Diatomic molecules electronic partition functions

In nitric oxide, which is an exception among stable diatomic molecules, each level has a multiplicity of two (A-type doubling), so that the electronic partition function is actually 4.0. 

We explicitly excluded molecules in our earlier treatment of the electronic partition function. Let us consider Select for molecules now, starting with a diatomic molecule and generalizing the result to other molecules. 

Because Dq is typically large and is a positive exponential, the first term in the equation above typically dominates, and we can approximate the diatomic molecule s electronic partition function as... 

Choose a diatomic gas and compute its translational, rotational, vibrational, and electronic partition functions at 298.15 K and 1.000 bar, looking up parameters as needed in Table A.22 in Appendix A or in some more complete table. Unless you choose NO or a similar molecule with an unpaired electron, assume that only the ground electronic state needs to be included. 

The partition function of the atomic species consists of the electronic and translational contributions only, but for the diatomic molecule A2 the partition function involves the electronic, translational and rotational factors, and also the contribution of one vibrational mode. The translational partition function is given by equation (16.16) as... 

Some values of Dq for diatomic molecules are given in Table 29.1. Note that Dq and are measurable while D is calculated from Eq. (29.66). For a polyatomic molecule in which the various vibrations are independent, it is convenient to combine the product of the electronic and vibrational partition functions. We have for qeQv,... 

Molecular Structure, III. Electronic Spectra and Electronic Structure of Polyatomic Molecules, Reprint edition (1991) (Krieger Publishing Company) with corrections of 2nd edition (1966) (D. Van Nostrand Company, Princeton, NJ, originally 1950, partition functions for diatomic molecules, p. 466 ff). 

In the molecular orbital method [8] the bonding is described in terms of linear combinations of atomic orbitals and the localised description of the chemical bond is lost, but as Mulliken [9] showed, it is possible to partition the electron density and thereby get an estimate of the spatial distribution and bonding character of an orbital. The procedure can be illustrated by the simple case of a diatomic molecule with one basis function per atom containing N electrons in a molecular orbital. Let the molecular orbital be written as ... 

Of the five parts of trans d can always be considered symmetric as far as the Pauli principle is concerned (no matter which type of particle—a fermion or a boson—the nucleus is). The electronic wavefunction eiect almost always symmetric. For homonuclear diatomic molecules, there is usually a + superscript on the term symbol of the ground electronic state that implies symmetric behavior however, some diatomic molecules—O2 is the noteworthy one—have a superscript minus (—) in their term symbol, indicating that the groimd electronic state is actually antisymmetric Ignoring these rare exceptions (but see the end-of-chapter exercises), ultimately the and the partition functions combine to determine the overall symmetry of Q for the molecule. 

The classical molecular partition function for dilute diatomic and polyatomic gases without electronic excitation contains three factors. The translational factor is the same as given by the formula in Eq. (27.4-12), since the translational motion of a molecule is the same as that of an atom ... 

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