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Related Concept Videos

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...
UV–Vis Spectroscopy: Woodward–Fieser Rules01:29

UV–Vis Spectroscopy: Woodward–Fieser Rules

UV–Visible absorption spectra of conjugated dienes arise from the lowest energy π → π* transitions. The light-absorbing part of the molecule is called the chromophore, and the substituents directly attached to the chromophore are called auxochromes. A strong correlation exists between the absorption maxima, λmax, and the structure of a conjugated π system. The Woodward–Fieser rules predict the value of λmax for a given structure by adding the contributions...
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...
UV–Vis Spectroscopy: Molecular Electronic Transitions01:16

UV–Vis Spectroscopy: Molecular Electronic Transitions

In Ultraviolet–Visible (UV–Vis) spectroscopy, the absorption of electromagnetic radiation is used to probe the electronic structure of molecules. This technique provides insights into molecular electronic transitions, particularly the movement of electrons between different molecular orbitals. Radiation is absorbed if the energy of the electromagnetic radiation passing through the molecule is precisely equal to the energy difference between the excited and ground states. During this process,...
¹H NMR of Conformationally Flexible Molecules: Variable-Temperature NMR01:15

¹H NMR of Conformationally Flexible Molecules: Variable-Temperature NMR

The axial and equatorial protons in cyclohexane can be distinguished by performing a variable-temperature NMR experiment. In this process, except for one proton, the remaining eleven protons are replaced by deuterium. The deuterium substitution avoids the possible peak splitting caused by the spin-spin coupling between the adjacent protons. The remaining proton flips between the axial and equatorial positions.

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Multimodal Nonlinear Hyperspectral Chemical Imaging Using Line-Scanning Vibrational Sum-Frequency Generation Microscopy
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Variational response-function formulation of vibrational circular dichroism.

Sonia Coriani1, Andreas J Thorvaldsen, Kasper Kristensen

  • 1Dipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Trieste, Via L. Giorgieri 1, I-34127 Trieste, Italy. coriani@units.it

Physical Chemistry Chemical Physics : PCCP
|February 2, 2011
PubMed
Summary
This summary is machine-generated.

This study presents a computationally efficient method for calculating the atomic axial tensor (AAT) in vibrational circular dichroism. The new approach reduces computational cost and improves accuracy for molecular property calculations.

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Published on: January 25, 2020

Area of Science:

  • Computational Chemistry
  • Spectroscopy
  • Quantum Chemistry

Background:

  • Vibrational circular dichroism (VCD) is a powerful technique for determining molecular structure.
  • Calculating the atomic axial tensor (AAT) is crucial for VCD but computationally intensive.
  • Existing methods for AAT calculation require solving computationally expensive response equations.

Purpose of the Study:

  • To develop a more computationally efficient method for calculating the atomic axial tensor (AAT).
  • To reformulate the AAT calculation within the density matrix-based quasienergy derivative Lagrangian approach.
  • To enable the use of London atomic orbitals for gauge-origin independence.

Main Methods:

  • The study utilizes the density matrix-based quasienergy derivative Lagrangian approach.
  • The atomic axial tensor is expressed as a frequency derivative of a linear response function.
  • The method avoids solving response equations for nuclear displacements, reducing computational cost.

Main Results:

  • A novel formulation for the atomic axial tensor (AAT) is derived, significantly reducing computational cost.
  • The approach allows for straightforward incorporation of London atomic orbitals to remove gauge-origin dependence.
  • The formalism is amenable to linear scaling for large molecular systems.

Conclusions:

  • The developed method offers a computationally efficient and accurate way to calculate the atomic axial tensor for VCD.
  • This advancement facilitates more accessible and scalable VCD calculations in computational chemistry.
  • The approach provides a robust framework for calculating molecular properties.