Determining internal coordinate sets for optimal representation of molecular vibration
Kemal Oenen1, Dennis F Dinu1, Klaus R Liedl1
1Department of General, Inorganic and Theoretical Chemistry, University of Innsbruck, Innrain 80, 6020 Innsbruck, Austria.
The Journal of Chemical Physics
|January 5, 2024
Summary
Normal modes describe molecular vibrations but are often complex. This study introduces a toolkit to find optimal internal coordinates, simplifying vibrational analysis and notation for better molecular understanding.
Area of Science:
- Computational Chemistry
- Molecular Spectroscopy
- Quantum Chemistry
Background:
- Normal modes simplify molecular vibrations into independent degrees of freedom, crucial for analyzing vibrational spectra and potential energy surfaces.
- Traditional Cartesian coordinate representations of normal modes present challenges, particularly for delocalized vibrations and clear notation.
- Internal coordinates offer a more intuitive representation but selecting an optimal set for normal mode analysis is not straightforward.
Purpose of the Study:
- To develop a systematic method for selecting optimal internal coordinates for normal mode analysis.
- To improve the clarity and descriptiveness of vibrational notations.
- To provide a computational tool for efficient representation of molecular vibrations.
Main Methods:
- Utilized a normal mode decomposition scheme based on the Hessian matrix.
- Screened potential internal coordinate sets considering topology and symmetry.
- Employed a metric to minimize coupling between internal coordinates for optimal set selection.
- Developed the Nomodeco toolkit to automate the selection of internal coordinate sets.
Main Results:
- Demonstrated a method to identify optimal internal coordinate sets for representing molecular vibrations.
- Showcased how the Nomodeco toolkit reduces the search space for suitable internal coordinate sets.
- Generated contribution tables that clarify vibrational notations by linking normal modes to internal coordinates.
- Successfully applied the scheme to small and mid-sized molecules.
Conclusions:
- The Nomodeco toolkit provides an effective strategy for selecting optimal internal coordinates for normal mode analysis.
- This approach enhances the interpretability of molecular vibrations and simplifies vibrational notation.
- The method offers a significant improvement over traditional Cartesian coordinate-based normal mode representations.
Related Concept Videos
01:16IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration
1.3K
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...
According to Hooke's law, the vibrational frequency is directly proportional to...
1.3K
01:24IR Spectroscopy: Molecular Vibration Overview
2.3K
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...
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...
2.3K
02:35Molecular Orbital Theory I
32.1K
Overview of Molecular Orbital Theory
32.1K
00:52¹H NMR of Conformationally Flexible Molecules: Temporal Resolution
847
At room temperature, the chair conformer of cyclohexane undergoes rapid ring flipping between two equivalent chair conformers at a rate of approximately 105 times per second. These two chair conformers are in equilibrium. The rapid ring flipping results in the interconversion of the axial proton to an equatorial proton and an equatorial to the axial proton. Such interconversions are too rapid and cannot be detected on the NMR timescale. Hence, the NMR spectrometer cannot distinguish between the...
847
02:40MO Theory and Covalent Bonding
10.5K
The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while...
10.5K
02:00Molecular Models
38.4K
Physical models representing molecular architectures of chemical compounds play essential roles in understanding chemistry. The use of molecular models makes it easier to visualize the structures and shapes of atoms and molecules.
38.4K