vibrational spectrum of SF4
Hank Wells
MAILER...@maroon.tc.umn.edu <MAILER...@maroon.tc.umn.edu> wrote:
>Your message was not delivered to the following recipients:
>
> n: User unknown
>
>---------------- Your original message ----------------
>Received: by maroon.tc.umn.edu; Fri, 31 Mar 95 16:03:55 -0500
>Message-Id: <2f7c7c4...@maroon.tc.umn.edu>
>Date: Fri, 31 Mar 95 16:03:55 -0500
>From: wel...@maroon.tc.umn.edu
>To: n
>Subject: vibrational spectrum of SF4
>
>
>Pascal Dietzel <uzs...@ibm.rhrz.uni-bonn.de> writes:
>
>> crus...@aol.com (CRUSTYMP) wrote:
>> >
>> > I was wondering why the vibrational spectra (ir annd Raman), of SF4 has 5
>> > peaks in each the IR and Raman, but if one determines the number of peaks
>> > using group theory, one comes up with 6 peaks, my question is WHY?
>>
>> SF4 has a trigonal bipyramidal structure with the free electron pair occupying
>> an equatorial position. The point-group should then be C2v, there should be 3N-6
>> (N=5, hence nine) normal modes of vibration.
>> I looked up the character table of the point group and found that there should
>> be four vibrations in symmetry class A1 (one is active IR and the other three Raman
>> active), one in A2 (Raman active), two in B1 and another two in B2 (in each, one is
>> IR active and one is Ra active). All in all you should expect six peaks in the
>> Raman spectrum and three in the infrared (=9).
>> Now, if you found more then that they might result from a combination (substraction
>> or addition) of two vibrations or it might be an overtone of one of the normal
>> modes (the frequency then is a multiple of the normal mode's frequency) or they might
>> result from Fermi resonance.
>>
>> Hope this helps,
>>
>> Pascal.
>
>
>On the right track, but incorrect. You do end up with 4 A1 vibrations,
>but ALL of these are going to be active in the IR and the Raman.
>Likwise, in the B1 and B2 irreducible representations ALL of these are
>IR and Raman active. So the totals are 9 for the Raman and 8 for the
>IR. The original poster observed less than that -- probably do to some
>energy overlap of these vibrations.
>
>I think I see where you're making your mistake in you analysis. If we
>look at the first two lines of the C2v character table we'd see this:
>
>C2v | E | C2 | (sigma) | (sigma') | |
>A1 | 1 | 1 | 1 | 1 | z | x2, y2, z2
>
>I think you're saying aha - 4 A1 modes and four entries in the last two
>columns. Three of those entries are quadratic terms (Raman active) and
>one is translational (IR active) so we must have 3 Raman and 1 IR. But
>that's incorrect.
>
>To see why, ask yourself what you'd have if you only had one A1? By
>the above logic you'd either have to pick one at random or assign 1/4
>of a mode being active in the IR!
>
>If you consult Cotton's _Chemical Applications of Group Theory_ you'd
>find the selection rule for IR which will remove all doubt: "A
>fundamental will be Infrared active (i.e. will give rise to an
>absorption band) if the normal mode which is excited belongs to the
>same representation as any one or several of the Cartesian
>coordinates." That means ALL A1 modes are IR active.
>
>You can not identify the 9 vibrational modes simply by coming up with
>3N-6 and seeing that there are 9 things other than Rx, Ry and Rz listed
>in the character table. In this case, it was sheer coincidence! You
>need to derive all of the vibrations for the molecule and subtract out
>the 3 from translation and 3 from rotational modes (in a non-linear
>molecule).
>
>If anyone would like to see how one can generate the reducible
>representation for all the vibrations in the SF4 molecule, let me know
>and I'll post it here or put something with better detail and pretty
>pictures on our web site.
>
>Enjoy.
>
>Rob
>
>-----------------------
>Professor Robert Toreki, Dept. of Chemistry, University of Kentucky
>rto...@pop.uky.edu. http://www.uky.edu/ArtsSciences/Chemistry/
>
>Additional affiliations at UK: 1) Center for Applied Energy Research
>(CAER) and 2) Applied Science and Technology Commercialization Center
>(ASTeCC).
>
If this hasn't been beaten to death already, a quick and dirty calculation
(below) suggests that several of the modes are very nearly degenerate,
which would account for the lower than predicted number of experimental
bands.
HyperChem log start -- Mon Apr 03 12:30:13 1995.
Vibrational Analysis, SemiEmpirical, molecule = D:\HYPER3\SF4.HIN.
PM3
Convergence limit = 0.0000100 Iteration limit = 50
Accelerate convergence = NO
UHF Calculation:
Singlet state calculation
Number of electrons = 34
in which
Number of Alpha Electrons = 17
Number of Beta Electrons = 17
Charge on the System = 0
Total Orbitals = 20
ENERGIES AND GRADIENT
Total Energy = -44916.2466485 (kcal/mol)
Total Energy = -71.577166090 (a.u.)
