J. Phys. Chem. A 2006, 110, 9805-9815
9805
Laser-Induced Fluorescence Spectra, Structure, and the Ring-Twisting and Ring-Bending Vibrations of 1,4-Benzodioxan in Its S0 and S1(π,π*) States Juan Yang, Martin Wagner, and Jaan Laane* Department of Chemistry, Texas A&M UniVersity, College Station, Texas 77843-3255 ReceiVed: April 21, 2006; In Final Form: June 16, 2006
The laser-induced fluorescence (LIF) spectra, both the fluorescence excitation spectra (FES) and single vibrational level fluorescence spectra (SVLF) from several different vibronic states, along with the ultraviolet (UV) absorption spectra of 1,4-benzodioxan have been recorded and analyzed. A detailed energy map has been constructed for four low-frequency vibrations and their combinations for both the S0 and S1(π,π*) electronic states. These are ν48 (ring-bending), ν25 (ring-twisting), ν47 (ring-flapping), and ν24 (skeletal-twisting). Both the experimental and ab initio calculations show the molecule to be twisted in both the S0 and S1(π,π*) states with high barriers to planarity. The experimentally determined ring-twisting quantum states, which are confined to the lower regions of the potential energy surface, were used to calculate one-dimensional potential functions in terms of the twisting coordinates, and the extrapolated barriers were estimated to be 5700 and 4200 cm-1 for the S0 and S1 states, respectively. Two-dimensional calculations, which included the interactions with the bending modes, gave values of 3906 and 1744 cm-1, respectively. The S0 value compares favorably with the ab initio value of 4095 cm-1.
Introduction In recent years, we have been studying the structures and conformations of bicyclic aromatic compounds utilizing the laser-induced fluorescence spectroscopy of jet-cooled molecules1-8 along with ultraviolet absorption spectra. Recent work has been published on molecules in the indan family3-6 and 1,2-dihydronaphthalene.8 In the present paper, we present our results on 1,4-benzodioxan (14BZD), which is related to the simpler molecule 2,3-dihydro-1,4-dioxin (DHD). We have already reported the ground-state vibrational frequencies (infrared and Raman) along with density functional theory (DFT) computations for this molecule as well as the related molecule tetralin (TET).9 In our work here, we concentrate on the ring-twisting and ringbending vibrational modes of 14BZD and utilize these to analyze the characteristics of the potential energy surfaces (PESs) for the conformational changes of this molecule in its S0 ground and S1(π,π*) electronic excited states. These PESs allow us to understand how electronic transitions affect the structures and forces of molecules, and, hence, some of the important contributions to photochemical reactions.
Experimental Section The sample of 1,4-benzodioxan (97% purity) was purchased from Aldrich Chemical Co. and further purified by vacuum distillation. Ultraviolet absorption spectra were recorded on a Bomem DA8.02 Fourier transform spectrometer using a deuterium lamp source, a quartz beam splitter, and a silicon detector in the 20 000-50 000 cm-1 region. The vapor-phase sample was
contained in a 20 cm glass cell with quartz windows. Ultraviolet absorption spectra were collected at ambient temperatures, and the vapor pressure within the cell was about 200 mTorr. Resolutions of 0.25 and 0.5 cm-1 were used, and more than 10 000 scans were averaged. The FES and SVLF spectra were recorded using a Continuum Powerlite 9020 Nd:YAG laser that pumped a Continuum Sunlite OPO and FX-1 ultraviolet extension unit. FES spectra were obtained at 0.5 cm-1 resolution, and SVLF spectra were taken with a spectral resolution of 1 cm-1. Both spectra were recorded under jet-cooled conditions. More details are provided elsewhere.1-8 Calculations Theoretical calculations were carried out using the GAUSSIAN 03 package.10 The calculations for the structure and vibrational frequencies for the S0 ground state have been reported previously.9 Preliminary calculations for the structural parameters and vibrational frequencies for the S1(π,π*) excited state have been carried out and can be found elsewhere.11 Table 1 lists the calculated energies for the planar (C2V) and bent (Cs) structures of 14BZD in its S0 state relative to the energy minima at twisted (C2) conformations. The twisting angle τ and the bending angle θ are as defined in Figure 1. By fixing the dihedral angle D(-O-C-C-O-), the twisting angle τ is confined to be a constant during the structural optimization. The energies for different conformations with different twisting angles were computed from the MP2/ 6-31G(d) calculations. A one-dimensional calculated potential energy curve for the 14BZD S0 state with respect to the twisting coordinate τ is presented in Figure 2. For this basis set the calculated barrier is 4431 cm-1. Similarly, by fixing the dihedral angle D(-CdC-O-C-), the bending angle θ can also be fixed during the optimization. The corresponding relative energies and the one-dimensional potential energy curve in the S0 state with respect to the bending coordinate θ are presented in Figure 3.
10.1021/jp062474b CCC: $33.50 © 2006 American Chemical Society Published on Web 07/22/2006
9806 J. Phys. Chem. A, Vol. 110, No. 32, 2006
Yang et al.
Figure 1. Definition of ring-twisting coordinate τ and the ring-bending coordinate θ for 1,4-benzodioxan and related molecules.
Figure 3. One-dimensional ring-bending potential energy curve from MP2/6-31G(d) calculations for 1,4-benzodioxan. The energy is relative to the twisting minima.
