Vibrational Spectra, Theoretical Calculations, and Two-Dimensional

Dec 16, 2014 - Department of Military Technology, Finnish National Defence University, P.O. Box 7, 00861 Helsinki, Finland. §. Department of Chemistr...
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Vibrational Spectra, Theoretical Calculations, and Two-Dimensional Potential Energy Surface for the Ring-Puckering Vibrations of 2,4,7Trioxa[3.3.0]octane Hye Jin Chun,† Niklas Meinander,‡ John R. Villarreal,§ and Jaan Laane*,† †

Department of Chemistry, Texas A&M University, College Station, Texas 77843-3255, United States Department of Military Technology, Finnish National Defence University, P.O. Box 7, 00861 Helsinki, Finland § Department of Chemistry, University of Texas-Pan American, Edinburg, Texas 78539, United States ‡

S Supporting Information *

ABSTRACT: 2,4,7-Trioxa[3.3.0]octane (247TOO) is an unusual bicyclic molecule which can exist in four different conformational forms which are determined by the directions of the two ring- puckering motions. The vibrational assignments of 247TOO have been made based on its infrared and Raman spectra and theoretical density functional theory (DFT) calculations. The two ring-puckering motions (in-phase and out-of-phase) were observed in the Raman spectra of the liquid at 249 and 205 cm−1 and these values correspond well to the DFT values of 247 and 198 cm−1. Ab initio calculations were utilized to calculate the structures and conformational energies for the four energy minima and the barriers to interconversion and the data was utilized to generate a two-dimensional potential energy surface (PES) for the two ring-puckering motions. The resulting quantum state energies for this PES were then calculated in order to better understand the patterns that are produced when the PES has four energy minima at different energy values. The wave functions corresponding to the different quantum states were also calculated. The NMR spectrum of 247TOO showed the presence of the two lowest energy conformations, consistent with the results of the ab initio calculations.

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INTRODUCTION For a number of decades we have been reporting both experimental and theoretical investigations of vibrational potential energy surfaces (PESs) for large-amplitude motions.1−3 Earlier reviews from other laboratories have also been published.4−8 Specific references to previous work from our laboratory and others can be found in these reviews. Relatively little work has been published on vibrational PESs outside our laboratory in recent years, although a number of papers have appeared on the study of internal rotations.9−15 Several of our recent studies have focused on determining two-dimensional PESs for bicyclic molecules in order to better understand how the two rings interact. We are aware of only one report of a twodimensional PES from another laboratory.16 In 2004 we presented our study of bicyclo[3.3.0]oct-1,5-ene17 (BCO) and showed that its PES could be represented by a function of the form V = a(x14 + x 2 4) + b(x12 + x 2 2) + cx12x 2 2 + dx1x 2

quantum states, wave functions, and predicted spectra were reported. For SSH, the PES has the form of eq 1 but does not require the x1x2 term. We recently also calculated the PES for two out-of-plane ring vibrations of 2-cyclopenten-1-one ethylene ketal19 (CEK) and analyzed its energy levels and wave functions. The two-dimensional PES for CEK has two pairs of energy minima at two different conformational energies. In the present study, we present our results for 2,4,7-trioxa[3.3.0]octane (247TOO). The infrared and Raman spectra were recorded and compared to predicted spectra from density functional theory (DFT) calculations. Ab initio calculations were used to calculate the structures and energies of the four conformational minima and the energy barriers between these conformations. A PES in terms of the two ring-puckering coordinates was then calculated, and the corresponding energy levels and wave functions were determined. This molecule is of particular interest since the anomeric effect is expected to cause puckering of the ring with two oxygen atoms (we label this the β ring) and torsional forces are expected to pucker the ring with the single oxygen (the α ring).

