Scalar Relaxation of the Second Kind — A Potential Source of Information on the Dynamics of Molecular Movements. 2. Magnetic Dipole Moments and Magnetic Shielding of Bromine Nuclei

Abstract

In this paper, we continue the exploration of possibilities, limitations, and methodological problems of the studies based on measurements of the nuclear spin relaxation rates running via the scalar relaxation of the second kind (SC2) mechanism. The attention has been focused on the (13)C-(79)Br and (13)C-(81)Br systems in organic bromo compounds, which are characterized by exceptionally small differences of Larmor frequencies, ΔωCBr, of the coupled nuclei. This unique property enables experimental observation of longitudinal SC2 relaxation of (13)C nuclei, which makes investigation of the SC2 relaxation rates an attractive experimental method of determination of spin-spin coupling constants and relaxation rates of quadrupole bromine nuclei, both types of parameters being hardly accessible by direct measurements. A careful examination of the methodology used in SC2 relaxation studies of carbon-bromine systems reveals, however, some disturbing facts that could burden the results with systematic inaccuracies. Namely, the way of calculating the Larmor frequency differences between (13)C and bromine isotopes, ΔωCBr, may cause some reservations. In this work, the values of (79)Br and (81)Br magnetogyric ratios have been rechecked using bromine NMR data for the KBr·Kryptofix 222 complex in acetonitrile solution and the results of the advanced calculations of the magnetic shielding of the bromine nucleus in the Br(-) anion. Moreover, it has been pointed out that in the case of (13)C-(79)Br, the magnetic shielding of the bromine nucleus in the investigated molecule must not be neglected during the calculation of the ΔωCBr parameter. Some recommendations concerning the exploitation of available theoretical methods to calculate bromine shielding constants for bromo compounds have also been formulated, keeping in mind relativistic effects.

Interpretation of the Longitudinal 13C Nuclear Spin Relaxation and Chemical Shift Data for Five Bromoazaheterocycles Supported by Nonrelativistic and Relativistic DFT Calculations

“…The differences between the resonance frequencies of brominated carbons and bromines were calculated according to the equation normalΔ ω CX = [ γ C false( 1 − σ normalC false) − γ X false( 1 − σ normalX false) ] B 0 where X = 79 Br or 81 Br . The needed isotropic magnetic shielding constants of carbon nuclei were calculated using the measured 13 C NMR chemical shifts and the relationship σ ( C 13 ) = σ TMS − δ ( C 13 ) where σ TMS = 186.6 ppm stands for the isotropic magnetic shielding constant of tetramethylsilane carbons.…”

“…The needed isotropic magnetic shielding constants of carbon nuclei were calculated using the measured 13 C NMR chemical shifts and the relationship σ ( C 13 ) = σ TMS − δ ( C 13 ) where σ TMS = 186.6 ppm stands for the isotropic magnetic shielding constant of tetramethylsilane carbons. The shielding constants of bromine nuclei for compounds 1 – 5 were calculated theoretically and corrected for relativistic effects using a method described elsewhere . These values were 2112, 2171, 2286, 1964, 2041, 1941, and 2027 ppm for 1 , 2 , 3 , 2-Br of 4 , 4-Br of 4 , 2-Br of 5 , and 4-Br of 5 , respectively.…”

“…The shielding constants of bromine nuclei for compounds 1−5 were calculated theoretically and corrected for relativistic effects using a method described elsewhere. 27 These values were 2112,2171,2286,1964,2041,1941, and 2027 ppm for 1, 2, 3, 2-Br of 4, 4-Br of 4, 2-Br of 5, and 4-Br of 5, respectively. The molecular geometry optimizations and calculations of NMR parameters were performed using in each case the same level of theory.…”

“…where X = 79 Br or 81 Br. 27 The needed isotropic magnetic shielding constants of carbon nuclei were calculated using the measured 13 C NMR chemical shifts and the relationship…”

Nuclear singlet relaxation by scalar relaxation of the second kind in the slow-fluctuation regime

“…In the high-field NMR of diamagnetic materials, the fastfluctuation regime of Equation 1 is only encountered when the I-spin relaxation is very rapid, which normally requires a quadrupolar relaxation mechanism for the I-spins. The cases of 13 C nuclei which are scalar-coupled to 79 Br, 81 Br and 14 N nuclei have been studied in detail [50][51][52][53][54] .…”