Figure 2. One-dimensional ring-twisting potential energy from MP2/ 6-31G(d) calculations for 1,4-benzodioxan.
TABLE 1: Calculated Relative Energies (cm-1) for Different Structures of 1,4-Benzodioxan in Its S0 Ground State HF
B3LYP
MP2
6-311++G 6-311++G 6-31G 6-311++G (d,p) (d,p) (d) (d,p) cc-pVTZ
structure C2V (planar) Cs (bent) C2 (twisted)
3572 2219 0
3265 2360 0
4431 2890 0
4509 2576 0
4095 2722 0
All energies are relative to the energy minima at the twist conformations. If both τ and θ are fixed at the same time, then the relative energies for conformations with specific twisting and bending coordinates can be calculated. By varying the fixed τ and θ values, a two-dimensional potential energy surface that consists of hundreds of data points can be generated, as shown in Figure 4. Vibrational Hamiltonian For molecules that have two strongly coupled large-amplitude vibrations, as is the case for 14BZD with its ring-twisting ν25 and the ring-bending ν48 vibrations, the two-dimensional vibrational Hamiltonian operator is given by
∂ p2 ∂ ∂ ∂ g (q , q ) + g (q , q ) + 2 ∂τ 44 4 5 ∂τ ∂τ 45 4 5 ∂θ ∂ ∂ ∂ ∂ g (q , q ) + g (q , q ) +V ˆ (τ, θ) (1) ∂θ 45 4 5 ∂τ ∂θ 55 4 5 ∂θ
H ˆ vib ) -
Figure 4. Two-dimensional potential energy for 1,4-benzodioxan S0 state from MP2/6-31G(d) calculations.
[
]
where τ and θ are the ring-twisting and ring-bending coordi-
nates, respectively. The g44 and g55 expressions are the reciprocal reduced masses for the ring-twisting and ring-bending vibrations, respectively. The g45 term is the interaction cross term for these two vibrations. The methodology and vectors for these calculations are published elsewhere.12 Assignment of Spectra 14BZD is related to 2,3-dihydro-1,4-dioxin (DHD), which we have studied previously.13 In 14BZD, a planar benzene ring replaces the double bond, but this molecule is also expected to have twisted C2 symmetry with a high barrier to planarity. The MP2/cc-pVTZ calculation predicts the molecule to have a barrier to planarity of 4095 cm-1 in the S0 state. With such a high barrier, the energy levels close to the bottoms of the twisting potential energy wells are nearly degenerate. The symmetry species of the nearly degenerate ground states (VT ) 0,1) are A1 and A2, respectively, assuming the molecule has perturbed C2V symmetry. Figures 5 and 6 show the jet-cooled fluorescence excitation spectrum (FES) and the room-temperature ultraviolet (UV) absorption spectrum of 14BZD in the 0-900 cm-1 and 9001800 cm-1 regions, respectively, relative to the electronic band origin 000 at 35 563.1 cm-1. Figure 7 shows the FES spectrum under relatively hot conditions compared with the UV absorption spectrum. This was achieved by decreasing the backing pressure of the He carrier gas and by increasing the distance from the nozzle to the laser beam. Table 2 presents the frequencies and
1,4-Benzodioxan in Its S0 and S1(π,π*) States
Figure 5. Fluorescence excitation spectra of jet-cooled 1,4-benzodioxan and ultraviolet absorption spectra at ambient temperature in the 0900 cm-1 region. The band origin 000 is at 35 563.1 cm-1.
Figure 6. Fluorescence excitation spectra of jet-cooled 1,4-benzodioxan and ultraviolet absorption spectra at ambient temperature in the 9001800 cm-1 region.
Figure 7. Ultraviolet absorption spectra and fluorescence excitation spectra of hot bands of 1,4-benzodioxan.
J. Phys. Chem. A, Vol. 110, No. 32, 2006 9807
Figure 8. Single vibronic level fluorescence spectra of jet-cooled 1,4benzodioxan with excitation of the 000 band at 35 563.1 cm-1 and the ultraviolet absorption spectra at ambient temperature.
Figure 9. Single vibronic level fluorescence spectra of jet-cooled 1,4benzodioxan with excitation of the 2510 band (000 + 139.6 cm-1) and the corresponding ultraviolet absorption spectra at ambient temperature.
Figure 10. Single vibronic level fluorescence spectra of jet-cooled 1,4-benzodioxan with excitation of the 4820 band (000 + 159.3 cm-1) and the ultraviolet absorption spectra at ambient temperature.
9808 J. Phys. Chem. A, Vol. 110, No. 32, 2006
Yang et al.
