Nuclear Magnetic Shielding Constants Research Articles

Probing the Solvent Shell with 195Pt Chemical Shifts: Density Functional Theory Molecular Dynamics Study of PtII and PtIV Anionic Complexes in Aqueous Solution

Ab initio molecular dynamics (aiMD) simulations based on density functional theory (DFT) were performed on a set of five anionic platinum complexes in aqueous solution. (195)Pt nuclear magnetic shielding constants were computed with DFT as averages over the aiMD trajectories, using the two-component relativistic zeroth-order regular approximation (ZORA) in order to treat relativistic effects on the Pt shielding tensors. The chemical shifts obtained from the aiMD averages are in good agreement with experimental data. For Pt(II) and Pt(IV) halide complexes we found an intermediate solvent shell interacting with the complexes that causes pronounced solvent effects on the Pt chemical shifts. For these complexes, the magnitude of solvent effects on the Pt shielding constant can be correlated with the surface charge density. For square-planar Pt complexes the aiMD simulations also clearly demonstrate the influence of closely coordinated non-equatorial water molecules on the Pt chemical shift, relating the structure of the solution around the complex to the solvent effects on the metal NMR chemical shift. For the complex [Pt(CN)(4)](2-), the solvent effects on the Pt shielding constant are surprisingly small.

Quantitative prediction of gas-phase N15 and P31 nuclear magnetic shielding constants

High-level ab initio benchmark calculations of the (15)N and (31)P NMR chemical shielding constants for a representative set of molecules are presented. The computations have been carried out at the Hartree-Fock self-consistent field (HF-SCF), density functional theory (DFT) (B-P86 and B3-LYP), second-order Moller-Plesset perturbation theory (MP2), coupled cluster singles and doubles (CCSD), and CCSD augmented by a perturbative treatment of triple excitations [CCSD(T)] level of theory using basis sets of triple zeta quality or better. The influence of the geometry, the treatment of electron correlation, as well as basis set and zero-point vibrational effects on the shielding constants are discussed and the results are compared to gas-phase experimental shifts. As for the first time a study using high-level post-HF methods is carried out for a second-row element, we also propose a family of basis sets suitable for the computation of (31)P shielding constants. The mean deviations observed for (15)N and (31)P are 0.9 [CCSD(T)/13s9p4d3f] and -3.3 ppm [CCSD(T)/15s12p4d3f2g], respectively, when corrected for zero-point vibrational effects. Results obtained at the DFT level of theory are of comparable accuracy to MP2 for (15)N and of comparable accuracy to HF-SCF for (31)P. However, they are not improved by inclusion of zero-point vibrational effects. The PN molecule is an especially interesting case with exceptionally large electron correlation effects on shielding constants beyond MP2 which, therefore, represents an excellent example for further benchmark studies.

Assessment of the CTOCD-DZ method in a hierarchy of coupled cluster methods

Gauge origin independent calculations of nuclear magnetic shielding tensors are carried out inside the formalism of the continuous transformation of the origin of the current density leading to formal annihilation of its diamagnetic contribution (CTOCD-DZ). We employ the unrelaxed linear response approach with a hierarchy of different coupled cluster methods in order to assess the importance of the level of approximation in the coupled cluster expansion. The basis set dependence of the computed nuclear magnetic shielding constants is also analyzed in the series of correlation consistent basis sets, with the aim of designing optimized basis sets of relatively small size.

A new experimental absolute nuclear magnetic shielding scale for oxygen based on the rotational hyperfine structure of H2O17

The hyperfine structure in the rotational spectrum of water containing (17)O has been investigated experimentally and by means of quantum-chemical calculations. The Lamb-dip technique has been used to resolve the hyperfine structure due to spin-rotation as well as spin-spin interactions and allowed the determination of the corresponding hyperfine parameters with high accuracy. The experimental investigation and, in particular, the analysis of the spectra have been supported by quantum-chemical computations at the coupled-cluster level. The experimental (17)O isotropic spin-rotation constant of H(2)(17)O has been used in a further step for the determination of the paramagnetic part of the corresponding nuclear magnetic shielding constant, whereas the diamagnetic contribution as well as vibrational and temperature corrections have been obtained from quantum-chemical calculations. This joint procedure leads to a value of 325.3(3) ppm for the oxygen shielding in H(2)(17)O at 300 K, in good agreement with pure theoretical predictions, and in this way provides the basis for a new absolute oxygen shielding scale.

