J. Phys. Chem. 1995,99, 12090-12098
12090
The 3s Rydberg Spectra and Conformations of Methyl-Substituted Cyclopentanones Alan R. Potts, Dale R. Nesselrodt, Tomas Baer,* and Jeffrey W. Driscollt Department of Chemistry, The University of North Carolina, Chapel Hill,North Carolina 27599-3290
J. Philip Bays Department of Chemistry, Saint Mary’s College, Notre Dame, Indiana 46556 Received: January 30, 1995; In Final Form: April 4, 1995@ Structural analysis of 17 methyl-substituted cyclopentanones (CPOs) was conducted using 2 -I- 1 resonanceenhanced multiphoton ionization (REMPI) spectroscopy via the 3s Rydberg state. The sharp spectra obtained with supersonically cooled samples show that methyl substitution leads to transition origin shifts with respect to CPO which depend on the position and orientation of the methyl group. Furthermore, multiple methyl substitutions give rise to shifts that are nearly equal to the addition of composite monomethyl shifts. Molecular mechanics and ab initio molecular orbital calculations indicate that CPO and most of the methyl-substituted derivatives have twisted geometries. The calculated potential energy barrier between various conformations was found to be no greater than 2.0 kcal/mol for the methyl-substituted derivatives, which is considerably smaller than the 3.8 kcaYmol barrier in unsubstituted CPO. One molecule, cis-2,Sdimethyl CPO, is predicted to be stable only in an envelope (bent) form, while others were found to have stable envelope and twist potential wells. A correlation was found between the 3s n REMPI spectra and 13CNMR carbonyl carbon chemical shifts. The I3C NMR shifts could be calculated from local van der Waals energies and electrostatic potentials at the carbonyl carbon. It was possible to calculate the energy of the 3s excited state from these nonbonded interactions on the basis of the observed correlation.
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Introduction Saturated five-membered rings have shallow energy wells in the twist and envelope conformations. In both, the substituents are oriented in equatorial and axial fashions, analogous to that found in the much more stable six-membered chair conformation of cyclohexane. However, in the five-membered rings, the difference between equatorial and axial is not as distinct as it is in the case of cyclohexane. Thus, these orientations are often referred to as pseudoequatorial and pseudoaxial.1%2In nonsymmetric molecular systems such as methyl-substitutedcyclopentanones (CPOs), a total of 10 distinct envelope and 10 distinct twist conformations can be constructed with molecular models. In the case of the envelope conformations, the flap of the envelope can be placed in five different locations, and in each the methyl group can be located either pseudoequatorially or pseudoaxially. Likewise for the twist forms, there are five distinct twist axes with each giving rise to two methyl group orientations. Although these 20 conformations are very close in energy, most of them are not located at stable minima. On the basis of far-IR spectro~copy,~.~ electron diffra~tion,~ microwave spectroscopy,6and W spectroscopy,’ as well as molecular mechanics calculation^,^^^ it is well established that the only stable conformation of the unsubstituted cyclopentanone is twisted (C2 symmetry) with the twist axis passing through the carbonyl group. The envelope (bent) structure appears to be a transition state of the pseudorotation motion that connects various conformations of this very flexible ~ y s t e m . ~ . ~Under ~.” C2 symmetry, pseudoaxial methyl substituents a to the carbonyl are equivalent, as are those /3 to the carbonyl group. Likewise, the pseudoequatorial positions are also equivalent. Therefore, substitution may occur at a total of four unique positions in the lowest-energy twist conformation: 2-equatorial (2-eq), 2-axial (2-ax), 3-equatorial (3-eq), and 3-axial (3-ax), where the * To whom correspondence should be addressed.
