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Frequency Analysis


A molecular vibration is the periodic motion of the atoms relative to each other. In this process, the center of molecular mass remains unchanged. A molecular vibration can be measured by vibration frequency (υ), which is the ratio of molecular absorbed energy (ΔE) to Planck's constant (h). Angular frequency (circular frequency, ω), represents the angular displacement per unit time. It is a physical quantity that describes the speed of the vibration of the object, related to the inherent property of the vibration system.

Molecular vibrational frequency analysis is an important approach to characterize molecular structures, chemical composition, chain orientation and describe the microstructure of materials. Also, it is critical for the analysis of thermal conductivity, finite-temperature stability, inorganic particles, and other transport properties of solids. Raman spectroscopy, one of the vibrational frequency analyses, can accurately determine the characteristic frequency of molecular vibration with polarizability. Another is infrared spectroscopy which plays a significant role in polymer analysis and pharmaceutical analysis. Frequency analysis with computational methods rather than time-consuming sample preparation increases the efficiency and simplifies the process.

Figure 1. The zero-dispersion frequenciesFigure 1. The zero-dispersion frequencies (Melchert, O.; et al. 2019)

Modes of Molecular Vibration Analysis

  • Symmetric and asymmetric stretching

Stretching vibration (υ) refers to the extension and contraction of atoms along the direction of the bond axis. The force constant of stretching vibration is usually larger than that of bending vibration and the stretching vibration of the same group therefore appears in the high-frequency region. Changes in the surrounding environment have little effect on the variation in frequency. Groups with atomic number greater than or equal to 3 can be divided into symmetric stretching vibration (υs) and asymmetric stretching vibration (aυs) due to the vibration coupling. Generally, aυs has a higher frequency than υs.

  • Bending

Bending vibration refers to the change of the bond angle of two chemical bonds with a common atom, or the movement of the whole group of atoms relative to other parts of the molecule that has nothing to do with the mutual movement of the atoms in a certain group of atoms. Bending vibration is also called deformation vibration and can be divided into symmetrical deformation vibration (δs) and asymmetrical deformation vibration (δas):

δs means that the angle formed by the three chemical bonds in the molecule and the molecular axis becomes smaller or larger at the same time. For example, the three carbon-hydrogen bonds of a methyl group change at the same angle to the axis at the same time.

δas means that the angle formed by the three chemical bonds in the molecule and the molecular axis alternately decreases and increases. For example, the three carbon-hydrogen bonds of a methyl group alternately change to the axis at the same angle at the same time.

  • Scissoring and rocking

As a type of bending vibration, in-plane bending vibration (β) refers to the bending vibration performed in a plane composed of several atoms. β can be divided into scissoring vibration and rocking vibration:

Scissor vibration means that the bond angle changes regularly during the vibration process which is like the opening and closing of scissors. The shear vibration of the methylene group shows a regular change in the angle between two carbon-hydrogen bonds.

Rocking vibration means the group swings as a whole in a plane composed of several atoms. The rocking vibration of the methylene group is represented by two carbon-hydrogen bonds swinging in the same direction and at the same angle.

  • Out-of-plane

Out-of-plane bending vibration refers to the bending vibration in the direction perpendicular to the plane composed of several atoms. It can be divided into out-of-plane wagging vibration (ω) and twisting vibration (τ):

ω means that the terminal atoms of a molecule or group vibrate in the same direction in a plane perpendicular to several atoms at the same time. For example, the two hydrogen atoms of the methylene group move in the same direction perpendicular to the plane at the same time.

τ means that the terminal atoms of the molecule or group vibrate in the opposite direction in the plane perpendicular to several atoms at the same time. For example, two hydrogen atoms of methylene group move in the opposite direction perpendicular to the plane at the same time.

Figure 2. Molecular vibrational frequenciesFigure 2. Molecular vibrational frequencies (Parks, H.L.; et al. 2019)

Our services

  • Electron spectroscopy

Electron energy spectroscopy is a general term for a collection of various surface analysis techniques. This analytical technology measures the binding energy of electrons in atoms or molecules by analyzing the energy of electrons emitted by various impact particles (single-energy photons, electrons, ions, atoms, etc.) after collisions with atoms, molecules or solids.

Our frequency analysis, especially molecular electronic vibrational transition, helps to explain the peak shape of electronic spectra and gain a deeper understanding of molecular excited state dynamics. We are capable of investigating various electronic energy spectra including X-ray photoelectron spectroscopy, auger electron spectroscopy, vacuum ultraviolet photoelectron spectroscopy, and electron energy loss spectroscopy.

  • Microstructures of matter

Frequency analysis provides a powerful approach to the microstructure of materials, such as the number and kind of functional groups, chemical bonds, and characteristic structures. At Alfa Chemistry, three-dimensional transmission electron microscopy (3D-TEM), thermal analysis, X-ray powder diffraction (XRD), X-ray fluorescence spectrometer (XRF), infrared nuclear magnetic (NMR), scanning electron microscopy (SEM) and so on are available to offer comprehensive insight into the microstructure of materials.


  • Our services provide ab initio methods for accurate molecular vibrational frequency prediction.
  • We are capable of developing multiple machine learning models to support frequency analysis.
  • Our analysis is of correctness, efficiency, and wide range.

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Project specification

  • Specific requirements of frequency analysis services
  • Analysis cycle

We deliver

  • Calculation algorithms and methods
  • Raw data
  • Analysis results

Our frequency analysis guarantees quick, specialized, and high-quality services for global customers. Using the most suitable algorithms, offering accurate results, saving time and human cost for our clients, and satisfying their research demands are our ultimate goals. If you are interested in our services, please contact us for more detailed information.


  • Melchert, O.; et al. Soliton molecules with two frequencies. Phys. Rev. Lett. 2019, 123(24): 243905.
  • Parks, H.L.; et al. Uncertainty quantification in first-principles predictions of harmonic vibrational frequencies of molecules and molecular complexes. J. Phys. Chem. C 2019, 123(7): 4072-4084.

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