118
J . Phys. Chem. 1990, 94, 118-124
-
incorporation of the carboxylic acid molecules and not by ion exchange of the chloride ions. The gallery height increases to 18 8, upon intercalation. The N H A molecules H bond to the chloride ions and are oriented with all the dipoles pointing in the Same direction. This bulk dipole moment leads to the manifestation of nonlinear second harmonic generation. This is particuolarly interesting, since crystals of pure N H A exhibit no frequency-
doubling characteristics.
Acknowledgment. We gratefully acknowledge the support of the National Science Foundation (CHE 8510614) and the DOD-university research instrumentation grant (DAAL 03-87G-0050). Registry No. NHA, 2645-07-0; [ LiAI2(0H),]CI, 68949-09-7.
Scaled ab Initio Force Fieid and Vibrational Spectra of Azetidine R. Dutler, A. Rauk,* and R. A. Shaw Department of Chemistry, University of Calgary, Calgary, Alberta, Canada T2N 1 N4 (Received: January 17, 1989; I n Final Form: May 9, 1989)
The vibrational spectra are reported for azetidine both in solution and in the vapor phase. A harmonic force field is derived by scaling the ab initio force constants calculated at the 6-31G* level, with the previously reported optimized geometry as the reference structure. The 6-31G* force field for oxetane is also evaluated and scaled to reproduce the literature assignments, so as to provide appropriate factors for the initial scaling of azetidine force field. The calculated frequencies for azetidine, together with the absorption intensities calculated with the 6-31G* atomic polar tensors, are sufficiently accurate that all major features in the experimental spectra are readily assigned. This confirms that only a single conformer, with the NH assuming the equatorial position, is present under the experimental conditions.
Introduction
Since the demonstration by Blom et a].' and Pulay and Meyer2 of the accuracy of ab initio methods in evaluating harmonic force constants, a dominant theme has been the derivation of force fields for small molecules incorporating unique structural aspects, Le., those that may be viewed as the smallest reasonable subdivisions of larger structures.3 The spectra of molecules too large for direct ab initio calculation may then be predicted on the basis of force constants calculated for such subunits. The small-to-medium sized rings are of particular interest in that there are unique and significant interactions among the ring-stretching coordinates even between nonadjacent bonds and also in that redundancy problems preclude the ring-deformational modes from being modeled realistically with force constants for individual torsional and angle-bending coordinates. Among the four-membered rings, complete scaled ab initio force fields have previously been reported for cyclobutane,4 oxetaneSb(both 4-21G), and thietane6 (3-21G), with the force constants scaled in each caseh%'to compensate for systematic overestimation of the diagonal force constants in particular. Although similar studies have not been carried out for azetidine, this compound has been the subject of a number of previous investigations, both experimental (IR,8-I0 (1) Blom, C. E.; Slingerland, P. J.; Altona, C. Mol. Phys. 1976, 31, 1359-1376. Blom, C. E.; Altona C. Ibid. 1976, 31, 1377-1391. (2) Pulay, P.; Meyer, W. J. Mol. Spectrosc. 1971, 40, 59-70. (3) For recent reviews, see, e.&: (a) Fogarasi, G.; h l a y , P. In Vibrational Spectra and Srrucrure; Durig, J. R., Ed; Elsevier: Amsterdam, 1985; Vol. 14, pp. 125-219. (b) Hess, B. A,; Schaad, L. J.; Carsky, P.; Zahradnik, R. Chem. Rev. 1986,86, 709-730. (4) Banhegyi, G.; Fogarasi, G.; Pulay, P. J . Mol. Strucr. 1982,89, 1-13. ( 5 ) (a) Kydd, R. A.; Wieser, H.; Kiefer, W. Specrrochim. Acra 1983,39A, 173-180. (b) Banhegyi, G.; Pulay, P.; Fogarasi, G. Specrrochim. Acra 1983, 39A, 761-769. (6) Shaw, R. A.; Castro, C.; Ibrahim, N.; Wieser, H. J. Phys. Chem. 1988, 92, 6528-6536. (7) Shaw, R. A.; Ursenbach, C.; Rauk, A,; Wieser, H. Can. J. Chem. 1988, 66, 1318-1332. (8) Carriera, L. A.; Lord, R. C. J. Chem. Phys. 1969, 51, 2735-2744. (9) Robiette, A. G.; Borgers, T. R.; Strauss, H. L. Mol. Phys. 1981, 42, 15 19-1 524. (IO) Gunther, H.; Schrem, G.; Oberhammer, H. J. Mol. Specrrosc. 1984, 104, 152-164.
