The structures of polyatomic molecules

Microwave spectroscopy often gives more definite and precise information on the structure of polyatomic molecules than vibration-rotation and electronic spectra. For example, consider the simplest oxime formald-oxime, CH2=NOH. There are two likely structural configurations for this... 

As might be expected, the rotational spectra of polyatomic molecules are more complex than those for diatomic molecules. For example, depending on their structures polyatomic molecules can have as many as three different moments of inertia. Although more complicated, the analysis of the structures of polyatomic molecules using rotational spectra follows the same principles as we have discussed for diatomic molecules. 

Understanding VER in condensed phases has proven difficult. The experiments are hard. The structurally simple systems (diatomic molecules) involve complicated relaxation mechanisms. The structures of polyatomic molecules are obviously more complex, but polyatomic systems are tractable because the VER mechanisms are somewhat simpler. 

NUMERICAL DATA ON THE STRUCTURE OF POLYATOMIC MOLECULES. CONNECTION WITH CHEMICAL BINDING... 

It is important to note that because the moment of inertia depends upon the masses of the atoms in the molecule, the microwave spectrum of a diatomic molecule will be sensitive to the isotopic composition of the molecule. The structure of polyatomic molecules can also be studied using microwave spectroscopy, although the procedure is more complicated than that considered here for diatomic molecules. 

The simple ideas that have been introduced in relation to diatomic molecules can be carried over to a brief discussion of bonding in polyatomic molecules in particular, the distinction between cr bonds and re—bonds. Moreover, the structure of polyatomic molecules can be rationahsed in terms of the atomic orbitals on neighbouring atoms that are used to create molecular orbitals for example, if one... 

Another example of reduced symmetry is provided by the changes that occur as H2O fragments into OH and H. The a bonding orbitals (ai and b2) and in-plane lone pair (ai) and the a antibonding (ai and b2) of H2O become a orbitals (see the Figure below) the out-of-plane bi lone pair orbital becomes a" (in Appendix IV of Electronic Spectra and Electronic Structure of Polyatomic Molecules, G. Herzberg, Van Nostrand Reinhold Co., New York, N.Y. (1966) tables are given which allow one to determine how particular... 

Mulliken introduced the term "orbital" distinct from "orbital wave function" in 1932 in the second of fourteen papers carrying the general title, "Electronic Structures of Polyatomic Molecules and Valence." Mulliken defined atomic orbitals (AOs) and molecular orbitals (MOs) as something like the... 

Mulliken, Life, 90. On the "orbital," Mulliken wrote in 1932 "From here on, one-electron orbital wave functions will be referred to for brevity as orbitals. The method followed here will be to describe unshared electrons always in terms of atomic orbitals but to use molecular orbitals for shared electrons." In Robert Mulliken, "Electronic Structures of Polyatomic Molecules and Valence," Physical Review 41 (1932) 4971, on 50. 

Information about the structure of gas molecules haB been obtained by several methods. Spectroscopic studies in the infrared, visible, and ultraviolet regions have provided much information about the simplest molecules, especially diatomic molecules, and a few polyatomic molecules. Microwave spectroscopy and molecular-beam studies have yielded very accurate interatomic distances and other structural information about many molecules, including some of moderate complexity. Molecular properties determined by spectroscopic methods are given in the two books by G. Herzberg, Spectra of Diatomic Molecules, 1950. and Infrared and Raman Spectra, 1945, Van Nostrand Co., New York. The information obtained about molecules by microwave spectroscopy is summarised by C. H. Townes and A. L. Schawlow in their book Microwave Spectroscopy of Gases, McGraw-Hill Book Co., New York, 1955. 

Herzberg, G., Molecular Spectra and Molecular Structure vol. I Spectra of Diatomic Molecules, Second Edition, 1950 vol. II Infrared and Raman Spectra of Polyatomic Molecules, 1945 vol. Ill Electronic Spectra and Electronic Structure of Polyatomic Molecules, 1966 Van Nostrand, Princeton, New Jersey. Very comprehensive treatments with many tabulations of experimental data. (The data in vols. I and II have been largely superseded by more recent work.)... 