’ Present address:
Aldrich Chemical Company, Inc., Milwaukee, WI 53233. Abstract published in Advance ACS Abstracts, July 15, 1995. @
“pseudo” prefix is assumed. Methyl substitution lowers the molecular symmetry to CI in all cases except for those in which the ring is symmetrically substituted with trans-dimethyl or tetramethyl groups. While unsubstituted five-membered rings have been extensively ~ t u d i e d , ~much - ~ less is known about the conformations of methyl-substituted five-membered rings. The addition of methyl groups at various locations can be expected to change considerably the energetics of the various conformations, possibly leading in some cases to multiple low-energy stable forms. In a series of papers, we have demonstrated the utility of the 3s n 2 1 resonance-enhanced multiphoton ionization (REMPI) spectroscopy for the identification of configurational and even conformational stereoi~omers.~~-l~ This technique is based on the fact that methyl groups substituted at various positions and orientations on the six-membered rings shift the transition origin by characteristic amounts which are additive and largely independent of other methyl groups around the ring. This has permitted us to differentiate, for instance, the two configurational isomers of cis- and trans-2,6-dimethylcyclohexanone (CHO), whose transition origins differ by 310 cm-I.l2 In addition, conformational isomers 2-eq,3-ax-dimethyl CHO and 2-ax,3-eq-dimethyl CHO exhibit transition origins that differ by 373 cm-I.’* The multiphoton technique employed here involves a twophoton absorption to the 3s Rydberg state followed by absorption of a third photon which causes ionization. For cyclic ketones and ethers the two-photon absorption promotes an electron from a nonbonding molecular orbital (oxygen) to the 3s Rydberg state which lies at the one-photon energy of about 50000 cm-I. Because ionization occurs with near unit efficiency once the Rydberg state is excited, collecting the total electron signal as a function of laser wavelength yields a UV absorption spectrum of the 3s state. Spectral congestion is reduced by cooling the sample in seeded supersonic molecular beams. Supersonic expansions +
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0022-365419512099-12090$09.00/0 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 32, 1995 12091
Conformations of Methyl-Substituted Cyclopentanones reduce translational and rotational temperatures of seed molecules to a few degrees Kelvin, while vibrational temperatures are generally cooled to 40-100 K, depending on the seed molecule and backing pressures used.I6 The low rovibrational temperature and the inherently long lifetimes of the 3s Rydberg state help reduce the absorption peak full width at half-maximum (fwhm) to 0.05 nm. Because the relative peak intensities for conformational isomers reflect the relative thermodynamic stabilities, it is possible to extract relative energies for these conformers. Both CHOs and tetrahydropyrans (THPs) exist predominantly in the chair conformation with significant barriers for the chair inversion which converts equatorial substituents into axial substituent^.'^^'^ Because the cooling in the molecular beam is extremely rapid, the conformations are frozen out before significant interconversion takes place. Thus the population ratio of the two conformations in the cold beam reflects their Boltzmann distribution at the temperature of the pulsed valve nozzle (usually 298 K). As alluded to earlier, CPOs have lowfrequency ring flexing modes with low barriers to interconversion between conformers. Unless the rate of cooling is much faster than the rate of interconversion for methyl-substituted CPOs, it is possible that the room-temperature equilibrium populations will not be frozen out because the barriers to interconversion are small. If the interconversion barrier between conformers is less than about 1.1 kcal/mol, then the less stable conformers may relax to the most stable s t r u ~ t u r e . ' ~ , ~ ~ NMR has been extensively used for analyzing conformations of cyclic compounds. It is especially useful for ketones where the carbonyl I3C NMR shifts can be employed to investigate not only configurational isomers but also interconverting conformational isomers if the rates can be slowed sufficiently by cooling of the sample. Li and Chesnut have shown that the I3C NMR chemical shift can be approximated by p and y substituent steric effects and the localized van der Waals (vdW) energies they give rise to on a particular carbon center for a vast array of molecules, including cyclic ethers and In comparing 3s n REMPI spectroscopy with I3C NMR, Cornish and Baer23noted an intriguing correlation between the I3C NMR chemical shift of the carbonyl carbon and the 3s n transition origin shifts for a wide range of cyclic and acyclic ketones. Since the NMR shifts can be accounted for by purely ground state properties such as steric effects, one might conclude that the observed optical shifts are also related to ground state properties. In this paper we explore the effectiveness of 3s n REMPI spectroscopy in analyzing the conformations of methylsubstituted cyclopentanonesand compare the results to I3CNMR shifts. The low interconversion barriers present a considerable challenge for NMR analysis because of the resulting rapid equilibration of conformers, a problem that is less severe in the spectroscopy of supersonically cooled samples.