0022-3654/90/2094-0118$02.50/0
Raman," ED,10,12 MW'O) and theoretical,'*16 aimed at elucidating the s t r u ~ t u r e ' ~ . 'and ~ - ~ potential ~ for ring p u ~ k e r i n g . ~ ~ ~ ~ ~ Calculations and experimental results are in agreement that azetidine exists as a single conformer, puckered, with a pyramidal N atom and the N-H bond in a pseudoequatorial orientation. As part of a combined MW/ED structure investigation, Gunther and co-workersIOhave reported the vapor-phase infrared absorption spectrum of azetidine (2-cm-1 resolution) and refined an empirical valence force field to fit their vibrational assignments. We have remeasured the vapor-phase absorption spectrum at a resolution of 0.12 cm-I and have also measured the infrared and Raman spectra of solution and neat liquid, respectively. The vibrational assignments are then reexamined through systematic scaling of the 6-31G* a b initio force constants, calculated in conjunction with a recent study of the ring inversion/NH inversion potential surface.16 To this end, a force field is also calculated for oxetane with the same basis set. Scaling factors optimized to fit the previously reported fundamental absorption frequencies of oxetane5 are then used as a means of predicting the azetidine spectrum and for confirming the final optimized azetidine force field as reasonable. The assignments of ref 10 are confirmed for the most part in the A' species, however, a number of revisions are required for the A" modes. Experimental Section
Azetidine was purchased from Aldrich (>98%), and the reported purity was confirmed by analytical GC. Vapor-phase and solution infrared spectra were run at 0.12- (400 scans) and 1-cm-I resolution (400 scans), respectively, with use of a Nicolet Model (1 I ) Carriera, L. A.; Carter, R. 0.; Durig, J. R. J. Chem. Phys. 1972.57, 3384-3387. (12) Mastryukov, V. S.; Dorofeeva, 0. V.; Vilkow, L. V.; Hargittai, I. J. Mol. Struct. 1981, 34, 99-1 12. (13) Catalan, J.; Mo, 0.; Yanez, M.J . Mol. Srrucr. 1978, 43, 251-257. (14) Skancke, P. N.; Fogarasi, G.; Boggs, J. E. J. Mol. Srrucr. 1980, 62, 259-273. ( 1 5 ) Cremer, D.; Dorofeeva, 0. V.; Mastryukov, V. S . J. Mol. Struct. 1981, 75, 225-240. (16) Dutler, R.; Rauk, A.; Sorenson, T.S . J . Am. Chem. SOC.1987,109. 3224-3228.
0 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 1. 1990 119
Force Field and Vibrational Spectra of Azetidine TABLE I: Observed Infrared Absorptions and Raman Lines
(a") for Azetidine
infrared peak no." 1
2 3 4 5 6 7 8 9
IO 11
12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
assignment
solutionb
vapoF
3339 vw 2994.2 m 2961.2 s 2930.1 m,dcn 2920.4 m,dcn 2871.0 m, dcn 2861.3 s, dcn 1491.7 w
3357.7 3003.0 (2974.2) 293 1.6 (2871 .O) 2861.9 1498.9
1446.5 m 1334.5 vs 1314.7 w, dcn 1249.4 m 1238.4 m 1198 vw
1450.1 1340.6 B 1320.5 1251.4 B 1244.4 B 1195.9
1146.7 m 1084.4 s 1021.7 m 983.2 s 949.0 w
1145.5 1088.4 B 1028.2 989.8 B 948.8
Ramand
this work
3330 m, p 2982 m, dp 2956 s, p 2934 s, p 2924 m, dp
741 .O s (C2C14) 658.1 s
910.4 891.4 824.6 736.4 647.9 207.2f
y2
~1 ~4
(2975), (2947),
~ 1 (2960) 7 ~ 1 (2934) 8
y5
y6
y19
1I94 m,p 1 I80 sh, dp 1 I50 m, p
y7 y20
y7
va
Y8
y2 1 y22
"9
Y19
y20
y9
y23 VI0
1078 w, dp 1022 vs, p 982 s, dp
y24
"I I y25
VI2
920 s, dp 902.1 s
y2
"3 y4
y17 via
2862 vs, p 1487 m, dp 1458 sh, dp 1446 m,dp 1337 vw, ? 1313 vw, ? 1247 w, dp
-
ref IOc VI
VI
y26
y25
815 vw, dp 755 w, dp 668 w, dp 217 w, ?
