# Temperature dependence of contact and dipolar NMR chemical shifts in paramagnetic molecules

## Abstract

Using a recently proposed equation for NMR nuclear magnetic shielding for molecules with unpaired electrons [A. Soncini and W. Van den Heuvel, J. Chem. Phys. 138, 021103 (2013)], equations for the temperature (T) dependent isotropic shielding for multiplets with an effective spin S equal to 1/2, 1, 3/2, 2, and 5/2 in terms of electron paramagnetic resonance spin Hamiltonian parameters are derived and then expanded in powers of 1/T. One simplifying assumption used is that a matrix derived from the zero-field splitting (ZFS) tensor and the Zeeman coupling matrix (g-tensor) share the same principal axis system. The influence of the rhombic ZFS parameter E is only investigated for S = 1. Expressions for paramagnetic contact shielding (from the isotropic part of the hyperfine coupling matrix) and pseudo-contact or dipolar shielding (from the anisotropic part of the hyperfine coupling matrix) are considered separately. The leading order is always 1/T. A temperature dependence of the contact shielding as 1/T and of the dipolar shielding as 1/T{sup 2}, which is sometimes assumed in the assignment of paramagnetic chemical shifts, is shown to arise only if S ≥ 1 and zero-field splitting is appreciable, and only if the Zeeman coupling matrix is nearly isotropicmore »

- Authors:

- Department of Chemistry, University at Buffalo, State University of New York, Buffalo, New York 14260-3000 (United States)

- Publication Date:

- OSTI Identifier:
- 22416068

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ANISOTROPY; CHEMICAL SHIFT; COUPLING; ELECTRON SPIN RESONANCE; ELECTRONS; HAMILTONIANS; MAGNETIC SHIELDING; MOLECULES; MULTIPLETS; NUCLEAR MAGNETIC RESONANCE; PARAMAGNETISM; SPIN; TEMPERATURE DEPENDENCE; TENSORS; ZEEMAN EFFECT

### Citation Formats

```
Martin, Bob, and Autschbach, Jochen, E-mail: jochena@buffalo.edu.
```*Temperature dependence of contact and dipolar NMR chemical shifts in paramagnetic molecules*. United States: N. p., 2015.
Web. doi:10.1063/1.4906318.

```
Martin, Bob, & Autschbach, Jochen, E-mail: jochena@buffalo.edu.
```*Temperature dependence of contact and dipolar NMR chemical shifts in paramagnetic molecules*. United States. doi:10.1063/1.4906318.

```
Martin, Bob, and Autschbach, Jochen, E-mail: jochena@buffalo.edu. Sat .
"Temperature dependence of contact and dipolar NMR chemical shifts in paramagnetic molecules". United States.
doi:10.1063/1.4906318.
```

```
@article{osti_22416068,
```

title = {Temperature dependence of contact and dipolar NMR chemical shifts in paramagnetic molecules},

author = {Martin, Bob and Autschbach, Jochen, E-mail: jochena@buffalo.edu},

abstractNote = {Using a recently proposed equation for NMR nuclear magnetic shielding for molecules with unpaired electrons [A. Soncini and W. Van den Heuvel, J. Chem. Phys. 138, 021103 (2013)], equations for the temperature (T) dependent isotropic shielding for multiplets with an effective spin S equal to 1/2, 1, 3/2, 2, and 5/2 in terms of electron paramagnetic resonance spin Hamiltonian parameters are derived and then expanded in powers of 1/T. One simplifying assumption used is that a matrix derived from the zero-field splitting (ZFS) tensor and the Zeeman coupling matrix (g-tensor) share the same principal axis system. The influence of the rhombic ZFS parameter E is only investigated for S = 1. Expressions for paramagnetic contact shielding (from the isotropic part of the hyperfine coupling matrix) and pseudo-contact or dipolar shielding (from the anisotropic part of the hyperfine coupling matrix) are considered separately. The leading order is always 1/T. A temperature dependence of the contact shielding as 1/T and of the dipolar shielding as 1/T{sup 2}, which is sometimes assumed in the assignment of paramagnetic chemical shifts, is shown to arise only if S ≥ 1 and zero-field splitting is appreciable, and only if the Zeeman coupling matrix is nearly isotropic (Δg = 0). In such situations, an assignment of contact versus dipolar shifts may be possible based only on linear and quadratic fits of measured variable-temperature chemical shifts versus 1/T. Numerical data are provided for nickelocene (S = 1). Even under the assumption of Δg = 0, a different leading order of contact and dipolar shifts in powers of 1/T is not obtained for S = 3/2. When Δg is not very small, dipolar and contact shifts both depend in leading order in 1/T in all cases, with sizable contributions in order 1/T{sup n} with n = 2 and higher.},

doi = {10.1063/1.4906318},

journal = {Journal of Chemical Physics},

number = 5,

volume = 142,

place = {United States},

year = {Sat Feb 07 00:00:00 EST 2015},

month = {Sat Feb 07 00:00:00 EST 2015}

}