Infrared and Raman Spectra, Theoretical Calculations, Conformations

Aug 18, 2014 - The infrared and Raman spectra of the bicyclic spiro molecule 2-cyclopenten-1-one ethylene ketal (CEK) have been recorded. Density func...
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Infrared and Raman Spectra, Theoretical Calculations, Conformations, and Two-Dimensional Potential Energy Surface of 2‑Cyclopenten-1-one Ethylene Ketal Hong-Li Sheu,† Niklas Meinander,‡ and Jaan Laane*,† †

Department of Chemistry, Texas A&M University, College Station, Texas 77843-3255 United States Department of Military Technology, Finnish National Defense University, P.O. Box 7, 00861 Helsinki, Finland

‡

S Supporting Information *

ABSTRACT: The infrared and Raman spectra of the bicyclic spiro molecule 2-cyclopenten-1-one ethylene ketal (CEK) have been recorded. Density functional theory (DFT) calculations were used to compute the theoretical spectra, and these agree well with the experimental spectra. The structures and conformational energies for the two pairs of conformational minima, which can be defined in terms of ring-bending (x) and ring-twisting (τ) vibrational coordinates, have also been calculated. Utilizing the results from ab initio MP2/cc-PVTZ computations, a twodimensional potential energy surface (PES) was calculated. The energy levels and wave functions for this PES were then calculated, and the characteristics of these were analyzed. At lower energies, all of the quantum states are doubly degenerate and correspond to either the lower-energy conformation L or to conformation H, which is 154 cm−1 higher in energy. At energies above the barrier to interconversion of 264 cm−1, the wave functions show that the quantum levels have significant probabilities for both conformations.

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INTRODUCTION We have been investigating the vibrational spectra, conformations, and potential energy surfaces (PESs) for several decades.1−3 Most recently, we reported the two-dimensional PES calculation for the two ring-puckering vibrations of 4-silaspiro-3,3-heptane (SSH).4 For this molecule, the two four-membered rings are identical, and each is puckered in its lowest-energy conformation. Therefore, the PES for SSH has four equivalent energy minima and gives rise to a most interesting pattern of four-fold degenerate quantum states. In the present study, we report our results for 2-cyclopenten-1-one ethylene ketal (CEK). We will present the experimental infrared and Raman spectra and compare these to the computed spectra using DFT calculations. We also report the calculated structures and conformational energies for its two low-energy conformations. We then present the calculated twodimensional PES in terms of its puckering and twisting coordinates along with the quantum energy states and wave functions that result from this PES. Unlike the case for SSH where all four energy minima have the same energy, CEK has two pairs of energy minimum at different energies. Therefore, its pattern of resulting quantum states is most instructive to analyze.

transform spectrometer equipped with a globar light source, a KBr beamsplitter, and a deuterium lanthanum triglycine sulfate (DLaTGS) detector for the mid-infrared region. For the farinfrared region, a Mylar beamsplitter and a mercury cadmium telluride (MCT) detector were used. Measurements were done with 1024 scans at 1.0 cm−1 resolution. The observed Raman spectra were collected using a Jobin-Yvon U-1000 spectrometer equipped with a frequency-doubled Nd:YAG Coherent Verdi-10 laser and a CCD detector. Laser excitation at 532 nm with a power of 1 W was utilized. The observed Raman spectra were obtained of the liquid sample in a quartz cuvette and measured in the 100−3400 cm−1 region at room temperature. The effective resolution was 0.7 cm−1. Parallel and perpendicular polarization measurements were made utilizing the standard accessory and scrambler. Due to the low vapor pressure of the sample, the vapor-phase far-infrared spectra of CEK could not be obtained.

