Molecular structures, conformations, and vibrational spectra of bicyclo[3.1.0]hexane and its oxygen analogues

Journal of Molecular Structure 519 (2000) 75–84 www.elsevier.nl/locate/molstruc

Molecular structures, conformations, and vibrational spectra of bicyclo[3.1.0]hexane and its oxygen analogues P. Kang a, J. Choo a,*, M. Jeong b, Y. Kwon b a

Department of Chemistry, Hanyang University, Ansan 425-791, South Korea Department of Chemistry, Hanyang University, Seoul 133-791, South Korea

b

Received 26 March 1999; accepted 16 May 1999

Abstract The molecular structures and ring-puckering potential energy profiles of bicyclo[3.1.0]hexane and its three oxygen analogues—6-oxabicyclo[3.1.0]hexane, 3-oxabicyclo[3.1.0]hexane, and 3,6-dioxa[3.1.0]hexane—have been reexamined using both ab initio (HF and MP2) and density functional theory (B3LYP) methods. The calculated structural parameters and ring-puckering potential profiles of those molecules have been compared to the previously reported microwave, electron diffraction, and far-infrared data. Our computational results show that the inclusion of electron correlation effects is crucial for the precise prediction of geometrical parameters of such bicyclic systems. The calculated ring-puckering potential energy profiles using the B3LYP method reproduce the experimental profiles more accurately than those predicted by MM3 force-field methods. Vibrational frequency calculations of 6-oxabicyclo[3.1.0]hexane have been also performed to compare with those measured from the infrared and Raman spectroscopy. Comparison of the calculated and experimental results indicates that the B3LYP method has led to the prediction of more accurate vibrational frequencies than the HF and MP2 methods. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Bicyclo[3.1.0]hexane; 6-Oxabicyclo[3.1.0]hexane; 3-Oxabicyclo[3.1.0]hexane; 3,6-Dioxa[3.1.0]hexane; Ring-puckering potential energy function; Density functional theory

1. Introduction Over the past two decades, there have been many studies of the molecular structures and conformations of bicyclo[3.1.0]hexane, I, and its oxygen analogues, II–IV [1–15]. Experimental methods such as microwave (MW) [1–4] and electron diffraction (ED) [5] have been extensively used to determine the structural parameters of each molecule in the gas phase. However, the structural parameters determined from the experimental methods include some experimental uncertain* Corresponding author. Tel.: 1 82-345-400-5505; fax: 1 82345-407-3863. E-mail address: [email protected] (J. Choo).

ties due to several independent structural parameters. In the process of determining the equilibrium geometry, some of the structural parameters are forced to fix at certain values to optimize the other parameters by fitting the observed microwave or electron diffraction patterns. Hence, such arbitrary assumptions may cause large uncertainties on the initial fixed parameters compared to the other structural parameters.

In order to solve such problems, quantum

0022-2860/00/$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S0022-286 0(99)00292-6