TABLE 2: Fluorescence Excitation Spectra (FES), Ultraviolet (UV) Absorption Frequencies (cm-1), and Assignments for 1,4-Benzodioxana GHb
this work FES
UV
-217
w
-190
vw
-166 -138
vw w
-78
-761.8 -734.7 -620.5 -594.1 -568.4 -561.5 -356.6 -246.7 -240.8 -233.7 -217.2 -216.0 -192.7 -190.1 -170.0 -167.3 -165.6 -138.4 -104.6 -93.6 -85.6 -81.4
w m w m m w w m m m w s s m w m s vs w m w m
vw
-26
w
-21
w
0
inferredc
vs
80
w
111
w
139 159
s s
236.5 278 297 306 318
s m m m m
358 363 374 395 435 443 455 465
m s m m w w w m
476 483
s m
-71.9 -67.4 -59.0 -52.3 -48.3 -31.1 -26.5 -24.5 -21.0 -12.0 -6.3 0.0 6.2 24.7 29.1 52.9
m w m m w vs vvs vs m w vs vvs m s s vs
58.4 79.5 85.8 112.8 133.6 139.6 159.3 166.9 190.6 237.2 278.3
m vw s vs s vs w m m m w
317.8 337.1 355.4 357.8 363.1 374.3
w m w vw m w
434.2 442.8
vw vw
465.1 467.2 470.0 476.2 483.1
vw w vw w w
-761.2 -734.7 -620.6 -594.1 -568.4 -561.5 -356.9 -241.6 -234.2 -217.3 -216.0 -192.1 -190.1 -171.0 -165.6 -137.8 -104.3 -93.1/-94.1 -85.8
assignment
FES
UV
14012511 1401 25112702 2702 1501 46014801 2712 ? 2534 25114802 47014810 2523 2512 25014811 25024820 ? 2501 47014820 4801 25024720/4844 25014810
-138
vvw
? -78.2 -73.0/71.6 -68.1 -59.9 -52.0 -48.4 -28.8 -26.0 -24.5
2533 47204803/4833 25104802 4721 2522 4822 1411 2511 4811 ?
-12.0 -6.3 0.0
2411 25014820 000 ? ?
30.9/29.5 52.9/55.0
2543 4810 2532 2521 25114820 2510 4820 16112510 ?
237.2/238.6 278.3 298.9 306.5 317.0/317.8 336.6 356.8 358.1 363.1 376.8 396.5 437.6 446.2 457.4 465.8 467.0 469.0 474.4/475.9 483.1
4720/4830 2520 25104820 2410 47204810/4840 23102511 231025014820 25204810 2310 25104720 47204820 25204820 24102510 25104840 24104820 16102511 16104811 4740/4860 3910
-240.88
vw
24224811
-216.10 -193.13 -189.98
w vw vw
2422 2512 25014811
-167.87 -166.06 -138.92
w w m
47014810 2501 2411
-94.33 -86.08 -81.88 -77.19 -71.67 -68.16
vvw vvw m m m w
4844
-53.81 -48.53
m m
2522 4822
2533 25224811 4833 47104834
-26
vw
-26.91 -24.66 -21.57
s s m
2511 4811 251147104801
0
vs
54
vvw
0 6.03 24.40 28.89 52.61 54.13
vs s m s s vw
000 47104801 251147304803 47204802 47304803 2410
114
vw s vw
237 278
vw vvw
m m vw s w w w w vw
2532 2521
139 159
85.31 112.39 133.38 139.30 159.39 166.50 190.43 236.72 278.36
2510 4820 251047204802 251047304803 4720 2520
363 374
w vvw
362.88 374.39
m vw
2310 25104720
4832/47204802 25114810/4821
58.7 79.8 85.8 112.7 133.3 139.6 159.3 168.7
assignment
1,4-Benzodioxan in Its S0 and S1(π,π*) States
J. Phys. Chem. A, Vol. 110, No. 32, 2006 9809
TABLE 2 (Continued) GHb
this work FES 493 502 511
UV s m w
519 531.5
m m
553 557 564
vw w w
599 609 622 632 639 642.5 653 658 669
w m m m m m w w m
690
w
698 702 706 716 727
m s vs m m
840 845 857 864 867 888
m s m m m m
938 943 948 951 967 980 984 1003
m s s vs m s m m
1063 1067 1087 1090
s m m s
1186 1202
s s
1253 1268 1282 1289 1316
vs m s m m
1392
s
493.5 503.3 510.3 513.3
m vw vw w
531.1 539.5 552.0
vw m vw
563.6 567.4
vw m
622.8 633.1 638.8 643.0 652.2 657.3
m w vw vw m vw
676.6 679.6 682.3
s vs s
696.8
m
inferredc
assignment
493.5 502.7 515.5 513.2 522.4 531.1 540.3 553.0 555.0 562.9 567.5 600.3 612 622.7 633.1 641.4 642.7 655.1 658.6 670.7 677.1 679.4 681.4 690.7
1610 23102510 25204720 14102512 23104820 1510 14102501 2540 47204840 39104810 141047014820 23104720 2420 25103910 16102510 23102520 39104820 16104820 231025104820 15102510 1421 14102511 14104811 15104820
FES
UV
678
vs
18102511
? 702.3 702.0 705.9
702.0 705.9
s vs
728.0 731.1 735.9 758.8 791.3 812.3 818.5 840.2 845.3 857.8 864.3 867.5 888.9 920.9 924.9 939.5 943.0 947.1 951.3 967.5 979.7 984.8 1003.4 1036.4 1062.9 1067.5 1086.8 1090.7 1110.1 1185.7 1202.4 1226.8 1253.1 1268.1 1280.8
m m m m m m m m m w w w m m s w m m vs m m vw m m m m m m w w w m s w m
726.2 730.6 735.0 758.8 791.7 812.9 818.7 839.5 845.5 856.6 865.5 867.6 888.9 920.2 924.8 939.2 943.1 947.1 951.3 966.2 980.3 984.2 1003 1037 1064 1069 1087 1091 1111 1188 1200 1229 1253
1315.8 1386.6 1392.6
vw m vw
1314 1386 1393
241047204820 2110 1410 ? 2320 ? 141047204802 141025114810 14102532 131047014820 14102521 21102510 14102510 16102310 14104820 23202510 3710 13101411 13102511 21104720 14104720 2010 1310 3920 21102520 14102520 141025104820 13102532 1520/13102521 14102310 20102510 13102510 13104820 13104720 14101610 13102520 1010 ? ? ? 13102310 14202511 10102510
GHb
this work assignment
704
vs
1810
842
w
21102510
924
s
14102511
950
s
1410
1228 1251
m s
12102511 1210
1278
m
1110
1385
s
18202511
FES
inferredc
UV
1404 1409 1413 1419 1431 1444 1552 1565 1571 1594 1613
m s vs m s m s m m s m
1650 1656 1671 1685 1767 1794 1839 1897
m vs m m m m m m
1957 1987 2013 2202 2363
s m m m m
1404.3 1408.6 1412.8 1419.7 1431.6 1444.2 1552.5 1565.1
m m s vw m w m vw
1594.2 1614.2 1629.1 1649.5 1656.5
m vw m m s
1685.3 1766.6 1795.2 1839.7 1897.1 1930.9 1958.0 1986.8
w m m w m m m m
2202.0 2363.1
m m
1404 1408 1412
assignment 2120 14102110 1420
FES
UV
assignment
1410
s
1820
1642
s
14101810
? ? ? 1553 1567 1572 1594
14202510 141021104820 14204820 14103710 ?