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THEORETICAL CALCULATIONS The structure and vibrational frequencies of CEK were calculated using the Gaussian 09 program.5 Ab initio calculations were done at the second-order Møller−Plesset (MP2) level of theory with the cc-PVTZ basis set for structure

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Special Issue: 25th Austin Symposium on Molecular Structure and Dynamics

EXPERIMENTAL SECTION CEK (95% purity) was purchased from Sigma-Aldrich. It was purified by trap-to-trap transfer on a vacuum line. The observed infrared spectra were obtained using a Bruker Vertex 70 Fourier © 2014 American Chemical Society

Received: May 30, 2014 Revised: August 15, 2014 Published: August 18, 2014 1478

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Figure 1. Calculated structures for the two conformations of CEK. Structure L on the left is for the lower-energy conformation, and structure H is for the conformation that is calculated to be 154 cm−1 higher in energy. Only the skeletal atoms are shown (no hydrogen atoms).

optimization. The Becke and Lee−Yang−Parr exchange− correlation function (B3LYP)6,7 with the cc-PVTZ basis set was utilized for the calculation of vibrational frequencies. A scaling factor of 0.964 was used for frequencies above 2000 cm−1, 0.969 for the 1400−2000 cm−1 region and 0.985 for frequencies below 1400 cm−1 based on our previous work.4,8−14 The Meinander−Laane DA2OPTN4 program15 was used to calculate the ring-puckering energy levels and wave functions for the two-dimensional PES.

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RESULTS AND DISCUSSION Molecular Structure. Figure 1 shows the calculated structures for the two low-energy conformations of CEK. For structure L (at lower energy), the ring-puckering angle for the olefinic ring (ring A) was calculated to be 22.1°, and the twisting angle for the dioxo ring (ring B) was calculated to be 24.1°. Structure H (at higher energy) was calculated to be 154 cm−1 higher in energy with a puckering angle of 20.1° and a twisting angle of 26.2°. The direction of the twisting relative to the puckering of the second ring is different for the two conformations. The calculated bond distances and angles are also shown in Figure 1, and these can be seen to be very similar for both structures. Vibrational Spectra. Figure 2 shows the calculated and experimental infrared spectra for liquid CEK, and Figure 3

Figure 2. Observed infrared spectrum for liquid CEK compared to the calculated spectra for conformations L and H. 1479

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Figure 3. Observed Raman spectrum for liquid CEK compared to the calculated spectra for conformations L and H.

compares the Raman spectrum of the liquid to the calculated spectrum. The calculated spectra are shown for both structure L and structure H. The experimental spectra result from the mixed sample, which, based on the calculated conformational energy difference between the two structures, is expected to be about 68% L and 32% H at 25 °C. Table 1 compares the observed vibrational frequencies and intensities to those calculated. For frequencies above 250 cm−1, the agreement between the observed and calculated values can be seen to be very good, and the calculated spectra for structures L and H can be seen to be very similar. The CEK molecule has four vibrational frequencies below 300 cm−1. These are the out-of-plane ring-bending (ringpuckering) and the twisting about the CC bond of ring A and the ring-bending and twisting of ring B with the two oxygen atoms. The two conformational minima of the molecule are achieved by optimizing the extent of ring-bending in ring A and the degree of twisting in B. The other two low-frequency vibrations do not play a significant role in establishing the conformations of the molecule. Hence, we placed our focus on the calculation of the conformational energies of the molecule as a function of the bending of A (x) and the twisting of B (τ). In the following section, we will discuss our results for the calculation of the two-dimensional PES in terms of x and τ for CEK. Vibrational PES. For CEK, we define the out-of-plane ringbending motion x in ring A (the one with the double bond) as the distance that carbon atom 4 is out of the plane of the other four carbon atoms. We choose this definition due to the complexity of this molecule. In previous work,1−3 we have defined the ring-puckering coordinate as half of the distance between the two ring diagonals, but the choice of that coordinate here would be very cumbersome. Nonetheless, our coordinate here can be related to this traditional puckering coordinate by the geometrical relationships presented elsewhere.8−10 The twisting coordinate τ for ring B (the one with two oxygen atoms) is defined as the angle between the O−C− O plane and the C−C bond. This is the same definition utilized in our previous work.16−18

Figure 4. Vibrational PES for CEK in terms of its ring-bending x and ring-twisting τ coordinates. The conformational energies (cm−1) are shown for the minima and for barriers to interconversion.