(1)

where x1 and x2 are the ring-puckering coordinates of the two rings and a, b, c, and d are potential energy parameters that are determined so that they best fit the two different conformational energies and energy barriers found from ab initio calculations. The complex nature of the ring-puckering quantum states and the resulting spectra were analyzed in detail. More recently, we reported the two-dimensional PES for the two ring-puckering vibrations of 4-silaspiro[3.3]heptane (SSH).18 The calculated © 2014 American Chemical Society

Received: November 12, 2014 Revised: December 15, 2014 Published: December 16, 2014 410

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The Journal of Physical Chemistry A

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EXPERIMENTAL SECTION Synthesis of 2,4,7-Trioxa[3.3.0]octane. 247TOO was prepared at the University of Texas-Pan American through a ring-closure condensation reaction of anhydroerythritol and paraformaldehyde. At the time of the synthesis, there was no mention in the chemical literature of this compound having been prepared. In a 500 mL three-neck flask, 0.25 mol of anhydroerythritol (Aldrich) was dissolved in 150 mL of dry benzene. The flask was charged with 15 g of paraformaldehyde, and a Dean−Stark trap was used to remove water over a 4 h period. The reaction contents were mixed in a separatory funnel with three successive 150 mL portions of 5% Na2CO3 and then with 150 mL portions of saturated NaCl and water. After overnight drying over anhydrous MgSO4, the mixture was concentrated via a 10 in. Vigreux column and distilled under vacuum (bp 105°−115°). The 247TOO was characterized by 13 C and 1H NMR spectrometry recorded on a JEOL Eclipse 300 MHz FT-NMR spectrometer. Infrared and Raman Spectra. Raman spectra were recorded with the right-angle scattering geometry using a Jobin Yvon U-1000 monochromator equipped with 1800 groove mm−1 holographic grating and CCD detection. The resolution was 0.7 cm−1. A Coherent Verdi-V10 laser operating at 532 nm was used and typically operated at a power of 6 W for vaporphase samples and 0.5 W for liquid-phase samples. For the vapor sample, a homemade single-pass gas cell20,21 was used to contain 247TOO at 300 Torr, achieved by heating the liquid sample to 200 °C. Spectra of the liquid were obtained from the sample contained in a quartz cuvette. The liquid-state mid-infrared spectrum of 247TOO was recorded on a Bruker Vertex 70 FT spectrometer equipped with a globar light source, a KBr beamsplitter, and a deuterated lanthanum triglycine sulfate (DLaTGS) detector.

Figure 1. Geometrical parameters and structure of 247TOO in its lowest-energy conformation.

Figure 2. Conformational minima and relative conformational energies (in cm−1) of 247TOO.

structure to another, and these are shown in Table 1. The puckering of the α ring results from the torsional strain between the CH2 group and the H−C−O grouping on the bridgehead carbon atom. This can be seen in Figure 3 which shows that eclipsing would result if this ring were planar. The puckering of the β ring is caused by the anomeric effect due to the O−C−O bonding configuration. We have observed this previously and discussed it in some detail in our studies of 1,3-dioxole24 and 1,3benzodioxole.25 While the puckering of each ring is readily understood, the quantitative reasons for the conformational energy differences among structures A, B, C, and D are less clear. Nuclear Magnetic Resonance Spectra. The 13C NMR spectrum shows three types of carbon atoms with chemical shifts at 96, 80, and 73 ppm. The 1H NMR spectrum shows five signals: 5.0 ppm (1 proton), 4.8 ppm (1 proton), 4.7 ppm (2 protons), 4.1 (2 protons), and 3.4 ppm (2 protons). The data support a bicyclic ring system in which the two protons of each of the methylene groups are not equivalent because of the conformations of the two rings and of the bicyclic system in general. The chemical shifts of the methylene groups and the bridgehead hydrogen atoms are consistent with those in the literature for similar groups (1,3-dioxolane, tetrahydrofuran, and 9oxabicyclo[6.1.0]nonane). Significantly, each of the NMR peaks shows up as a closely spaced doublet, indicating that two different conformers have significant abundance in the liquid at room temperature. These clearly arise from conformers A and B, which are calculated to be 181 cm−1 apart in conformational energy. Conformations C and D, which are calculated to be 745 and 1148 cm−1 higher in energy, were not observed in the NMR spectra. Vibrational Spectra. Figure 4 shows the infrared spectrum of liquid 247TOO and compares it to the calculated spectra of the four conformers. Figure 5 compares the observed Raman spectra of the vapor and liquid to the calculated spectra. As can be seen, the observed spectra agree quite well with that of structure A, which is the predominant one in the sample and calculated to be 181 cm−1 lower in energy than conformer B. This molecule has Cs symmetry with the plane of symmetry passing through the

