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.     

Calculations of the magnetic shielding constants of heavy nuclei in polyatomic molecules

Coupled Hartree-Fock perturbation theory has been applied to compute the nuclear magnetic shielding tensors for ¹⁷O, ¹⁴N, and ¹³C in the molecules of water, ammonia, and methane with four wave functions of increasing accuracy, expanded over basis sets of Gaussian functions. The agreement with the experimental data available for ammonia and methane is very good. Quantities necessary to evaluate the shilding for an arbitrary gauge are also given. The degree of gauge-invariance of the calculated properties is nt satisfactory in the ammonia, while better results are found for water.     

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.     

Electric quadrupole polarizabilities of nuclear magnetic shielding in some small molecules

Computational procedures, based on (i) the Ramsey common origin approach and (ii) the continuous transformation of the origin of the quantum mechanical current density-diamagnetic zero (CTOCD-DZ), were applied at the Hartree-Fock level to determine electric quadrupole polarizabilities of nuclear magnetic shielding for molecules in the presence of a nonuniform electric field with a uniform gradient. The quadrupole polarizabilities depend on the origin of the coordinate system, but values of the magnetic field induced at a reference nucleus, determined via the CTOCD-DZ approach, are origin independent for any calculations relying on the algebraic approximation, irrespective of size and quality of the (gaugeless) basis set employed. On the other hand, theoretical estimates of the induced magnetic field obtained by single-origin methods are translationally invariant only in the limit of complete basis sets. Calculations of electric quadrupole polarizabilities of nuclear magnetic shielding are reported for H(2), HF, H(2)O, NH(3), and CH(4) molecules.     

Density-functional calculations of relativistic spin-orbit effects on nuclear magnetic shielding in paramagnetic molecules

Terms arising from the relativistic spin-orbit effect on both hyperfine and Zeeman interactions are introduced to density-functional theory calculation of nuclear magnetic shielding in paramagnetic molecules. The theory is a generalization of the former nonrelativistic formulation for doublet systems and is consistent to O(alpha4), the fourth power of the fine structure constant, for the spin-orbit terms. The new temperature-dependent terms arise from the deviation of the electronic g tensor from the free-electron g value as well as spin-orbit corrections to hyperfine coupling tensor A, the latter introduced in the present work. In particular, the new contributions include a redefined isotropic pseudocontact contribution that consists of effects due to both the g tensor and spin-orbit corrections to hyperfine coupling. The implementation of the spin-orbit terms makes use of all-electron atomic mean-field operators and/or spin-orbit pseudopotentials. Sample results are given for group-9 metallocenes and a nitroxide radical. The new O(alpha4) corrections are found significant for the metallocene systems while they obtain small values for the nitroxide radical. For the isotropic shifts, none of the three beyond-leading-order hyperfine contributions are negligible.     

Connection between the nuclear electric shielding tensor and the infrared intensity

The integrated IR intensity can be directly related to the electric shielding tensor of the nuclei in a molecule. This allows us to measure, by IR spectroscopy, the effective electric field at the nuclei of a molecule immersed in an external electric field. Relations exist with the dynamic polarizability and the magnetizability, which implies the possibility of a unified treatment of electric and magnetic second-order properties.     

Calculations of influence of electric field on proton magnetic shielding in molecule,by means of Gell-Mann-Feynman theorem

A method is proposed for calculating the electric-field-linear contribution to the processional magnetic shielding of the nucleus, based on application on the Gell-Mann-Feyman theorem, using the Pade approximant. Calculational formulas have been derived for the first derivatives of the precessional magnetic shielding of the nucleus with respect to the electric field strength, these formulas containing either experimentally determinable characteristics of the molecules or characteristics obtained by interpolation of the observed properties of isoelectronic molecules. No calculations of wavefunctions are required. For hydrogen and hydrogen halide molecules, values have been calculated for the derivatives, with respect to electric field strength, of the precessional _H ⁽¹⁾ , prec and total _H ⁽¹⁾ proton magnetic shielding. The results are in good agreement with experimental data.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 4, July–August, 1985.     

MNDO Calculations of silicon-containing molecules

A comparison is made of MNDO and MINDO /3 calculations for saturated silicon-containing molecules, and with experimental values, for heats of formation, molecular geometries, charge distributions, and ionization potentials. Except for bond angles, it is found that with the published parameter values the MINDO /3 program gives more reliable results than MNDO . For unsaturated molecules, a comparison of bond lengths and stabilities of Si multiple bonds as given by the two programs and ab initio methods is made, and large discrepancies between predicted structures are pointed out. Some reasons for the dicrepancies are discussed.     

