Dipolar contributions to nuclear magnetic shielding by anisotropic molecules

Simple analytical expressions are given for the dipolar contributions to isotropic magnetic shielding outside axially-symmetric molecules. Except for certain paramagnetic metal-ion complexes the new expressions for the shielding expanded in spheroidal harmonics are preferable to the McConnell formula.     

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.     

Leading-order relativistic effects on nuclear magnetic resonance shielding tensors

We present perturbational ab initio calculations of the nuclear-spin-dependent relativistic corrections to the nuclear magnetic resonance shielding tensors that constitute, together with the other relativistic terms reported by us earlier, the full leading-order perturbational set of results for the one-electron relativistic contributions to this observable, based on the (Breit-)Pauli Hamiltonian. These contributions are considered for the H(2)X (X = O,S,Se,Te,Po) and HX (X = F,Cl,Br,I,At) molecules, as well as the noble gas (Ne, Ar, Kr, Xe, Rn) atoms. The corrections are evaluated using the relativistic and magnetic operators as perturbations on an equal footing, calculated using analytical linear and quadratic response theory applied on top of a nonrelativistic reference state provided by self-consistent field calculations. The (1)H and heavy-atom nuclear magnetic shielding tensors are compared with four component, nearly basis-set-limit Dirac-Hartree-Fock calculations that include positronic excitations, as well as available literature data. Besides the easy interpretability of the different contributions in terms of familiar nonrelativistic concepts, the accuracy of the present perturbational scheme is striking for the isotropic part of the shielding tensor, for systems including elements up to Xe.     

Relativistic corrections to the diamagnetic term of the nuclear magnetic shielding: analysis of contributions from localized orbitals

We have calculated the relativistic corrections to the diamagnetic term of the nuclear magnetic shielding constants for a series of molecules containing heavy atoms. An analysis of the contributions from localized orbitals is performed. We establish quantitatively the relative importance of inner core and valence shell molecular orbitals in each correcting term. Contributions from the latter are much less important than those from the former. The calculated values of the correction sigma(L-PSO), first derived within the linear response elimination of small component formalism, show a power-law dependence on the nuclear charge approximately Z(3.5), in contrast with the approximately Z(3.1) behavior of the mass-velocity external-field correction to the paramagnetic term previously reported.     

Use of locally dense basis sets for nuclear magnetic resonance shielding calculations

The locally dense basis set approach to the calculation of nuclear magnetic resonance shieldings is one in which a sufficiently large or dense set of basis functions is used for an atom or molecular fragment containing the resonant nucleus or nuclei of interest and fewer or attenuated sets of basis functions employed elsewhere. Provided the dense set is of sufficient size, this approach is capable of determining chemical shieldings nearly as well as a calculation with a balanced basis set of quality equal to the locally dense set, but with considerable savings of CPU time. Detailed comparisons are provided of locally dense and balanced calculations in the gauge including atomic orbital (GIAO) method for the individual principal values, the isotropic shieldings, and the tensor orientations for hydrogen, carbon, nitrogen, oxygen, fluorine, and phosphorus nuclei. It is seen that chemical functional groups can often define the appropriate molecular fragment to be taken locally dense. While the present test cases are for the most part small molecules, the value of the method is that it will allow calculations on systems that would otherwise presently be computationally expensive or inaccessible. © John Wiley & Sons, Inc.     

Estimation of the contribution of vibronic interaction to the isotope effect on the nuclear magnetic shielding constant of a hydrogen bridge

A nonadiabatic correction to the H/D isotope effect on the constant of electronic magnetic shielding of a nucleus was estimated within the framework of the first-order perturbation theory. The procedure consists in the ab initio calculation of frequencies and relative intensities in the vibronic spectrum for H and D forms of a molecule taking into account only the transitions allowed in the magnetic-dipole approximation. With the elementary assumptions (case of Herzberg vibronic interaction), the semiquantitative estimation of adiabatic (geometrical) and nonadiabatic contributions to the H/D isotope effect on the ¹⁵N shielding constant of a complex with the HF-pyridine hydrogen bond was carried out. These two contributions to the isotope effect are comparable in the order of magnitude, at least for unsaturated molecules with low-lying excited electronic states. A correct solution to the problem requires ab initio calculation that is not based on the Born-Oppenheimer approximation.     

Introduction to nuclear magnetic resonance

The basic principles of nuclear magnetic resonance (NMR) are presented in an elementary form using classical and elementary quantum mechanics and the experimental technique 1s explained. The motion of the magnetization by r.f. pulses, free induction decay and spectrum, transverse and longitudinal relaxation, local field and spin echo are described and the effects of molecular motion are discussed. The concepts of spin temperature and spin diffusion are presented and the advantage of using quadrupole nuclei is stressed. Finally, the specific problems of NMR in interface studies are considered and a typical example is given.     

