Authors: Kolja Them
Source: Journal of Physics Communications (preprint, 2021-01-05)
Field: Chemistry — Spectroscopy

From molecular quantum electrodynamics at finite temperatures to nuclear magnetic resonance Abstract The algebraic reformulation of molecular Quantum Electrodynamics (mQED) at finite temperatures is applied to Nuclear Magnetic Resonance (NMR) in order to provide a foundation for the reconstruction of much more detailed molecular structures, than possible with current methods. Conventional NMR theories are directly related to the effective spin model, which idealizes nuclei as fixed points in a lattice <?CDATA ${{\mathbb{Z}}}^{3}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi mathvariant="double-struck">Z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:math> . However, the delocalization of spins due to the thermal energy is more realistically described by the amplitude square of the nuclear wave function ∣Ψ β ( X )∣ 2 with <?CDATA $X\in {{\mathbb{R}}}^{3n}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>X</mml:mi> <mml:mo>∈</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> <mml:mi>n</mml:mi> </mml:mrow> </mml:msup> </mml:math> , instead of fixed points in <?CDATA ${{\mathbb{Z}}}^{3}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi mathvariant="double-struck">Z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:math> . In addition, the phenomenological integration of thermalization only allows an investigation of the molecular structure based on the position of the punctiform center of an NMR signal, but not based on the width and shape of NMR signals. Hence, a lot information on molecular structures remain hidden in experimental NMR data. In this document it is shown how ∣Ψ β ( X )∣ 2 , <?CDATA $X\in {{\mathbb{R}}}^{3n}$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>X</mml:mi> <mml:mo>∈</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> <mml:mi>n</mml:mi> </mml:mrow> </mml:msup> </mml:math> can be reconstructed from NMR data. To this end, it is shown how NMR spectra can be calculated directly from mQED at finite temperatures without involving the effective description. The new method connects all data points—the positions, widths, heights and shapes—of NMR signals directly with the molecular structure, which allows more detailed investigations of the underlying system. Furthermore, it is shown that the presented method corrects wrong predictions of the effective spin model. The fundamental problem of performing numerical calculations with the infinite-dimensional radiation field is solved by using a purified representation of a KMS state on a W * -algebra. It is outlined that the presented method can be applied to any molecular system whose electronic ground state can be calculated using a common quantum chemical method. Therefore, the presented method can replace the effective description which forms the basis for NMR theory since 1950. Delocalized electron ; Physics ; Quantum ; Spin (aerodynamics) ; Quantum mechanics Advanced NMR Techniques and Applications ; Electron Spin Resonance Studies ; Molecular spectroscopy and chirality