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¹H NMR: Interpreting Distorted and Overlapping Signals01:02

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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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At room temperature, the chair conformer of cyclohexane undergoes rapid ring flipping between two equivalent chair conformers at a rate of approximately 105 times per second. These two chair conformers are in equilibrium. The rapid ring flipping results in the interconversion of the axial proton to an equatorial proton and an equatorial to the axial proton. Such interconversions are too rapid and cannot be detected on the NMR timescale. Hence, the NMR spectrometer cannot distinguish between the...
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NMR Spectroscopy: Spin–Spin Coupling01:08

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The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved...
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2D NMR: Overview of Homonuclear Correlation Techniques01:16

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Homonuclear correlation spectroscopy (COSY) is a powerful technique used in Nuclear Magnetic Resonance (NMR) spectroscopy to study the correlations between nuclei of the same type within a molecule. It provides information about scalar couplings between adjacent nuclei, which helps determine connectivity and structural information. There are several COSY variants, each with its unique strengths and experimental parameters.
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Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a heteronucleus. The HSQC experiment is similar to the heteronuclear correlation experiment (HETCOR) but is more sensitive. In the HSQC spectrum, the proton chemical shift is plotted on the horizontal F2 axis, while the 13C chemical shift is plotted on the vertical F1 axis. The corresponding proton and 13C spectra are also shown. The HSQC contour plot does...
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Irradiation of a spin-active nucleus causes an increase or decrease in the signal intensity of neighboring nuclei that are not necessarily chemically bonded or involved in J-coupling.  This phenomenon, called the Nuclear Overhauser Enhancement (NOE), results from through-space interactions between the nuclear spins. The NOE effect decreases with increasing internuclear distance and is generally not observed beyond 4 angstroms. In NOE, dipole-dipole interactions between neighboring...
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Quantum computation of molecular structure using data from challenging-to-classically-simulate nuclear magnetic

Thomas E O'Brien1, Lev B Ioffe1, Yuan Su1

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|January 10, 2023
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This study introduces a quantum algorithm to determine molecular nuclear spin Hamiltonians using nuclear magnetic resonance (NMR) measurements. The quantum approach efficiently learns complex molecular dynamics, offering potential advancements in structural analysis.

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Area of Science:

  • Quantum Computing
  • Molecular Biophysics
  • Nuclear Magnetic Resonance (NMR) Spectroscopy

Background:

  • Inferring molecular nuclear spin Hamiltonians is crucial for understanding molecular structure and dynamics.
  • Classical simulation of anisotropic dipolar interactions within Hamiltonians presents significant computational challenges.
  • Nuclear magnetic resonance (NMR) provides time-resolved measurements of spin-spin correlators, a key data source for Hamiltonian inference.

Purpose of the Study:

  • To develop and demonstrate a quantum algorithm for inferring molecular nuclear spin Hamiltonians.
  • To focus on learning the anisotropic dipolar term, which is computationally intensive for classical methods.
  • To explore the application of quantum computation for analyzing molecular structures using NMR data.

Main Methods:

  • Proposing a quantum algorithm utilizing time-resolved spin-spin correlator measurements from NMR.
  • Implementing algorithms for both noisy near-term and fault-tolerant quantum computers.
  • Estimating the Jacobian and Hessian of the learning problem directly on a quantum computer to learn Hamiltonian parameters.
  • Benchmarking the method on a protein (ubiquitin) confined on a membrane, analyzing small spin clusters.

Main Results:

  • Demonstrated the quantum algorithm's ability to learn Hamiltonian parameters by estimating Jacobian and Hessian.
  • Showcased the algorithm's convergence on a model system (spin clusters of ubiquitin).
  • Observed a correlation between the multifractal dimension of eigenstates and the learnability of Hamiltonian parameters across a phase transition.

Conclusions:

  • The developed quantum algorithm offers a promising approach for inferring molecular nuclear spin Hamiltonians, particularly the anisotropic dipolar term.
  • Quantum computation, especially on near-term devices, shows potential as an early beyond-classical application for molecular structure analysis.
  • The findings suggest that quantum methods could enhance the interpretation and development of novel NMR techniques.