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Experimental Approach The apparatus used to obtain our REMPI spectra has been described p r e v i o u ~ l y .Briefly, ~~ an excimer-pumped dye laser (Lumonics) operating at 15 Hz was used to generate light over the wavelength range of 390-415 nm. This light was focused into the ionization region of the spectrometer by a 25 cm focal length lens where it perpendicularly intersected the molecular beam. Molecular beams of argon, seeded with (3-5%) analyte, were generated from a Laser Technics pulsed valve (model LPV). A high electric field, 1000 Vlcm, was used to accelerate the electrons down a 10 cm flight tube to the detector, where they were collected with a dual microchannel plate detector. Output
from the microchannel plates was amplified before passing onto a Stanford Research Systems gated integrator with a 3 ns gate. The laser power at each wavelength was monitored with a Scientech calorimeter. Both signals was digitized and recorded with a computer. All spectra were power normalized by dividing the observed signal by the laser power dependence, I", where n was determined for each compound. Values of n ranged from 2 I n 5 3. cis- and trans-2,5-dimethyl CPO were synthesized by simple methylation of 2-methyl CPO under kinetically controlled conditions. The crude reaction mixture contained side products from the thermodynamic reaction channel. The undesired products were separated out by preparative GC using an SF 96 column. However, it was not possible to separate cis and trans isomers by this method. The presence of both cis and trans isomers was confirmed by analytical GCMS on a PLOT column. Synthesis of 3,3-dimethyl CPO was carried out by hydrogenating 4,4-dimethyl-2-cyclopenten-l-one.All other compounds were purchased from Aldrich or Wiley with '98% purity. Samples were frozen with liquid nitrogen and thawed under vacuum several times prior to injection into the valve. Molecular mechanics calculations were performed using Allinger's MM3 program? Local van der Waals (vdW) energies for the carbonyl carbon and oxygen were calculated from the p, y , and 6 through-space interactions with the rest of the atoms in the molecule. E values, describing the hardness of the atom, were taken from the molecular mechanics program. c for sp3 carbon, sp2 carbonyl carbon, carbonyl oxygen, and hydrogen are 0.044, 0.044, 0.05, and 0.047, respectively. vdW radii for each atomic center type are 1.900, 1.940, 1.740, and 1.500, respectively. Ab initio calculations using GAUSSIAN9225were performed with various basis sets up to 6-31G*. Input geometries for these ab initio calculations were obtained from converged structures from the molecular mechanics output. Results and Discussion
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REMPI Spectra and the Transition Origin Shifts. The 3s n 2 1 REMPI spectra of a series of methyl-substituted CPOs were obtained. Each spectrum displays a dominant 3s n transition origin with several less intense vibronic transitions at higher energies. The transition origins appear in the one-photon energy range of 48 600 to 50 600 cm-' . Figure 1 displays the spectra of unsubstituted, monomethyl- (Mel), trimethyl- (Me3), and tetramethyl- (Me4) substituted CPOs, while Figure 2 contains the REMPI spectra of all dimethyl- (Me2) substituted CPOs. While each spectrum shows a dominant transition origin, the complexity of the vibrational structure varies substantially from compound to compound. The 3s n transition origin energies are summarized in Table 1 As previously mentioned, some of the configurational dimethyl CPOs could not be separated on a preparative GC column. In the case of the 3,4-Me2 CPO, a pure cis-3,4-Me2 CPO sample was commercially available. The spectrum of pure cis-3,4-Me2 CPO could be subtracted from that of the cisltrans mixture, thus providing a clean trans-3,4-Me2 CPO spectrum. While the cis- and trans-2,3-Me2 CPOs could not be separated, their spectra are sufficiently different with the minor cis component lying to the red of the transition origin of the trans spectrum so that their spectra can be assigned with (considerable)confidence. The spectrum of cis-2,3-Me2 CPO was taken with increased laser power so that a better signal to noise ratio could be obtained. The cis- and trans-2,4-Me2 CPO spectra were not sufficiently different to enable a similar unambiguous assign-
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+
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Potts et al.
12092 J. Phys. Chem., Vol. 99, No. 32, 1995
TABLE 1: REMPI Transition Energies and 13C NMR Carbonyl Carbon Shifts Relative to Unsubstituted Cyclopentanone I3CNMR carbonyl REMPI 3s n compound transition origin (cm-I) shift (cm-I) R carbon shift (ppm)" shift (ppm) 1.50 219.4 50070 CPO -369 1.5 0.78 220.9 2-Mel 49701 C 91 50161 3-Mel ax 218.7 -0.7 0.86 248 50318 3-Mel eq -604 222.3 2.9 1.40 49466 trans-2,5-Me2 ? ? ? 222.7 3.3 cis-2,5-Mez 1.6 -259 0.5 1 221.0 49811 trans-2,4-Me2 2-ax, 4-eq 0.6 0.66 -110 49960 220.0 cis-2,4-Mez 1.37 220.3 0.9 26 50096 trans-2,3-Mez 1.5 0.87 -680 49390 220.9 cis-2,3-Mez 2-eq, 3-ax 0.50 -1100 223.4b 4.0 48970 2.2-Me2 1.30 -2.1 217.3 466 50536 trans-3,4-Me2 -0.8 0.70 14 218.6 50084 cis-3,4-Me2 0.1 0.84 139 219.5b 50209 3,3-Me2 0.8 0.35 -134 49939 220.2 2,4,4-Me3 0.22 2.6 -855 492 15 222.0 2,2,4-Me3 4.7 224.1 - 1066 0.56 49004 2,2,5-Me35-eq 7.0 -1366 1.32 226.4 48704 2,2,5,5-Me4
-
a
Reference 35. Reference 40. No polarization ratio could be obtained.