Solvent Dependence of (14)N Nuclear Magnetic Resonance Chemical Shielding Constants as a Test of the Accuracy of the Computed Polarization of Solute Electron Densities by the Solvent.

Although continuum solvation models have now been shown to provide good quantitative accuracy for calculating free energies of solvation, questions remain about the accuracy of the perturbed solute electron densities and properties computed from them. Here we examine those questions by applying the SM8, SM8AD, SMD, and IEF-PCM continuum solvation models in combination with the M06-L density functional to compute the (14)N magnetic resonance nuclear shieldings of CH3CN, CH3NO2, CH3NCS, and CH3ONO2 in multiple solvents, and we analyze the dependence of the chemical shifts on solvent dielectric constant. We examine the dependence of the computed chemical shifts on the definition of the molecular cavity (both united-atom models and models based on superposed individual atomic spheres) and three kinds of treatments of the electrostatics, namely the generalized Born approximation with the Coulomb field approximation, the generalized Born model with asymmetric descreening, and models based on approximate numerical solution schemes for the nonhomogeneous Poisson equation. Our most systematic analyses are based on the computation of relative (14)N chemical shifts in a series of solvents, and we compare calculated shielding constants relative to those in CCl4 for various solvation models and density functionals. While differences in the overall results are found to be reasonably small for different solvation models and functionals, the SMx models SM8, and SM8AD, using the same cavity definitions (which for these models means the same atomic radii) as those employed for the calculation of free energies of solvation, exhibit the best agreement with experiment for every functional tested. This suggests that in addition to predicting accurate free energies of solvation, the SM8 and SM8AD generalized Born models also describe the solute polarization in a manner reasonably consistent with experimental (14)N nuclear magnetic resonance spectroscopy. Models based on the nonhomogeneous Poisson equation show slightly reduced accuracy. Scaling the intrinsic Coulomb radii to larger values (as has sometimes been suggested in the past) does not uniformly improve the results for any kind of solvent model; furthermore it uniformly degrades the results for generalized Born models. Use of a basis set that increases the outlying charge diminishes the accuracy of continuum models that solve the nonhomogeneous Poisson equation, which we ascribe to the inability of the numerical schemes for approximately solving the nonhomogeneous Poisson equation to fully account for the effects of electronic charge outside the solute cavity.

Quantitative prediction of gas-phase O17 nuclear magnetic shielding constants

Benchmark calculations of (17)O NMR chemical shifts for a series of 19 molecules with 22 chemical shifts are presented. This includes calculations at the HF-SCF, DFT (BP86 and B3-LYP), MP2, CCSD(T), and for a special case full CCSDT level of theory using basis sets of quadruple zeta quality and better. The effects of the quality of the geometry, electron correlation, basis set, and the inclusion of zero-point vibrational and temperature corrections are discussed in detail and the results are compared to gas-phase experimental values. Mean and standard deviations are 6 and 24 ppm for HF-SCF, -20 and 14 ppm for BP86, -20 and 13 ppm for B3-LYP, and 26 and 12 ppm for MP2. Results at the CCSD(T)/pz3d2f level of theory using geometries optimized at the CCSD(T)/cc-pVTZ level of theory exhibit a mean deviation of 16 ppm and a standard deviation of 6 ppm. A mean deviation of 6 ppm and a standard deviation of 4 ppm are obtained if these values are corrected for zero-point vibrational and temperature effects.

Nuclear magnetic shielding constants calculated from numerical hartree-fock wave functions

Numerical Hartree-Fock wave functions for neutral atoms (for the ground state) calculated by Froese [1] have been used to calculate nuclear magnetic shielding constants (σ) for all the atoms from helium (Z = 2) to radon (Z = 86). From the analysis of the partial contributions to σ from the various shells in xenon it is pointed out that the innermost shells make the largest contribution in agreement with the observation of Malli and Fraga [2] reported earlier.

Four-component relativistic theory for NMR parameters: Unified formulation and numerical assessment of different approaches

Several four-component relativistic approaches for nuclear magnetic shielding constant have recently been proposed and their formal relationships have also been established [Xiao et al., J. Chem. Phys. 126, 214101 (2007)]. It is shown here that the approaches can be recast into a unified form via the generic ansatz of orbital decomposition. The extension of the formalisms to magnetizability (and nuclear spin-spin coupling) is straightforward. Exact analytical expressions are also derived for both the shielding constant and magnetizability of the hydrogenlike atom in the ground state. A series of calculations on Rn(85+) and Rn is then carried out to reveal the performance of the various methods with respect to the basis set requirement, leading to the conclusion that it is absolutely essential to explicitly account for the magnetic balance condition. However, different ways of doing so lead to quite similar results. It is also demonstrated that only extremely compact negative energy states are important for the total shieldings and their effects are hence essentially canceled out for chemical shifts. This has important implications for further theoretical developments.