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THEORETICAL CALCULATIONS To calculate the infrared and Raman spectra, DFT computations were carried out using the Gaussian 09 package22 with the B3LYP functional and the cc-pVTZ basis set. Scaling factors of 0.985 for frequencies below 2000 cm−1 and 0.961 for the higher frequencies were used. Ab initio computations with the MP2/ccpVTZ method were used to calculate the conformational structures and potential energy surface. The Meinander−Laane DA2OPTN4 program23 was used to calculate the ring-puckering energy levels and wave functions.

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RESULTS AND DISCUSSION Structure. Figure 1 shows the calculated structure and geometrical parameters of 247TOO in its lowest-energy conformation, which we label as structure A. Both rings are puckered up, and the dihedral angles of puckering are 41.9° for the α ring with the single oxygen and 36.0° for the β ring with two oxygens. The molecule also has three additional conformational energy minima resulting from whether the two rings pucker up or down relative to each other, and we label these as structures B, C, and D in order of increasing energy. Figure 2 shows all four conformations along with their calculated relative energies and puckering angles. The bond distances and angles other than the directions of the two puckering angles differ little from one 411

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The Journal of Physical Chemistry A Table 1. Bond Distances (in Å) and Angles (in deg) Calculated for the Four Conformations of 247TOO parameter

A

C−C C−O C−H (CH2) ∠CCO ∠COC ∠CCC ∠HCH puckering angle bridge C−C C−H (CH)

1.524 1.423 1.086/1.097 105.6 103.9 103.0 109.8 +41.9 1.554 1.086

C−O O−CH2 C−H (CH2) ∠CCO ∠COC ∠OCO ∠HCH puckering angle conformational energy (cm−1)

1.421 1.411 1.086/1.094 104.3 105.8 106.3 111.5 +36.0 0

B α Ring 1.519 1.420 1.086/1.067 105.5 104.4 103.2 109.9 +41.5 1.550 1.091 β Ring 1.423 1.406 1.086/1.098 104.2 105.0 106.4 111.2 −38.4 189

Figure 3. Eclipsing of the CH2 and H−C−O groups when the α ring is planar. The eclipsing interaction is enclosed in the circle.

D

1.527 1.422 1.085/1.095 105.0 105.0 103.2 109.9 −40.7 1.550 1.090

1.532 1.422 1.092/1.096 105.5 105.0 103.3 109.2 −41.1 1.550 1.085

1.423 1.410 1.086/1.098 104.7 104.7 106.5 111.1 +38.7 797

1.421 1.410 1.085/1.097 104.5 104.6 106.6 110.8 −39.1 1130

Figure 5. Observed Raman spectra of 247TOO and calculated Raman spectra of its four conformations.

where the A1 and B2 modes are in actuality the A′ modes and the A 2 and B 2 modes are the A″ modes. Utilizing the C 2v approximation, however, allows us to distinguish the A1 and B1 in-plane ring modes from the A2 and B2 out-of-plane modes. Table 2 presents a listing of the observed infrared and Raman bands according to C2v symmetry and compares these to the calculated frequencies and intensities for all of the conformations of the molecule. The Raman bands in the vapor spectrum are sharp and readily observed for the A1 modes but are broad with small peak heights for the nontotally symmetric modes. Our primary interests are the low-frequency modes of 247TOO. The vibration of lowest frequency is the skeletal twisting motion in which the two rings twist in opposite directions. This is calculated to be at 92 cm−1. The next two lowest-frequency vibrations are the ring-puckering motions, calculated to be at 198 and 247 cm−1 for a vapor sample. Although we did not observe these in the vapor spectrum, they appear in the liquid spectrum at 205 and 249 cm−1. The lower frequency results from the two rings puckering in phase (we label this υ+) while the higher frequency (υ−) has the β and α rings puckering in opposite directions. We will focus on the potential energy surface governing these vibrations since they determine the conformation of the molecule.

