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

IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration

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 the...
IR Spectroscopy: Molecular Vibration Overview01:24

IR Spectroscopy: Molecular Vibration Overview

When Infrared (IR) radiation passes through a covalently bonded molecule, the bonds transition from lower to higher vibrational levels. The fundamental vibrational motions that result in infrared absorption can be classified as stretching or bending vibrations.
Stretching vibrations are vibrational motions that occur along the bond line, changing the bond length or distance between two bonded atoms. They are further distinguished as symmetric or asymmetric. In symmetric stretching, the...
IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations01:08

IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations

Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single stretching vibration...
Two-Dimensional (2D) NMR: Overview01:12

Two-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.
2D NMR: Overview of Homonuclear Correlation Techniques01:16

2D 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...
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H 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...

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Related Experiment Video

Updated: May 9, 2026

Multimodal Nonlinear Hyperspectral Chemical Imaging Using Line-Scanning Vibrational Sum-Frequency Generation Microscopy
08:49

Multimodal Nonlinear Hyperspectral Chemical Imaging Using Line-Scanning Vibrational Sum-Frequency Generation Microscopy

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Two-dimensional spectroscopy of coupled vibrations with the optimized mean-trajectory approximation.

Mallory Gerace1, Roger F Loring

  • 1Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University , Ithaca, New York 14853, United States.

The Journal of Physical Chemistry. B
|August 9, 2013
PubMed
Summary

The optimized mean-trajectory (OMT) approximation now calculates nonlinear vibrational response functions for coupled anharmonic vibrations. This method efficiently computes multidimensional infrared spectra, capturing quantum dynamics with classical trajectories.

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Area of Science:

  • * Computational Chemistry
  • * Quantum Dynamics
  • * Spectroscopy

Background:

  • * The optimized mean-trajectory (OMT) approximation is a semiclassical method for calculating nonlinear vibrational response functions.
  • * Previous work assessed the OMT for a single anharmonic degree of freedom.
  • * Computing multidimensional infrared spectra requires accurate quantum dynamics approximations.

Purpose of the Study:

  • * To generalize the OMT approximation for multiple coupled anharmonic vibrations.
  • * To develop an efficient numerical method for calculating two-dimensional infrared spectra using the OMT.
  • * To assess the OMT's ability to reproduce quantum response function features.

Main Methods:

  • * Extended the OMT derivation to semiclassical approximations of double-sided Feynman diagrams for coupled anharmonic vibrations.
  • * Developed an efficient numerical procedure for computing two-dimensional infrared spectra.
  • * Utilized classical trajectories linked by discontinuities to approximate quantum dynamics.

Main Results:

  • * The OMT approximation was successfully generalized to systems with multiple coupled anharmonic vibrations.
  • * An efficient numerical method for calculating two-dimensional infrared spectra was established.
  • * The OMT approximation accurately reproduced key quantum response function characteristics, including coherence and population dynamics.

Conclusions:

  • * The generalized OMT approximation provides a robust semiclassical method for simulating complex vibrational dynamics.
  • * The developed numerical procedure enables efficient computation of multidimensional infrared spectra for coupled anharmonic systems.
  • * The OMT approximation serves as a valuable tool for understanding quantum effects in molecular vibrations.