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Related Concept Videos

Two-Dimensional (2D) NMR: Overview01:12

Two-Dimensional (2D) NMR: Overview

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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....
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IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration01:16

IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration

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A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
According to Hooke's law, the vibrational frequency is directly proportional to...
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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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Mass Spectrometry: Complex Analysis01:21

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Mass spectrometry is an important technique for the identification of pure compounds. However, it has some limitations for the analysis of complex mixtures, often due to excessive fragmentation making the spectrum too complicated to decipher. Mass spectrometry can be combined with suitable separation methods in sequence, forming hyphenated methods, which are useful in the analysis of complex mixtures.
GC–MS is a powerful hyphenated method commonly used in forensics and environmental...
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Spectrophotometry: Introduction01:16

Spectrophotometry: Introduction

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Spectrophotometry is the quantitative measurement of the absorption, reflection, diffraction, or transmission of electromagnetic radiation through a material as a function of the intensity and wavelength of the radiation. A spectrophotometer is a device used to measure the change in the radiation intensity caused by its interaction with the material.
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Molecular Spectroscopy: Absorption and Emission01:14

Molecular Spectroscopy: Absorption and Emission

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Molecules possess discrete energy levels called quantum states. Unlike atoms, which have simpler energy levels, molecules possess additional rotational and vibrational energy levels. Each energy level is separated by an energy gap, with the gaps between adjacent electronic, vibrational, and rotational levels varying significantly. The three types of energy levels in a diatomic molecule are shown in Figure 1.
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Related Experiment Video

Updated: Apr 15, 2026

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
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Analytical calculation of two-dimensional spectra.

Joshua D Bell, Rebecca Conrad, Mark E Siemens

    Optics Letters
    |April 2, 2015
    PubMed
    Summary
    This summary is machine-generated.

    We present an analytical method for calculating two-dimensional (2D) coherent spectra. This approach simplifies the analysis of electronic and vibrational resonances, offering a direct fit to experimental data.

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    Area of Science:

    • Spectroscopy
    • Quantum Optics
    • Physical Chemistry

    Background:

    • Two-dimensional (2D) coherent spectroscopy is a powerful technique for probing molecular dynamics.
    • Analytical solutions for 2D spectra are often complex, limiting their application.
    • Understanding resonance behavior requires advanced spectral analysis methods.

    Purpose of the Study:

    • To develop a fully analytical method for calculating 2D coherent spectra.
    • To provide a simplified approach for analyzing electronic and vibrational resonances.
    • To enable direct fitting of theoretical results to experimental 2D spectra.

    Main Methods:

    • Solving optical Bloch equations for a two-level system in the 2D time domain.
    • Applying projection-slice and Fourier-shift theorems for analytical 2D Fourier transforms.
    • Developing a theoretical framework for arbitrary resonance inhomogeneity.

    Main Results:

    • A complete analytical calculation of 2D coherent spectra is demonstrated.
    • The method allows for a fully analytical 2D Fourier transform.
    • The derived results accurately fit experimental 2D coherent spectra, even with inhomogeneous broadening.

    Conclusions:

    • The developed analytical method offers a significant simplification in 2D coherent spectroscopy.
    • This approach facilitates the interpretation of complex spectral data.
    • The findings provide a valuable tool for researchers studying molecular resonances.