2,2.5,5-Me,
2,2,5-Me~
2,2,4-Me~
I
2.2-Mez
2,4,4-Me~
A
2-Me1
CIS
4
I I
CPO
1 50000
& trans 2,4-Mez
cis & trans 2,5-Men
I
48000
51 000
49000
Energy (c m-')
+
-
Figure 1. 2 1 REMPI 3s n spectra of cyclopentanone and some mono-, tri-, and tetramethyl-substituted derivatives. ment. The peak at 49 811 cm-I is without question a transition origin for one of the isomers. The spectrum was scanned 1000 cm-' to the red of the transition origin, and unlike 2,3-Mez CPO, no other peaks were detected. Thus, the other isomer most likely appears to the blue. Only with the aid of empirical arguments can the assignment of the other configurational isomer be extracted from the spectrum of the first. Another major problem occurs with the cis- and trans-2,5-Mez CPOs. It is tempting to assign the two largest peaks, one at 49 572 cm-I and the other at 49 466 cm-', to the cis and trans configurations. However, as will be pointed out, this is inconsistent with empirical arguments based on shift additivities. Hence, considerable uncertainty surrounds the 3s n origins of the configurational isomers of cis- and trans-2,5-Me2 CPO and cisand trans-2,4-Mez CPO. The effect on transition origins of adding equivalent methyl groups is shown in Figure 3. The most stable conformer of 3-Me1 CPO has the methyl group directed in the equatorial
-
48000
49000
50000
51 000
Energy ( c m - ' )
-
Figure 2. 2 + 1 REMPI 3s n spectra of dimethyl-substituted cyclopentanone derivatives. The spectrum of trans-3,4-Me2CPO was obtained by subtraction of the cis isomer spectrum from a spectrum of the mixture of cis and trans isomers. The spectra of cis- and trans2,3-Me2 CPO were obtained from a mixture of the two isomers. The cis-2,3-Me2 isomer spectrum was obtained at a higher laser power. orientation. Similarly, the most stable form of the truns-3,4Me2 CPO has both methyl groups directed in the equatorial orientations. It is thus evident from the bottom three spectra of Figure 3 that the addition of equatorial methyl groups at the 3 or at the equivalent 4 position shifts the transition origin to the blue by about 250 cm-I. A similar shift was noted in the spectra of the methyl-substituted cyclohexanones, where an equatorial 3-methyl group shifts the origin to the blue by 124 & 15 cm-I.I5 A comparison of the CPO and 2-Me1 CPO spectra in Figure 3 shows that the addition of a methyl group at the 2-position shifts the transition origin to the red by 369 cm-'. Since the dominant conformation of the 2-Mel CPO has the methyl group directed in the equatorial orientation, we associated this red shift with equatorial substitution at the 2-position. The analysis of
Conformations of Methyl-Substituted Cyclopentanones
J. Phys. Chem., Vol. 99, No. 32, 1995 12093
trans 2.5-Me2
b
v
500
1
I
/ ,* 0 -
-500
-
2.2-MezCPO
x
.-c Ln c
P
a, 4
trans 3,4-Me2
3-Mel
* I/ I
Figure 3. 2
50000 Energy ( c m - ' )
49000
CPO
51 000
+ 1 REMPI 3s - n spectra.
Upper set of three spectra shows additivity at the 2-equatorial position. Lower set of three spectra shows additivity at the 3-equatorial position.
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shifts introduced by additional methyl groups at the 2-position is made difficult by the uncertain assignment of the 3s n transition origin in the cis- and truns-2,5-Mez CPO mixture. The position of the first peak in the 2,5-Me2 CPO spectrum is shifted by 235 cm-' from the peak in the 2-Me1 CPO spectrum. Although it is considerably less than the shift introduced by the first methyl group, it does suggest that this first peak is associated with the truns-2,5-Me2 CPO transition. This assignment can be checked by looking at other pairs of molecules which differ simply by the addition of a methyl group in the 2-equatorial position. For instance, when a methyl group is added to CPO at the 5-position, it does so in an equatorial orientation, giving the 2,4,4-Me3 CPO molecule. The shift resulting from this addition at the 2-position is 270 cm-I. In general, at a given ring position, axial methyl groups shift the transition origins farther to the red than equatorial methyl group^.'^.'^ Thus, we expect to see the cis-2S-Me2 CPO peak to the red of the truns isomer transition origin in Figure 3. Yet, to the red of the truns origin are only small peaks which we attribute to thermodynamic side products (2,2-Me2, 2,2,5-Me3, 2,2,5,5-Me4 CPO) that could not be completely separated by preparatory GC from the crude reaction product. Thus, we cannot make an assignment for the cis isomer. A nonlinear least-squares Levenberg-Marquardt fitting procedure (eq 1) was utilized to determine the best values for the shift parameters describing the additivity of the transition origin shifts upon methyl substitution. An explanation of this procedure has been given before.I5 S=sxM
C
,?