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mechanical calculations can be applied to do the initial bond parameters under constraint. Recently, Shen et al. [6] performed ab initio calculations at the HF level to determine more reliable structural parameters using a combined analysis of molecular orbital constrained electron diffraction (MOCED) and microwave data. Several ab initio studies at the HF levels were also reported for a series of bicyclo[n.1.0]alkanes [7–11]. However, the HF-predicted structural parameters still show a considerable discrepancy between the experimental and calculated ones due to the neglect of electron correlation effects. Therefore, more time-consuming methods, such as the second-order Møller–Plesset perturbation (MP2) or density functional theory (DFT) including electron correlation effects, are required to get more accurate structural parameters for the bicyclic molecules. In the present study, theoretical calculations with ab initio and DFT methods have been performed in order to investigate more precise geometrical parameters for molecules I–IV. In addition to the structural analyses, we also investigated the fundamental vibrational frequencies for 6-oxabicyclo[3.1.0] hexane, II, using both experimental and theoretical methods. In addition, we reinvestigated the potential energy profiles in terms of the ring-puckering coordinate for molecules I–IV using the DFT method at the B3LYP level. The ring-puckering potential energy profiles of the molecules were determined from the far-infrared and Raman spectroscopy reported in the 1970s [12– 14]. Very recently, more reliable potential profiles were determined from far-infrared data along with kinetic energy expansions and the results were compared to those calculated by the molecular mechanics (MM3) method [15]. For each of these molecules, however, the MM3-predicted potential profile incorrectly predicted double minima, in complete contrast to a single minimum in the potential profile. The inconsistency of potential profiles between far-infrared and MM3 results has prompted us to reinvestigate the potential energy profiles from a quantum mechanical point of view. To date the conformational analyses of the bicyclic molecules I–IV have been well studied by experimental methods [1–6,12–15] as well as by ab initio SCF calculations [7–11]. To the best of our knowledge, however, there have been no precise theoretical studies including electron correlation effects. In an

attempt to better characterize the experimental uncertainties of the structural determination as well as the inconsistencies of potential profiles between farinfrared and MM3 results, we reinvestigated the structural properties and conformational behaviour for molecules I–IV using the MP2 and B3LYP methods. Our theoretical calculations will give a valuable insight into better understanding the structural behaviour as well as the spectroscopic properties of the bicyclic systems. 2. Experimental The gas-phase infrared and liquid-phase Raman spectra of 6-oxabicyclo[3.1.0]hexane, II, have been measured and assigned. 6-Oxabicyclo[3.1.0]hexane was purchased from Aldrich Chemical and used without further purification. The gas-phase midinfrared spectra of molecule II were recorded on a Bio-Rad FTS-6000 interferometer equipped with a cryogenic MCT detector. Gas-phase spectra were recorded at a resolution of 0.5 cm 21 at 40 Torr of pressure in a 10 cm gas cell with KBr windows, while liquid-phase far-infrared spectra were recorded at a resolution of 1.0 cm 21 using a DTGS detector and a 2.0 mm wavelength polyethylene cell. Liquid-phase Raman spectra were recorded on a Bruker IFS-55 FTRaman spectrophotometer using Nd:Yag laser as an excitation source, in which the laser line at 1064 nm was used with 200 mW of power at the sample. Spectral resolutions between 1 and 2 cm 21 were employed for the Raman measurements. 3. Calculations The molecular geometries, infrared and Raman frequencies, vibrational intensities, and potential energy profiles of bicyclo[3.1.0]hexane, I, and its three oxygen analogues, II–IV, were calculated using the Gaussian94 program [16]. All the calculations were performed at the HF, MP2, and B3LYP levels of theory with the 6-31G** basis set. Vibrational frequency calculations have been performed using the HF, MP2, and B3LYP methods in order to compare the calculated frequencies with those observed. Most of the recent publications indicate that the B3LYP functional is the preferred method

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Fig. 1. Numbering scheme of bicyclo[3.1.0]hexane and its oxygen analogues. Table 1 Structural parameters of bicyclo[3.1.0]hexane, I Structural parameters

C1 –C2 C3 –C4 C4 –C5 C4 –C6 C2 –H9 C2 –H10 C3 –H11 C3 –H12 C4 –H13 C5 –H15 C5 –H16 C1 –C2 –C3 C2 –C3 –C4 C3 –C4 –C6 H7 –C1 –H8 H9 –C2 –H10 H15 –C5 –H16 ac bd a

Experimental values MW a

ED b

1.530 1.530 1.513 1.513 1.092 1.092 1.092 1.092 1.082 1.082 1.082 107.9 100.8 108.1 109.3 109.3 116.0 38.0 63.0

1.553 1.531 1.509 1.511 1.095 1.095 1.096 1.096 1.087 1.087 1.087 103.6 104.3 107.6 – – – – –