Utilizing the ab initio calculations, we computed the conformational energy in cm−1 for CEK as a function of x (Å) and τ (radians) for the energy minima, for the central barrier at x = τ = 0, and for the barriers where either x or τ was fixed at its minimum-energy value. In addition, several additional conformational energy values were calculated for additional values of x and τ. The data were then used to calculate a PES that closely fits all of these data points. This PES was found to be V (x , τ ) = 9970.9x 4 − 2650.6x 2 + 33385.3τ 4 − 12829.0τ 2 − 183.2x 2τ 2 − 2008.2xτ + 277.0x 3τ + 7585.0xτ 3 + 1494

(1)

This is shown in Figure 4. As can be seen, there are two pairs of energy minima for structure L at the two lowest energies and structure H at the two energies 154 cm−1 higher. The puckering barrier when the twisting τ is at its minimum value is 264 cm−1, and the twisting barrier when the bending x is at its minimum value is 1318 cm−1. When x and τ are both zero, the central barrier is 1494 cm−1. We have calculated the ring-puckering and ring-twisting energy levels for this surface, and these results will be discussed in some detail. In order to calculate the energy levels for the PES in eq 1, it is necessary to have the reduced mass values corresponding to x and τ. Because of the complexity of the molecule, these were 1480

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Table 1. Observed and Calculated Vibrational Spectra (cm−1) of CEK calculateda

observed ν

approximate description

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

CH sym. stretch (A) CH antisym. stretch (A) CH2 antisym. stretch (A) CH2 antisym. stretch (B) CH2 antisym. stretch (B) CH2 antisym. stretch (A) CH2 sym. stretch (A) CH2 sym. stretch (A) CH2 sym. stretch (B) CH2 sym. stretch (B) CC stretch (A) CH2 deformation (B) CH2 deformation (B) CH2 deformation (A) CH2 deformation (A) C−H in-plane wag (A) CH2 wag (B) CH2 wag (B) CH2 wag (A) CH2 wag (A) CH2 twist (A/B) CH2 twist (A/B) CH2 twist (B) ring stretch (A) CH2 twist (A) ring stretch (A) ring stretch (A) C−H in-plane wag (A) ring stretch (B) ring stretch (B) ring stretch (B) ring stretch (A) C−H out-of-plane wag (A) CH2 rock (A) CH2 rock (B) CH2 rock (B) CH2 rock (A) C−H out-of-plane wag (A) ring stretch (A/B) ring stretch (A/B) ring angle bend (B) ring angle bend (A) ring angle bend (B) skeletal twist skeletal twist ring angle bend (A) skeletal twist ring twisting (A) ring twisting (B) ring puckering (A) ring bending (B)

infrared

b

Raman

c

3059 m

3065 (46)

2980 s 2948 ms

2980 (43) 2944 (67) 2938 (67)

2883 s 1619 m

2884 (70) 1616 (86)

1477 m 1452 m 1430 m 1364 s

1474 (15) 1450 (23) 1428 (18) 1362 (7)

1302 m 1264 m

1298 (6) 1262 (1)

1210 ms

1211 (10)

1154 s 1080 s

1078 (25)

1048 s 1027 s 979 ms

1023 (23) 977 (5)

947 s

946 (57)

909 s

916 (60)

786 s 758 m

821 (15) 790 (15) 758 (19)