Prediction of gas‐phase 13C nuclear magnetic shielding constants using ONIOM and optimally selected basis functions

AbstractThe wave functions for calculating gas‐phase 13C nuclear magnetic shielding constants of 22 molecules have been optimally selected using factorial design as a multivariate technique. GIAO and CSGT methods were used for computation of shielding constants. Different wave functions for different types of carbons were recommended. A wave function as the best level of the theory is proposed for almost similar carbons. ONIOM approach for molecules with different types of carbons is applied. The results of GIAO method using the proposed wave function are in very good agreement with the experimental values. An additional series (21 carbons) were used as test sets and their results confirmed the validity of the approaches. © 2008 Wiley Periodicals, Inc.Concepts Magn Reson Part A 32A: 449–461, 2008.

Nuclear Magnetic Shielding of the 113Cd(II) Ion in Aqua Solution: A Combined Molecular Dynamics/Density Functional Theory Study

We present a combined molecular dynamics simulation and density functional theory investigation of the nuclear magnetic shielding constant of the (113)Cd(II) ion solvated in aqueous solution. Molecular dynamics simulations are carried out for the cadmium-water system in order to produce instantaneous geometries for subsequent determination of the nuclear magnetic shielding constant at the density functional theory level. The nuclear magnetic shielding constant is computed using a perturbation theory formalism, which includes nonrelativistic and leading order relativistic contributions to the nuclear magnetic shielding tensor. Although the NMR shielding constant varies significantly with respect to simulation time, the value averaged over increasing number of snapshots remains almost constant. The paramagnetic nonrelativistic contribution is found to be most sensitive to dynamical changes in the system and is mainly responsible for the thermal and solvent effects in solution. The relativistic correction features very little sensitivity to the chemical environment, and can be disregarded in theoretical calculations when a Cd complex is used as reference compound in (113)Cd NMR experiments, due to the mutual cancelation between individual relativistic corrections.

The isotropic nuclear magnetic shielding constants of acetone in supercritical water: A sequential Monte Carlo/quantum mechanics study including solute polarization

The nuclear isotropic shielding constants sigma((17)O) and sigma((13)C) of the carbonyl bond of acetone in water at supercritical (P=340.2 atm and T=673 K) and normal water conditions have been studied theoretically using Monte Carlo simulation and quantum mechanics calculations based on the B3LYP6-311++G(2d,2p) method. Statistically uncorrelated configurations have been obtained from Monte Carlo simulations with unpolarized and in-solution polarized solute. The results show that solvent effects on the shielding constants have a significant contribution of the electrostatic interactions and that quantitative estimates for solvent shifts of shielding constants can be obtained modeling the water molecules by point charges (electrostatic embedding). In supercritical water, there is a decrease in the magnitude of sigma((13)C) but a sizable increase in the magnitude of sigma((17)O) when compared with the results obtained in normal water. It is found that the influence of the solute polarization is mild in the supercritical regime but it is particularly important for sigma((17)O) in normal water and its shielding effect reflects the increase in the average number of hydrogen bonds between acetone and water. Changing the solvent environment from normal to supercritical water condition, the B3LYP6-311++G(2d,2p) calculations on the statistically uncorrelated configurations sampled from the Monte Carlo simulation give a (13)C chemical shift of 11.7+/-0.6 ppm for polarized acetone in good agreement with the experimentally inferred result of 9-11 ppm.

Basis-set convergence of nuclear magnetic shielding constants in molecular HF and MP2 calculations

Recently, segmented contracted basis sets of double, triple, quadruple and quintuple zeta valence quality plus polarization functions (XZP, X = D, T, Q and 5) for the atoms from H to Ar were presented by Jorge et al. We report a systematic study of basis sets required to obtain accurate values for nuclear magnetic shielding tensors for 20 molecules at their experimental equilibrium geometries. Two methods were examined: Hartree–Fock (HF) and second-order Møller–Plesset perturbation theory (MP2). Gauge-invariant atomic orbitals were used to guarantee origin-independent values of magnetic properties. By direct calculations or by fitting the directly calculated values through two extrapolation schemes, estimates of the HF and MP2 complete basis-set limit have been obtained. Comparison with experiment and benchmark results reported in the literature is made.

