H.‐Jörg Osten

Theoretical Aspects of Isotope Effects on Nuclear Shielding

Publisher Summary This chapter presents the theoretical basis for the interpretation of isotope shifts in NMR. The interpretation of isotope shifts largely involves consideration of the vibrational and rotational averaging of nuclear shielding. Therefore, the isotope shift is intimately related to the observed temperature dependence of nuclear shielding in the gas phase in the zero-pressure limit. The theory considered essentially provides a good account of generally observed trends along with some of the more specific correlations with electronic structure and with other molecular properties. Isotope shifts are because of rovibrational effects and can be described by an electronic factor multiplied by a dynamic factor. The nearly uniform sign (negative) that is observed in one-bond isotope shifts comes from the nearly uniform sign (negative) of the electronic factor combined with the widely observed shortening of the average bond length upon heavy isotope substitution. The dynamic factor largely depends on the masses of the atoms involved in the bond. The mass factor confirms the observed dependence of isotope shifts on the fractional change in mass. It favors the observation of isotope shift upon substitution of light atoms while observing heavy nuclei.

The additivity of NMR isotope shifts

One of the most interesting and useful aspects of the isotope effect on nuclear magnetic shielding is the proportionality of the shift to the number of substituted atoms in equivalent positions. In this paper we show the quantitative basis for the additivity of isotope shifts in NMR, using the CX4−nYn (X,Y=H,D,T) system and the linear triatomic systems CO2, NNO, and OCS as examples. We also predict small deviations from additivity and find that these deviations are consistent with those observed for 14N shifts in the NH4−nD+n homologous series. Furthermore, we determine the mass dependence of the one‐bond isotope shift.

The dependence of the 13C and the 1H nuclear magnetic shielding on bond extension in methane

The mean bond displacements 〈Δr〉 in the methane isotopic homologous series 13/12CX4−nYn  (X, Y=H, D, T) at 300 K, and the temperature dependence of 〈ΔrCH〉 in 13CH4 from 250 to 350 K were calculated. With the assumption that the linear terms are sufficient to account for the isotope shifts, we determine from the 2/1H‐induced 13C isotope shift an empirical value of(∂σC/∂ΔrCH)e=−35±3 ppm/A. This predicts a temperature dependence in the 13C resonance in CH4 gas in the zero‐pressure limit of 2.7×10−2 ppm over 100 °, which explains why it could not be observed. We observed the 13/12C‐induced 1H isotope shift in CH4, −0.0024 ppm. With the same mean bond displacements, this isotope shift gives an estimate of (∂σHi /∂ΔrCHi )e=−38±3 ppm/A. From the reported 2/1H‐induced two‐bond 1H isotope shift in CH4, −0.016 ppm, using the mean bond displacements and the derivative obtained from the 13/12C‐induced one‐bond isotope shift, we get an estimate of (∂σHi/ ∂ΔrCHj) e=−1.3±0.2 ppm/A.

The NMR isotope shift in polyatomic molecules. Estimation of the dynamic factors

In a continuing study of the factors which determine the isotope shifts in NMR we consider here substitution of end atoms in molecular types in which the bond angle deformation does not play a significant role. We show that in molecules of the type AXn the rovibrational correction to shielding of nucleus A can be obtained directly from the isotope shift without dynamical calculations. We propose a method for estimating 〈Δr〉, knowing only the equilibrium bond length, the masses, and the rows of the Periodic Table of the atoms in the bond. We test this on diatomic molecules for which we are able to calculate 〈Δr〉 directly from the spectroscopic constants and examine its dependence on bond order. We apply the estimation method to polyatomic molecules for which we have completed a full dynamical calculation using the best available force fields. We use the estimated 〈Δr〉 for other molecular systems and obtain estimates of the shielding derivatives from the observed isotope shifts. The results compare well wit...

Systematic trends in the variation of 19F nuclear magnetic shielding with bond extension in halomethanes

A modified Urey-Bradley force field using the same set of quadratic constants for all halomethanes, augmented by Morse stretching and Lennard-Jones non-bonded anharmonic force constants, is used to calculate mean bond displacements in two series of halomethanes CF4, CF3Cl, CF3Br, CF3I and CF4, CF3Cl, CF2Cl2, CFCl3. The temperature dependence of the T in these molecules is used in a one-parameter fit to the observed temperature dependence of the 19F shielding at the zero-pressure limit, [σ0(T) - σ0(300)]. The empirical derivatives (∂σF/∂Δr CF)e are then used to calculate the 13/12C-induced 19F isotope shifts at room temperature. The calculated isotope shifts are in satisfactory agreement with experimental values. The derivatives are: (∂σF/∂Δr CF)e = -1180, -1630, -1850, -1950, -2000, and -2400 ppm A-1 respectively for CF4, CF3Cl, CF3Br, CF3I, CF2Cl2, and CFCl3. The CF3 X molecules exhibit a nearly linear plot of (∂σF/∂Δr CF)e vs. σe. For the series CF4-n Cl n the derivative varies linearly with n. F...