Predicting 9Be nuclear magnetic resonance chemical shielding tensors utilizing density functional theory

The structures of a series of beryllium containing complexes have been optimized at the B3LYP/6-31G(d) level and their (9)Be magnetic shielding values have been determined using B3LYP/6-311G+g(2d,p) and the gauge-including atomic orbital (GIAO) method. The calculated chemical shifts are in excellent agreement with experimental values. The performance of a variety of NMR methods (SGO, IGAIM, CSGT) were also examined but were found to be inferior to the GIAO method at the chosen level of theory employed. The theoretical method has been utilized to predict the beryllium chemical shifts of structurally characterized complexes for which no measured (9)Be NMR spectrum exists, and to investigate a literature complex with an unusual (9)Be NMR chemical shift. A new standard for beryllium NMR in nonaqueous solvents has been suggested.     

Parity nonconservation contribution to the nuclear magnetic resonance shielding constants of chiral molecules: a four-component relativistic study

A systematic four-component relativistic study of the parity nonconservation (PNC) contribution to the (isotropic) NMR shielding constants of chiral molecules is presented for the P enantiomers of the series H(2)X(2) (X=(17)O,(33)S,(77)Se,(125)Te,(209)Po). The PNC contributions are obtained within a linear response approach at the Hartree-Fock level. A careful design of the basis sets is necessary. The four-component relativistic results based on the Dirac-Coulomb Hamiltonian are compared with the nonrelativistic Levy-Leblond results and those obtained by the spin-free modified Dirac Hamiltonian. The calculations confirm the nonrelativistic scaling law Z(2.4) of the PNC contribution with respect to nuclear charge Z. However, the calculations also show that the overall scaling is significantly modified by relativistic effects. The scalar relativistic effect scales as Z(4.7) for the selected set of molecules, whereas the spin-orbit effect, of opposite sign, scales better than Z(6) and completely dominates the PNC contribution for the heaviest elements. This opens up the intriguing possibility of the experimental observation of PNC effects on NMR parameters of molecules containing heavy atoms. The presented formalism is expected to be valuable in assisting the search for suitable candidate molecules.     

Effect of perturbation of the atomic basis on nuclear magnetic shielding constants for small molecules

We have calculated the components of the paramagnetic part of the magnetic shielding tensor for nuclei in molecules of LiH, HF, and H₂O within the uncoupled variant of Hartree-Fock-Roothaan perturbation theory, taking into account the dependence of the original basis set of Slater-type AO's (STO's) on the perturbation parameter. We have shown that it is necessary to take into account such a dependence when calculating the components of the magnetic shielding tensor in minimal basis sets of STO's. We have carried out a comparative analysis of the data obtained with results of other approaches.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 24, No. 5, pp. 527–532, September–October, 1988     

Systematic studies on the computation of nuclear magnetic resonance shielding constants and chemical shifts: the density functional models

We present a systematic density functional investigation on the prediction of the 13C, 15N, 17O, and 19F NMR properties of 23 molecules with 21 density functionals. Extensive comparisons are made for both 13C magnetic shieldings and chemical shifts with respect to the gas phase experimental data and the best CCSD(T) results. We find that the OPBE and OPW91 exchange-correlation functionals perform significantly better than some popular functionals such as B3LYP and PBE1PBE, even surpassing, in many cases, the standard wavefunction-based method MP2. Further analysis has been performed to explore the individual role played by various exchange and correlation functionals. We find that the B88 and PBE exchange functionals have a too strong tendency of deshielding, leading to too deshielded magnetic shielding constants; whereas the OPTX exchange functional performs remarkably well. We claim that the main source of error arises from the exchange functional, but correlation functional also makes important contribution. We find that the correlation functionals may be grouped into two classes. class A, such as LYP and B98, leads to deshielded NMR values, deteriorating the overall performance; whereas class B, such as PW91 and PBE, generally increases the absolute shieldings, which complements the exchange functionals, leading to improved results in the calculation of NMR data.     