Ref. [4]. Ref. [6]. c 1808—/(C1C3C4C6 –C1X2C3). d 1808—/(C1C3C4C6 –C4X5C6). b

HF/6-31G**

MP2/6-31G**

B3LYP/6-31G**

1.542 1.520 1.499 1.500 1.085 1.084 1.086 1.088 1.076 1.078 1.076 105.3 104.8 108.2 107.3 106.7 113.6 28.0 68.1

1.539 1.516 1.505 1.510 1.090 1.090 1.092 1.093 1.082 1.082 1.081 105.0 104.5 107.9 107.6 106.9 114.1 31.5 68.3

1.548 1.524 1.511 1.516 1.095 1.094 1.097 1.098 1.087 1.088 1.087 105.2 104.9 108.0 107.1 106.6 113.5 29.6 67.9

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Table 2 Structural parameters of oxygen-containing bicyclo[3.1.0]hexane analogues, II–IV Molecule

Structural parameters

MW a

HF/6-31G**

MP2/6-31G**

B3LYP/6-31G**

II

C1 –C2 C3 –C4 C4 –O5 C4 –C6 C2 –H9 C2 –H10 C3 –H11 C3 –H12 C4 –H13 C1 –C2 –C3 C2 –C3 –C4 C3 –C4 –C6 H7 –C1 –H8 H9 –C2 –H10 ab bc C1 –O2 C3 –C4 C4 –C5 C4 –C6 C3 –H11 C3 –H12 C4 –H13 C5 –H15 C5 –H16 C1 –O2 –C3 O2 –C3 –C4 C3 –C4 –C6 H7 –C1 –H8 H15 –C5 –H16 a b C1 –O2 C3 –C4 C4 –O5 C4 –C6 C3 –H11 C3 –H12 C4 –H13 C1 –O2 –C3 O2 –C3 –C4 C3 –C4 –C6 H7 –C1 –H8 a b

1.530 1.513 1.436 1.471 1.092 1.092 1.092 1.092 1.082 108.6 98.3 109.6 109.3 109.3 40.7 64.3 1.410 1.530 1.513 1.513 1.092 1.092 1.082 1.082 1.082 111.3 101.1 105.4 109.3 116.0 40.7 64.5 1.410 1.513 1.436 1.471 1.092 1.092 1.082 112.8 99.7 107.8 109.3 39.3 63.9

1.543 1.511 1.410 1.450 1.083 1.085 1.085 1.088 1.077 105.6 103.7 109.5 107.7 107.6 28.1 74.1 1.407 1.515 1.497 1.498 1.084 1.090 1.074 1.077 1.076 109.5 105.2 105.3 108.5 114.6 30.7 68.9 1.406 1.506 1.406 1.448 1.083 1.089 1.075 111.2 105.2 106.8 109.0 22.1 73.7

1.540 1.509 1.448 1.466 1.087 1.089 1.091 1.093 1.084 105.4 103.4 109.0 107.9 108.0 31.0 73.9 1.432 1.511 1.502 1.508 1.091 1.097 1.081 1.082 1.080 106.9 105.2 105.2 109.0 115.4 34.6 69.3 1.430 1.506 1.442 1.462 1.090 1.097 1.083 108.8 105.4 106.7 109.2 26.5 73.5

1.550 1.517 1.440 1.470 1.092 1.094 1.095 1.097 1.089 105.5 103.8 109.2 107.5 107.6 28.7 73.4 1.430 1.519 1.509 1.514 1.096 1.102 1.086 1.086 1.086 108.1 105.6 105.3 108.4 114.8 31.8 68.6 1.428 1.513 1.436 1.466 1.095 1.103 1.088 109.8 105.7 106.7 108.6 23.4 72.9