Figure 4. Observed infrared spectrum of 247TOO and calculated infrared spectra of its four conformations.

oxygen atom of the α ring and the CH2 group of the β ring. With Cs symmetry, the molecule has 23 A′ and 19 A″ modes. Visualizing and assigning the vibrations are facilitated if we assume that the molecule takes on a totally planar skeletal structure and has C2v symmetry. The vibrations are then distributed as Γ = 14A1 + 7A 2 + 12B1 + 9B2

C

(2) 412

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The Journal of Physical Chemistry A Table 2. Observed and Calculated Infrared and Raman Spectra of 247TOO calculatedd

2,4,7-trioxa[3.3.0]octane symmetry

descriptiona

A1 (A′)

CH sym. str. CH2 sym. str. (β) CH2 sym. str. (i.p.) (α) CH2 def. (β) CH2 def. (i.p.) (α) CH2 wag (i.p.) (α) CH wag (i.p.) ring str. (i.p.) ring str. (i.p.) ring str. (i.p.) ring str. (i.p.) ring str. (i.p.) ring bending ring bending CH2 antisym. str. (o.p.) (α) CH wag (o.p.) CH2 twist (β) CH2 twist (o.p.) (α) CH2 rock (o.p.) (α) ring twist ring twist CH2 sym. str. (o.p.) (α) CH antisym. str. CH2 def. (o.p.) (α) CH2 wag (β) CH2 wag (o.p.) (α) CH wag (o.p.) ring str. (o.p.) ring str. (o.p.) ring str. (o.p.) ring bending ring str. (o.p.) skeletal bend CH2 antisym. str. (β) CH2 antisym. str. (i.p.) (α) CH wag (i.p.) CH2 twist (i.p.) (α) CH2 rock (β) CH2 rock (i.p.) (α) ring flap ring puckering (o.p.) ring puckering (i.p.)

A2 (A″)

B1 (A″)

B2 (A′)

infrared (liquid)b

Raman (vapor)c

Raman (liquid)c

A

B

C

D

2977 (m, br) 2858 (s, br) 2858 (s, br)

2983 (51) 2877 (16) 2850 (51)

2986 (41, br) 2861 (29, br) 2861 (9, br)

2978 (41, 1101) 2866 (74, 505) 2850 (92, 1260)

2926 (98, 1129) 2821 (100, 882) 2852 (84, 1198)

2975 (8, 889) 2833 (45, 428) 2873 (54, 1577)

3003 (36, 768) 2896 (62, 931) 2958 (20, 1278)

1505 (9) 1462 (12) 1368 (3) 1225 (10) 1060 (12) 1015 (22) 922 (37) 873 (2) 827 (100) 727 (9) 719 (5) 2986 (41, br)

1523 (1, 42) 1481 (5, 35) 1373 (0.2, 12) 1216 (4, 10) 1060 (59, 32) 1002 (6, 39) 926 (27, 38) 874 (7, 7) 814 (13, 100) 722 (0.2, 11) 715 (28, 8) 2991 (18, 376)

1519 (2, 60) 1479 (6, 41) 1379 (1, 11) 1228 (1, 14) 1076 (100, 20) 1010 (16, 41) 928 (22, 45) 888 (11, 9) 816 (16, 100) 747 (15, 21) 701 (16, 12) 2993 (19, 423)

1523 (2, 45) 1495 (3, 68) 1369 (0.2, 20) 1233 (2, 18) 1083 (100, 28) 1021 (5, 51) 956 (27, 34) 824 (10, 100) 926 (8, 31) 728 (1, 20) 609 (2, 30) 2986 (27, 875)

1518 (1, 66) 1495 (3, 43) 1374 (0, 17) 1239 (1, 20) 1089 (100, 26) 976 (4, 32) 926 (12, 26) 821 (8, 100) 966 (7, 23) 732 (0.3, 7) 604 (4, 27) 3059 (18, 630)