-1500
2
-1
500
- 1 000
-500
0
500
Observed REMPI Shift (cm-l)
I/ 48000
s l
(1)
M is a 4 x 11 matrix containing rows of the form [2-eq 2ax 3-eq 3-axI in which the elements are the occupation number for the four methyl group orientations for each of the 11 compounds where high confidence of the transition origin assignment was made. For example, the form of the row corresponding to 2-Me] CPO with its one equatorial methyl group would be [l 0 0 01 and cis-3,4-Me2 CPO with its one equatorial and one axial methyl group would be [0 0 1 13. S
Figure 4. Levenberg-Marquardt-predicted REMPI shifts correlated with experimentally observed REMPI shifts. Filled circles represent origins assigned with confidence. Open circle represent cases of uncertainty. The point marked cis-2,3-Mez CPO is the 2-eq/3-ax conformer. The point marked truns-2,4-Me2 CPO is the 2-ad4-eq conformer. See text.
TABLE 2: Optimized Shift Parameters from the Least-Squares Analysis (See Text) shift parameter
REMPI shift (cm-I)
"C NMR chemical shift (ppm)
2-equatorial 2-axial 3-equatorial 3-axial
-308 f 35 -390 18 226 f 6 -65 f 71
1.5 i 0.03 2.1 i 0.08 -0.9 i 0.1 I 0.5 i 0.25
*
is a 1 x 11 matrix containing observed transition origin REMPI shifts relative to the transition origin of unsubstituted CPO. Optimized shift parameters are obtained by adjusting s, the (1 x 4) matrix of shift parameters [2-eq, 2-ax, 3-eq, 3-ax], in order to minimize X2 where
Optimized shift parameters and their standard deviations can be found in Table 2, and a plot of predicted versus observed transition origins is shown in Figure 4. A best fit gives standard deviations of 6-70 cm-' for each substituent. On average, the error associated with predicting the transition origin with respect to CPO is ~ 6 cm-' 0 over an 1800 cm-' range for transition origins. Thus, in predicting the shift for 3,3-Me2 CPO, addition of 3-eq and 3-ax shifts yield 108 cm-' compared to the experimentally observed value of 139 cm-'. A linear regression of the data gives a correlation coefficient of 0.9890. Evidently, the assumption that the transition origin shifts are governed by additive single methyl group shifts is well justified. However, the deviations are somewhat larger than they were for the methyl-substituted CHOs.I5 The Levenberg-Marquardt analysis in Figure 4 was carried out only with the well-established transition origins (filled circles). Both the 2,2-Me2 and 2,2,4-Me3 CPO data points were removed from the correlation because of the uncharacteristic intense vibrational progressions, indicating a large geometry change in the 3s state. Previous studies by Driscoll and Baeri5 suggest that the methyl group additivity effect is considerably reduced when the 3s geometry is very different from that of the ground state. These compounds are discussed more fully in the next section. In cases where multiple conformerg and inseparable configurational isomers are present, assignment of transition origins was made solely with the aid of these empirical parameters. Attention has already been drawn to the assignment of the trans
Potts et al.
12094 J. Phys. Chem., Vol. 99, No. 32, 1995 TABLE 3: Dihedral Angles and Energies Calculated Using MM3 Molecular Mechanics and ab Initio MO Methods MM3 energy geometry (kcdmol) LC5-Cl-C2-C3
ab initio
~
compound CPO 2-Me 3-Me
conf
Me eq Me ax Me eq trans-2.5-Me2 Di eq cis-2,5-Me2 trans-2,4-Me2 Me2 ax Me2 eq cis-2.4-Me~ Di eq trans-2.3-Me2 Di eq cis-2,3-Me2 Me2 ax Me2 eq 2.2-Me2 trans-3,4-Mez Di eq cis-3,4-Me2 3,3-Me2 2,2,4-Me3 Me4 eq 2,4,4-Me3 Me2 eq 2,2,5-Me3 Me5 eq 2,2,5,5-Med
LC5-Cl-C2-C3 -11.4 16.2 -12.9 12.3 -12.0 19.7 -6.4 -15.0 15.1 -16.7 -11.6 19.6 -12.6 -12.3 -13.2 -14.3 10.7 -13.2 8.4 11.4
LC2-Cl-C5-C4
twist twist
-11.3 7 .O -9.8 11.4 -12.1 2.8 -16.9 -7.9 9.2 -7.4 - 12.2 4.2 - 10.0 -12.3 -11.3 -8.7 13.0 -10.1 15.0 11.4
twist twist
twist envelope
twist twist twist twist twist envelope
twist twist twist
twist twist twist twist
twist
3-Met
X
c t s & t r o i s - 2 , 4-Me2
15.2 16.6 16.9 15.7 18.2 19.0 18.3 18.3 17.2 17.6 19.7 19.5 19.8 16.8 18.7 18.1 20.3 19.6 21.1 24.1
-12.0 16.5 -17.9 -14.2 12.3 22.7 4.8 10.2 -16.4 -19.4 12.0 24.5 14.5 -12.3 -7.7 19.7 -17.1 -32.2 -6.9 11.1
LC2-Cl-C5-C4 -12.0 6.9 -5.5 - 10.2 12.3 0.5 18.9 13.2 -8.1 -4.9 12.1 -0.3 8.4 -12.3 -17.3 3.9 27.1 13.0 -16.6 11.2
geometry twist twist twist
twist twist envelope envelope twist
twist envelope twist enveloDe
twist twist twist envelope envelope envelope twist
twist