1630 1650 1657 1672 1686 1769 1797
131014102511 20102110 13101410 14103920 141021102520 14101520 131014102510 ?
1902
1320 ?
1959
10101410 ? ?
2204 2364
10101310 13101420
a Abbreviations: s, strong; m, medium; w, weak; v, very. b From ref 14. c Inferred combination frequencies are based on assignments of individual vibrations.
9810 J. Phys. Chem. A, Vol. 110, No. 32, 2006
Yang et al.
Figure 12. Experimental and calculated energy levels for the onedimensional potential energy function of the ring-twisting vibration of 1,4-benzodioxan in its S0 state.
Figure 11. Energy level diagram for the low-frequency modes of 1,4benzodioxan in its S0 and S1(π,π*) states.
assignments in the FES and UV absorption spectra. Assignments up to 2400 cm-1 higher than the 000 excitation are presented. The results from the earlier work of Gordon and Hollas14 (GH) are also listed for comparison. The difference in assignments is obvious. The spectra in our work are much more comprehensive and thus have allowed a much clearer interpretation to be attained. For example, GH did not observe any bands in the 280-360 cm-1 region, but there are four bands evident in our FES and each band has a clear assignment. GH assigned the band at -138 cm-1 to be 2411 and the band at 54 cm-1 to be 2410, which would make the fundamental frequency of the double bond twisting vibration ν24 in the S0 state be 192 cm-1. This is not the case because the vapor-phase Raman spectrum9 clearly shows the fundamental frequency of ν24 to be 317 cm-1. Moreover, there is no band observed near 54 cm-1 in our work. The FES band at 306 cm-1 in our work is assigned to be 2410, which is close to the computed frequency of 299 cm-1 from the CIS/6-311++G(d,p) basis set calculations for the S1 excited state. Table 2 shows more than 130 assignments, almost all of which were made with considerable certainty. These were used to determine approximately 40 quantum states for both S0 and S1 states, and, therefore, the energy levels are each typically well-defined by several different spectroscopic transitions. It should be noted that a number of the observed transitions are not totally symmetric, and in principle these should be forbidden. However, as was the case for our work on phthalan, the highly anharmonic and larger amplitude vibrations often lead to violations of the first-order selection rules. Figure 8 shows the single vibrational level fluorescence (SVLF) spectra collected from exciting the 000 band at 35 563.1 cm-1. These frequencies and assignments are shown in Table 3. The fundamental frequencies obtained from vapor IR and vapor Raman spectra as well as those from B3LYP/6-311++G(d,p) calculations are also listed for comparison.9 Figures 9 and 10 show the SVLF spectra from exciting the 2510 and 4820 bands, which are 139.2 and 158.6 cm-1 higher than the 000 band, re-
Figure 13. Representation of the two-dimensional potential energy for the ring-twisting and ring-bending vibrations of 1,4-benzodioxan in the S0 state. P ) planar; T ) twisted; B ) bent structure.