650 w 496 m 468 m 436 m 328 w 267 w

691 (1) 650 (2) 496 (8) 465 (6) 432 (100) 330 (3) 263 (4)

lower well

upper well

3091 (9, 71) 3061 (11, 59) 3004 (13, 28) 2986 (28, 60) 2980 (35, 80) 2959 (16, 60) 2938 (17, 52) 2914 (30, 84) 2893 (68, 19) 2882 (42, 100) 1631 (6, 100) 1475 (0.2, 15) 1468 (2, 38) 1451 (6, 41) 1427 (2, 32) 1370 (47, 13) 1359 (2, 8) 1347 (2, 3) 1309 (2, 10) 1272 (12, 6) 1238 (4, 10) 1230 (23, 14) 1211 (4, 22) 1184 (89, 21) 1168 (17, 5) 1149 (86, 3) 1130 (24, 1) 1087 (100, 31) 1057 (19, 1) 1042 (23, 2) 1028 (29, 36) 972 (4, 2) 966 (6, 6) 938 (12, 25) 919 (20, 10) 906 (16, 17) 887 (8, 9) 828 (8, 11) 784 (23, 13) 755 (3, 8) 737 (9, 5) 695 (1, 3) 640 (2, 6) 492 (11, 7) 450 (6, 1) 427 (1, 19) 333 (1, 1) 266 (1, 3) 201 (0.2, 3) 76 (1, 2) 48 (5, 1)

3093 (8, 76) 3066 (9, 59) 3016 (14, 35) 3014 (22, 70) 2986 (31, 68) 2971 (22, 79) 2960 (9, 42) 2929 (18, 100) 2928 (59, 53) 2903 (36, 64) 1591 (7, 18) 1474 (0.1, 3) 1464 (2, 6) 1448 (6, 6) 1430 (2, 8) 1371 (44, 2) 1355(2, 2) 1346 (2, 1) 1310 (3, 2) 1282 (4, 1) 1241 (17, 2) 1236 (25, 2) 1209 (2, 2) 1207 (45, 6) 1172 (4, 2) 1138 (100, 1) 1134 (4, 1) 1083 (83, 6) 1062 (18, 0.3) 1045 (23, 1) 1026 (23, 6) 977 (4, 1) 959 (6, 1) 945 (13, 4) 918 (7, 4) 910 (31, 2) 889 (3, 1) 849 (4, 2) 793 (8, 20) 759 (8, 1) 748 (13, 1) 680 (1, 1) 641 (2, 1) 508 (8, 2) 454 (7, 0.2) 432 (2, 3) 323 (2, 0.4) 285 (1, 0.4) 196 (0.3, 1) 94 (0.4, 1) 52 (4, 0.1)

a

Relative infrared and Raman intensities are given in parentheses (IR, Raman); vibrational frequencies were calculated using the B3LYP level of theory; the scaling factor used was 0.964 for frequencies above 2000 cm−1, 0.969 for the 1400−2000 cm−1 region and 0.985 for frequencies below 1400 cm−1. bAbbreviations: s, strong; m, medium; w, weak. cRelative Raman intensities are given in parentheses.

not calculated rigorously but were calculated so that the fundamental bending and twisting frequencies would match those obtained from the DFT calculation. This procedure was found to work well in previous studies.4,19−23

The lowest quantum states correspond to either structure L at the lowest energy or to structure H at the higher energy. They can be labeled according to (νB,νT), indicating how many quanta of bending or twisting are excited. We have also labeled 1481

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Figure 5. Quantum states (νB,νT) for the ring-bending (B) and ring-twisting (T) vibrations of CEK. Each quantum state is also labeled sequentially in terms of increasing energy so that the lowest level (0,0) is also labeled as 0, level (1,0) is labeled as 1, and so on. Note that each level is actually doubly degenerate.