The major changes in the new edition are as follows There are three new chapters. Chapter 1 is a review and summary of aspects of quantum mechanics and electronic structure relevant to molecular spectroscopy. This chapter replaces the chapter on electronic structure of polyatomic molecules that was repeated from Volume I of Quantum Chemistry. Chapter 2 is a substantially expanded presentation of matrices. Previously, matrices were covered in the last chapter. The placement of matrices early in the book allows their use throughout the book in particular, the very tedious and involved treatment of normal vibrations has been replaced by a simpler and clearer treatment using matrices. Chapter 7 covers molecular electronic spectroscopy, and contains two new sections, one on electronic spectra of polyatomic molecules, and one on photoelectron spectroscopy, together with the section on electronic spectra of diatomic molecules from the previous edition. In addition to the new material on matrices, electronic spectra of polyatomic molecules, and photoelectron... 

This section attempts a systematic classification of the covalent bonding schemes, in terms of VB theory, exhibited by atoms of the Main Group elements. The aim is to enable the reader to fit together the structure of a molecule or polyatomic ion by identifying the appropriate bonding scheme for each atom. You should try not to memorise by rote the tables in this section the material should be studied in conjunction with a text which covers the descriptive chemistry in some detail. The lists of bonding schemes are not exhaustive, but they contain the most important ones. 

R. S. Mulliken, Electronic structures of polyatomic molecules and valence. VI. On the method of molecular orbitals, Journal of Chemical Physics 3 (1935) 375-378. 

Although gas-phase structures of polyatomic molecules which are derived by ED or MW cannot be compared strictly with each other, differences between ra and rz or between ra or r0 lie in general within the combined experimental uncertainties of both methods. The comparison between bond distances derived in the gas phase and those obtained by X-ray crystallography, however, is much more difficult, if not impossible. Three different effects may cause systematic differences ... 

G. Herzberg, Molecular Spectra and Molecular Structure. III. Electronic Spectra and Electronic Structure of Polyatomic Molecules, Van Nostrand, New York, 1966. See Subject Index for tables for individual symmetry groups. (In the text of the present article this book is often referred to as Herzberg s Polyatomics.)... 

There are many challenging areas, for example, the energies and accurate structures of polyatomic molecules of the heavy elements, where the reliability... 

POLYATOMIC MOLECULES Specifying the three-dimensional structure of polyatomic molecules requires that we include bond angles and bond lengths. Any successful theory of bonding must explain and predict these structures. Let s test the VB approximation on the second-period hydrides, the structures of which we have already examined in Chapter 3 using VSEPR theory. 

We shall see shortly that it is really quite easy to obtain the structures of diatomic molecules to very high accuracy. Also, for a relatively minor number of small polyatomic molecules (such as OCS, SO2, CO2, CH4), it has been possible to determine rg structures. Certainly, when possible, this is the desired result. As we shall shortly describe, the task is formidable once the molecule reaches 4 or 5 atoms or more, in general. Indeed, for an important prototype organic molecule such as ethane (C2H5), a true r structure (as described below)... 

New experimental teehniques have increased the capacity of rotationally resolved spectroscopy tremendously. They are generating experimental data at an unprecedented rate and with excellent precision. As a result of all these developments, we know a lot more with much greater precision and accuracy about many more molecules. This includes equilibrium structures of polyatomic molecules. 

The model Hamiltonian of Section II captures some of the essential features of the electronic and vibrational structure of polyatomic molecules, like benzene and 5ym-triazine, that have both nondegenerate and degenerate, Jahn-Teller active, electronic levels. In this section interference experiments are described which will be sensitive to the geometric phase development accompanying adiabatic nuclear motion on either of the electronic potential energy surfaces in the Jahn-Teller pair. 

So far we have discussed chemical bonding only in terms of electron pairs. However, the properties of a molecule cannot always be explained accurately by a single structure. A case in point is the O3 molecule, discussed in Section 9.8. There we overcame the dilemma by introducing the concept of resonance. In this section we will tackle the problem in another way—by applying the molecular orbital approach. As in Section 9.8, we will use the benzene molecule and the carbonate ion as examples. Note that in discussing the bonding of polyatomic molecules or ions, it is convenient to determine fust the hybridization state of the atoms present (a valence bond approach), followed by the formation of appropriate molecular orbitals. 

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