Symmetry formaldehyde

In Eq. (I.l) Ja, Jt>, and Je stand for the a, b, and c-components of the overall angular momentum measured in units of h. They are referred to the principal axis system of the molecular moment of inertia tensor. Because of the mutual compensation of positive and negative contributions, the absolute values of the g-tensor elements are usually smaller than 1 (typically on the order of 0.01 to 0.1 as may be checked in Table AI of the Appendix). In many cases the off-diagonal elements of the g-tensor in Eq. (I.l) will be zero because of molecular symmetry. Formaldehyde or 1,2-difluorobenzene may serve as examples. 

An example will help illustrate these ideas. Consider the formaldehyde molecule H2CO in C2v symmetry. The configuration which dominates the ground-state waveflinction has doubly occupied O and C 1 s orbitals, two CH bonds, a CO a bond, a CO n bond, and two 0-centered lone pairs this configuration is described in terms of symmetry adapted orbitals as follows (Iai22ai23ai2lb2 ... 

The teehniques used earlier for linear moleeules extend easily to non-linear moleeules. One begins with those states that ean be straightforwardly identified as unique entries within the box diagram. For polyatomie moleeules with no degenerate representations, the spatial symmetry of eaeh box entry is identieal and is given as the direet produet of the open-shell orbitals. For the formaldehyde example eonsidered earlier, the spatial symmetries of the nji and nn states were A2 and Ai, respeetively. 

In a molecule such as the asymmetric rotor formaldehyde, shown in Figure 5.1(f), the a, b and c inertial axes, of lowest, medium and highest moments of inertia, respectively, are defined by symmetry, the a axis being the C2 axis, the b axis being in the yz plane and the c axis being perpendicular to the yz plane. Vibrational transition moments are confined to the a, b or c axis and the rotational selection mles are characteristic. We call them... 

Having assigned symmetry species to each of the six vibrations of formaldehyde shown in Worked example 4.1 in Chapter 4 (pages 90-91) use the appropriate character table to show which are allowed in (a) the infrared specttum and (b) the Raman specttum. In each case state the direction of the transition moment for the infrared-active vibrations and which component of the polarizability is involved for the Raman-active vibrations. 

The A A2 X Ai, n -n system of formaldehyde (see Section 7.3.1.2) is also electronically forbidden since A2 is not a symmetry species of a translation (see Table A.l 1 in Appendix A). The main non-totally symmetric vibration which is active is Vq, the hj out-of-plane bending vibration (see Worked example 4.1, page 90) in 4q and d transitions. 

Here are the energies and symmetry designations for the next set of molecular orbitals for formaldehyde ... 

Formaldehyde belongs to the symmetry group Czv and the electronic states can be classified into the four irreducible representations Ai, A 2, B, and B -... 

Problem 10-7. Formaldehyde, CH2O, has C2v symmetry. The ground state has symmetry species Ai, and low-lying excited states have symmetry species A2, B2, and Ai. To which excited states are transihons allowed What are the direchons of polarizahon of the allowed transihons ... 

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. 

Like water, it has the symmetry of point group C2e. When the MOs of formaldehyde molecule as given in the figure are subjected to the symmetry operations of this group, n-orbital is observed to transform as bx and n orbital as ba as shown below ... 

Figure 3.11 Symmetry and charge distribution m molecular orbitals of formaldehyde n (b2), n (bj) and w (bj) and o (r ).

The electronic configuration of formaldehyde under different types of electronic transitions can be represented in terms of electron occupancy (Table 3.2). To obtain the molecular state symmetry the symmetry of singly occupied orbitals need only be considered for the direct product (Section 2.9). 

The energy state, electronic configuration, molecular state symmetry and the nature of transition in formaldehyde 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 ... 

Write down the electronic configurations for the ground states of the molecules water, carbon dioxide, formaldehyde, ethene, benzene, and the nitrogen dioxide radical. The occupied MO s shall be given using the full point group symmetry of the molecule. 

Formaldehyde has symmetry operations which place it in the point group C2V. The character table for C2V was given in Table 6-1. Since 0(py) transforms as b2 and 0(pz) as bx, the ground... 

The carbon-oxygen double bond in aldehydes and ketones is similar and can be described in either of these two ways. If we adopt the iocalised-orbital description, formaldehyde will have two directed lone pairs in place of two of the C-H bonds in ethylene. In this case the axes of these hybrid orbitals will be in the molecular plane (unlike the oxygen lone pairs in water). Either the components of the double bond or the lone pairs can be transformed back into symmetry forms. The alternative description of the lone pairs would he one er-type along the 0-0 direction and one jr-type with axis perpendicular to the 0-0 bond hut in the molecular plane. It is the latter orbital which has the highest energy, so that an electron is removed from it in. ionisation or excitation to the lowest excited state. 

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