Figure 7. Ring-twisting potential energy function in terms of τ and energy levels calculated for x at its minimum-energy value. The ringtwisting energy levels are also shown for νB = 0. Figure 6. Ring-bending potential energy function in terms of x and energy levels calculated for τ fixed at its minimum-energy value. The ring-bending energy levels are also shown for νT = 0.

we show the L levels on the left side of the figure separated from those in the higher well on the right side of the figure. Levels for νB ≥ 8 are shown in the center because these have nearly equal probabilities for either L or H. To understand the origin of these quantum states, it is helpful to also simultaneously examine Figure 6, which shows the potential energy curve and energy levels for the ring-bending coordinate when the ring-twisting coordinate τ is at its minimum-energy value. Similarly, Figure 7 shows the potential energy curve

them sequentially beginning with 0 for the lowest-energy state (0,0). Figure 5 shows the quantum states calculated for the PES of eq 1 and Figure 4. The lowest quantum states are almost totally localized in either the lower potential energy well for structure L or in the higher well for structure H. Consequently, 1482

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Figure 8. Wave functions calculated for selected quantum states for the PES of eq 1. Each energy level shown in Figures 5−7 is doubly degenerate; therefore, there are two wave functions A and B for each level. Levels 0, 1, 2, and 4 are almost totally confined to conformation L, while 3 is almost totally in conformation H. Higher levels show probabilities for both conformations. The energy level values in cm−1 do not include zero-point energies. Additional wave functions can be found in the Supporting Information.

Figure 7 is 103 cm−1. Figure 6 shows why levels (0,0), (1,0), (2,0), and (4, 0) are almost totally isolated in well L while (3,0) and (5,0) are isolated in the higher well H. Levels (νB,0) for νB = 6−8 tend to favor one well or the other but begin to show significant probability in the second well also. By νB ≥ 8, the wave functions show substantial probability for both wells.

along the ring-twisting coordinate when the bending x is at its minimum-energy value. For the one-dimensional functions in these figures, the energy levels have been adjusted so that they do not include the zero-point energy of the other vibration. Thus, for Figure 6, only the bending zero-point energy of 38 cm−1 is included, while the zero-point energy for the twisting in 1483

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wave functions. This material is available free of charge via the Internet at http://pubs.acs.org.

Figure 8 shows a selection of wave functions corresponding to several of the quantum states, and these support the description given above. In the figure, the levels are identified by their sequence number, and the symmetric and antisymmetric components are labeled as A and B, respectively. The energy level values are given relative to the lowest state at 0.0 cm−1 with the zero-point energy excluded. We show both the A and B components for levels 0−3, but for higher levels, only the A component is shown. In the Supporting Information, we show all of the wave functions through level 34 (2 × 35 = 70 functions). The Supporting Information also contains the calculated energy values for all of these levels. In Figure 8, levels 0, 1, 2, and 4 can be seen to correspond to conformation L. Levels 1 and 2 are excited states of the bending, as confirmed by the fact that the functions change sign along the x direction. Similarly, level 4 changes sign along τ and thus corresponds to the excited state of the twisting as level (0,1), Level 3 is the lowest-energy state for conformation H, and this is clearly shown in the figure. Levels 5 and 6 are mostly constrained to conformations L and H, respectively, but both begin to show probabilities for the other potential energy well. Levels 9 and 12 are the (1,1) and (2,1) states with both the bending and twisting motions being excited, and this is evident as their wave functions show directionality along both x and τ. Level 10 (or 8,0) lies above the puckering barrier to interconversion and shows almost equal probability for structures L and H. In other words, the molecule is essentially puckering freely between L and H while passing through the planar structure of ring A. Level 13 corresponds to H and has directionality along τ, indicating that it is the first excited twisting state for this structure. The wave functions for several other states are also shown, and these confirm the assignments that we have given in Figure 5. Figure 5 shows that for each of the twisting excited states with νT ≥ 1, the sequence of puckering levels is fairly similar, as expected, although the energy separations differ more between the lower and higher wells. For example, in the higher well, the lowest puckering transition is about 59 versus 76 cm−1 for the lower well. As Figure 7 shows, because of the high twisting barrier, the lowest eight twisting quantum states are highly localized in one well or the other. Because the ground state of the higher well is labeled as (3,0), each of the twisting levels in Figure 8 is labeled as (3,νT), indicating no additional excitation of the ring-bending.

