Formaldehyde symmetry coordinates

Figure 10.6. Symmetry coordinates of formaldehyde. (From Fig. 2 of reference [23])...

In this section an example of calculations employing the APZT formalism is presented. Atomic polarizability tensors for formaldehyde-do and foimaldehyde-d2 are evaluated. The initial data are taken from RHF/6-31G(d,p) db initio MO calculations [332]. Molecular geometry, static polarizability tensor and definition of symmetry coordinates are given in Table 9.11. The orientation of the molecule in the Cartesian space, definition of internal coordinates and numbering of atoms are shown in Fig. 3.1. 

The state symmetries of formaldehyde can easily be deduced from group theoretical considerations. The wave functions of rr, rt and tt orbitals are pictorially represented in Figure 3.11 with coordinate axes as used for the molecule. 

Once the state symmetries have been established it only remains to be shown that the direct product of the species of the ground state symmetry, the coordinate translational symmetries and the excited state symmetry belong to the totally symmetric species A. Let us take the n-wr transition in formaldehyde. The ground state total wave function has the symmetry Ax. The coordinate vectors x, y and z transform as By, Bf and Ax respectively (refer Character Table for C2k Section 2.9, Table 2.2), The excited state transforms as symmetry species A2. The direct products are ... 

In 1979 the results of ab initio calculations at the 4-3IG and 6-3IG level on the same complex as well as a formaldehyde/H+ complex were reported. Structural and energetic ctxnparisons of the two complexes showed that while Li+ prefers a linear geometry for electrostatic ion-dipole bonding, the proton coordinates to the carbonyl through a largely covalent bond, resulting in a bent structure (Cs symmetry)... 

Molecular geometry, static polarizability and definition of symmetry vibrational coordinates for formaldehyde ... 

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