron correlation as described by the B3LYP exchange-correlation functional on the pure vibrational and electronic hyperpolarizabilities and compare the computed hyperpolarizabilities with available experimental data. The effects of electron correlation on the pure vibrational corrections vary signficantly even between these structurally very similar molecules, making it difficult to estimate these effects without explicit calculations at the density functional theory level. As expected, the frequency-dependent first hyperpolarizability, which determines the experimentally observed second-harmonic generation, is dominated by the electronic term, whereas for the static hyperpolarizability, the vibrational contribution is equally important. As a consequence, frequency extrapolation of the measured optical hyperpolarizabilities can only provide an estimate for the electronic contribution to the static hyperpolarizability, not its total value. The relative values of the hyperpolarizabilities for different molecules, obtained from the calculations, are in reasonable agreement with experimental data.

Spin-rotation and NMR shielding constants in HCl.

The spin-rotation and nuclear magnetic shielding constants are analysed for both nuclei in the HCl molecule. Nonrelativistic ab initio calculations at the CCSD(T) level of approximation show that it is essential to include relativistic effects to obtain spin-rotation constants consistent with accurate experimental data. Our best estimates for the spin-rotation constants of (1)H(35)Cl are CCl = -53.914 kHz and C(H) = 42.672 kHz (for the lowest rovibrational level). For the chlorine shielding constant, the ab initio value computed including the relativistic corrections, σ(Cl) = 976.202 ppm, provides a new absolute shielding scale; for hydrogen we find σ(H) = 31.403 ppm (both at 300 K). Combining the theoretical results with our new gas-phase NMR experimental data allows us to improve the accuracy of the magnetic dipole moments of both chlorine isotopes. For the hydrogen shielding constant, including relativistic effects yields better agreement between experimental and computed values.

Weak intermolecular interactions in gas-phase nuclear magnetic resonance.

Gas-phase nuclear magnetic resonance (NMR) spectra demonstrating the effect of weak intermolecular forces on the NMR shielding constants of the interacting species are reported. We analyse the interaction of the molecular hydrogen isotopomers with He, Ne, and Ar, and the interaction in the He-CO(2) dimer. The same effects are studied for all these systems in the ab initio calculations. The comparison of the experimental and computed shielding constants is shown to depend strongly on the treatment of the bulk susceptibility effects, which determine in practice the pressure dependence of the experimental values. Best agreement of the results is obtained when the bulk susceptibility correction in rare gas solvents is evaluated from the analysis of the He-rare gas interactions, and when the shielding of deuterium in D(2)-rare gas systems is considered.

NMR shielding constants in PH3, absolute shielding scale, and the nuclear magnetic moment of 31P.

Ab initio values of the absolute shielding constants of phosphorus and hydrogen in PH(3) were determined, and their accuracy is discussed. In particular, we analyzed the relativistic corrections to nuclear magnetic resonance (NMR) shielding constants, comparing the constants computed using the four-component Dirac-Hartree-Fock approach, the four-component density functional theory (DFT), and the Breit-Pauli perturbation theory (BPPT) with nonrelativistic Hartree-Fock or DFT reference functions. For the equilibrium geometry, we obtained σ(P) = 624.309 ppm and σ(H) = 29.761 ppm. Resonance frequencies of both nuclei were measured in gas-phase NMR experiments, and the results were extrapolated to zero density to provide the frequency ratio for an isolated PH(3) molecule. This ratio, together with the computed shielding constants, was used to determine a new value of the nuclear magnetic dipole moment of (31)P: µ(P) = 1.1309246(50) µ(N).

DFT calculations of 31P spin-spin coupling constants and chemical shift in dioxaphosphorinanes.

One-bond heteronuclear spin-spin coupling constants (1)J(PX) (X=H, O, S, Se, C and N) between the phosphorus atom and axial and equatorial substituents in dioxaphosphorinanes are computed using density functional theory (DFT). The experimental values of these coupling constants for a variety of substituents can be applied to identify different diastereoisomers. The DFT calculations confirm the systematic trend observed in experiment, and indicate that the computed (1)J(PX) coupling constants are related to the length of the axial and equatorial bonds. A similar relation between the phosphorus chemical shift and the R(PX) bond length appears to be valid, with the exception of selenium substituents.