The effects of molecular diffusion in ultrafast two-dimensional nuclear magnetic resonance

The so-called "ultrafast" nuclear magnetic resonance (NMR) methods enable the collection of multidimensional spectra within a single scan. These experiments operate by replacing traditional t(1) time increments, with a series of combined radiofrequency-irradiation/magnetic-field-gradient manipulations that spatially encode the effects of the indirect-domain spin interactions. Barring the presence of sizable displacements, the spatial patterns thus imparted can be read out following a mixing period with the aid of oscillating acquisition gradients, leading to a train of t(2)-modulated echoes carrying in their positions and phases the indirect- and the direct-domain spin interactions. Both the initial spatial encoding as well as the subsequent spatial decoding procedures underlying ultrafast NMR were designed under the assumption that spins remain static within the sample during their execution. Most often this is not the case, and motion-related effects can be expected to affect the outcome of these experiments. The present paper focuses on analyzing the effects of diffusion in ultrafast two-dimensional (2D) NMR. Toward this end both analytical and numerical formalisms are derived, capable of dealing with the nonuniform spin manipulations, macroscopic sample sizes, and microscopic displacements involved in this kind of sequences. After experimentally validating the correctness of these formalisms these were used to analyze the effects of diffusion for a variety of cases, including ultrafast experiments on both rapidly and slowly diffusing molecules. A series of prototypical schemes were considered including discrete and continuous encoding modes, constant- and real-time manipulations, homo- and heteronuclear acquisitions, and single versus multiple quantum modalities. The effects of molecular diffusion were also compared against typical relaxation-driven losses as they happen in these various prototypical situations; from all these situations, general guidelines for choosing the optimal ultrafast 2D NMR scheme for a particular sample and condition could be deduced.     

Decomposition of nuclear magnetic resonance spin-spin coupling constants into active and passive orbital contributions

The theory of the J-OC-PSP (decomposition of J into orbital contributions using orbital currents and partial spin polarization) method is derived to distinguish between the role of active, passive, and frozen orbitals on the nuclear magnetic resonance (NMR) spin-spin coupling mechanism. Application of J-OC-PSP to the NMR spin-spin coupling constants of ethylene, which are calculated using coupled perturbed density functional theory in connection with the B3LYP hybrid functional and a [7s,6p,2d/4s,2p] basis set, reveal that the well-known pi mechanism for Fermi contact (FC) spin coupling is based on passive pi orbital contributions. The pi orbitals contribute to the spin polarization of the sigma orbitals at the coupling nuclei by mediating spin information between sigma orbitals (spin-transport mechanism) or by increasing the spin information of a sigma orbital by an echo effect. The calculated FC(pi) value of the SSCC (1)J(CC) of ethylene is 4.5 Hz and by this clearly smaller than previously assumed.     

Detecting pore size distribution of activated carbon by low-field nuclear magnetic resonance

In this study, the transverse relaxation time (T₂) of activated carbon (AC) in different relative environment humidity was detected firstly by low-field nuclear magnetic resonance (LFNMR). The pore size (diameter) of AC distributions was calculated by the relationship between T₂ and surface relaxation rate (ρ), where ρ was obtained by the detection of nine porous materials with known pore size. The results showed that the pore size distributions of AC calculated by ρ < 0.19 nm/ms were in good agreement with that obtained by nitrogen adsorption method and proved that LFNMR as a new detection method was feasible for characterizing AC pore size distribution.     

Improved description of nuclear magnetic resonance chemical shielding constants using the M06-L meta-generalized-gradient-approximation density functional

The performance of the M06-L density functional has been tested for four databases of NMR isotropic chemical shielding constants. Comparison with the B3LYP, BLYP, HCTH, KT1, KT2, LSDA, OPBE, OLYP, PBE, TPSS, and VSXC functionals shows that M06-L has improved performance for calculating NMR chemical shielding constants, especially for highly correlated systems. We also found that VSXC and M06-L have encouraging accuracy for calculating (13)C chemical shielding constants, and both functionals perform very well for the chemical shielding constants in the o-benzyne molecule.     

Relativistic effects on the nuclear magnetic resonance shielding of FX (X = F, Cl, Br, I, and At) molecular systems

We present ab inito full four-component and spin-free calculations of the NMR shielding parameter, σ, in the FX (X = F, Cl, Br, I and At) molecular systems. A different expression that overcomes the traditional non-relativistic (NR) approximation used to calculate the relationship between spin-rotation constants and the paramagnetic terms of σ(p) are given. Large deviations from NR results are obtained for σ(X; X = I and At) and for σ(F; FAt). σ(∥)(p)(I; FI) is zero within the NR approach but -447.4 parts per million from our calculations. The electronic origin of relativistic corrections are analyzed. All passive SO contributions are obtained as a difference between full four-component calculations and spin-free ones. Considering relativistic effects on the anisotropy, we obtain a deviation of 10% for I and 25% for At. σ(∥)(SO)(X) is always negative and σ(∥)(SF)(X) is always positive; the passive SO becomes larger than the SF one for X = Br, I, and At. Both σ(∥)(SO)(X) and σ(⊥)(SO)(X) have a functional dependence such as a Z(X)(b) being the exponent 3.5 and 3.65, respectively. The passive SO contribution to the anisotropy has a similar functional dependence with an exponent of 3.60, meaning that its perpendicular component is larger than its corresponding parallel component.