The gradient of a molecular wavefunction and its relation to the nuclear electric shielding

The electric shielding of a nucleus in a molecule can be expressed in terms of the gradient of the molecular wavefunction. This gradient can be evaluated analytically via perturbation theory, introducing the Hamiltonian in the acceleration gauge.     

Polarized basis sets and the calculation of infrared intensities from nuclear electric shielding tensors

The idea of the basis set polarization which follows from the known dependence of basis set functions on the perturbation strength is applied to the calculation of the dipole moment derivatives with respect to nuclear displacements. The differentiation of the dipole moment function is replaced by the straightforward evaluation of derivatives of the intramolecular electric field with respect to the external electric field strength. The method and its efficiency are illustrated by a series of calculations of the dipole moment derivatives for the water molecule. Already a polarized basis set of 26 CGTO's derived from the minimal CGTO basis set provides fairly reasonable results.     

CNDO calculations of diamagnetic shielding in molecules

An approximate procedure for the calculation of diamagnetic shielding in molecules is presented. The method proposed is based on the ‘complete neglect of differential overlap’ (CNDO) molecular wave functions and is formulated according to the zero differential overlap (ZDO) approximation. The results obtained with several CNDO-type wave functions for diatomic and polyatomic molecules are in very good agreement with non-empirical SCF calculations. The ¹⁴N diamagnetic shielding constants in several molecules were computed and some approximations usually adopted in the interpretation of ¹⁴N chemical shifts are critically discussed. It was shown that in some cases the observed ¹⁴N chemical shifts cannot be interpreted solely in terms of the paramagnetic contribution to the shielding constant.     

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     

Nuclear electric dipole shielding in molecular ions

A formula, which includes the effects of finite nuclear masses, is derived for the force on a nucleus in a (possibly molecular) ion in a spatially uniform (possibly time dependent) electric field.     

Calculations of the orbital diamagnetic contribution to nuclear spin-spin coupling constants for molecules with multiple bonds

Ab initio SCF and Cl calculations of the orbital diamagnetic contribution to nuclear spin-spin coupon constants have been performed for a series of molecules containing multiple bonds. A striking feature of the results is the prediction of consistently large contributions to vicinal (trans) and geminal proton-proton couplings which oppose and dominate the corresponding orbital paramagnetic contributions.     

Self‐consistent shielding in atoms and molecules

The orbital exponents of trial wave functions for simple systems can be found from the potential energy terms alone. Shielding of the nuclear charge by one electron on another is determined by the relative values of the nuclear–electron attraction and the electron–electron repulsion. For two electrons in the same orbital, the shielding is divided equally. For different orbitals, only the inner electron shields the outer. The systems tested are first‐row atoms, using Slater orbitals. It appears that if this approach can be generalized, it may not be necessary to calculate kinetic energies in chemical systems, since they will be determined by the orbital exponents. This would be useful if trial wave functions were not available, but trial electron density functions were. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

An alternative NMR method to determine nuclear shielding anisotropies for molecules in liquid-crystalline solutions with (13)C shielding anisotropy of methyl iodide as an example

An alternative NMR method for determining nuclear shielding anisotropies in molecules is proposed. The method is quite simple, linear and particularly applicable for heteronuclear spin systems. In the technique, molecules of interest are dissolved in a thermotropic liquid crystal (LC) which is confined in a mesoporous material, such as controlled pore glass (CPG) used in this study. CPG materials consist of roughly spherical particles with a randomly oriented and connected pore network inside. LC Merck Phase 4 was confined in the pores of average diameter from 81 to 375 A and LC Merck ZLI 1115 in the pores of average diameter 81 A. In order to demonstrate the functionality of the method, the (13)C shielding anisotropy of (13)C-enriched methyl iodide, (13)CH(3)I, was determined as a function of temperature using one dimensional (13)C NMR spectroscopy. Methane gas, (13)CH(4), was used as an internal chemical shift reference. It appeared that methyl iodide molecules experience on average an isotropic environment in LCs inside the smallest pores within the whole temperature range studied, ranging from bulk solid to isotropic phase. In contrast, in the spaces in between the particles, whose diameter is approximately 150 microm, LCs behave as in the bulk. Consequently, isotropic values of the shielding tensor can be determined from spectra arising from molecules inside the pores at exactly the same temperature as the anisotropic ones from molecules outside the pores. Thus, for the first time in the solution state, shielding anisotropies can easily be determined as a function of temperature. The effects of pore size as well as of different LC media on the shielding anisotropy are examined and discussed.     

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.