Raman Spectroscopy: An Intensity Approach

An Intensity Approach

Guozhen Wu

• Publisher: WSPC
• Year: 2016
• ISBN:
  9789813143517
• Topic: Physical Sciences
• Subtopic: Physical & Theoretical Chemistry

This book summarizes the highlights of our work on the bond polarizability approach to the intensity analysis. The topics covered include surface enhanced Raman scattering, Raman excited virtual states and Raman optical activity (ROA). The first chapt

Chapter 1

Raman effect

1.1Basics: the Raman virtual state

Raman effect was discovered by C. V. Raman in 1928^[1-3]. It is an inelastic two-photon process, in which the scattering photon is first absorbed by the scatterer, for instance a molecule (in the followings, we will specify the scatterer to molecule without loss of generality). The photon-perturbed molecule is excited/disturbed and then relaxes and emits a secondary photon instantaneously. What excited/disturbed in the photon-perturbed molecule is its charges/electrons (from the ground state). During this process, the energy of the excited/disturbed charges may exchange with the molecular internal quanta, such as vibration through the so-called vibronic(vibration-electronic) coupling, so that the energy of the emitted photon may be different from the scattering photon. This energy difference is called the Raman shift. Raman shift is expressed in wavenumber (cm⁻¹, wavenumber multiplied by the velocity of light, 3 × 10¹⁰cm/sec, gives the actual frequency). Raman shift gives the information of the molecular internal motion. For molecular vibration, Raman shift gives its frequency which is related to the molecular structure (geometry and atomic masses) and bond strengths. In fact, this information can also be obtained from other effects, such as infrared absorption. Hence, we know that the Raman shift is not the core information that we can obtain from the Raman effect.

The real core information lies in the Raman intensity which offers the dynamics of the photon-perturbed molecule. The photon-perturbed molecule, in general, may not be in its excited eigenstates. In such case, we call it the non-resonant the Raman process and the photon-perturbed molecule including its relaxation, the Raman excited virtual state, or simply the Raman virtual state. However, we have to stress that the Raman virtual state is a real physical entity, not just by our imagination. The word virtual should not be exaggerated to imply a physical meaning. The Raman virtual state is like a wave packet.

It is a common daily experience that in a pan full of water, there can be standing waves which are shaped by the pan. When a pebble is thrown into the pan, the water inside will be splashed above or even out of the pan in a random way. Similarly, when a molecule (the pan) absorbs a light quantum (the pebble), its electronic distribution (the water) will be disturbed. The disturbed (excited) electronic distribution in such an excitation is, in general, not stationary (the splashing water) or non-resonant and does not correspond to an eigenstate (the standing wave). We know that the eigenstates are governed by the molecular nuclei and can be accurately predicted by Schroedinger equation (just as that the patterns of the standing waves are defined by the pan boundary) while the non-stationary excitation including its relaxation, called virtual state, is not well defined by the nuclei and is hard to figure out though not impossible. This is the physical concept of the Raman virtual state. Just like that we cannot say that the splashing water is not a physical reality due to it is not a standing wave, we cannot say that the Raman virtual state is not a real physical entity due to that it is simply not an eigenstate or resonant one!

Back to the core issue: how to retrieve the information of the Raman virtual state from the Raman intensity? This is the central issue for the Raman study and the core topic we will cover in this book.

Before going to the issue of Raman intensity study, we will first introduce briefly the classical and quantum mechanical treatments of the Raman effect. If the readers are familiar with them, these sections may be skipped, except the Comments in Section 1.3.

Comments

If Raman excitation is to an eigenstate, we call the process resonant. In general, this is not the case, then the process is called non-resonant. In such case, no doubt that the electrons are disturbed and the molecule is in the so-called Raman virtual state. Hence, the virtual state is a physical reality, albeit the molecule is not in an eigenstate. Do not try to interpret the phenomenon from the vocabulary—virtual. It is only a word, a nomenclature for the phenomenon, not a deduction based on any physical considerations.

1.2The classical treatment

As a molecule is hit by the visible light (called the scattering light), the nuclear motion (vibration) will not be disturbed since its frequency is much less than that of the light. However, the electrons will be disturbed by the light. This disturbance of electrons by the external light is described by the electronic polarizability, which is a measure how easily the electrons can be affected by the light. As the electrons are more tightly bound to the nuclei and harder to be disturbed by the light, the electronic polarizability is smaller, otherwise, it is larger. The dimension of the electronic polarizability is volume. Its physical significance is the space occupied by the electrons. It is also proportional to the amount of electron numbers (charges). Since the electronic distribution of a molecule(or the molecular configuration/shape) is, in general, not spherical, the electronic polarizability is direction dependent, or a tensor. However, for the convenient elucidation of its physical significance, we will not go that far but simply consider it as a scalar in this book as we will pay more attention to the electronic polarizability of a bond. This will not affect the retrieval of the physical concepts of the topics concerned. For convenience, electronic polarizability is often shortened as polarizability.

Suppose the electric field of the scattering light with angular frequency ω is

and the vibration is described by the normal mode (at least, in the low exci...