Calculations of nuclear electric shielding in molecules

The electric shielding tensor at nuclei in the molecules H₂O, NH₃, CH₄ and CO has been evaluated via coupled Hartree-Fock perturbation theory. The average trace of the shielding tensor is linearly dependent on atomic electronegativities in the isoelectronic series H₂O, NH₃, CH₄.     

Calculations of electric dipole polarizabilities of polyatomic molecules

Coupled and uncoupled Hartree–Fock theories are used to compute the electric dipole polarizability of water, ammonia, and methane with three different GTO basis sets. Bounds for the geometric approximation to uncoupled polarizabilities are also computed to examine the accuracy of calculated values. The results are compared with those obtained by a variational-perturbation method proposed by Rebane. The numerical tests provide some information on the correlation terms affecting total computed polarizabilities. The computed values are shown to be in fair or good agreement with experimental data for the largest basis sets. The reliability of Rebane's method with respect to coupled HF procedure is also discussed.     

Calculations of electric dipole hyperpolarizability of polyatomic molecules

Coupled Hartree-Fock perturbation theory is employed to compute electric dipole hyperpolarizabilities of water, ammonia and methane with three different GTO basis sets. The results were extremely sensitive to the form of zero-order HF wave-functions. In some cases large discrepancies between computed and experimental values suggest that the latter ones must be reviewed. A comparison with other computations is also made.     

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     

Zero-point vibrational corrections to isotropic hyperfine coupling constants in polyatomic molecules

The present work addresses isotropic hyperfine coupling constants in polyatomic systems with a particular emphasis on a largely neglected, but a posteriori significant, effect, namely zero-point vibrational corrections. Using the density functional restricted-unrestricted approach, the zero-point vibrational corrections are evaluated for the allyl radical and four of its derivatives. In addition for establishing the numerical size of the zero-point vibrational corrections to the isotropic hyperfine coupling constants, we present simple guidelines useful for identifying hydrogens for which such corrections are significant. Based on our findings, we critically re-examine the computational procedures used for the determination of hyperfine coupling constants in general as well as the practice of using experimental hyperfine coupling constants as reference data when benchmarking and optimizing exchange-correlation functionals and basis sets for such calculations.     

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.     

NMR shielding constants for hydrogen guest molecules in structure II clathrates

Proton NMR shielding constants and chemical shifts for hydrogen guests in small and large cages of structure II clathrates are calculated using density-functional theory and the gauge-invariant atomic-orbital method. Shielding constants are calculated at the B3LYP level with the 6-311++G(d,p) basis set. The calculated chemical shifts are corrected with a linear regression to reproduce the experimental chemical shifts of a set of standard molecules. The calculated chemical shifts of single hydrogen molecules in the small and large structure II cages are 4.94 and 4.84 ppm, respectively, which show that within the error range of the method the H2 guest molecules in the small and large cages cannot be distinguished. Chemical shifts are also calculated for double occupancy of the hydrogen guests in small cages, and double, triple, and quadruple occupancy in large cages. Multiple occupancy changes the chemical shift of the hydrogen guests by approximately 0.2 ppm. The relative effects of other guest molecules and the cage on the chemical shift are studied for the cages with multiple occupancies.     

Calculation of nuclear magnetic shielding constants in molecules by the extended Hückel method with expansion by Gaussian functions

Theoretical and Experimental Chemistry -     

Quantitative prediction of gas-phase 19F 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.     

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).     

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.