y27 y14 VI5
y16
y16
4Corresponds to peak numbering in Figures 1-3. bCC14solution unless otherwise indicated (Figures I , 2). Abbreviations: s = strong; m = medium; w = weak; sh = shoulder; dcn indicates band resolved for measurement using Fourier self-deconvolution.22 Cobservedband contour is A, C, or A/C hybrid unless designated as B. dSpectrum of neat liquid (see Figure 3). Abbreviations: p = polarized; dp = depolarized. ePositions in brackets denote observed positions reported in ref IO. 'Vapor-phase position from ref 8.
8000 FT-IR spectrometer (see Figure 1 and 2). Solution spectra were run in both CCI, and C2CI4and are virtually identical over common spectral windows and are unchanged upon dilution. Only the CCI, spectrum is included here. Polarized and depolarized Raman spectra (Figure 3) were measured for a neat sample with a Jarrell-Ash 25-100 triplegrating monochromator interfaced to an IBM PC to allow for multiple scans. The 514.5-nm line of an Ar+ laser (Coherent Radiation) was selected for all measurements, with a typical power of 500 mW measured at the sample. The measured band positions (Table I) are from a spectrum run with no polarizer, 7-cm-' slits, and I-cm-I step between data points and averaged over 4 scans.
Calculations The optimized 6-3 lG* structure of azetidine has been reported previously.16 Analytical Cartesian force constants were evaluated at that geometry with the same basis set by the GAUSSIAN82 program,17 modified to run on the Cyber 205 supercomputer at the University of Calgary.l* The force constants were then transformed to a nonredundant set of local symmetry coordinates (Table 11) and scaled according to Fij = (CiCj)1/2Kij, where represents the ab initio force constants and Fij the corresponding scaled value. Full symmetry coordinates were constructed so as to provide clearer descriptions of the normal modes (see Table IV). These are not included for reasons of space; however, they correspond exactly to the local symmetry coordinates for modes involving only atoms lying in the plane of symmetry at equilibrium (e.g., P-CH, and NH stretches and bends), as well as for the ring pucker and in-plane deformation. For the ring stretches and a-CH2 modes, normalized in-phase and out-of-phase combinations of the symmetry-related coordinates were constructed. Least-squares optimizations of the scaling factors were accomplished using a program that minimized the average deviation ()7).Binkley, J . S.; Frisch, M. J.; DeFrees, D. J.; Ragavachari, K.; Whiteside, R. A.; Schlegel, H.B.; Fluder, E. M.; Pople. J. A. GAUSSIAN
82; Department of Chemistry, Carnegie-Mellon University: Pittsburgh, PA,
1983. (18) Rauk, A.; Dutler, R. J . Comp. Chem. 1987, 8, 324-332.
270~
21
127
r
rOO
550
700
850
1000
1150
1300
lr50
WRVENUN6ERS
Figure 1. Midinfrared absorption spectra of azetidine. From bottom: vapor phase (IO-cm path; pressure, 8 Torr for lower plot, 98 Torr for inset); CC14solution (0.1-mm path, 1.35 M). Uppermost trace represents spectrum calculated for force field run 5 (see Table IV), assuming Aullz
= 10 cm-I.
between the observed and calculated frequency parameters X i = ( ~ T C U ) with ~ , the observed positions weighted by (1/Xpb)2. Infrared absorption intensities were evaluated from the atomic polar tensors'9 and Raman scattering activities calculated with use of
Dutler et al.
