Question

1. The combination of infrared (IR) and Raman spectroscopies constitutes the field of vibrational spectroscopy, which is a powerful tool in analyzing molecular structure. Let us consider the vibrational spectroscopy of XY₂. Let us propose that there are four candidate structures for XY₂. I. Bent, with X central, but the X-Y bonds of different length (C_s symmetry); II. Bent, symmetric, with X central (C_2v symmetry); III Linear, with X central (D_∞h); IV. Linear with Y central (C_∞v).

       In each case, the vibrational representation would be:

                     I                II            III                                      IV

       Γ_vib              3a΄      2a₁ + b₁             Σ_g⁺ +Σ_u^- + Π_u            Σ⁺ + Σ^- +Π                            

Referring to the appropriate character tables, and recalling that modes that transform as (x,y,z) are IR active, and that modes that transform as (x²,xy,…) are Raman active, we can summarize the number of each type of mode as:

# modes             I             II                 III              IV

(or “bands”)

       IR active      3 (3a΄)          3 (2a₁ + b₁)        1     (Π_u)      2 (Σ⁺ + Π)

       Raman   active    3 (3a΄)          3 (2a₁ + b₁)        1     (Σ_g⁺)      2 (Σ⁺ + Π)

       Polarized^*    3 (3a΄)          2 (2a₁)                     1     (Σ_g⁺)     1 (Σ⁺)

       Concident^@     3 (3a΄)         3 (2a₁ + b₁)        0            2 (Σ⁺ + Π)

* A polarized Raman band is essentially totally symmetric.

^@ “Coincident” denotes that the same band is active in both IR and Raman.

Examination of the IR and Raman spectra for XY₂ would reveal which candidate structure is correct.

(i)   Fill in the table below for NH₃ and H₂CO in the style of the one above. (NOTE. You looked at both molecules in detail in a previous homework.)

                   G_vib(NH₃) = ________           G_vib(H₂CO) = ________

# modes:

                            NH₃ (C_3v)                   H₂CO (C_2v)

IR active        ______                  _____­­

       Raman active             _______                  _____­

       Polarized^*           _______                  _____­

       Coincident^@          _______                  _____­

(ii) A molecule X₂Y₂ is suspected to have one of the following symmetries:

            C_2v, D_2h, C_2h or C_s

Working each possible geometry through, we find:

       Γ_vib = 3a₁ + a₂ + 2 b₁      (C_2v)

       Γ_vib = 3a_g + a_u + 2 b_u      (C_2h)

       Γ_vib = 5a_’ + a_”                    (C_s)

       Γ_vib = 2a_g + b_1g + b_1u + b_2u + b_3u      (D_2h) (x axis through the X atoms.)

The vibrational spectroscopy gives us the following information. What is the geometry of the molecule?

IR active        ___3___             

       Raman   active           ___3___             

       Polarized^*           ___2___              ­

       Coincident^@          ___0___

Answer 1

(i) The principle of mutual exclusion reveals that the molecule having (i) the symmetry element i , the IR and the Raman modes would be mutually exclusive.

The following rule makes the question straightforward.

In the first problem the NH3 belongs to the C3v point group which doesnt have the i.

The no. of modes of vibration are 6. Among which all are both RAMAN and IR active.

Then H2CO has 6 modes of vibration and having point group of C2v( NO i).

All modes are IR and Raman active modes i.e coincident modes.

(ii) For the question we see that the Ir and Raman modes are not coincident. It says that the molecule doesnt have ANY (I) OR THE POINT OF INVERSION. Among the point groups given the C2h only has the (i) . THus the C2h point group would be taken.

Geomtry is C2h.

The no of modes will be 3* 4 - 6 (taking non-linear) = 6.

Hence the vibrational modes are also given 6.