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Related Concept Videos

IR Spectroscopy: Molecular Vibration Overview01:24

IR Spectroscopy: Molecular Vibration Overview

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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...
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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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¹³C NMR: Distortionless Enhancement by Polarization Transfer (DEPT)01:20

¹³C NMR: Distortionless Enhancement by Polarization Transfer (DEPT)

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When proton-coupled carbon-13 spectra are simplified by a broadband proton decoupling technique, structural information about the coupled protons is lost. Distortionless enhancement by polarization transfer (DEPT) is a technique that provides information on the number of hydrogens attached to each carbon in a molecule. While the DEPT experiment utilizes complex pulse sequences, the pulse delay and flip angle are specifically manipulated. The resulting signals have different phases depending on...
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IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations01:08

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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...
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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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UV–Vis Spectroscopy: Molecular Electronic Transitions01:16

UV–Vis Spectroscopy: Molecular Electronic Transitions

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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...
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Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
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Calculating vibrational spectra of molecules using tensor train decomposition.

Maxim Rakhuba1, Ivan Oseledets1

  • 1Skolkovo Institute of Science and Technology, Skolkovo Innovation Center, Building 3, 143026 Moscow, Russia.

The Journal of Chemical Physics
|October 27, 2016
PubMed
Summary

We developed a new algorithm for calculating molecular vibrational spectra using tensor train decomposition. This method efficiently computes spectra, requiring minimal memory and time, even on a standard laptop.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Applied Mathematics

Background:

  • Calculating molecular vibrational spectra is crucial for understanding molecular properties and reactions.
  • Traditional methods often require significant computational resources, limiting their application to smaller systems.
  • The assumption of low-rank tensor structure for eigenfunctions offers a potential pathway for computational efficiency.

Purpose of the Study:

  • To introduce a novel algorithm for computing molecular vibrational spectra.
  • To leverage tensor train decomposition for efficient representation of molecular eigenfunctions.
  • To demonstrate the algorithm's performance on a realistic molecular system.

Main Methods:

  • Utilizing tensor train decomposition to represent molecular eigenfunctions.
  • Applying iterative methods (e.g., LOBPCG, inverse iteration) for solving linear systems.
  • Solving linear systems inexactly along a low-parametric manifold of low-rank tensors.

Main Results:

  • Accurate computation of 84 vibrational states for the acetonitrile (CH3CN) molecule.
  • Demonstration of the algorithm's efficiency, completing calculations on a laptop in one hour.
  • Significant memory reduction, using only 100 MB to store all computed eigenfunctions.

Conclusions:

  • Tensor train decomposition provides an efficient approach for calculating molecular vibrational spectra.
  • The proposed algorithm offers a computationally feasible method for high-accuracy spectral calculations.
  • This technique has the potential to enable detailed vibrational analysis of larger and more complex molecules.