Related Experiment Video
Updated: May 16, 2026
09:25
NMR 15N Relaxation Experiments for the Investigation of Picosecond to Nanoseconds Structural Dynamics of Proteins
Published on: November 1, 2024
Exact two-component relativistic theory for NMR parameters: general formulation and pilot application
Qiming Sun1, Yunlong Xiao, Wenjian Liu
1Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871, People's Republic of China.
The Journal of Chemical Physics
|November 14, 2012
Summary
This study reformulates the exact two-component (X2C) relativistic theory for nuclear magnetic resonance (NMR) parameters. The enhanced X2C-NMR method offers accurate calculations comparable to four-component methods, simplifying complex relativistic NMR computations.
Area of Science:
- Quantum Chemistry
- Relativistic Quantum Theory
- Nuclear Magnetic Resonance Spectroscopy
Background:
- Nuclear Magnetic Resonance (NMR) spectroscopy is crucial for molecular structure determination.
- Relativistic effects become significant for heavy elements, necessitating advanced theoretical treatments.
- Existing four-component relativistic methods for NMR are computationally demanding.
Purpose of the Study:
- To reformulate the exact two-component (X2C) relativistic theory for NMR parameters.
- To unify various balancing and decoupling schemes within the X2C-NMR framework.
- To develop computationally efficient approximations for practical applications.
Main Methods:
- The exact two-component (X2C) relativistic theory is reformulated.
- Integration of two kinetic balance schemes, five magnetic balance schemes, and three decoupling schemes.
- Inclusion of three spin magnetization definitions in the coupled-perturbed Kohn-Sham equation.
- Development of approximate schemes for the first-order coupling matrix and two-electron integrals.
Main Results:
- The reformulated X2C-NMR theory provides a unified framework for various theoretical treatments.
- Diamagnetic and paramagnetic terms in X2C-NMR individually agree with four-component results for any finite basis.
- Approximate schemes significantly reduce computational cost, making X2C-NMR comparable to approximate two-component methods.
- The method maintains accuracy while improving computational efficiency.
Conclusions:
- The enhanced X2C-NMR theory offers a robust and versatile approach for calculating relativistic NMR parameters.
- The developed approximations enable accurate and efficient NMR calculations for systems with significant relativistic effects.
- This work advances the computational methodology for studying heavy-element chemistry using NMR spectroscopy.
Related Concept Videos
01:12Two-Dimensional (2D) NMR: Overview
The 1D NMR spectrum of large and complex molecules like natural products has complicated splitting patterns and overlapping signals, which can be easily interpreted using 2-dimensional (2D) NMR. Unlike 1D NMR, 2D NMR has two frequency axes that provide the coupling information between the nucleus A and nucleus B in a molecule. The process from which 2D spectra are obtained has four steps.
The first step is the preparation period, during which nucleus A is excited with a radiofrequency pulse.
The first step is the preparation period, during which nucleus A is excited with a radiofrequency pulse.
01:162D NMR: Overview of Homonuclear Correlation Techniques
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.
COSY90 is the standard two-dimensional (2D) COSY experiment that...
COSY90 is the standard two-dimensional (2D) COSY experiment that...
01:182D NMR: Overview of Heteronuclear Correlation Techniques
Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other axis.
01:02¹H NMR: Interpreting Distorted and Overlapping Signals
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.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
01:10Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule
In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1 triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others.
01:20Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)
Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...