III

IV

a

Ref. [4]. 1808—/(C1C3C4C6 –C1X2C3). c 1808—/(C1C3C4C6 –C4X5C6). b

P. Kang et al. / Journal of Molecular Structure 519 (2000) 75–84

for the vibrational analysis [17–21]. Thus, we evaluated the utility of the B3LYP method for calculating the vibrational frequencies of molecule II. In this connection, the root mean square (RMS) deviations of vibrational frequencies from the experiments have been calculated to compare the frequency prediction capability of each computational method. Vibrational frequency analyses at all levels of calculation indicate that optimized structures of all molecules are at stationary points corresponding to local minima without imaginary frequencies. The calculated infrared and Raman spectra of molecule II were fit using Lorentzian band shapes in order to compare to the observed frequencies. The ring-puckering potential energy profile of each molecule was calculated by specifying the puckering coordinate of five-membered ring, while all other parameters were optimized.

4. Results and discussion 4.1. Molecular structures of bicyclo[3.1.0]hexane and its oxygen analogues The numbering of atoms in bicyclo[3.1.0]hexane and its three oxygen analogues is depicted in Fig. 1. The calculated optimized geometries of bicyclo[3.1.0]hexane, I, with the HF, MP2 and B3LYP methods are listed in Table 1. Previously reported experimental geometries from MW [1–4] and HFconstrained ED [5,6] methods are also included for comparison. As shown in the table, exceptional large discrepancies between the calculated and MW values are found for the bond angles, C1 –C2 –C3 and C2 –C3 –C4, and the dihedral angles, a (1808— (C1C3C4C6 –C1X2C3)) and b (1808—(C1C3C4C6 – C4X5C6)) in molecule I. The C1 –C2 –C3 and C2 –C3 – C4 bond angles differ from the microwave data by 22.6, 22.9 and 22.78 and by 4.0, 3.7 and 4.18 for the HF, MP2 and B3LYP levels, respectively. Similarly, the calculated dihedral angles a and b deviate by 10.0, 6.5 and 8.48 and by 5.1, 5.3 and 4.98 for the HF, MP2 and B3LYP levels, respectively. These bond angle discrepancies are also found in the other three oxygen analogues, II–IV, as shown in Table 2. The consistent discrepancies of the four angles between theoretical calculations and the MW experiment may be ascribed to the experimental uncertainties.

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In the microwave study of molecules I–IV, the C1 – C2 –C3 bond angle was first kept fixed and then adjusted in order to better reproduce the rotational constants using the linear least squares method, which results in rather considerable uncertainties on C1 –C2 –C3, a and b compared to the other bond angles. There also exists a larger uncertainty on the C2 –C3 –C4 bond angle since it is closely related to a . On the other hand, the C1 –C2 –C3 and C2 –C3 –C4 bond angles determined from the ED analysis using HF/631G* constraints are much closer to those determined from the computational methods. This is because the arbitrary initial parameters for molecule I were constrained to values obtained from the HF calculation. However, the bond lengths in particular among the structural parameters at the HF levels are a little underestimated, whereas the inclusion of electron correlation at the MP2 level makes them closer to the ED data. The overall structural parameters at the B3LYP level are very close to the MP2 results and represent definite improvements on the HF results. The MP2- and B3LYP-predicted geometries agree fairly well with the expected accuracy of about ˚ for bond lengths and 2 degrees for bond 0.02 A angles. The C–H bond lengths of molecule I are rather accurately predicted at the MP2 level. On the contrary, the bond lengths except the C–H bonds at the B3LYP level are in better agreement with the experimental bond lengths than those determined at the MP2 level. Similar tendencies are also found in the other three oxygen analogues, II–IV, as shown in Table 2. Unfortunately, we could not compare our MP2 and B3LYP-predicted structural parameters to more reliable ED or MW data since no precise experimental studies using ab initio constraints for molecules II–IV are available yet. 4.2. Vibrational analysis of 6oxabicyclo[3.1.0]hexane Both experimental and computational results indicate that the equilibrium structure of molecule II has a boat form [1–5,8,12–15]. Thus, this molecule belongs to Cs symmetry and has 36 fundamental modes distributed as 20 A 0 1 16A 00 : The gas-phase infrared and liquid-phase Raman spectra of 6-oxabicyclo[3.1.0]hexane, II, are given in Figs. 2 and 3, respectively. The theoretical infrared and Raman