The Journal of Physical Chemistry, Vol. 94, No. 1 , 1990
120
TABLE 11: Local Symmetry Coordinate Definitions for Azetidine” 8
I
I 2 3 4
C-N stretch
5 6
a-CH stretch
6
C(2)-N C(4)-N c(4j-c(3 j v - c ( 31 C(4)-H( 11) C(4)-H(10)
C-C stretch
12 13 14
C(4) C(2) C(4) C(2) C(4) C(2) C(4) C(2)
a-CH2 scissor a-CH, scissor a-CH, wag a-CH2 wag a-CH2 twist a-CH, twist a-CH, rock a-CH2 rock P-CH, scissor P-CH, wag P-CH, rock P-CH, twist ring deformn ring pucker N-H bend (in-plane) N-H bend (out-of-plane)
15
16 17 18
19 20 21 22 23 24 25 26 27
7 8
a-CH stretch
9 10
6-CH stretch
II
N-H stretch
C(2)-H(7) C(21-H(6) ci3j-~(9j C(3)-H(8)
410-4-1 1) a(6-2-7) p(1-4-11) p(1-4-10) -p(3-4-11)-(3(3-4-10) @(I-2-7) p(1-2-6) - p(3-2-7) - p(3-2-6) p(3-4-10) p(1-4-11) - p(1-4-10) -/3(3-4-11) p(3-2-6) p(1-2-7) - p(1-2-6) - p(3-2-7) p(1-4-11) - O(1-4-10) p(3-4-11) - p(3-4-10) p(1-2-7) - p(l-2-6) + p(3-2-7) - p(3-2-6) a(8-3-9) p(4-3-9) - p(2-3-8) - p(2-3-9) p(4-3-8) p(4-3-8) - p(4-3-9) + p(2-3-8) - O(2-3-9) p(2-3-9) p(4-3-8) - p(4-3-9) - p(2-3-8) o(2-1-4)- e(i-4-3) o(4-3-2) - e(3-2-11 T(2-1-4-3) - ~(1-4-3-2) + ~(4-3-2-1) - ~(3-2-1-4) p(5-1-4) - b(5-1-2) D(5-1-4) + p(5-1-2)
+ +
+
+
+
+
+
+
depolarization ratios calculated for the final scaled force field are included in Table IV and the theoretical infrared spectra plotted with the experimental results in Figures 1 and 2 .
600
x30
Assignments and Force Field Refinements
-
c
‘E
150
I
G
4
X125
!7
2’6 i y Zn-2
ZiZZ
1
-
\ 313C 371; &-9L C? J T 5 f s =
353-
I
333Z
I t C -
Figure 2. CH/NH stretching region of the infrared absorption spectrum of azetidine. From bottom: vapor phase (10-cm path; pressure, 8 Torr for lower plot, 98 Torr for Inset); CC14 solution (0.1-mmpath, 1 35 M; 1 .O-mm path, 1 45 M for expansion); calculated spectrum (see caption to Figure I ) . The absorption at 3282 cm-I (not numbered) in the solution spectrum is believed to correspond to the OH stretch of trace water, hydrogen-bonded to azetidine. See text.