1225 (10) 1201 (8)

1343 (1, 7) 1214 (0.1, 33) 1202 (2, 17)

1347 (0, 7) 1220 (2, 41) 1205 (2, 32)

1352 (0.1, 9) 1216 (1, 27) 1202 (7, 39)

1359 (1, 0) 1219 (0.1, 38) 1206 (6, 30)

983 (1)

983 (1, 4)

1067 (19, 5)

1115 (5, 1)

1077 (21, 1)

375 (3)

391 (1, 2) 92 (1, 2) 2993 (6, 671)

366 (2, 3) 98 (1, 2) 2995 (6, 734)

395 (3, 4) 87 (0.1, 5) 2993 (29, 1919)

380 (0.2, 5) 35 (1, 2) 3062 (13, 1025)

2911 (23, 349) 1467 (1, 53) 1404 (6, 31) 1329 (1, 12) 1292 (0, 14) 1104 (84, 3) 1018 (24, 2) 963 (69, 4) 830 (1, 0.2) 850 (16, 5) 587 (1, 21) 2980 (32, 830)

2968 (0.1, 269) 1486 (0.3, 57) 1400 (3, 25) 1307 (0.1, 24) 1280 (1, 29) 1083 (48, 7) 1033 (14, 6) 947 (41, 10) 728 (0, 5) 898 (33, 11) 577 (3, 17) 2979 (32, 770)

2987 (3, 287) 1485 (0.1, 50) 1402 (2, 37) 1315 (0, 24) 1291 (0, 5) 1111 (16, 5) 1025 (4, 2) 927 (57, 7) 912 (5, 13) 712 (2, 3) 588 (1, 15) 3055 (18, 807)

1504 (vvw) 1504 (vvw) 1396 (vw) 1226 (vw) 1060 (s) 1016 (m) 922 (ms) 874 (vw) 827 (ms) 719 (ms) 2977 (m, br)

1365 (2) 1063 (4) 1015 (5) 933 (13) 827 (100) 748 (5) 718 (6) 2996 (40)

1226 (vw) 1200 (vw)

2977 (m, br)

2996 (40)

2986 (41, br)

2977 (m, br) 1462 (w) 1396 (vw) 1324 (vw) 1264 (w) 1099 (vs) 1076 (s) 963 (vs) 874 (vw)

2983 (51)

2986 (41, br) 1450 (11) 1396 (5) 1322 (7) 1266 (10) 1099 (6) 1075 (7) 963 (2) 873 (2)

574 (w) 2977 (m, br)

2983 (44)

575 (11) 2986 (41, br)

2966 (12, 302) 1470 (1, 51) 1407 (6, 15) 1325 (2, 18) 1272 (0.1, 25) 1107 (56, 3) 1075 (24, 4) 956 (100, 6) 876 (6, 5) 810 (8, 0.3) 572 (4, 16) 2967 (50, 774)

2858 (s, br)

2850 (51)

2861 (29, br)

2845 (35, 207)

2847 (36, 214)

2868 (25, 160)

2954 (20, 112)

1266 (10) 1168 (1) 1099 (6) 406 (5) 249 (2)

1334 (3, 19) 1265 (12, 30) 1165 (61, 3) 1112 (80, 12) 415 (8, 4) 247 (5, 6)

1330 (8, 28) 1266 (11, 30) 1167 (66, 4) 1102 (72, 13) 393 (5, 8) 262 (8, 1)

1331 (3, 20) 1260 (5, 31) 1165 (48, 4) 1041 (2, 27) 429 (7, 12) 257 (11, 5)

1328 (5, 25) 1262 (2, 22) 1169 (25, 2) 1060 (6, 10) 419 (2, 14) 235 (8, 2)

205 (5)

198 (7, 3)

181 (3, 4)

175 (2, 4)

193 (1, 3)

1264 (w) 1166 (s) 1099 (vs)

