Electronic Spectra of Polyatomic Molecules

A basic theoretical understanding of stable isotope fractionations can help researczzzhers plan and interpret both laboratory experiments and measurements on natural samples. The goal of this chapter is to provide an introduction to stable isotope fractionation theory, particularly as it applies to mass-dependent fractionations of non-traditional elements and materials. Concepts are illustrated using a number of worked examples. For most elements, and typical terrestrial temperature and pressure conditions, equilibrium isotopic fractionations are caused by the sensitivities of molecular and condensed-phase vibrational frequencies to isotopic substitution. This is explained using the concepts of vibrational zero-point energy and the partition function, leading to Urey’s (1947) simplified equation for calculating isotopic partition function ratios for molecules, and Kieffer’s (1982) extension to condensed phases. Discussion will focus on methods of obtaining the necessary input data (vibrational frequencies) for partition function calculations. Vibrational spectra have not been measured or are incomplete for most of the substances that Earth scientists are interested in studying, making it necessary to estimate unknown frequencies, or to measure them directly. Techniques for estimating unknown frequencies range from simple analogies to well-studied materials to more complex empirical force-field calculations and ab initio quantum chemistry. Mossbauer spectroscopy has also been used to obtain the vibrational properties of some elements, particularly iron, in a variety of compounds. Some kinetic isotopic fractionations are controlled by molecular or atomic translational velocities; this class includes many diffusive and evaporative fractionations. These fractionations can be modeled using classical statistical mechanics. Other kinetic fractionations may result from the isotopic sensitivity of the activation energy required to achieve a transition state, a process that (in its simplest form) can be modeled using a modification of Urey’s equation (Bigeleisen 1949).

Theoretical estimates of isotopic fractionations are particularly powerful in systems that are difficult to characterize experimentally, or when empirical …

Applying Stable Isotope Fractionation Theory to New Systems

This paper presents a chart giving probable positions of characteristic infra-red absorption bands for certain molecular groupings. Both original and published data were used in its preparation. The reliability of the various correlations is discussed in the text.

Spectra-Structure Correlations in the Infra-Red Region

http://theop11.chem.elte.hu/main_index_files/1990_Allen_ChemPhys_145_427_LinMol.pdf

A systematic study of molecular vibrational anharmonicity and vibration-rotation interaction by self-consistent-field higher-derivative methods. Linear polyatomic molecules

Calculation of inertia defect: Part I. General formulation

212. Structure of benzene. Part II. Direct introduction of deuterium into benzene and the physical properties of hexadeuterobenzene

The infrared spectra of H2S, HDS and D2S have been examined up to 15 μ with a monochromating prism spectrometer, and the results compared with the Raman spectra. The fundamental frequencies have been assigned with reasonable certainty, and a calculation has been made of the frequencies corresponding to infinitesimal amplitude. The cruder methods of the vibrational‐rotational spectrum suggest a vertical angle of 110°, as compared with 92° obtained previously from a rotational analysis.

The Infrared Absorption Spectra of H2S, HDS and D2S

218. Structure of benzene. Part VIII. Assignment of vibration frequencies of benzene and hexadeuterobenzene

The total number of valence electrons in this compound is 3 + 3 × 7 = 24 = 3 × 8, and in accordance with Zachariasen’s rule (1931) the boron atom should lie at the centre of the triangle formed by the three fluorine atoms. If this total number is expressible as n × 8 + m × 2, then the central atom is displaced from the plane, as in SO3--. It was partly with a view to determining whether the extreme ionic nature of fluorine made any difference to this principle that this infra-red investigation was undertaken. The results obtained were completed by the recent publication of the Raman spectrum of this substance (Anderson, Lassettre and Yost 1936) in both the gaseous and liquid states.

C. R. Bailey

Papers

212. Structure of benzene. Part II. Direct introduction of deuterium into benzene and the physical properties of hexadeuterobenzene

The Infrared Absorption Spectra of H2S, HDS and D2S

218. Structure of benzene. Part VIII. Assignment of vibration frequencies of benzene and hexadeuterobenzene

The Molecular Structure of Boron Trifluoride, BF$_{3}$

The Infrared Absorption Spectra of Some Polyatomic Fluorides