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13: Molecular Spectroscopy

Last updated

Nov 15, 2022
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- 12.T: Correlation Tables
- 13.1: The Electromagnetic Spectrum

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Spectroscopy generally is defined as the area of science concerned with the absorption, emission, and scattering of electromagnetic radiation by atoms and molecules, which may be in the gas, liquid, or solid phase. Visible electromagnetic radiation is called light, although the terms light, radiation, and electromagnetic radiation can be used interchangeably. Spectroscopy played a key role in the development of quantum mechanics and is essential to understanding molecular properties and the results of spectroscopic experiments. It is used as a “stepping stone” to take us to the concepts of quantum mechanics and the quantum mechanical description of molecular properties in order to make the discussion more concrete and less abstract and mathematical.

13.1: The Electromagnetic Spectrum
This page explores the role of Molecular Spectroscopy in Physical Chemistry, highlighting how molecules interact with their environment through electromagnetic radiation. It discusses the wave-particle duality of radiation and its properties like wavelength and energy. Spectroscopic techniques measure energy transfer, unveiling molecular energy transitions that inform physical properties such as bond lengths and temperature based on frequency analysis.
13.2: Rotations Accompany Vibrational Transitions
This page explains the rovibrational spectra of diatomic gas molecules, detailing vibrational and rotational transitions influenced by quantum selection rules and bond length changes. It covers energy quantization, resulting in P- and R-branches, and discusses the rotational constant $B$ and the Q-branch in spectroscopy.
13.3: Unequal Spacings in Vibration-Rotation Spectra
This page discusses the differences between real and ideal rovibrational spectra, emphasizing the effects of rotational-vibrational coupling and centrifugal distortion on line spacing in R-branch and P-branch as energy varies. It notes how bond length influences vibrational states and the rotational constant, detailing how the spacing in R-branch decreases with increasing J values, while P-branch spacing increases as J decreases.
13.4: Unequal Spacings in Pure Rotational Spectra
This page discusses the vibrational energy of non-rigid rotators, emphasizing flexible internuclear distances. It explains how centrifugal force necessitates a restoring force, resulting in potential energy. The text derives energy equations, showing differences in energy levels between rigid and non-rigid rotators, and highlights the impact of the centrifugal stretching constant ( $\tilde{D}$ ) on energy levels at higher angular momentum, enhancing the accuracy for spectral observations.
13.5: Vibrational Overtones
This page discusses the limitations of the harmonic oscillator model for molecular vibrations, particularly at higher energy levels where anharmonic effects become significant. The anharmonic oscillator model, incorporating higher-order terms, offers more accurate predictions and allows for transitions between various vibrational states, resulting in overtones. Observed frequencies align better with anharmonic models, especially for higher energy levels, leading to weaker intensity lines.
13.6: Electronic Spectra Contain Electronic, Vibrational, and Rotational Information
This page discusses how molecules undergo electronic transitions during microwave and infrared absorptions, linked to vibrational and rotational states. It explains that energy levels come from electronic potential energy curves and that electronic transitions simplify calculations by being independent of rotational effects.
13.7: The Franck-Condon Principle
This page explains the Franck-Condon Principle, detailing how electronic transitions in spectroscopy occur with minimal nuclear change. It highlights the significance of the Franck-Condon overlap integral, connecting transition probabilities to vibrational wavefunction overlaps.
13.8: Rotational Spectra of Polyatomic Molecules
This page provides an overview of the angular motion and rotational dynamics of diatomic and polyatomic molecules. It begins with the Schrödinger equation for rigid diatomic molecules and introduces rotational energy levels governed by quantum number $J$ . The text further explores polyatomic molecules using an inertia tensor and discusses spherical tops with equal principal moments of inertia.
13.9: Normal Modes in Polyatomic Molecules
This page discusses normal modes as independent vibrational motions in molecules, defined by symmetries and their roles in IR and Raman spectroscopy. Molecules have 3N degrees of freedom, with nonlinear and linear molecules having 3N-6 and 3N-5 vibrational degrees, respectively. Each vibrational mode acts as a harmonic oscillator, contributing to energy. Normal coordinates aid in analyzing vibrations by simplifying equations.
13.10: Irreducible Representation of Point Groups
This page discusses normal coordinates and their relation to irreducible representations of molecular vibrations, categorized by point group symmetry. It highlights the water molecule (C2v symmetry) as an example, having three normal modes classified as v1, v2, and v3. The complexity of determining normal modes rises with the number of atoms, prompting the use of modern simulations for calculations, illustrated by the complex [PtCl4]2- species with numerous vibrational degrees of freedom.
13.11: Time-Dependent Perturbation Theory
This page discusses quantum mechanics' time-independent and time-dependent perturbation theories, introduced by Schrödinger and Dirac. Time-independent perturbation deals with static Hamiltonians, while time-dependent perturbation examines dynamic Hamiltonians, emphasizing state evolution and energy levels.
13.12: The Selection Rule for the Rigid Rotor
This page explains selection rules that govern transition probabilities between quantum levels during the absorption or emission of electromagnetic radiation. It discusses gross and specific selection rules, emphasizing that a molecule must have a permanent dipole moment for rotational spectra and outlines the rule $\Delta J = \pm 1$ for absorptive transitions. These principles are relevant for both electronic and orbital angular momentum transitions.
13.13: The Harmonic Oscillator Selection Rule
This page discusses selection rules in spectroscopy and physical chemistry, which govern the allowed transitions of particles in quantized atomic systems, including electronic, rotational, and vibrational transitions. These rules assist chemists in identifying substances by analyzing light wavelengths that induce transitions, revealing properties like molecular structure and bond strength.
13.14: Group Theory Determines Infrared Activity
This page explains how to determine if molecular normal modes are infrared (IR) or Raman active, requiring changes in dipole moment for IR activity and changes in polarizability for Raman activity. It uses water (H2O) as an example to show the application of group theory in identifying active modes. The analysis confirms the vibrational transitions related to different symmetry representations, detailing the IR and Raman active modes along with their energy levels.
13.E: Molecular Spectroscopy (Exercises)
This page outlines Chapter 13 homework exercises from McQuarrie and Simon's "Physical Chemistry," focusing on molecular spectroscopy involving diatomic molecules. It covers vibrational energy levels, dissociation energies, and practical calculations for molecules like H2, Na2, and O2. Key concepts include the harmonic oscillator model, anharmonicity, and moments of inertia, illustrating how molecular structure affects rotational dynamics.

Thumbnail: White light is dispersed by a prism into the colors of the visible spectrum. (CC BY-SA 3.0; D-Kuru).

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