spectively. The corresponding UV absorption spectra are also shown. The SVLF spectra were recorded from nine different excitation bands including 000. These corresponding results are summarized in Table 4. These data were very helpful in confirming the energies of the quantum levels for the S0 ground state and also for determining the descriptions of the vibronic levels from which the transitions occur. Figure 11 presents the energy level diagram for both the S0 and S1(π,π*) states, based on all of these spectra. The four lowest-frequency ring vibrations ν48, ν25, ν47, and ν24 are labeled as A, B, C, and D, respectively, and the corresponding quantum levels for the S1 state are indicated by primes in both Table 4 and Figure 11. Table 5 compares the frequency assignments for several of the fundamental vibrations of 14BZD in its S0 and S1(π,π*) states. Potential Energy Surface (PES) for the S0 Ground State On the basis of the assignments of the low-frequency modes presented in Tables 3 and 4 and shown in Figure 11, both a one-dimensional potential energy function in terms of the ringtwisting vibration and a two-dimensional PES in terms of the
1,4-Benzodioxan in Its S0 and S1(π,π*) States
J. Phys. Chem. A, Vol. 110, No. 32, 2006 9811
TABLE 3: Frequencies (cm-1) and Assignments of Single Vibronic Level Fluorescence (SVLF) Spectra of Jet-Cooled 1,4-Benzodioxan with Excitation of the 000 Band at 35 563.1 cm-1 a this work SVLF 0 -104 -166 -207 -297 -330 -377 -400 -412 -464 -494 -553 -562 -569 -594 -630 -643 -659 -697 -717 -727 -735 -747 -756 -843 -871 -881 -888 -893 -901 -918 -953 -959 -1019 -1028 -1043 -1061 -1067 -1079 -1105 -1122 -1130 -1138 -1150 -1195 -1255 -1268 -1282 -1289 -1296 -1303 -1421 -1433 -1448 -1469
UV vvs vw s vw vw ms w m vw m m m s s w w w w vw m m vs m m m w w w m s m w w m s m m m m m m ms m w m s m s s ms s m m m s
from ref 9 inferredb
0.0 -104.6 -165.6
vs w s
-297.1
w
assignment 0
-208 -330 -400.0
vw
-464.0
vw
-552.2 -561.5 -568.4 -594.1
vw w m m
-734.7
m
-755.5
vw
-401 -412 -463 -494
-568 -594 -630 -660/-658 -698 -719 -728 -735 -754 -871 -883 -890 -901
-958 -1017 -1044 -1063 -1067 -1106 -1124 -1131 -1138 -1194 -1271
-1297 -1304 -1421 -1434 -1448 -1470
000 4801 2501 4802 4701 2502 4001 47014801 4804 1601/4601/25014701 3901/2503 2301 1501 46014801 4702 16012501/25014601 3801 25013901/2504 47024801 2201/23012501 15012501 1401/250146014801 4501 4002 2101 39014001 22012501 4703 1301 14012501 4401 2001 16013901/39014601 16012301/23014601 1201 45014701 3601/390146014801 14012502 1101 1901/2302
vapor IR
calcdc
vapor Raman 105 167
(8) (15)
104 165
297
(4)
297 376
565
vw
645
vw
463 495 552 566
(42) (3) (11) (2)
462 494 555 571
642
720 733 746
893
vw s
ms
732 746
(100) (7)
734 747
842
vvw
845
891
(1)
886 925 952
1025
(65)
1029 1059
1074
s
1074 1107
(1) (4)
1066 1105
1151 1194 1250
w w s
1151
(3)
1249
(25)
1157 1189 1252
1280
s
1280
(29)
1286 1285
1307
ms
1306
(11)
1321
1465
w
1462
(3)
1473
1502 150146014801 46024802 1001 3401/12012501 901 19012501 1801 3301 14011501 801/140146014801 9012501 2202 18012501 601/1402
9812 J. Phys. Chem. A, Vol. 110, No. 32, 2006
Yang et al.
TABLE 3 (Continued) this work SVLF
UV
-1493 -1500 -1588 -1602 -1628 -1635 -1649 -1671 -1686 -1762 -1815 -1823 -1837 -1843 -1849 -1856 -1919 -1929 -1989 -2001 -2014 -2022 c
m m m ms m m m m m s m m m m s m w m s m s ms
from ref 9
inferredb
assignment
-1494
4502 501 12011501 401 13011401 6012501/14022501 110146014801 20012201 2102 12011401 11011401 90146014801 4402 15011801 180146014801/15013301 330146014801 1602390239024602 14013401 9011401 44022501 14011801 14013301
-1590 -1628 -1635 -1648 -1670 -1686 -1763 -1814 -1824 -1836 -1844 -1851 -1858 -1918 -1930 -1990 -2003 -2017 -2014
vapor IR
calcdc
vapor Raman
1496
vs
1494
(0.5)
1502
1609
vw
1609
(4)
1602
a Abbreviations: s, strong; m, medium; w, weak; v, very. b Inferred combination frequencies are based on assignments of individual vibrations. Calculated using the B3LYP/6-311++G(d,p) basis set with GAUSSIAN 03.
TABLE 4: Single Vibronic Level Fluorescence (SVLF) Frequencies (cm-1) and Assignments from Various Excitation Bands of 1,4-Benzodioxana A′
B′
2A′
2C′
2B′
2A′ + B′
4A′
A′ + 2B′
assignment
inferredb
0c vs
+80 w
+139 s
+159 s
+237 s
+278 m
+297 m
+318 m
+358 m
A B 2A A+B C 2B 2A + B 4001 A+C 4A 1601/4601 3B/3901 ? 2A + 2B 2301 1501 46014801 2C 16012501/25014601 3801 4B/25013901 ? A + 2C 2201/23012501 15012501 1401/250146014801
-104.3 -165.6 -207.7 -268.7 -297.1 -330.3 -371.1
-104 vw -166 s -207 vw
-104 s
-166 vs -208 vw -270 vw
-166 m -208 vs
-166 w -207 vs
-165 s
-166 vw -207 ms
-165 vw -207 m
-295 vw -330 w -374 m
-374 m
-332 m -373 s
-328 s
-400 s
-399 s
-496 w
-464 w -493 m
excitation:
-400.0 -411.9 -462.7 -494.3
000
-297 vw -330 ms
-271 m -296 s
-377 w -400 m -412 vw -464 m -494 m
-401 vw -465 vw -494 m -499 m
-538
-594.1
-657.7 -697
-553 m -562 s -569 s -594 w -630 w -643 w -659 w -697 vw -717 m -727 m -735 vs
-332 s -374 vw
-553 w -566 m
-631 w
-665 m -698 w
-400 s -412 w
-400 m
-494 w
-498 m
-539 ms
-377 vs
-566 m
-567 w
-566 s
-553 m -566 ms
-594 m
-594 s
-594 m
-594 m
-660 w -665 vw -717 w -727 m -734 s
-332 s
-659 w -665 w
-735 w
-734 w
-733 w
-270 vw
-411 vw -462 w -493 vw -540 m
-659 vw -697 w
-733 m
a Abbreviations: s, strong; m, medium; w, weak; v, very. b Frequency values inferred from the energy level diagram in Figure 11. c The excitation of 000 is at 35 563.1 cm-1; the frequencies of all other excitation bands are relative to the 000.