analytical polarizability derivatives, provided by the G A U S S I A N ~ ~ program.20 The infrared and Raman intensities and Raman
The first stage of the vibrational analysis involves nonuniform scaling of the ab initio force constants using factors previously optimized for analogous coordinates in related compounds. This then permits assignment of those experimental features that are well removed from others and those for which infrared vapor-phase contours or Raman polarization measurements confirm the correct symmetry species; the initial scaling factors may then be refined to fit these firm assignments and the less obvious assignments pursued following the guidance of the adjusted force field. Unfortunately, there are very few scaled 6-31G* force fields in the literature to date. As a means of deriving appropriate starting values for azetidine, we have evaluated the optimized structure and force constants for oxetane using the same basis set and refined four alternate sets of scaling factors to fit the published assignm e n t ~ .The ~ refined values are listed in Table 111. The four individual runs differ according to the number of scaling factors defined and provide an indication as to whether only a limited number, some of which scale large groups of coordinates, is sufficient (run 1) or whether it is necessary to further subdivide the coordinate set into smaller groups (runs 2, 3) or even to assign separate factors for each coordinate type (run 4). We have shown previously6.’ that for the 3-21G basis set significant differences may arise among factors scaling coordinates that are similar in type. For both runs 3 and 4, there are factors (P-CH, twist and a-CH2 rock, respectively) that deviate markedly from those for other bending coordinates. However from earlier work,5 (19) (a) Biarge, J. A.; Herranz, J.; Morcillo, J. An. R. SOC.ESP.Pis. Qim., Ser. A . 1961, 57, 81. (b) Person, W. B.; Newton, J. H. J. G e m . Phys. 1974, 61, 1040-1049. (20) Frisch, M. J.; Binkley, J. S.; Schlegel, H. B.; Raghavachari, K.; Melius, C. F.; Martin, L. R.; Seeger, R.; Whiteside, R. A,; Fox, D. J.; Fluder, E. M.; Pople, J. A. GAUSSIAN 86; Department of Chemistry, Carnegie-
Mellon University: Pittsburgh, PA, 1984.
Force Field and Vibrational Spectra of Azetidine
The Journal of Physical Chemistry, Vol. 94, No. 1, 1990 121 6.7
1
I
I
3400
3300
3200
3100
3000
2900
2800
19
I
20
I
1600
1400
1200
1000
800
600
400
200
UAVENUMBERICM- I
Figure 3. Raman spectrum of azetidine (neat liquid). For each section (1600-lOO cm-l and 3400-2800 cm-I), the perpendicular (lower) and
parallel (upper) polarized spectra are included. Each trace represents the average of four scans, with 2 cm-l between data points and I-s dwell at each point. it is clear that for oxetane the scaling factors for A2 and B1 coordinates may be inaccurate due to possible misassignment or incomplete assignments (A2), the influence of anharmonic coupling with the ring puckering mode ( B l ) and uncertainty in choosing the appropriate reference geometry (planar or puckered ring) for evaluating the force field. We therefore attach less significance to the factors for the rocking and twisting coordinates of runs 3 and 4. The quality of the fit for oxetane deteriorates only moderately as the number of variables decreases, the average deviation ranging from 10.6 (optimizing thirteen separate scaling factors) to 13.6 cm-’ (four factors) over ninety-five input frequencies for oxetane and four partially deuterated species. This suggests that the scaling factors of run 1 should be sufficient to provide reliable predicted frequencies for azetidine. Each of these sets of scaling factors was transferred to scale the calculated azetidine force constants. Fourteen of the twenty-seven fundamental transitions could then be assigned unequivocally on the combined evidence of their predicted positions together with experimental evidence. For example, the A” transitions were expected to exhibit distinctive B contours in the vapor-phase absorption spectrum, and five of the A” modes were readily assigned on that basis. Raman polarization measurements confirmed assignments for two additional Af modes (vIo and v l I ) . Several other modes including three of the C-H stretches of A’ symmetry (v2, u4. and us), the two CH2 scissors V6 and v7, the @CH2 rock vI4, and the ring deformation vis, were assigned readily on the basis of their predicted positions and vapor-phase infrared band shapes that preclude their assignment to the A” species. The calculated absorption intensities were also helpful in some cases, for example in confirming the assignments for and v,,-both
