Benzene (D 6h Symmetry)

Transcription

1 Lec 29 Mon-Wed 27,29 Mar17 Vibrations of a Polyatomic Molecule Benzene (D 6h Symmetry)

2 The word "totally symmetric" refers to a function that ALWAYS goes into itself upon ALL symmetry operations for the molecule. Typically called A 1g or A g, it is the irreducible representation type whoses characters are ALL = 1 The x transition dipole integral, Ψ 1 * x Ψ2dτ Example: operator x = E 1u, and ψ 1 is A g ground state, then need ψ 2 = E 1u i.e., only transition to E 1u are dipole allowed. x and y are equivalent. 2

3 Opt Frequency calculation for benzene with high correlation + large basis (required for accurate frequencies and normal modes) %chk=c:\564-17\benzene-vibs.chk #b3lyp/ g(d,p) pop =reg opt freq benzene b3lyp/ g(d,p) pop =reg opt 0 1 C C C C C C H H H H H H

4 benzene #b3lyp/ g(d,p) pop=reg opt (3 minutes on PC) Frequencies in cm -1 numbered by order of increasing frequency AU B3U AG(E2G) B2U B3G AG B3G(E2G) B3U B2G B1G B2G AU B3U AG B2G B1U B2U B1U B2U B3G B2U B1U B3G AG B1U B3G AG B2U B1U AG

5 Figure from: "1B2u 1A1g spectroscopy of jetcooled benzene: Single vibronic level fluorescence studies" Thomas A. Stephenson, Patricia L. Radloff, and Stuart A. Rice Citation: J. Chem. Phys. 81, 1060 (1984); doi: /

6 Numbered by mode convention e 2g x B 2u = E 1u one-photon Herzberg- Teller active two-photon Herzberg- Teller active Figure from: "1B2u 1A1g spectroscopy of jetcooled benzene: Single vibronic level fluorescence studies" Thomas A. Stephenson, Patricia L. Radloff, and Stuart A. Rice Citation: J. Chem. Phys. 81, 1060 (1984); doi: /

7 1599 cm -1 ν 8 e 2g 1516 in ground 1570 cm -1 ν 14 b 2u 1309 in ground 923 cm -1 ν 1 a 1g 993 in ground Only a 1g modes are FC-active (non-zero Franck-Condon factors) 522 cm -1 ν 6 e 2g 608 in ground 522 cm -1 ν 6 e 2g 608 in ground

8 The word "totally symmetric" refers to a function that ALWAYS goes into itself upon ALL symmetry operations for the molecule. Typically called A 1g or A g, it is the irreducible representation type whoses characters are ALL = 1 The x transition dipole integral, Ψ 1 * x Ψ2dτ e 2g x B 2u = E 1u only 1 quantum of e2g vibrations make significant intensity Herzberg-Teller activity: operator x = E 1u, and ψ 1 is A g ground state, then need ψ 2 = e 2g x B 2u = E 1u vibronic state which is formally 8 dipole allowed. only 1 quantum of e2g vibrations make significant intensity

9 Absorbance cm (1 00 ) (1 00 ) 521 cm Benzene vapor, room temperature cm -1

10 Electronic symmetry vibrational Vibronic symmetry symmetry e 2g E 1u e 2g E 1u e 2g E 1u cm -1 ν 1 a 1g B 2u B 2u cm -1 ν 6 e 2g E 1u 0 a 1g B 2u Hot bands (have Boltzmann factor. 0-0 f 1 01 f 993 cm -1 ν 1 a 1g Ground A 1g cm -1 ν 6 e 2g f= forbidden red = allowed

11 2.0 D Benzene vapor, room temperature Absorbance cm -1

12 2.0 D Benzene vapor, room temperature Absorbance cm -1 Benzene in cold jet (vib. temperature is about 50 K. Figure from: "1B2u 1A1g spectroscopy of jetcooled benzene: Single vibronic level fluorescence studies" Thomas A. Stephenson, Patricia L. Radloff, and Stuart A. Rice Citation: J. Chem. Phys. 81, 1060 (1984); doi: /

13 E 2g Figure from: "1B2u 1A1g spectroscopy of jetcooled benzene: Single vibronic level fluorescence studies" Thomas A. Stephenson, Patricia L. Radloff, and Stuart A. Rice Citation: J. Chem. Phys. 81, 1060 (1984); doi: / E 2g

14 π MOs of Benzene f 23 xy LUMOs x 2 -y y HOMOs x 20 s

15 After CIS (y xy) (x x 2 y 2 ) (x xy) (y x 2 y 2 ) 2-1/2 (y xy)+(x x 2 y 2 ) 2-1/2 (x xy)+(y x 2 y 2 ) 2-1/2 (y xy)-(x x 2 y 2 ) 1 B a,b, 1 E 1u 1 L a, 1 B 1u 2-1/2 (x xy)-(y x 2 y 2 ) 1 L b, 1 B 2u Ground

16 A 1g -E 1u Transition Density Looks like a dipole (Reduced) 1 st order Transition Density is Product of Ground and Excited state wavefunctions (integrated over all but one electron) B 2u Vibration Mode 14 A 1g -B 2u Transition Density

17 E 2g vibrations induce weak one-photon absorption E 2g + E 2g + E 2g - 1,2,3 substitution gives very weak one-photon absorption E 2g - B 2u - B 1u + E 1u - E 1u - E 1u + E 1u +

18 The previous slide has a wealth of information. It is answering the question: what perturbation symmetry will mix E 1u (the x,y symmetry) into the one-photon forbidden B 2u and B 1u states to make them one-photon allowed. It also answers the question: what perturbation symmetry will mix A 1g and E 2g (the x 2 + y 2, and x 2 - y 2,xy, symmetries) into the two-photon forbidden B 2u and B 1u states to make them two-photon allowed. (We will study two-photon absorption briefly in a later lecture to understand the reason for these symmetries) One-photon absorption: <B 2u H E 1u > 0 requires H = e 2g B 2u requires an e 2g perturbation (H ) because B 2u x e 2g = E 1u experimentally, nu 6 is the primary Herzberg-Teller active vibration for benzene; it is weak because the transition density is on the atoms, not the bonds. inductive perturbations due to substituents e.g., fluoro make strong allowedness in various patterns because the transition density is on the atoms: 1,4 difluoro will be 4 times more intense than mono-sustitution. 1,2,3 will provide no intensity although allowed by symmetry because of cancellations! B 1u also requires an e 2g perturbation because B 1u x e 2g = E 1u nu 8 is very strongly HT-active, making B 1u have molar extinction =10,000(!) because it is bond stretching. inductive perturbations have little effect because the transition density is in the bonds, as shown on the next slide. Two-photon absorption: <B 2u H A 1g > or <B 2u H E 2g > 0 requires H be B 2u or E 1u the Kekule vibration perturbation overlaps the B 2u transition density very strongly and mixes the B 2u electronic state so strongly with the ground state that the frequencies are affected (pseudo Jahn-Teller effect) and creates extremely strong two-photon absorption. The B 1u state has weak vibrationally induced intensity, but inductive perturbations induce strong intensity because the transition density is on the atoms, as shown in a slide below.

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20 Two-Photon Fluor. Excitation Spectrum Benzene in hexane (1 00 ) B 1u B 2u 1500 cm Solvent induced Fluoro-Benzene in hexane A 1g -B 2u Transition Density A 1g -B 1u Transition Density