ring-twisting and ring-bending modes were calculated. Because the barrier to inversion through the twisting mode is very high and because the observed transitions only reach quantum states
about 700 cm-1 above the energy minima, for both the one and two-dimensional calculations only the lower region of the PESs can be determined with considerable accuracy. Hence, the
1,4-Benzodioxan in Its S0 and S1(π,π*) States
J. Phys. Chem. A, Vol. 110, No. 32, 2006 9813 frequencies and barriers are the same in both cases. In reduced coordinates, the function that best fits the data is
TABLE 5: Comparison of Experimental Vibrational Frequencies (cm-1) for 1,4-Benzodioxan in Its S0 Ground and S1(π,π*) Excited States
V(cm-1) ) 8.10(z4 - 52.86z2)
ν sym. C2V(C2) A1 (A)
A2 (A)
B1 (B) B2 (B)
C2V
C2
description
S0a
S1b
10 13 14 15 16 20 21 23 24 25 37 39 47 48
12 17 19 21 23 16 18 22 24 25 41 44 47 48
C-H wag (op,op′) sat. ring (C-C) stretch benzene C-C stretch benzene ring bend sat. ring bend C-H wag (op, op′) C-H wag (op, ip′) benzene ring bend skeletal twist sat. ring twist benzene ring bend sat. ring bend sat. ring flap sat. ring bend
1151 893 735 562 463 953 843 553 317 166 834 494 297 104
1253 951 706 531 493 947 702 363 306 140 889 483 (119)c 80
a Experimental frequencies are inferred from Table 4 and ref 9. Experimental frequencies are inferred from Table 3. c Only overtone frequency of 237 cm-1 was observed for ν47.
where z is the reduced coordinate. This function, which is shown in Figure 12, has a barrier to inversion of 5672 cm-1, and the calculated frequencies agree well with the observed values, as shown in Table 6 and Figure 12. The coordinate z can be transformed to the dimensioned coordinate τ using15
τ ) (2µA)-1/2 pz
V(τ) ) aτ4 + bτ2
(2)
where τ is the ring-twisting coordinate, as defined in Figure 1. This calculation can be done in either reduced coordinates15 or dimensioned coordinates, and the resulting calculated transition
(4)
where µ ) 1/g44 is the reduced mass. The reduced mass that was calculated12 for the simple twisting model is 30.0 au, but this large-amplitude vibration is clearly much more complicated than this model. If this reduced mass value is used, then the dimensioned potential function becomes
V(cm-1) ) (1.68 × 103)τ4 - (6.18 × 103)τ2
b
estimation of the barrier by extrapolation of the potential function in either case cannot be expected to be very accurate. For the one-dimensional calculation, the potential energyfunction is given by
(3)
(5)
where τ is in radians. This function, however, has minima corresponding to ridiculously high twist angle values of (77°. Part of the discrepancy is apparently related to the fact that the extrapolated barrier is 40% higher than the ab initio value of 4095 cm-1 and thus the minima are moved to higher τ values. The difficulty in having an accurate description of the vibrational model also contributes because a reliable reduced mass cannot be readily calculated. In addition to the twisting, the vibration no doubt also involves contributions from the out-of-plane and in-plane ring-bendings as well as CH2 motions, particularly the rocking and twisting. To provide some perspective on the significance of the reduced mass, a reduced mass of µ ) 100.0 au
TABLE 6: Observed and Calculated One-Dimensional and Two-Dimensional Transition Frequencies (cm-1) and the Corresponding Potential Energy Parameters for the 1,4-Benzodioxan S0 Ground State one-dimensionala parameters µtwist a (cm-1/rad4) b (cm-1/rad2) c (cm-1/rad2) d (cm-1/rad4) A B barriers (cm-1) τmin (rad) τmin (degree) (0,0)-(2,0) (2,0)-(4,0) (4,0)-(6,0) (6,0)-(8,0) (0,1)-(2,1) (0,2)-(2,2) (0,0)-(0,1) (0,1)-(0,2) (0,2)-(0,3) (0,3)-(0,4) (0,4)-(0,5) (0,5)-(0,6) (0,6)-(0,7) (2,0)-(2,1) (2,1)-(2,2) (2,2)-(2,3) (2,3)-(2,4) (4,0)-(4,1) (4,1)-(4,2) a
observed
calcd I 30.0 1.68 × 103 -6.18 × 103
165.6 164.7 164.0 163.4 164.4 163.4 104.3 103.4 102.5 101.7 101.0 100.3 99.8 103.1 102.4 101.8 101.3 102.8 102.0
8.10 -52.86 5672 1.35 77° 165.7 164.8 163.9 163.4
two-dimensionalb calcd II
calcd III
calcd IV
100.0 1.87 × 104 -2.06 × 104
29.9 6.4 × 103 -1.0 × 104 2.8 × 103 1.0 × 103 12.68 -35.10 3906 0.88 50° 166.7 164.8 163.2 162.4 166.6 166.6 104.1 103.9 103.8 103.7 103.5 103.4 103.2 104.0 103.9 103.8 103.6 104.0 103.9
84.3 3.7 × 104 -2.8 × 104 2.8 × 103 2.3 × 103 11.43 -43.23 5339 0.61 35° 166.0 164.6 163.4 163.1 165.6 165.2 104.3 104.2 104.1 104.0 103.8 103.7 103.6 103.9 103.8 103.6 103.5 103.5 103.4
8.10 -52.86 5672 0.74 42° 165.7 164.8 163.9 163.4
The one-dimensional potential function is given by V ) aτ4 + bτ2. b The two-dimensional potential function is given by V ) aτ4 + bτ2 + cθ2 + dτ2θ2.