calculated and observed to be the strongest absorptions through the midinfrared. The calculated positions for runs 1 (4 scaling factors) and 4 (17 scaling factors) are listed in Table IV, where the 14 assignments discussed above are highlighted by boldfaced type. So as to gauge the relative accuracy of these two predictions, we compare them in their ability to reproduce this limited set of firm assignments. In both cases, the fit to the 11 midinfrared positions is good (6.9 and 6.0 cm-I, respectively, excluding the C-H stretches, see Table III), suggesting that a single factor is sufficient to scale all bending force constants. The larger differences among the CN, CC, and C H stretching factors are certainly justified. Even the subtle distinction between the (r-CHz and @CH2 stretching factors is merited, as evidenced by the accuracy of run 4 (average error of 5.8 cm-’ including C-H stretches; scaling factors of 0.808 and 0.832, respectively), as compared to run 1 (average error of 8.3 cm-’ including C-H stretches), for which a single factor of 0.818 was used for all C H stretches. To complete the remaining assignment, run 4 was used to guide the search for the C H stretches, while both runs 1 and 4 were considered in searching for the as yet unassigned midinfrared modes. These assignments are discussed below. A’Modes. The N H stretch vI is extremely weak in the infrared; however, this transition is clear in the Raman spectrum at 3330 cm-’. The N H stretching region of the infrared spectrum of azetidine has been examined previouslyz1in CC14 solution and at a longer (IO-cm) path length. A broad absorption at 3339 cm-’ was reported, with a higher frequency shoulder also present at 3387 cm-I, which were assigned, respectively, as the N H stretching mode of the axial and equatorial conformers. The former corresponds to a very weak A-type band in our vapor-phase absorption spectrum at 3357.7 cm-I (Figure 2), which has also been detected previously at a longer path length (1 1.75 m) and assigned by Gunther and co-workersI0 as the N H stretch v I . Finding no evidence of the axial conformer elsewhere in the midinfrared and C H stretching region, we also adopt the assignment of Gunther et al., placing the corresponding solution infrared and Raman bands at 3339 and 3330 cm-l, respectively. The features observed to low frequency of the N H stretch in all of our spectra are ascribed to the O H stretch of trace amounts of water, hydrogen-bonded to azetidine. The solution absorption at 3282 cm-’ (Figure 2) is accompanied by a relatively sharp feature at 3678 cm-I (not shown) that is then assigned as the free O H stretch. The C H stretch v3 is assigned to the solution infrared absorption band observed at 2961.2 cm-I (peak no 3, Figures 1-3), corresponding to a sequence of transitions spread over the range 2940-2980 cm-’ in the vapor-phase absorption spectrum. The strong polarized Raman feature at 2956 cm-’ confirms this assignment. The A-type band appearing at 1320.5 cm-I as a low-frequency shoulder (peak no. 14, Figure 1) on v20 (peak no. 13) is confirmed as the in-phase (r-CH2 wag (v& with the calculated absorption intensity relative to that of the neighboring vzO, matching the experimental ratio very closely. It is of some concern that the calculated position is in error by over 20 cm-’ for run 1, although the corresponding out-of-phase wag is predicted within 10 cm-I of that observed. This disparity is discussed further below. The a-CH2twist, v9, is predicted with very low intensity in the infrared spectrum, and is believed to give rise to the very weak vapor-phase transition at 1195.9 cm-] (peak no. 15, Figure 1). The associated Raman band is quite intense (see Figure 3). Close inspection of the spectrum over the 1150-1 200-cm-I range suggests the band to be partially polarized, with a third transition at 1172 cm-I (vz3) partially responsible for the residual feature in the perpendicularly polarized spectrum. This interpretation of the Raman spectrum is also supported by the vapor-phase Raman spectrum reported in ref 11, where this spectral region shows a very sharp, weak emission that we assign as v9, superimposed upon a broader feature ( v ~ ~ ) . Both u12and u I 3are predicted to lie in the 900-950-~m-~ range,
-
(21) Krueger, P. J.; Jan, J. Can. J . Chem. 1970, 48, 3236-3248.
122
The Journal of Physical Chemistry, Vol. 94, No. I , 1990
Dutler et al.