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Corresponding Author

*E-mail: [email protected]. Phone: 979-845-3352. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This paper is dedicated to the memory of Jim Boggs, a colleague and a friend for more than 40 years. The authors wish to thank the Robert A. Welch Foundation (Grant A-0396) for financial support. Calculations were carried out on the Texas A&M Department of Chemistry Medusa computer system funded by the National Science Foundation, Grant No. CHE0541587.

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REFERENCES

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CONCLUSION We have calculated the two-dimensional PES of CEK in terms of the two low-frequency, large-amplitude vibrations that govern the conformational energies of this molecule. The PES has two pairs of energy minima that are at two different energies, and this creates a most interesting case for the study of its quantum state patterns. Figures 5−7 elucidate what the characteristics of these energy levels are, and Figure 8 displays the rather fascinating wave functions. Although the PES for CEK was generated from ab initio computations and is only approximate, the energy level patterns and wave functions calculated should provide a fairly accurate description for this molecule.

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AUTHOR INFORMATION

ASSOCIATED CONTENT

S Supporting Information *

A table with the listing of all of the energy levels for the PES of CEK. Also included is a figure showing all of the calculated 1484

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Prediagonalized Harmonic Basis and the Distributed Guassian Basis. J. Mol. Struct. 2001, 569, 1−24. (16) Laane, J.; Harthcock, M. A.; Killough, P. M.; Bauman, L. E.; Cooke, J. M. Vector Representation of Large Amplitude Vibrations for the Determination of Kinetic Energy Functions. J. Mol. Spectrosc. 1982, 91, 286−299. (17) Harthcock, M. A.; Laane, J. Calculation of Kinetic Energy Terms for the Vibrational Hamiltonian: Application to Large Amplitude Vibrations Using One-, Two-, and Three-Dimensional Models. J. Mol. Spectrosc. 1982, 91, 300−324. (18) Schmude, R. W.; Harthcock, M. A.; Kelly, M. B.; Laane, J. Calculation of Kinetic Energy Functions for the Ring-Puckering of Asymmetric Five-Membered Rings. J. Mol. Spectrosc. 1987, 124, 369− 378. (19) Chun, H. J.; Laane, J. Theoretical Calculations, Far-Infrared Spectra and the Potential Energy Surfaces of Four Cyclic Silanes. Chem. Phys. 2014, 431−432, 15−19. (20) Chun, H. J.; Colegrove, L. F.; Laane, J. Vibrational Spectra, Theoretical Calculations, and Structures for 1,3-Disilacyclopent-4-ene and 1,3-Disilacyclopentane and Their Tetrachloro Derivatives. J. Mol. Struct. 2013, 1049, 172−176. (21) Grubbs, G. S., II; Novick, S. E.; Pringle, W. C., Jr.; Laane, J.; Ocola, E. J.; Cooke, S. A. A Bis-trifluoromethyl Effect: Doubled Transitions in the Rotational Spectra of Hexafluoroisobutene, (CF3)2CCH2. J. Phys. Chem. A 2012, 116, 8169−8175. (22) McCann, K.; Wagner, M.; Guerra, A.; Coronado, P.; Villareal, J. R.; Choo, J.; Kim, S.; Laane, J. Spectroscopic Investigations and Potential Energy Surfaces of the Ground and Excited Electronic States of 1,3-Benzodioxan. J. Chem. Phys. 2009, 131, 044302/1−044302/9. (23) Al-Saadi, A. A.; Laane, J. Vibrational Spectra, Ab Initio Calculations, and Ring-Puckering Potential Energy Function for γCrotonolactone. J. Phys. Chem. A 2007, 111, 3302−3305.

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