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infrared and Raman experiments are found to be 40.8, 21.1, and 13.8 cm 21 for HF, MP2, and B3LYP calculations, respectively. The RMS deviations indicate that the vibrational frequencies calculated from the B3LYP method are in better agreement with the experimental values than those obtained from the MP2 method. It is also obvious that the effects of electron correlation should be taken into account by MP2 or B3LYP methods because the HF method is less accurate in predicting the vibrational frequencies than the B3LYP and MP2 methods.

Fig. 2. Observed and calculated infrared spectra of 6-oxabicyclo[3.1.0]hexane: (a) gas-phase mid-infrared spectrum; (b) liquidphase far-infrared spectrum; and (c) calculated infrared spectrum at the B3LYP/6-31G** level.

spectra simulated from the B3LYP calculations are also shown in the figures for comparison. All the calculated results including vibrational frequencies and intensities are compared to the experimental data in Table 3. A full geometry optimization was performed to find a minimum energy structure, and then the calculations of harmonic force constants and normal modes in Cartesian coordinate were performed. For a better comparison, the calculated frequencies are uniformly scaled by 0.8953, 0.9434 and 0.9614 at the HF, MP2 and B3LYP levels, respectively [22]. Overall root mean square (RMS) deviations of scaled vibrational frequencies from the

Fig. 3. Observed and calculated Raman spectra of 6-oxabicyclo[3.1.0]hexane: (a) liquid-phase FT-Raman spectrum; (b) calculated Raman spectrum at the B3LYP/6-31G** level.

4.3. Asymmetric ring-puckering potential energy profiles of bicyclo[3.1.0]hexane and its oxygen analogues In order to evaluate the capabilities to reproduce the ring-puckering potential energy profiles for the bicyclic systems, a series of computations at the B3LYP level was carried out. More details on the definition of ring-puckering coordinate for the bicyclic rings can be found elsewhere [12–15]. Fig. 4 compares the experimentally determined ring-puckering potential energy profiles to those obtained from the MM3 [23–25] and B3LYP calculations for the bicyclic systems I–IV. The comparisons between the experimental and the MM3 potential profiles were previously reported [15]. The MM3-predicted potential profile for each molecule, however, predicted a double minimum shape and failed to reproduce the experimental single potential well accurately. On the contrary, our B3LYP calculations for molecules I–IV show the single minimum potential shapes and predict the experimental profiles better than do the MM3 calculations. As mentioned above, the previously reported MW and ED data indicate that the boat conformations are the most stable for molecules I–IV due to the nonbonded interactions of the hydrogen atoms on C1 and C3 with the hydrogen atoms on C4 and C6. The boat conformation leads to the preferred staggered arrangement of the hydrogen atoms, whereas the chair form in the eclipsed arrangement of the hydrogen atoms is unstable. Our computational results are also found to be totally consistent with the fact that each molecule possesses the boat conformations as its equilibrium structure. In Fig. 5 we illustrated the projection diagrams for both conformations. The

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Table 3 Observed and calculated vibrational frequencies (cm 21) of 6-oxabicyclo[3.1.0]hexane, II (abbreviations: s ˆ strong, m ˆ medium, w ˆ weak, v ˆ very. Numbers in the brackets are infrared frequencies observed from pure-liquid far-infrared spectra) Vibrational descriptions (Cs)

