Vibrational contributions to cubic response functions from vibrational configuration interaction response theory
Mikkel Bo Hansen1, Ove Christiansen
1The Lundbeck Foundation Center for Theoretical Chemistry, Department of Chemistry, University of Århus, DK-8000 Århus C, Denmark. mbh@chem.au.dk
The Journal of Chemical Physics
|October 28, 2011
Summary
This study introduces the pure vibrational cubic response function for vibrational configuration interaction wave functions. It also details combined electronic and vibrational cubic response functions, advancing computational chemistry methods.
Area of Science:
- Computational Chemistry
- Theoretical Chemistry
- Quantum Chemistry
Background:
- Building upon recent work on vibrational quadratic response functions.
- Addressing the need for higher-order response properties in theoretical models.
Purpose of the Study:
- To derive and implement the pure vibrational cubic response function.
- To present combined electronic and vibrational cubic response functions.
- To discuss challenges in calculating these response functions.
Main Methods:
- Utilizing vibrational configuration interaction wave functions.
- Employing sum-over-states expressions within the Born-Oppenheimer framework.
- Applying response theory for analytic calculations.
Main Results:
- Successful derivation and implementation of the pure vibrational cubic response function.
- Formulation of combined electronic and vibrational cubic response functions.
- Identification of complicating factors in the calculations.
Conclusions:
- The developed implementation enables analytic computation of the pure vibrational cubic response function.
- This function is a component of the broader vibronic cubic response function.
- Advances theoretical capabilities for molecular property calculations.
Related Concept Videos
01:24IR Spectroscopy: Molecular Vibration Overview
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...
01:16IR 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...
According to Hooke's law, the vibrational frequency is directly proportional to the...
02:46Crystal Field Theory - Tetrahedral and Square Planar Complexes
Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
02:58Crystal Field Theory - Octahedral Complexes
Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
01:08IR 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...
02:38Valence Bond Theory and Hybridized Orbitals
According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.
A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is...
A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is...