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Solid State Nuclear Magnetic Resonance

NMR and relative quantum theory

Stanley Clough

Published Nov 1, 1997• 10 citations
Publisher
DOI
10.1016/s0926-2040(97)00042-8

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Abstract The origins, history, and present status of the controversy surrounding a quantum description of the NMR signal as being due to radio waves are traced. With the Principle of Relativity and Coulomb's Law as formal starting points and the minimum of mathematics needed for understanding, the derivation of a classical electromagnetic theory of signal reception is first given. The agreement between that classical theory and a recent NMR experiment is then presented, leading to proof that, except for the highest field imaging experiments, there is no significant contribution of radio waves to the signal. Attention is drawn to the very different properties of the near and far energy, momenta, and fields inherent in the derivation. The role of the Correspondence Principle in formulating a quantum description is then emphasized and it is shown that the standard NMR interpretation of Dicke's theory of coherent spontaneous emission—that the latter is responsible for the NMR signal—cannot be correct. Finally, the author speculates on some of the intriguing relationships found in the classical electrodynamics of NMR signal reception and attempts to relate them to a common quantum electrodynamic precept of near field interaction: that the free induction decay voltage present at the terminals of an open‐circuit receiving coil is based on an exchange of virtual photons between the nuclei in a sample and the free electrons in a receiving coil. © 2009 Crown in the right of Canada. Concepts Magn Reson Part A 34A: 193–216, 2009.

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Multiple quantum (MQ) NMR methods1 are applied to the analysis of various problems of quantum information processing. It is shown that the two-spin/two-quantum Hamiltonian1 describing MQ NMR dynamics is related to the flip-flop Hamiltonian of a one-dimensional spin system in the approximation of the nearest neighbor interactions. As a result, it is possible to organize quantum state transfer along a linear chain. MQ NMR experiments are performed on quasi-one-dimensional chains of 19F nuclei in calcium fluorapatite Ca5(PO4)3F. Relaxation of the MQ NMR coherences is considered as the simplest model of decoherence processes. A theory of the dipolar relaxation of the MQ NMR coherences in one-dimensional systems is developed. A good agreement of the theoretical predictions and the experimental data is obtained.

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Abstract The origins, history, and present status of the controversy surrounding a quantum description of the NMR signal as being due to radio waves are traced. With the Principle of Relativity and Coulomb's Law as formal starting points and the minimum of mathematics needed for understanding, the derivation of a classical electromagnetic theory of signal reception is first given. The agreement between that classical theory and a recent NMR experiment is then presented, leading to proof that, except for the highest field imaging experiments, there is no significant contribution of radio waves to the signal. Attention is drawn to the very different properties of the near and far energy, momenta, and fields inherent in the derivation. The role of the Correspondence Principle in formulating a quantum description is then emphasized and it is shown that the standard NMR interpretation of Dicke's theory of coherent spontaneous emission—that the latter is responsible for the NMR signal—cannot be correct. Finally, the author speculates on some of the intriguing relationships found in the classical electrodynamics of NMR signal reception and attempts to relate them to a common quantum electrodynamic precept of near field interaction: that the free induction decay voltage present at the terminals of an open‐circuit receiving coil is based on an exchange of virtual photons between the nuclei in a sample and the free electrons in a receiving coil. © 2009 Crown in the right of Canada. Concepts Magn Reson Part A 34A: 193–216, 2009.
Absolute nuclear magnetic shielding constants and relative chemical shifts are second-derivative response properties that underpin the interpretation of Nuclear Magnetic Resonance (NMR) spectra and provide critical insights into the structural and electronic environments of diverse chemical systems. However, their accurate computation is often constrained by the need for method-specific, analytical response implementation, and therefore is particularly challenging for non-variational, correlated wavefunction methods where analytical second derivatives are frequently unavailable. Here we present a scalable framework that computes NMR shielding tensors through finite magnetic field differentiation of complex-valued, gauge-including atomic-orbital (GIAO) based self-consistent field (SCF) calculations. By combining hybrid MPI and OpenMP parallelization and resolution-of-identity (RI) approximation-based Coulomb (J) and Exchange (K) implementation and mixed numerical/analytical derivatives computational scheme, we achieve very good efficiency for hybrid density functional theory (DFT) NMR shielding, relative to existing state-of-the-art analytic implementations across realistic chemical systems of various sizes. Forward differentiation with optimal step sizes derived from rigorous error analysis retains favorable numerical errors much smaller than experimental uncertainty or intrinsic DFT errors. The results demonstrate that RI-accelerated finite magnetic field calculations can obtain DFT-level NMR shielding constants very precisely, providing a scalable foundation for extensions to more advanced quantum chemistry methods in future work.
Multiple quantum (MQ) NMR methods1 are applied to the analysis of various problems of quantum information processing. It is shown that the two-spin/two-quantum Hamiltonian1 describing MQ NMR dynamics is related to the flip-flop Hamiltonian of a one-dimensional spin system in the approximation of the nearest neighbor interactions. As a result, it is possible to organize quantum state transfer along a linear chain. MQ NMR experiments are performed on quasi-one-dimensional chains of 19F nuclei in calcium fluorapatite Ca5(PO4)3F. Relaxation of the MQ NMR coherences is considered as the simplest model of decoherence processes. A theory of the dipolar relaxation of the MQ NMR coherences in one-dimensional systems is developed. A good agreement of the theoretical predictions and the experimental data is obtained.