depends on their potential well depth. These were calculated by both molecular mechanics and ab initio molecular orbital methods. A molecular mechanics conformational search was carried out on each structure using the MM3 force field as implemented in Spartan.26 For flexible rings, Spartan employs the method of Goto and O ~ a w to a ~altemately ~ pucker the ring up and down in order to explore conformational space. The resulting conformations were then exported to Allinger’s MM39 program in order to eliminate those structures which did not represent true conformational minima; Le., conformations having a negative vibrational frequency were discarded. The ab initio calculations were carried out using the GAUSSIAN9225program with various basis sets up to 6-31G*. Table 3 shows the results of the conformational search in the form of the dihedral angles LC~-CI-CZ-C~and L C ~ - C I - C ~ - C (WAC). ~ On the basis of these dihedral angles, we assigned the structure as either a twist or an envelope (bent). In a pure twisted conformation, all dihedral angles associated with the carbon atoms are equal to about 112’1, while for the bent structure, one of the dihedral angles is equal to 0”. The assignment of twist or bent geometries becomes nearly arbitrary in some cases because the structure deviates markedly from pure twist and pure envelope. Thus, we arbitrarily assigned a bent structure if one of the dihedral angles is less than 15’1. The most stable form for nearly all molecules is the twist conformation, in which the twist axis passes through the carbonyl group. This is so, independent of the substituents. It is interesting that all of the bent structures had the “flap” of the envelope well away from the carbonyl group. That is, the flap passed through either carbon atom locations 2 and 4 or 3 and 5 . These are identical for the case of CPO but become unique for some of the other species. The MM3 and the ab initio calculations agreed remarkably well in most respects. On the basis of these calculations, the one structure that is predicted to be stable only in an envelope conformation is cis2,5-Me~CPO. Unfortunately, this is precisely the molecule for which we could not assign its REMPI spectrum with confidence. Consider again the spectrum of the cis and trans mixture of 2,5-Me2 CPO in Figure 3. The major peak is assigned to the trans configuration. It is possible that the other large peak to the blue at 49 572 cm-’ is due to the cis configuration. If the configuration were a twisted structure, its transition origin would
J. Phys. Chem., Vol. 99, No. 32, 1995 12095
Conformations of Methyl-Substituted Cyclopentanones be expected to lie to the red of the trans configuration. However, since we find the cis configuration to have a bent structure, its transition origin may not be predicted very well by the Levenberg-Marquardt scheme. This problem may be resolved when the physical separation of these two configurational isomers can be achieved. Finally, several of the twisted structures have two conformations that reside in relatively deep wells. Among these is the 3-Me1 CPO which can orient the methyl group either equatorially or axially (much like their six-membered ring counterparts). Microwave experiments indicate that the equatorial methyl conformer is more stable.2s The equatorial orientation, as calculated by both molecular mechanics and ab initio (631G* basis set) methods, is more stable by about 1 kcdmol, while the barrier between them, as determined by molecular mechanics, is 1.4 kcdmol. This barrier was calculated by varying the LC2-C3-C4-C3 dihedral angle in regular intervals and optimizing the structure at each point. Interestingly, both trans-2,4-Me2 and cis-2,3-Me2 CPO are predicted to be stable in both the twist and the envelope conformations. Further, trans2,4-Me2 CPO is calculated to reside in two nearly isoenergetic wells in which the methyl groups are both axial or equatorial (Le., the two conformers would be 2-axl4-eq and 2-eql4-ax). The barrier for this case was found to be 1.7 kcal/mol. The calculated barriers between these equilibrating conformations range from 1.4 to 2.0 kcal/mol. The reliability of these calculated barrier heights can be obtained from the barrier in CPO. Laane et al.4 have recently determined the barrier for pseudorotation (which is nearly isoenergetic with the planar form) by far-infrared spectroscopy. They obtained a barrier of 3.88 kcdmol. Our molecular mechanics calculated barrier for pseudorotation in CPO is 2.96 kcal/mol. Therefore, it appears that the calculations underestimate the barrier energies. According to Gutowsky and c o - w o r k e r ~ a, ~ban-ier ~ ~ ~ ~of 1 kcdmol should be sufficiently high to freeze out conformations in a molecular beam. Our calculated barriers are slightly above this limit, so that we expect to see evidence for multiple structures in our spectra. However, only in the case of the 3-Me CPO were we able to assign a peak to the less stable conformer. This is shown as an inset to the red of the main peak in Figure 5. The possibility of a hot band was eliminated