TABLE 111: Scalina Factors for Azetidine Predictions and Refinement azetidine predictions" run I 0.748 (0.8) 0.854
coordinate CO (CN) str CC str NH str a-CH str 6-CH str ring deformn ring pucker a-CH2 scissor a-CH2 rock a-CH2 wag a-CH2 twist @-CHIscissor P-CH, rock &CH2 wag P-CH, twist NH bend (in-plane) NH bend (out-of-plane) av error in calc positn oxetane azetidine (excl C-H str.) azetidine (incl C-H str.)
run 2 0.748 (0.8)
0.818 0.794 0.8
run 3 0.750 (0.8) 0.867 (0.808) 0.808 0.832 0.797 0.8 0.780 0.857 0.758 0.789 0.775 0.783 0.788) 0.788)
(0.788) 13.6 6.9 8.3
13.4 7.3 8.6
11.0 7.0 6.6
run 5 (azetidine refinement)* 0.784 0.883 0.792 0.809 0.827
run 4 0.748 (0.8) 0.872 (0.808) 0.808 0.832 0.795 0.8 0.779 0.798 0.769 0.783 0.788 0.796 0.759 0.832 (0.788) (0.788)
0.785
10.6 6.0 5.8
5.1 4.8
'Optimized 6-31G* scaling factors for oxetane, with alternative scaling procedures. Values in brackets (NH bends, C N stretch) for runs 2-4 were estimated as the average of oxetane bending and skeletal stretching factors from run I . The N H stretch factor of runs 1 and 2 was inferred by comparing the observed and 6-31G* calculated N H stretching frequencies for methylamine (ref 23). *Scaling factors optimized to fit those assigned frequencies in bold-faced type in Table IV. Calculated frequencies are listed under the heading "final refinement" in Table IV. CFor azetidine, average error includes only those transitions in bold-faced type in Table IV.
TABLE IV: Observed and Calculated Fundamental Transition Frequencies (cm-') for Azetidine
Y
calc positionC
peak no.'
calc intensityC
_______
IR
YObS
Raman
assignment/
A' 1
1
2 3 4 5 6 7 8 9 IO
2 3 4 7 8
11
12 13 14 15 16
3357.7 3003.0 2961.2 s o h 2931.6 2861.9 1498.7 1450.1 1320.5 1 195.9 1145.5 1028.2 948.8 9 10.4 136.4 647.9 217 R
3411.5 2987.7 2950.5 2937.2 2881.1 1503.4 1452.7 1343.4 1 187.9 1144.3 1023.2 938.6 906.0 739.4 636.6 198.7
3390.6 301 1.9 2968.3 2927.3 2863.3 1496.2 1451.7 1331.3 1186.0 1150.1 1027.7 940.1 909.4 741.3 639.1 200.2
3357.7 3003.2 2960.0 2928.2 2865.1 1500.7 1450.0 1342.2 1186.1 1142.1 1025.8 939.9 904.4 737.8 635.2 198.3
2 51 45 47 80
2920.4 s o h 287 1 .O s o h 1458 sh,R 1340.6 1251.4 1244.2 (1 180) sh,R 1088.4
2926.8 2858.1 1468.2 1363.3 1254.0 1234.7 1187.9 1088.7 998.2 922.2 810.9
2928.1 2859.4 1473.7 1361.1 1256.0 1250.9 1174.8 1082.8 990.5 928.1 802.1
76 99 8 19 3 8 1 17
105 27 3 4
11
10
920 R 815 R
2944.8 2875.7 1476.6 1363.7 1256.9 1253.1 1175.5 1086.1 997.5 918.8 802.9
u l . uI6)
8.3 9.6
5.8 6.4
4.8 7.0
IO 12 15 17 19 21 23 26 27 28
1 1
2 1 15 5 2 28 56 47 4
107 65 115 80 161 13 14 2 19 1 29 2 5 3 2 0.3
0.32 0.75 0.05 0.37 0.17 0.71 0.74 0.10 0.75 0.62 0.10 0.43 0.75 0.71 0.68 0.32