1105 (2)

i.p.= in phase; o.p. = out of phase; α = α ring; β = β ring. bs = strong; m = medium; w = weak; v = very; br = broad. cRelative intensities; br = broad. The frequencies and relative intensities (IR, Raman) were calculated using the B3LYP/cc-pVTZ method. Scaling factors of 0.985 and 0.961 were used for frequencies below and above 2000 cm−1, respectively.

a

d

Potential Energy Surface (PES). Figure 2 shows the four conformations and their relative energies calculated for 247TOO. Each conformation can be defined in terms of its ring-puckering coordinates x1 and x2, which are defined in Figure 6. Our ab initio calculations provided the energy and x1 and x2 coordinate values for each of the minima as well as for the four

barriers between the minima. In addition, the central barrier value of 3141 cm−1 at x1 = x2 = 0 was calculated. Over 100 data points were used to calculate a potential energy surface that fits all of the values from the ab initio computations quite closely. In particular, we chose the potential energy parameters so that the 413

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Figure 6. Definition of the ring-puckering coordinates x1 and x2 for the α and β rings, respectively. Each coordinate is half the distance between two ring diagonals.

Figure 10. One-dimensional slice of the PES for 247TOO along x1 with x2 fixed at its energy minimum. It should be noted that the levels (n,0) for n = 2, 4, 6, and 8 are within the B well. The energy levels for υ− are also shown. Figure 7. PES corresponding to eq 3 for 247TOO. The conformational energies of the energy minima and barriers (in cm−1) are also shown.

data at lower energies would be fit well. The function determined, which at first glance looks excessively complicated, is V = 1.309·105x16 + 1.039· 104x15 + 6.324· 105x14 + 2.250·104x13 − 6.551· 104x12 − 3.116· 103x1 − 9.946·104x 2 6 − 8.653· 104x 2 5 + 1.781· 106x 2 4 + 2.766·104x 2 3 − 9.851· 104x 2 2 − 1.589· 103x 2 + 2.001·103x1x 2 + 3.223· 105x12x 2 2 − 4.809· 103x13x 2 + 4.443·104x1x 2 3 − 3.136· 105x13x 2 3 + 9.827 ·106x14x 2 2 − 1.391·107x12x 2 4 + 9.684· 105x15x 2 + 8.336· 104x1x 2 5 − 3141

(3) −1

In eq 3, the potential energy V is in units of cm , and the puckering coordinates x1 and x2 are in Å. A large number of terms, above and beyond those used in eq 1, were required to reproduce the conformational energies of this highly asymmetric PES. In eq 1 no terms above fourth-power were utilized, but eq 3 also uses sixth-power terms, and this may seem troublesome. However, these higher-power terms have been used to tweak the PES only somewhat and have considerably smaller contributions than it might seem. For example, the x16 term contributes about 40 times less at the energy minima than the x14 term since its coefficient is about 8 times smaller and its value is about 5 times less there. Similarly, the x26 term contributes about 90 times less than the x24 term. Without the higher-power terms, however, the overall PES would not be fit so well. Figure 7 shows the twodimensional PES corresponding to eq 3. Having determined this PES, we were then able to use the Meinander−Laane DA2OPTN4 program10 to calculate the energy levels for this surface. The calculation also requires the utilization of the kinetic energy (reciprocal reduced mass) terms. We made realistic estimates of these by choosing their values so that our program reproduces the ring-puckering frequencies calculated using DFT. The DFT frequencies were calculated on the basis of the harmonic approximation, and it is well-known that deep within a potential well the harmonic oscillator approximation works quite well for predicting frequencies.26

Figure 8. Energy levels calculated for the different conformations of 247TOO. The levels are labeled sequentially and also in the (v−, v+) format.

Figure 9. One-dimensional slice of the PES for 247TOO along x2 with x1 fixed at its energy minimum. The energy levels for υ+ are also shown.

414

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Figure 11. Selected wave functions calculated for the PES of 247TOO.