9814 J. Phys. Chem. A, Vol. 110, No. 32, 2006
Yang et al.
Figure 14. Two-dimensional potential energy surface for the ringtwisting coordinate τ and the ring-bending coordinate θ of 1,4-benzodioxan in its S0 state.
was arbitrarily utilized to recalculate the dimensioned potential function and this was found to be
V(cm-1) ) (1.87 × 104)τ4 - (2.06 × 104)τ2
(6)
For this function, the twisting angles are (42°, which are much closer to the ab initio values of (30°. The experimental data in this case, therefore, do not do a particularly good job of determining the barrier because they only show the barrier to be very high. The experimental results can be stated to be 5000 ( 2000 cm-1 for the one-dimensional model. Prediction of the twisting angle is even worse. Again only the fact that there is a large twist angle can be ascertained.
Figure 15. Experimental and calculated energy levels for the onedimensional potential energy function of the ring-twisting vibration of 1,4-benzodioxan in its S1 state.
To account for some of the vibrational coupling involving the ring-twisting mode, a two-dimensional calculation with the out-of-plane ring-bending coordinate added, was also carried out. Figure 13 presents a graphical view, based on the ab initio calculations, of the relative energies of the twisted (T), bent (B), and planar (P) conformations. The molecule is trapped in its twisted structure where the twisting frequency is 166 cm-1 and the bending frequency is 104 cm-1. The molecule can undergo hindered pseudorotation and pass over a saddle point at 2722 cm-1 corresponding to a bent configuration. This is a lower energy pathway than that ascending over the planar structure at 4095 cm-1. Although the bent form is considerably lower in energy than the planar form, the data for the bending vibration, which extend to about 700 cm-1 above the ground state, are also not sufficient to yield a reliable experimental
TABLE 7: Observed and Calculated One-Dimensional and Two-Dimensional Transition Frequencies (cm-1) and the Corresponding Potential Energy Parameters for the 1,4-Benzodioxan S1(π,π*) Excited State one-dimensionala parameters µtwist a (cm-1/rad4) b (cm-1/rad2) c (cm-1/rad2) d (cm-1/rad4) A B barriers (cm-1) τmin (rad) τmin (degree) (0,0)-(2,0) (2,0)-(4,0) (4,0)-(6,0) (6,0)-(8,0) (0,1)-(2,1) (0,2)-(2,2) (0,0)-(0,1) (0,1)-(0,2) (0,2)-(0,3) (0,3)-(0,4) (0,4)-(0,5) (0,5)-(0,6) (2,0)-(2,1) (2,1)-(2,2) (4,0)-(4,1) (4,1)-(4,2) a
observed
calcd I 28.5 1.04 × 103 -4.17 × 103
139.6 138.7 137.8 136.9 138.7 137.7 79.8 79.5 79.3 79.2 79.1 79.0 78.9 78.5 79.5 76.4
7.15 -48.22 4158 1.41 81° 139.6 138.7 137.9 137.1
two-dimensionalb calcd II
calcd III
calcd IV
100.0 1.29 ×104 -1.46 × 104
28.3 4.4 × 103 -5.5 × 103 2.1 × 102 3.2 × 103 11.61 -24.51 1744 0.79 45° 139.5 138.9 137.8 136.9 138.4 137.3 80.3 79.9 79.4 79.0 78.6 78.2 79.2 78.7 77.7 77.3
72.0 2.6 × 104 -1.3 × 104 4.9 × 102 7.1 × 103 11.61 -24.51 1672 0.50 29° 140.3 138.7 137.2 136.4 139.2 138.0 80.5 79.9 79.4 78.9 78.4 78.0 79.3 78.8 78.0 77.5
7.15 -48.22 4158 0.75 43° 139.6 138.7 137.9 137.1
The one-dimensional potential function is given by V ) aτ4 + bτ2. b The two-dimensional potential function is given by V ) aτ4 + bτ2 + cθ2 + dτ2θ2.