Rovibrational effects on nuclear shielding of apex nuclei in bent molecules

The isotope shifts of non‐end nuclei with lone pairs are generally larger than those of nuclei without lone pairs. Using the bent triatomic molecule as a prototype, we examine the mass and temperature dependence of the mean bond angle deformation and the mean displacement along a bond due to centrifugal stretching and anharmonic vibration. We find that the temperature dependence of 〈Δα〉 determines whether the temperature dependence of the shielding of the apex nucleus will be normal [(dσ0/dT)<0] or abnormal. The dominant contribution of the rotation to the temperature dependence of 〈Δα〉 in the hydrides can lead to opposing temperature effects on shielding while the mass effects lead to normal isotope shifts. We performed similar calculations for the trigonal pyramidal molecules in order to explain the observed abnormal temperature dependence of the 15N and 31P nuclear shielding in NH3 and PH3.

The effect of anharmonic vibration and centrifugal distortion on nuclear shielding in linear triatomic molecules: NNO and CO2

The temperature dependence of the mean bond displacement in linear triatomic molecules NNO and CO2 have been determined using the well‐established anharmonic force fields for these molecules. The results are applied to explain the temperature dependence of the nuclear shielding observed in the zero‐pressure limit for the 15N and 13C nuclei in 15N15NO and 13CO2. By fitting the observed σ0(T)−σ0(300 K) for T=250–350 K, empirical values of (∂σ/∂Δr)e=−220 ppm/A (CO2), −1030 ppm/A (NN*O), and −5190 ppm/A (N*NO) are obtained. These derivatives are discussed in comparison to similar molecular types. The average shielding for the vibrational states (000) and (0110) are calculated for both 15N nuclei in NNO and compared with values obtained from experimental spin‐rotational constants. The empirical derivatives are also used to calculate NMR isotope shifts from the mass‐dependent 〈Δr〉.

Deuterium‐induced 19F isotope shifts in fluoroethenes

Deuterium‐induced 19F isotope shifts in the NMR spectra of 17 fluoroethenes are reported here together with other NMR parameters (1H and 19F chemical shifts and FF, HF, DF, and DH coupling constants). The two‐bond (gem) and three‐bond (trans) isotope shifts exhibit correlations with nuclear spin–spin coupling constants 2Jgem (HF) and 3Jtrans (HF). The isotope shifts are interpreted using derivatives of nuclear shielding with respect to bond extension derived from the 19F temperature dependence at the zero‐pressure limit, and the changes in the mean bond lengths due to isotopic substitution. The latter are calculated using the previously reported Urey–Bradley force fields for these molecules. The analysis of the isotope shifts lead to estimates of the change of 19F nuclear shielding due to extension of a bond which is located at a gem, cis, or trans position relative to the resonant nucleus. These 19F nuclear shielding derivatives correlate with the nuclear spin–spin coupling constants 2Jgem(HF) , 3Jcis (H...

The mean bond displacements and the derivatives of 19F shielding in CF2=CFX and CF2=CH2

The mean bond displacements 〈Δr〉 for molecules CF2=CFX (X=H, F, Cl, Br, I) and CF2=CH2 have been calculated as a function of temperature using a Urey–Bradley force field augmented by stretching anharmonic terms and cubic nonbonded interactions. The temperature dependence of the 19F nuclear shielding in the isolated molecule limit is interpreted in terms of 〈ΔrCF〉T and an electronic factor (∂σF/∂ΔrCF)e which is found by fitting the experimental data with σ0(T)−σ0(300 K)=(∂σF/∂ΔrCF)e[〈ΔrCF〉T −〈ΔrCF〉300] . The derivatives for each of the three F sites in the CF2=CFX molecules vary systematically with the absolute shielding of the F site. The 19F nucleus gem to the X substituent exhibits the greatest change of shielding with bond displacement. For X=Cl, Br, I, the derivatives (∂σF/∂ΔrCF)e are (−1940, −2000, −1950 ppm A−1) for the F nucleus trans to X; (−2190, −2290, −2300 ppm A−1) for the F nucleus cis to X; and (−2550, −2890, −3160 ppm A−1) for the F nucleus gem to X. In CF2=CF2 and CF2=CH2 the derivatives a...

Quadrupolar spin relaxation due to electric field gradients induced by vibrations and collisions

The spin relaxation of quadrupolar nuclei in highly symmetric electronic environments via vibrationally-induced electric field gradients is considered. A model is presented for tetrahedral molecules which yields a nuclear quadrupole coupling constant for 189Os in an excited vibrational state of OsO4 which is in reasonable agreement with experimentally observed values. The nuclear quadrupole coupling constants for the central nucleus in excited E and F2 vibrational states of GeCl4, GeBr4, RuO4, OsO4 molecules as well as the MO n- 4 ions (M = V, Cr, Mn, Mo, Tc, Re) are calculated using this model. These coupling constants lead to quadrupolar relaxation rates which are orders of magnitude too small compared to experiment. Alternate mechanisms, collisional-deformation by long-range van der Waals interactions and fields induced by octopole moments, are proposed. A binary collision model is used in which the fluctuating electric fields associated with London dispersion forces during a collision create electric ...