A0 n 1 CH sym. stretch n 2 CH2 antisym. stretch n 3 CH2 antisym. stretch n 4 CH2 sym stretch n 5 CH2 sym. stretch n 6 CH2 deformation n 7 CH2 deformation n 8 CH in-plane wag n 9 CH2 wag n 10 in-plane ring mode n 11 in-plane ring mode n 12 CH2 twist n 13 CH out-of-plane wag n 14 CH out-of-plane wag n 15 CH2 rock n 16 in-plane ring mode n 17 in-plane ring mode n 18 in-plane ring mode n 19 ring flap n 20 ring pucker A 00 n 21 CH antisym. stretch n 22 CH2 antisym. stretch n 23 CH2 sym. stretch n 24 CH2 deformation n 25 CH in-plane wag n 26 CH2 wag n 27 CH2 wag n 28 CH2 twist n 29 CH2 twist n 30 CH out-of-plane wag n 31 in-plane ring mode n 32 in-plane ring mode n 33 CH2 rock n 34 in-plane ring mode n 35 in-plane ring mode n 36 ring twist

Infrared (vapour)

Raman (liquid)

Scaled a HF/6-31G**

MP2/6-31G**

B3LYP/6-31G**

3041 vs 3028 vs 2969 s 2955 s 2927 s 1468 w 1440 w 1394 vs 1269 vw 1213 s 1203 w 1093 s – 936 s – 843 vs 759 w [657]m [403]m [220]w

3039 vs – – 2909 s 2923 s 1470 m 1444 s 1392 s 1284 w 1211 s 1192 s 1087 m 975 w 936 s 890 vs 842 m – 637 m 406 w 221 vw

2989 (45.0/155.3) b 2934 (49.8/62.2) 2902 (33.7/92.6) 2889 (38.0/107.0) 2857 (28.5/145.3) 1468 (3.3/4.5) 1446 (1.2/11.0) 1433 (17.6/10.1) 1321 (5.9/0.6) 1247 (5.4/6.7) 1211 (6.5/18.5) 1107 (10.8/1.7) 1016 (6.6/13.8) 933 (21.5/6.7) 853 (3.1/15.0) 843 (38.0/13.4) 786 (0.6/2.0) 642 (4.0/1.3) 396 (11.5/0.5) 206 (1.1/0.1)

3067 (33.0) c 3050 (20.3) 3013 (21.4) 2989 (21.9) 2952 (16.2) 1468 (2.2) 1450 (1.7) 1398 (10.3) 1298 (0.3) 1232 (3.6) 1195 (2.7) 1081 (4.0) 1014 (0.5) 923 (7.7) 865 (0.0) 835 (33.0) 792 (0.8) 632 (2.4) 389 (9.8) 228 (1.1)

3037 (43.6/135.6) b 3010 (30.3/64.1) 2975(18.8/135.9) 2963(18.8/103.7) 2925 (22.0/149.9) 1456(2.3/9.2) 1438(0.9/10.3) 1396 (14.8/2.6) 1286 (0.2/116.2) 1229(3.4/26.2) 1195 (4.2/14.5) 1079 (5.4/4.5) 996 (0.5/128.0) 923 (11.1/8.0) 859 (0.5/19.7) 829 (32.1/6.6) 782 (0.6/11.9) 635(2.9/1.5) 390 (9.3/2.5) 209 (1.2/1.8)

3032 vs 2987 vs 2917 vs 1438 m 1304 m 1298 s 1244 m – – – 1018 m 923 s – 799 w [638]m [336]w

– 2959 s 2854 s – 1332 w 1297 m 1245 m – – – 1024 m 934 s 870 vw 796 m 638 m 312 w

2976 (26.5/75.2) 2903 (26.5/100.0) 2856 (51.6/19.6) 1446 (0.9/9.0) 1341 (0.3/0.6) 1308 (0.4/4.0) 1286 (0.8/2.1) 1190 (0.1/6.7) 1164 (0.2/0.1) 1075 (0.1/2.6) 1000 (1.0/9.0) 923 (11.9/1.9) 867 (0.0/2.3) 807 (1.0/2.3) 639 (1.7/2.9) 320 (2.9/0.1)