Quantitative prediction of gas-phase F19 nuclear magnetic shielding constants

Benchmark calculations of (19)F nuclear magnetic shielding constants are presented for a set of 28 molecules. Near-quantitative accuracy (ca. 2 ppm deviation from experiment) is achieved if (1) electron correlation is adequately treated by employing the coupled-cluster singles and doubles (CCSD) model augmented by a perturbative correction for triple excitations [CCSD(T)], (2) large (uncontracted) basis sets are used, (3) gauge-including atomic orbitals are used to ensure gauge-origin independence, (4) calculations are performed at accurate equilibrium geometries [obtained from CCSD(T)/cc-pVTZ calculations correlating all electrons], and (5) vibrational averaging and temperature corrections via second-order vibrational perturbation theory (VPT2) are included. For the CCSD(T)/13s9p4d3f calculations corrected for vibrational effects, mean and standard deviation from experiment are -1.9 and 1.6 ppm, respectively. Less elaborate theoretical treatments result in larger errors. Consideration of relative shifts can reduce the mean deviation (through an appropriately chosen reference compound), but does not change the standard deviation. Density-functional theory calculations of absolute and relative (19)F nuclear magnetic shielding constants are found to be, at best, as accurate as the corresponding Hartree-Fock self-consistent-field calculations and are not improved by consideration of vibrational effects. Molecular systems containing fluorine-oxygen, fluorine-nitrogen, and fluorine-fluorine bonds are found to be more challenging than the other investigated molecules for the considered theoretical methods.

Systematic investigation on the geometric dependence of the calculated nuclear magnetic shielding constants

We perform a systematic examination on the dependence of the calculated nuclear magnetic shielding constants on the chosen geometry for a selective set of density functional methods of B3LYP, PBE0, and OPBE. We find that the OPBE exchange-correlation functional performs remarkably well when either the optimized geometries or the experimental geometries are used. The popular B3LYP and PBE0 functionals have a clear tendency of deshielding, giving shieldings that are usually too low and shifts that are usually too high, at the experimental geometries. Combined with the Hartree-Fock geometries, however, much improved magnetic constants are obtained for B3LYP and PBE0, due to the compensation effect from the systematic underestimation of bond lengths by the Hartree-Fock method.

Effect of molecular size on the parity-non-conserving contributions to the nuclear magnetic resonance shielding constant

We present density-functional theory studies on the effects of molecular size on the parity-violating contribution to the nuclear magnetic shielding constant. We focus on models with different backbone and side chain lengths, as well as the details of geometry optimization for certain helical polysilylenes and investigate the parity-violating contribution to the shielding constant of the 29Si nucleus of the backbone. Our calculations show that the molecular geometry has a large influence on the magnitude of the parity-violating shielding contribution, a result that is in line with the previous studies on much smaller molecules. In addition, we find convergence in the magnitude of the PV effect with respect to system size, when using geometries that preserve the helical Si backbone structure optimized for the largest of the present systems. This can be interpreted in terms of the non-size-extensive nature of the parity-violating operator influencing the leading-order effect on nuclear magnetic shielding, as opposed to the size-extensive interaction affecting the energy difference between enantiomers. Our molecules are truncated models of large polysilylene systems, for which a difference in the 29Si chemical shift between enantiomers has been observed to be 0.06 ppm (Fujiki in Macromol Rapid Commun 22, 669–674, 2001). As expected based on earlier first principles studies of small molecules, we do not find support for the difference to be of the parity-violating origin. Instead, the predicted parity-violation-induced splitting of the 29Si resonance is found to converge at values around 10−8 ppm with increasingly large Si backbone.

Basis Set Convergence of Nuclear Magnetic Shielding Constants Calculated by Density Functional Methods.

The previously proposed polarization consistent basis sets, optimized for density functional calculations, are evaluated for calculating nuclear magnetic shielding constants. It is shown that the basis set convergence can be improved by adding a single p-type function with a large exponent and allowing for a slight decontraction of the p functions. The resulting pcS-n basis sets should be suitable for calculating nuclear magnetic shielding constants with density functional methods and are shown to perform significantly better than existing alternatives for a comparable computational cost.