Binding Energy = -327.2958065 (kcal/mol)
Isolated Atomic Energy = -44588.9508420 (kcal/mol)
Electronic Energy = -106496.1746645 (kcal/mol)
Core-Core Interaction = 61579.9280161 (kcal/mol)
Heat of Formation = -185.3358065 (kcal/mol)
Gradient = 0.0100765 (kcal/mol/Ang)
EIGENVALUES(eV)
Alpha Orbitals:
-32.233673 -25.940624 -25.938349 -22.137585 -18.876678
-18.622414 -18.410736 -18.409178 -17.440266 -17.440159
-16.692230 -16.578417 -16.574537 -15.907902 -15.907273
-15.600335 -10.411344 -0.960399 -0.499631 -0.489184
Beta Orbitals:
-32.233673 -25.941080 -25.937895 -22.137585 -18.876678
-18.622414 -18.410711 -18.409203 -17.440231 -17.440193
-16.692234 -16.578367 -16.574583 -15.907991 -15.907185
-15.600335 -10.411345 -0.960401 -0.499510 -0.489304
ATOMIC ORBITAL ELECTRON POPULATIONS
Alpha Orbitals:
0.914923 0.425329 0.424778 0.558994 0.879258
0.977504 0.829854 0.983918 0.878367 0.865228
0.940318 0.983504 0.878376 0.864972 0.940367
0.983707 0.882389 0.985655 0.985608 0.816951
Beta Orbitals:
0.914924 0.424778 0.425346 0.558977 0.878083
0.977399 0.827248 0.983652 0.878953 0.866683
0.940209 0.983644 0.878964 0.866439 0.940260
0.983838 0.882389 0.985605 0.985655 0.816952
NET CHARGES AND COORDINATES
Atom Z Charge Coordinates(Angstrom)
x y z
1 16 1.351951 -0.37806 0.16148 -0.43296
2 9 -0.336917 -0.37884 1.73363 -0.18861
3 9 -0.336905 0.98169 -0.62378 -0.17667
4 9 -0.336924 -1.74020 -0.62331 -0.18785
5 9 -0.341205 -0.38487 0.16592 1.20036
Dipole (Debyes) x y z Total
Point-Chg. 0.016 -0.011 -3.883 3.884
sp Hybrid -0.007 0.004 1.599 1.599
pd Hybrid 0.000 0.000 0.000 0.000
Sum 0.010 -0.006 -2.284 2.284
**********************************
****** Vibrational Analysis ******
**********************************
==== Force Constant Matrix in Milli-Dynes / Angstrom ====
(I -- Atom Index Z Atomic Number)
I Z I Z I Z I Z I Z I Z
1 16 2 9 3 9 4 9 5 9
1 16 4.58046 1.64033 1.64133 1.64043 1.58579
2 9 1.64033 2.05090 0.17651 0.17654 0.76402
3 9 1.64133 0.17651 2.05055 0.17651 0.76556
4 9 1.64043 0.17654 0.17651 2.05092 0.76427
5 9 1.58579 0.76402 0.76556 0.76427 2.61014
==== Principal Moments of Inertia ====
(Ix, Iy, Iz in Gram-Cm2 X 1.0e-40 and A, B, C in 1/Cm)
Ix = 175.47716 Iy = 175.48375 Iz = 233.72841
A = 0.15953 B = 0.15952 C = 0.11977
==== Zero Point Energy of Vibration in kcal / mol ====
6.70968
=================================
========== IR Spectrum ==========
=================================
---- Normal Mode Frequencies of Vibration in 1/cm.
---- Integrated Infrared Band Intensities in km/mol.
---- Derivatives of Dipole Moments with Respect
to Normal Coordinates in Debye/Angstrom/AMU.
*****************************************************************************
Normal Mode Frequency 190.90
1 Intensity 0.22853
Derivatives of Dipole Moment -0.0676 -0.0888 -0.0001
Normal Mode Frequency 192.35
2 Intensity 0.17888
Derivatives of Dipole Moment 0.0807 -0.0568 0.0007
Normal Mode Frequency 441.27
3 Intensity 53.38676
Derivatives of Dipole Moment 0.0064 -0.0042 -1.7055
Normal Mode Frequency 498.25
4 Intensity 16.45117
Derivatives of Dipole Moment -0.9035 -0.2827 -0.0019
Normal Mode Frequency 506.91
5 Intensity 15.43701
Derivatives of Dipole Moment -0.2784 0.8738 -0.0024
Normal Mode Frequency 555.39
6 Intensity 5.78790
Derivatives of Dipole Moment 0.0025 -0.0017 -0.5615
Normal Mode Frequency 754.89
7 Intensity 95.12641
Derivatives of Dipole Moment 2.2498 0.3479 0.0088
Normal Mode Frequency 756.29
8 Intensity 96.14738
Derivatives of Dipole Moment -0.3523 2.2615 -0.0079
Normal Mode Frequency 823.08
9 Intensity 22.41153
Derivatives of Dipole Moment 0.0054 -0.0034 -1.1050
Translation Frequency 1.60
1 Intensity 0.00000
Derivatives of Dipole Moment 0.0000 0.0000 0.0000
Translation Frequency 0.37
2 Intensity 0.00000
Derivatives of Dipole Moment 0.0000 0.0000 0.0000
Translation Frequency -0.03
3 Intensity 0.00000
Derivatives of Dipole Moment 0.0000 0.0000 0.0000
Rotation Frequency 23.60
1 Intensity 0.90647
Derivatives of Dipole Moment -0.0306 -0.2201 0.0005
Rotation Frequency -51.52
2 Intensity 0.90583
Derivatives of Dipole Moment -0.2200 0.0305 -0.0010
Rotation Frequency 0.14
3 Intensity 0.00000
Derivatives of Dipole Moment 0.0000 0.0000 0.0000
*****************************************************************************
HyperChem log stop -- Mon Apr 03 13:47:00 1995.