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Molecular Spectroscopy: Absorption and Emission01:14

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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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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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UV–Vis Spectroscopy: Molecular Electronic Transitions01:16

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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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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.
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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.
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2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)01:19

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Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a heteronucleus. The HSQC experiment is similar to the heteronuclear correlation experiment (HETCOR) but is more sensitive. In the HSQC spectrum, the proton chemical shift is plotted on the horizontal F2 axis, while the 13C chemical shift is plotted on the vertical F1 axis. The corresponding proton and 13C spectra are also shown. The HSQC contour plot does...
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Molecular Spectra Calculations Using an Optimized Quasi-Regular Gaussian Basis and the Collocation Method.

Shane W Flynn1, Vladimir A Mandelshtam1

  • 1Department of Chemistry, University of California, Irvine, California 92697, United States.

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This study enhances the collocation method for molecular vibrational calculations. Optimized quasi-regular grids (QRGs) with distributed Gaussian basis functions significantly improve accuracy and reduce computational cost for vibrational eigenenergies.

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Area of Science:

  • Quantum chemistry
  • Molecular spectroscopy
  • Computational physics

Background:

  • The collocation method offers a simplified approach to computing molecular vibrational spectra.
  • Distributed localized basis sets, like Gaussian functions, are key to this method.
  • Optimizing basis function placement and shape is crucial for efficiency.

Purpose of the Study:

  • To explore the optimization of basis function placement and shape within the collocation method.
  • To investigate the efficacy of quasi-regular grids (QRGs) for basis set optimization.
  • To improve the accuracy and efficiency of calculating molecular vibrational energies.

Main Methods:

  • Revisiting the Manzhos and Carrington collocation method.
  • Employing a distributed localized Gaussian basis set.
  • Utilizing quasi-regular grids (QRGs) for basis function optimization.
  • Solving the generalized eigenvalue problem for the molecular vibrational Hamiltonian.

Main Results:

  • Demonstrated the superiority of QRG-based distributed Gaussian basis sets.
  • Achieved accurate computation of eigenenergies for formaldehyde.
  • Showcased significant reduction in basis size through optimized basis functions.

Conclusions:

  • Quasi-regular grids represent an effective strategy for optimizing basis sets in the collocation method.
  • The enhanced method offers a computationally efficient and accurate route to molecular vibrational spectra.
  • This approach provides a flexible and numerically stable alternative for vibrational structure calculations.