by repeating the spectrum with various final beam temperatures. The ratio of areas between the equatorial transition origin peak and the peak assigned to the axial conformer did not change over a wide range of backing gas conditions. Further, a hot band, well separated from the axial conformer transition origin, was observed to grow into the spectrum as a function of increased final beam temperature. Finally, the intensity of the axial conformer is about as expected on the basis of a roomtemperature Boltzmann distribution. If the transition origin for an alternate conformation lies to the blue of the major transition, it cannot be readily distinguished from a vibrational peak of the major conformation. Our inability to find evidence for multiple conformations in the spectra of the other molecules is due in part to the fact that we have not yet analyzed the spectra of these molecules in detail. Consider the spectrum of cis-2,3-Mez CPO in Figure 5. The molecular mechanics and a b initio MO calculations both agree that two conformers should have nearly equal populations with the 2-eq/ 3-ax conformer being slightly more stable. If they freeze out in the beam, we should observe both spectra. However, we see only a single strong peak which is red-shifted by 680 cm-I. This peak can be assigned to the more stable 2-eql3-ax conformation with a predicted shift of -373 cm-I. The less stable 2-axI3-eq conformation has a predicted transition origin shift of -164 cm-I.
2 . 2-Me2
L
46800
49200
49600 Energy (cm-1)
50c100
50400
Figure 6. Strong vibronic progressions observed for the molecules 2,2-Me2 and 2,2,4-Me3 CPO are 295 and 255 cm-I, respectively.
It is worthwhile noting that just because a conformational barrier is larger than 1 kcal/mol does not mean that the two conformations will necessarily freeze out in the expansion. This energy criterion is only approximate because the criterion for freezing out ultimately depends upon the rate of equilibration and the rate of cooling in the beam. The activation energy is one factor, while the entropy of activation for the equilibration reaction is the other. Finally, collisional vibrational relaxation rate differences among molecules can also be ~ i g n i f i c a n t . ' ~ , ~ ~ , ~ ~ The Cases of 2,2-Mez CPO and 2 , 2 , 4 - M ~CPO. It is apparent that the predicted shifts for the 3s n transition origin for 2,2-Me2 and 2,2,4-Me3 CPO lie rather far from the correlation line. Before we attempt to explain the origin of these anomalous transition energies, it should be noted that the correlation is empirical in nature and no arguments based on first principles have been made to explain its existence. This increases considerably the challenge of finding a reason for its breakdown! Nevertheless, we note that, of all the cyclopentanones investigated, these two molecules have the most complex vibrational structure in their 3s n spectrum. Figure 6 shows these spectra in more detail. Well-spaced vibrational progressions with frequencies of 295 and 255 cm-' for the 2,2Me2 and 2,2,4-Me3 CPO spectra, respectively, show that the geometry of the molecule changes considerably upon excitation to the 3s Rydberg state. The low-frequency mode giving rise to the progression is tentatively assigned to the ring-CH2 symmetric rock on the basis of ab initio frequencies calculated at the 6-31G* level. A similar analysis of methyl derivatives of the cyclohexanone molecule also showed that the axial 2-methyl groups cause shifts that cannot be explained by a sum of single methyl group shifts. Rather, a second tier of rules for the axial 2-methyl group was proposed.15 Such a simple approach does not work for the case of five-membered ring compounds, most likely because this much more flexible system has many more options for minimizing energies. Analysis of Twist or Bent Structures from Polarization Ratios. Polarization ratios are reported in Table 1, where SE = Zc,JZlin. It is well known that when the excited state is of different symmetry than the ground state, an Q equal to 3/2 should be ~ b s e r v e d . ~If~the . ~ ground ~ and excited states have the same symmetry, then an Q value less than 1 should be observed. These differences are very clear-cut for the case of the six-membered rings cyclohexanone (Q = 1.50) and tetrahydropyran (Q = O.l), where the different Q values can be correlated with different HOMO ground state symmetries.12.'4 The excited 3s state has the same symmetry for both molecules. In addition, the spectra of several symmetrically oriented methylsubstituted cyclohexanones are characterized by Q = 1.5 values. In contrast to the situation in the six-membered rings, the
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12096 J. Phys. Chem., Vol. 99, No. 32, I995
Potts et al.