1,4-Benzodioxan in Its S0 and S1(π,π*) States
J. Phys. Chem. A, Vol. 110, No. 32, 2006 9815
energy value for the bent structure. Therefore, the following two-dimensional form of the PES was utilized
V(τ, θ) ) aτ4 + bτ2 + cθ2 + dτ2θ2
(7)
where τ and θ are the ring-twisting and ring-bending coordinates defined in Figure 1. For this PES the a and b coefficients define the twisting energetics. The parameter c is the coefficient for the harmonic term for the bending because this motion is very nearly harmonic in the region of the twisting minima (T). The data do not allow for a determination of the energy of the bent saddle points (B). Finally, the parameter d represents the interaction between the two modes. The two modes also interact through the g45 kinetic energy cross term discussed earlier. The parameters that best fit the data are a ) 6.4 × 103 cm-1/rad4, b ) -1.0 × 104 cm-1/rad2, c ) 2.8 × 103 cm-1/rad2, and d ) 1.0 × 103 cm-1/rad4, and these correspond to a twisting barrier of 3906 cm-1, which is much closer to the ab initio value of 4095 cm-1. Here again, however, the energy minima depend on the reduced mass values. The computed two-dimensional value of 29.9 au for the twisting produces minima at (50°. A value of 84.3 au would be required to match the ab initio value of (30°. The calculated frequencies for the two-dimensional PES are shown in Table 6, and Figure 14 shows this surface. The frequency agreement is excellent because it does not depend on the reduced mass values. Because no quadratic term was used in the potential energy function for the bending angle θ, this surface cannot show the presence of a saddle point along the bending axis although it is almost certainly present. Potential Energy Surface for the S1(π,π*) Excited State Similar procedures were carried out for studying the S1(π,π*) excited state, and the data in Table 2 and Figure 11 were used. The one-dimensional potential energy function for the ringtwisting vibration in reduced coordinate is
V(cm-1) ) 7.15(z4 - 48.22z2)
(8)
This function has a barrier of 4158 cm-1 and is shown in Figure 15. Table 7 shows the agreement between observed and calculated transition frequencies, and this is nearly perfect. If the calculated reduced mass of 28.5 au is used to transfer to the dimensioned coordinate τ, then the potential energy function becomes
V(cm-1) ) (1.04 × 103)τ4 - (4.17 × 103)τ2
(9)
and this function has minima at (81°, which again is ridiculously high. As shown in Table 7, the arbitrary reduced mass of 100.0 au would produce twisting angles of (43°.
A two-dimensional calculation based on eq 7 was also carried out, and the parameters determined are a ) 4.4 × 103 cm-1/ rad4, b ) -5.5 × 103 cm-1/rad2, c ) 2.1 × 102 cm-1/rad2, and d ) 3.2 × 103 cm-1/rad4. For this case, the calculated barrier is 1744 cm-1 and the energy minima are at (45°. The limited experimental data along with the inaccuracy of ab initio calculations for the excited state, however, do not give much confidence in these results. Because the twisting frequencies decrease from the 166 cm-1 in the S0 ground state to 140 cm-1 in the S1 excited state, this does indicate that the excited-state barrier is lower. Moreover, the one-dimensional potential energy calculations, based on our experimental data which yield a drop of 5672 cm-1 to 4158 cm-1, strongly support this view. An educated guesstimate is that the S1 excited-state barrier is about 3600 ( 2000 cm-1 versus 5000 ( 2000 cm-1 for the S0 ground state. Acknowledgment. We thank the National Science Foundation (Grant CHE-0131935) and the Robert A. Welch Foundation (Grant A-0396) for financial assistance. We also thank Dr. Jaebum Choo for performing some complementary calculations. References and Notes (1) Laane, J. J. Phys. Chem. A 2000, 104, 7715. (2) Laane, J. Intl. ReV. Phys. Chem. 1999, 18, 301. (3) Sakurai, S.; Bondoc, E.; Laane, J.; Morris, K.; Meinander, N.; Choo, J. J. Am. Chem. Soc. 2000, 122, 2628. (4) Bondoc, E.; Sakurai, S.; Morris, K.; Chiang, W.-Y.; Laane, J. J. Chem. Phys. 2000, 112, 6700. (5) Arp, Z.; Meinander, N.; Choo, J.; Laane, J. J. Chem. Phys. 2002, 116, 6648. (6) Yang, J.; Wagner, M.; Okuyama, K.; Morris, K.; Arp, Z.; Choo, J.; Meinander, N.; Laane, J. J. Chem. Phys., submitted for publication, 2006. (7) Arp, Z.; Laane, J.; Sakamoto, A.; Tasumi, M. J. Phys. Chem. 2002, 106, 3479. (8) Autrey, D.; Arp, Z.; Choo, J.; Laane, J. J. Chem. Phys. 2003, 119, 2557. (9) Autrey, D.; Yang, J.; Laane, J. J. Mol. Struct. 2003, 661, 23. (10) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (11) Yang, J. Ph.D. Dissertation, Texas A&M University, 2006. (12) Yang, J.; Laane, J. J. Mol. Struct., in press, 2006. (13) Tecklenburg, M. M. J.; Laane, J. J. Am. Chem. Soc. 1989, 111, 6920. (14) Gordon, R. D.; Hollas, J. M. J. Mol. Spectrosc. 1994, 163, 159. (15) Laane, J. Appl. Spectrosc. 1970, 24, 73.
