564-17 Lec 29 Mon-Wed 27,29 Mar17 Vibrations of a Polyatomic Molecule Benzene (D 6h Symmetry)
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
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/6-311++g(d,p) pop =reg opt freq benzene b3lyp/6-311++g(d,p) pop =reg opt 0 1 C 1.20809735 0.69749533-0.00000000 C 0.00000000 1.39499067-0.00000000 C -1.20809735 0.69749533-0.00000000 C -1.20809735-0.69749533-0.00000000 C 0.00000000-1.39499067-0.00000000 C 1.20809735-0.69749533-0.00000000 H 2.16038781 1.24730049-0.00000000 H 0.00000000 2.49460097-0.00000000 H -2.16038781 1.24730049-0.00000000 H -2.16038781-1.24730049-0.00000000 H 0.00000000-2.49460097-0.00000000 H 2.16038781-1.24730049-0.00000000
benzene #b3lyp/6-311++g(d,p) pop=reg opt (3 minutes on PC) Frequencies in cm -1 numbered by order of increasing frequency 1 2 3 AU B3U AG(E2G) 410.7349 411.6070 622.2315 16 17 18 B2U B3G AG 1174.8619 1197.4179 1197.6082 4 5 6 B3G(E2G) B3U B2G 622.2429 685.7410 718.7617 7 8 9 B1G B2G AU 860.6162 863.1904 986.4942 10 11 12 B3U AG B2G 988.0685 1011.6087 1014.4673 13 14 15 B1U B2U B1U 1023.3723 1059.1425 1059.4801 19 20 21 B2U B3G B2U 1337.3288 1381.2370 1510.5350 22 23 24 B1U B3G AG 1510.8040 1634.4257 1634.4289 25 26 27 B1U B3G AG 3157.3697 3166.8865 3166.9359 28 29 30 B2U B1U AG 3182.5618 3182.6543 3192.7553
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: 10.1063/1.447800
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: 10.1063/1.447800
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
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
Absorbance 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 608 cm -1 6 10 (1 00 ) 6 0 1 (1 00 ) 521 cm -1 6 01 1 0 1 601 1 0 2 1 0 0 916.8 896.5 929.7 Benzene vapor, room temperature 6 01 1 0 3 937 6 01 1 0 4 0.0 37000 38000 39000 40000 41000 42000 43000 cm -1
Electronic symmetry vibrational Vibronic symmetry symmetry 6 1 1 3 e 2g E 1u 6 1 1 2 e 2g E 1u 6 1 1 1 e 2g E 1u 1 1 923 cm -1 ν 1 a 1g B 2u B 2u 0 6 1 521 cm -1 ν 6 e 2g E 1u 0 a 1g B 2u 6 0 1 6 01 1 0 1 6 01 1 0 2 6 1 0 1 10 6 0 1 Hot bands (have Boltzmann factor. 0-0 f 1 01 f 993 cm -1 ν 1 a 1g Ground A 1g 0 606 cm -1 ν 6 e 2g f= forbidden red = allowed
2.0 D 1.8 1.6 1.4 1.2 Benzene vapor, room temperature Absorbance 1.0 0.8 0.6 0.4 0.2 0.0-0.2 39400 39450 39500 39550 39600 39650 cm -1
2.0 D 1.8 1.6 1.4 1.2 Benzene vapor, room temperature Absorbance 1.0 0.8 0.6 0.4 0.2 0.0-0.2 39400 39450 39500 39550 39600 39650 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: 10.1063/1.447800
6 01 1 0 1 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: 10.1063/1.447800 8 0 1 E 2g
π MOs of Benzene f 23 xy LUMOs x 2 -y 2 22 21 y HOMOs x 20 s
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
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
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 +
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.
Two-Photon Fluor. Excitation Spectrum Benzene in hexane 14 0 1 (1 00 ) B 1u B 2u 1500 cm -1 1 00 Solvent induced Fluoro-Benzene in hexane A 1g -B 2u Transition Density A 1g -B 1u Transition Density