Preparation, GIAO NMR calculations and acidic properties of some novel 4,5-dihydro-1H-1,2,4-triazol-5-one derivatives with their antioxidant activities.

Six novel 3-alkyl(aryl)-4-(p-nitrobenzoylamino)-4,5-dihydro-1H-1,2,4-triazol-5- ones (2a-f) were synthesized by the reactions of 3-alkyl(aryl)-4-amino-4,5-dihydro-1H- 1,2,4-triazol-5-ones (1a-f) with p-nitrobenzoyl chloride and characterized by elemental analyses and IR, (1)H-NMR, (13)C-NMR and UV spectral data. The newly synthesized compounds 2 were titrated potentiometrically with tetrabutylammonium hydroxide in four non-aqueous solvents such as acetone, isopropyl alcohol, tert-butyl alcohol and N,N-dimethylformamide, and the half-neutralization potential values and the corresponding pK(a) values were determined for all cases. Thus, the effects of solvents and molecular structure upon acidity were investigated. In addition, isotropic (1)H and (13)C nuclear magnetic shielding constants of compounds 2 were obtained by the gauge-including-atomic-orbital (GIAO) method at the B3LYP density functional level. The geometry of each compound has been optimized using the 6-311G basis set. Theoretical values were compared to the experimental data. Furthermore, these new compounds and five recently reported 3-alkyl-4-(2-furoylamino)-4,5-dihydro-1H-1,2,4-triazol-5-ones (3a-c,e,f) were screened for their antioxidant activities.

Geometric Dependence of the B3LYP-Predicted Magnetic Shieldings and Chemical Shifts

We perform a systematic investigation of how the B3LYP/6-311+G(2d,p) calculated 13C nuclear magnetic shielding constants depend on the 6-31G(d)-optimized geometries for a set of 18 molecules with various chemical environments. For absolute shieldings, the Hartree-Fock (HF)-optimized geometries lead to a mean absolute deviation (MAD) of 5.65 ppm, while the BLYP- and B3LYP-optimized geometries give MADs of 13.07 and 10.14 ppm, respectively. For chemical shifts, the HF, BLYP and B3LYP geometries lead to MADs of 2.36, 5.80, and 4.43 ppm, respectively. We find that the deshielding tendency of B3LYP can be effectively compensated by using the HF-optimized geometries. When we apply the B3LYP//HF protocol to versicolorin A and 5alpha-androstan-3,17-dione, MADs of 1.86 and 1.41 ppm, respectively, are obtained for chemical shifts, in satisfactory agreement with the experiment.

A study of some atomic properties for He-like selected ions

The atomic properties have been studied for He-like ions (He atom, Li+, Be2+ and B3+ions). These properties included, the atomic form factor f(S), electron density at the nucleus , nuclear magnetic shielding constant and diamagnetic susceptibility ,which are very important in the study of physical properties of the atoms and ions. For these purpose two types of the wave functions applied are used, the Hartree-Fock (HF) waves function (uncorrelated) and the Configuration interaction (CI) wave function (correlated). All the results and the behaviors obtained in this work have been discussed, interpreted and compared with those previously obtained.

Four-component relativistic theory for nuclear magnetic shielding constants: Critical assessments of different approaches

Both formal and numerical analyses have been carried out on various exact and approximate variants of the four-component relativistic theory for nuclear magnetic shielding constants. These include the standard linear response theory (LRT), the full or external field-dependent unitary transformations of the Dirac operator, as well as the orbital decomposition approach. In contrast with LRT, the latter schemes take explicitly into account both the kinetic and magnetic balances between the large and small components of the Dirac spinors, and are therefore much less demanding on the basis sets. In addition, the diamagnetic contributions, which are otherwise "missing" in LRT, appear naturally in the latter schemes. Nevertheless, the definitions of paramagnetic and diamagnetic terms are not the same in the different schemes, but the difference is only of O(c(-2)) and thus vanishes in the nonrelativistic limit. It is shown that, as an operator theory, the full field-dependent unitary transformation approach cannot be applied to singular magnetic fields such as that due to the magnetic point dipole moment of a nucleus. However, the inherent singularities can be avoided by the corresponding matrix formulation (with a partial closed summation). All the schemes are combined with the Dirac-Kohn-Sham ansatz for ground state calculations, and by using virtually complete basis sets a new and more accurate set of absolute nuclear magnetic resonance shielding scales for the rare gases He-Rn have been established.