TABLE 4: Electrostatic Potentials and Local van der Waals Interactions from ab Initio 3-216*Basis Set Level Calculations carbonyl carbon (electrostatic potential (C2/m)and P and y van der Waals interactions (kcaymol)) compound
elec. pot.
P
CPO 2-Mel 3-Mel ax 3-Mel eq truns-2.5-Me2 cis-2,5-Mez truns-2.4-Me2 2 equatorial truns-2,4-Me2 2 axial cis-2,4-Me? truns-2.3-Mez cis-2,3-Me2 e equatorial cis-2,3-Me2 2 axial 2,2-Me2 truns-3,4-Me2 cis-3,4-Me2 3.3-Me2 2,4,4-Me3 2,2,4-Me3 2,2,5-Me3 2,2,5,5-Me4
-0.430" -0.509 -0.433 -0.428 -0.53 1 -0.529 -0.480 -0.478 -0.473 -0.474 -0.482 -0.475 -0.545 -0.418 -0.432 -0.433 -0.470 -0.537 -0.599 -0.679
0.056 0.468 0.055 0.096 0.729 0.925 0.393 0.509 0.434 0.462 0.606 0.382 0.893 0.123 0.121 0.102 0.456 0.897 1.244 1.811
a
carbonyl oxygen @, y , and 6 van der Waals interactions (kcal/mol))
Y
B
Y
0.053 0.128 0.059 0.047 0.245 0.275 0.168 0.126 0.161 0.177 0.134 0.193 0.223 0.044 0.049 0.053 0.174 0.235 0.324 0.378
-0.089 -0.137 -0.096 -0.093 -0.049 -0.044 -0.052 -0.131 -0.047 -0.025 -0.137 -0.078 -0.130 -0.096 -0.102 -0.101 -0.042 -0.114 -0.104 -0.191
6
-0.062 -0.017 -0.050 -0.017 -0.018 -0.017 -0.016 -0.072 -0.034 -0.079 -0.086 -0.103 -0.075
Values multiplied by 2.57 x
polarization ratios for the five-membered rings are more complex. The only molecule in our series of methyl-substituted cyclopentanones which exhibits an Q = 1.5 is the unsubstituted CPO. Even the trans-3,4-Me2 CPO, which has perfect C:! symmetry, has an Q = 1.3. The less symmetric cis-3,4-Me2 CPO has a reduced Q value of 0.7. Although the trend is in the right direction, it is curious that the rather unsymmetric trans2,3-Me2 CPO also has an Q of 1.37. However, the cis isomer has again a lower Q value of 0.87. Another high Q value of 1.32 is observed for the symmetrical molecule 2,2,5,5-Me4 CPO. Thus there is some consistency to the results, with the highly symmetric molecules as well as the di-equatorially substituted molecules having high Q values. It is for this reason that we have considerable confidence that the peak assigned to the trans2,5-Me2 CPO is correct. It has an Q value of 1.4 which is expected of a twisted di-equatorial conformation. Correlation between 13CNMR Shifts and 3s n REMPI Transitions. Good correlations of I3C and I7ONMR chemical shifts have been made with n* n transitions in ketone^.^^,^^ I3C resonances shift to higher field with increasing absorption wavelength while I7O resonances shift to lower field. Several years ago, Cornish and Baer23noted a correlation between I3C NMR shifts (carbonyl group) and the shifts in 3s n transition origins for a series of cyclic and linear ketones. This correlation for the methyl-substituted CPOs of this study is shown in Figure 7. Cornish and Baer23have described the possible correlation factor for these optical 3s n and NMR shifts for a series of ketones. Methyl substitution on the CPO ring affects the diamagnetic shielding contribution, which gives rise to a change in the ground state wave function. The energies of the diffuse 3s molecular orbital and the ground state dictate the shifts in the optical spectrum, while electrostatic potentials of the carbonyl carbon determine the NMR shifts. The negative slope indicates that an upfield shift is correlated with a lowering of the optical transition energy to the 3s Rydberg state, contrary to the observations made at the n*state. I3CNMR is a measure of ground state interactions whereas REMPI is a measure of both ground and 3s Rydberg excited state interactions. While the NMR technique may be influenced by solvent effects,35the REMPI spectra are obtained in a collision-free environment. It has been well documented in the literature that nonbonded steric interactions play a significant role in determining I3C
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0 0
...
o
REMPIlcm-l, = -21 5.4 * ''C
