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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...
Van der Waals Equation01:10

Van der Waals Equation

The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
The Van der Waals Equation01:26

The Van der Waals Equation

The ideal gas law is based on two simplifying assumptions: first, that there are no intermolecular attractions between gas molecules, and second, that the volume occupied by the molecules themselves is negligible compared with the volume of the container. However, these assumptions don't hold up under all conditions - specifically, at high pressures and low temperatures, as gas tends to deviate from ideal gas behavior.The van der Waals equation is an enhanced version of the ideal gas law,...
Van der Waals Interactions01:24

Van der Waals Interactions

Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions between particles with permanent, partial, or temporary charges. The intermolecular forces between neutral atoms and molecules are ion–dipole, dipole–dipole, and dispersion forces, collectively known as van der Waals forces.Polar molecules have a partial positive charge on one end and a partial negative charge on the other end of the molecule,...
Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation04:01

Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws.
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...

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Thermochemical Studies of Ni(II) and Zn(II) Ternary Complexes Using Ion Mobility-Mass Spectrometry
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Toward large scale vibrational configuration interaction calculations.

Michael Neff1, Guntram Rauhut

  • 1Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany.

The Journal of Chemical Physics
|October 2, 2009
PubMed
Summary

A new configuration-selective vibrational configuration interaction (cs-VCI) method efficiently handles large molecular systems. This computational chemistry approach offers advantages over traditional grid-based methods for accurate vibrational energy calculations.

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Accurate calculation of molecular vibrational energies is crucial for understanding chemical reactions and spectroscopy.
  • Traditional methods like grid-based algorithms face challenges with computational scaling for large systems.
  • The vibrational configuration interaction (VCI) method offers a powerful framework but requires efficient implementation.

Purpose of the Study:

  • To present a novel state-specific configuration-selective vibrational configuration interaction (cs-VCI) approach.
  • To demonstrate the advantages of this cs-VCI method over existing grid-based algorithms.
  • To enable the handling of significantly larger variational spaces in vibrational structure calculations.

Main Methods:

  • Implementation of a state-specific configuration-selective vibrational configuration interaction (cs-VCI) approach.
  • Utilizing a polynomial representation of the potential energy surface.
  • Employing a configuration selection criterion combined with simultaneous exclusion of irrelevant configurations.
  • Incorporating an internal contraction scheme to manage large variational spaces.
  • Applying a modified iterative Jacobi-Davidson diagonalization for eigenpair determination.

Main Results:

  • The developed cs-VCI approach effectively manages large variational spaces, reaching up to 2x10(7) configurations.
  • Benchmark calculations demonstrate the method's capability in handling systems with three-mode couplings.
  • The approach shows advantages compared to traditional grid-based algorithms for vibrational structure problems.
  • Efficient determination of relevant internal eigenpairs within the selected configuration space was achieved.

Conclusions:

  • The presented state-specific cs-VCI method provides an efficient and scalable solution for calculating vibrational energies.
  • This approach overcomes limitations of grid-based methods, enabling studies of larger and more complex molecular systems.
  • The combination of selection criteria and diagonalization techniques offers a robust framework for advanced quantum chemistry calculations.