3056 (15.0) 3014 (11.6) 2951 (32.6) 1448 (1.3) 1326 (0.3) 1296 (5.1) 1270 (1.1) 1174 (0.1) 1143 (0.0) 1050 (0.0) 1003 (2.7) 918 (9.4) 881 (0.3) 793 (1.6) 626 (2.3) 312 (2.0)

3025 (22.4/5.3) 2976(33.6/154.4) 2924(39.4/47.1) 1436 (1.3/20.7) 1319 (0.5/10.0) 1286 (5.8/1.8) 1269 (0.8/12.2) 1167(0.1/35.8) 1138 (0.0/39.5) 1048 (0.0/168.0) 995 (4.2/22.2) 903 (11.5/7.1) 862 (0.3/18.5) 791 (2.0/52.1) 630 (3.0/7.2) 316 (1.8/3.1)

a

Calculated vibrational frequencies scaled by 0.8953, 0.9434 and 0.9614 for the HF, MP2 and B3LYP frequencies, respectively. Calculated infrared/Raman intensities. c Calculated infrared intensities. b

calculated dihedral angles H11C3C4H13 and H12C3C4H13, for molecules I–IV are listed in Table 4 in order to show the relative orientations of hydrogen atoms for the boat, planar, and chair

forms. As the five-membered ring puckers down from (a) to (c) in Fig. 5, the hydrogen atoms become more eclipsed with an increase of the potential energy.

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Fig. 4. Comparisons of experimental and calculated ring-puckering potential energy functions for bicyclo[3.1.0]hexane and its oxygen analogues.

Table 4 Comparison of dihedral angles and relative energies for the boat, planar and chair conformations of bicyclo[3.1.0]hexane and its oxygen analogues at the B3LYP/6-31G** level Molecule

I

II

III

IV

Conformation

Boat Planar Chair Boat Planar Chair Boat Planar Chair Boat Planar Chair

Puckered angle of five-membered ring (8)

30 0 2 30 30 0 2 30 30 0 2 30 30 0 2 30

Relative energy (cm 21)

Dihedral angle (8)

H11C3C4H13 (A)

H12C3C4H13 (B)

76.2 94.8 116.2 67.8 85.5 106.0 83.6 98.3 116.4 74.9 88.9 106.2

42.6 23.0 2.7 51.4 32.5 13.5 38.7 22.4 5.4 47.2 31.9 16.3

0.6 1062.4 1129.3 4.2 897.4 1393.2 7.7 1050.8 1582.9 75.5 434.2 1182.8

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spectra of the selected bicyclic molecules I–IV. On the basis of our computational results, we have concluded that the effects of electron correlation on the geometry optimization should be taken into account by using the MP2 or B3LYP method for more precise determination of structural parameters. We have also shown the accuracy of DFT method using the B3LYP hybrid functional in predicting the vibrational frequencies and absorption intensities for molecule II. According to our calculations, the boat conformation for each molecule is the most stable structure due to the preferred staggered arrangement of the hydrogen atoms, whereas the eclipsed arrangement increases the potential energy as the ring puckers to the opposite direction. Finally we can conclude that the B3LYP method can reproduce the experimental potential energy functions better than the MM3 forcefield method. Acknowledgements The authors wish to acknowledge the financial support of the Korea Research Foundation (Grant Numbers BSRI-98-2448 and 98-001-D00200) made in the program year of 1998. This work is partly supported by the Hanyang University Research Fund of the academic year 1999. J.C. is also grateful to the SERI Supercomputer Center in Korea for the use of a CRAY C90 system. References

Fig. 5. Projection diagrams for the bicyclic system: (a) boat conformation; (b) planar conformation; (c) chair conformation.

5. Conclusions In the present study we have performed ab initio and the B3LYP calculations to better understand the conformational properties as well as the vibrational

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