Origin of Molecular Spectra

As a first approximation, the energy of the molecule can be separated into three additive components associated with (1) the motion of the electrons in the molecule, (2) the vibrations of the constituent atoms, and (3) the rotation of the molecule as a whole  

The basis for this separation lies in the fact that electronic transitions occur on a much shorter timescale, and rotational transitions occur on a much longer timescale, than 10 vibrational transitions. The translational energy of the molecule may be ignored in this discussion because it is essentially not quantized. 

If a molecule is placed in an electromagnetic field (e.g., light), a transfer of energy from the field to the molecule will occur when Bohr s frequency condition is satisfied  

Infrared and Raman Spectra of Inorganic and Coordination Compounds, Sixth Edition, Part A Theory and Applications in Inorganic Chemistry, by Kazuo Nakamoto Copyright 2009 John Wiley Sons, Inc. 

Although the dimensions of v and v differ from one another, it is convenient to use them interchangeably. Thus, an expression such as a frequency shift of 5 cm is used throughout this book. 

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At the beginning of the twentieth century a general understanding of the origins of molecular spectra was achieved with the advent of the quantum theory. According to the basic principle of quantum mechanics, the energy associated... 

Interpretation of molecular spectra involves four basic steps. First, major skeletal and functional group components of the molecule are identified, either from assumptions about the compound origin or from features of the spectra. Second, non-localized molecular properties such as the molecular weight, elemental composition, and chromatographic behavior are considered. These global constraints can be used to eliminate unlikely functional groups, deduce the presence of groups and skeletal units which have no distinctive features in the spectra, and detect multiple occurrences of... 

Structural investigations, using the molecular origin of the spectra to provide information which is often in support of nuclear magnetic resonance (NMR) or mass spectrometry studies. 

Molecular spectroscopy is now a mature field of study. It is, however, difficult to find references superior to the classic treatise written by Herzberg nearly 50 years ago (1). The origin of vibrational spectra is usually considered in terms of mechanical oscillations associated with mass of the nuclei and interconnecting springs (9). Vibrational spectroscopy considers the frequency, shape, and intensity of internuclear motions due to incident electromagnetic fields. In the harmonic approximation, the vibrational bands are associated with transitions between nearest vibrational states. When higher order transitions, resonance, and coupling between vibrational motions require analysis, quantum mechanical treatment is mandated (1). Improvements and advancements in poljuner spectroscopy are driven by the many problems of interest in the polymer community. 

AHQP, Interview with Pauling. In a report on work in progress prepared in 1930, MulUken stressed the importance of molecular spectra for both physicists and chemists "[Band Spectra s] methods of analysis are those of physics both in the experimental and theoretical steps of the process the application of results is of special interest to chemistry. In other words this field of molecular spectroscopy is of interest to both physicists and chemists, although it is pure science from the standpoint of the physicist, but more nearly applied science from that of the chemist" in MP, Box 84, Folder 10, Draft of Information to the President, March 15, 1930, emphasis not in original. 

The analysis of molecular spectra is complicated because of the very large number of lines that is obtained simultaneously in normal excitation or absorption experiments. With narrow-band laser excitation an individual excited rotational-vibrational level can be populated selectively and only the decays originating in the excited state are observed. A similar simphfica-tion in absorption measurements is very desirable. Through the possibility of saturating optical transitions, a certain lower level can be labelled by depleting the population with a laser pump laser). If this laser is switched on and off repetitively, all absorption lines originating in the labelled level will be modulated when induced with a second (probe) laser [9.69, 9.70]. A number of schemes for modulation detection are indicated in Fig. 9.6. Several schemes can be used to ascertain that absorption has ocemred, as discussed... 

Since bulk properties, of either solid or liquid phases, clearly are not always appropriate to describe these reactions and molecular states at electrode/electrolyte phase boundaries, it is evident that these unique systems require innovative spectroscopic techniques and theoretical advancements to enable us to understand fully the origins of their spectra. Development of in situ techniques is especially important because crystalline electrode surfaces can restructure when removed from an electrolyte to vacuo, e.g.. Ref. 1, or by... 

Practically all CNDO calculations are actually performed using the CNDO/ 2 method, which is an improved parameterization over the original CNDO/1 method. There is a CNDO/S method that is parameterized to reproduce electronic spectra. The CNDO/S method does yield improved prediction of excitation energies, but at the expense of the poorer prediction of molecular geometry. There have also been extensions of the CNDO/2 method to include elements with occupied d orbitals. These techniques have not seen widespread use due to the limited accuracy of results. 

There is a small peak one mass unit higher than M m the mass spectrum of ben zene What is the origin of this peak d What we see m Figure 13 40 as a single mass spectrum is actually a superposition of the spectra of three isotopically distinct benzenes Most of the benzene molecules contain only and H and have a molecular mass of 78 Smaller proportions of benzene molecules contain m place of one of the atoms or m place of one of the protons Both these species have a molecular mass of 79... 

A number of reviews of mass spectra of carbohydrates have been published from which references to the original papers are available (4, 9, 11, 24, 26). The application of mass spectrometry to this field was initially limited by the relatively low volatility of free carbohydrates and by the complex spectra obtained from some derivatives. These limitations have been partially overcome by new inlet techniques and by pioneering studies on classes and derivatives in order to understand the characteristic fragmentations and rearrangements of the molecular ions of a wide range of carbohydrates. 

The approach to the evaluation of vibrational spectra described above is based on classical simulations for which quantum corrections are possible. The incorporation of quantum effects directly in simulations of large molecular systems is one of the most challenging areas in theoretical chemistry today. The development of quantum simulation methods is particularly important in the area of molecular spectroscopy for which quantum effects can be important and where the goal is to use simulations to help understand the structural and dynamical origins of changes in spectral lineshapes with environmental variables such as the temperature. The direct evaluation of quantum time- correlation functions for anharmonic systems is extremely difficult. Our initial approach to the evaluation of finite temperature anharmonic effects on vibrational lineshapes is derived from the fact that the moments of the vibrational lineshape spectrum can be expressed as functions of expectation values of positional and momentum operators. These expectation values can be evaluated using extremely efficient quantum Monte-Carlo techniques. The main points are summarized below. 

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