Figure 8 shows the calculated energy levels for the PES of eq 3. The lowest-energy quantum states are isolated in the potential energy wells for structures A and B, with those for the latter starting 181 cm−1 higher. The vibrationally excited states can be described by the number of quanta for each puckering motion (v−, v+), and they are also labeled sequentially starting at 0. Thus, the lowest ring-puckering level is (0,0) or 0 and corresponds to structure A. The next level, (0,1) or 1, corresponds to structure B and lies 181 cm−1 higher in energy. In the figure, the levels for structures A, B, C, and D are shown separately since at lower energies each level is isolated in one well or another. The complete listing of the lowest 100 calculated energy levels is

available in the Supporting Information. The energy levels in Figure 8 are shown so that those for υ+ with the lower puckering frequency are in a vertical column and those for υ− are shown progressing to the right. Thus, the lowest puckering transition for structure A is for υ+ and is (0,0) → (0,2) or 0 → 2 for the sequential levels. For structure B the lowest puckering transition is (0,1) → (0,3) or 1 → 4. The corresponding transitions for the υ− puckering are (0,0) → (1,0) or 0 → 3 for structure A and (0,1) → (2,1) or 1 → 6 for structure B. Most of the levels shown represent states for which both puckering motions have been excited at the same time. The (v−, v+) labels can become confusing since the lowest energy level, (0,0), corresponds to 415

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The Journal of Physical Chemistry A structure A while the next one, (0,1), corresponds to structure B. Figures 9 and 10 show one-dimensional slices of the twodimensional PES, displaying the energy levels associated with υ+ and υ−, respectively. The former shows the function for the puckering of ring β along x2 with x1 at its minimum-energy value. Figure 10 shows the potential energy curve for the α ring as a function of x1 with x2 at its minimum-energy value. These provide additional perspective and help in understanding the distribution of the quantum states between the potential wells for structures A, B, and C. The fourth well D and its energy levels are at much higher energies, as can be seen in Figures 7 and 8. Figure 11 shows a selection of the wave functions calculated for the energy levels in the different wells of the PES. The Supporting Information presents many more of these. The figure clearly shows that the lowest eight quantum states are clearly isolated in either well A (levels 0, 2, 3, 5, and 7) or B (levels 1, 4, and 6). Level 9 is almost totally in B but begins to show a tiny bit of probability in well A. Higher levels begin to show progressively more and more probability in both wells. Yet higher levels wind up isolated in conformation C (18, 30, 44, 47, and 50) or D (42, 57, and 61). In addition to showing where the conformational probabilities lie, the wave functions also show the expected nodes for each of the PES wells. Level 0 is the lowest state for conformation A, and level 1 is the lowest state for conformation B. Hence, neither has a node in the wave function. Levels 2 and 4 are the first excited vibrational levels for A and B, respectively, and each has one node. For higher levels, the number of nodes increases progressively. Careful inspection of the functions also shows that there is a directionality of the functions either along x1 or x2 or a combination of both. These correspond as expected on the basis of where the levels lie in Figures 9 and 10. For the very highest levels, which lie along all but the central barrier (such as 174 and 199), the conformational probabilities correspond to all of the conformations (A, B, C, and D).

ACKNOWLEDGMENTS

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REFERENCES

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CONCLUSIONS We have synthesized 247TOO for the first time and analyzed its infrared and Raman spectra with the aid of theoretical calculations. Ab initio calculations showed that the molecule could exist in four different conformational forms and provided conformational energy data for determining the two-dimensional PES for the out-of-plane modes of the two rings. The NMR spectra of the molecules showed the presence of the two lowestenergy conformations. The energies of the quantum states corresponding to each of the four potential energy wells were calculated along with their corresponding wave functions. The results provide a comprehensive understanding of both the energy-level patterns and the nature of the wave functions. ASSOCIATED CONTENT

S Supporting Information *

Listing of the calculated energies for the lowest 200 quantum states (Table S1) and many additional wave functions (Figure S1). This material is available free of charge via the Internet at http://pubs.acs.org.

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The authors thank the Robert A. Welch Foundation (Grant A0396) 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 CHE0541587). J.L. thanks Linda Redd for editorial assistance.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 416

DOI: 10.1021/jp511353r J. Phys. Chem. A 2015, 119, 410−417

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DOI: 10.1021/jp511353r J. Phys. Chem. A 2015, 119, 410−417