N H stretch @CH2 asym str &CHI sym str a-CH, str (eq) a-CH2 str (ax) a-CH2 scissor @-CHIscissor a-CH, wag a-CH, twist a-CH, rock 0.5 C N str 0.4 C C str 0.3 CC str + 0.2 N H bend (out-of-plane) 0.2 C N str 0.3 ring deformn 0.2 N H bend (out-of-plane) + 0.1 C N str 0.5 P-CH, rock + 0.4 N H bend (out-of-plane) + 0.2 a-CH2 twist 0.7 ring deformn 0.3 N H bend (out-of-plane) 0.2 a-CH2 rock ring pucker
+
+ +
+
+
A"
17 18 19 20 21 22 23 24 25 26 27
5 6 9 11
13 14 16 18 20 22 25
av error (cm-') boldface overall (excl
989.9
0.1 0.1
4
2 6 3 11 0.4
a-CH, str (eq) a-CH, str (ax) a-CH, scissor N H bend (in-plane) a-CH, wag 0.7 P-CH, wag + 0.3 a-CH, wag 0.4 @-CH2twist + 0.3 a-CH2 twist 0.5 a-CH, twist 0.2 a-CH, rock CN str CC str 0.6 a-CH, rock + 0.3 P-CH, twist
+
'Corresponding to peaks labeled in Figures 1-3. *Transitions designated by boldfaced type are those whose assignments are completely unambiguous in light of the predicted frequencies and experimental evidence and were used to gauge the accuracy expected in the frequencies predicted for less obvious assignments. See text. All positions are from the vapour phase unless otherwise noted (R = Raman, s o h = solution measurement). 'See Table 111 for scaling factors. dSix scaling factors (see Table 111) refined to fit boldfaced assignments only. See Figures 1 and 2 for plots of theoretical spectra. eCalculated intensities for Run 5 force field. Units of km mol-' for infrared and A4 amu" for Raman scattering activity. The third column lists the Raman depolarization ratio. 'From potential energy distribution in full symmet:y coordinates.
which is congested by what appear to be a number of combination bands involving the ring puckering mode. The distinctive Q branch at 948.8 cm-' (peak no. 21) is assigned as u 1 2 , with the corre-
sponding Raman emission concealed by peaks no. 20 and 22. The final A' mode is predicted to lie in the region of 900-910 cm-l. This region is congested in the vapor-phase absorption spectrum,
Force Field and Vibrational Spectra of Azetidine
The Journal of Physical Chemistry, Vol. 94, No. 1, 1990 123
TABLE V Scaled Force Constants for Azetidine“ 1 1
1 6
1 1 1 1
11
3 3 3 3 3 5 5 5 5 6 6 6 6 6 9 9 10
IO II I1 12 12 12 14 14 14 16 16 16 18 18 20 22 24 26
16 21 26 6 11
16 21 26 8 13 18 23 6 12 17 22 27 14 24 12 22 12 22 13 18 23 14 19 24 17 22 27 22 27 27 24 24 26
4.28 12 -0.01 74 -0.0162 -0.0238 -0.0229 -0.0700 0.0691 0.0039 -0.0686 0.1793 0.0068 0.0036 -0.0088 0.0855 0.02 I7 4.7072 0.1014 0.00 I O -0.0098 -0.01 23 -0.002 1 -0.06 56 -0.0026 0.0687 0.001 1 -0.01 23 0.0096 -0.0006 -0.0072 0.7703 -0.0002 0.0225 -0.0040 -0.05 13 -0.0168 0.0082 -0.0072 -0.02 16 0.0474 1.4184 0.6908
1 1 1 1 1 1
3 3 3 3 3 5 5 5 5 6 6 6 6 9 9 9 10
IO 11 11
12 12 12 14 14 14 16 16 18 18 20 21 22 24 27
2 7 12 17 22 27 7 12 17 22 27 9 14 19 24 8 13 18 23 9 16 25 14 24 14 24 14 19 24 15 20 25 18 23 18 23 20 21 25 25 27
-0.1415 0.1829 0.0359 0.0495 -0.0109 0.2257 -0.0102 -0.1549 0.0017 -0.0250 0.0379 0.0186 -0.0049 0.0010 0.0091 0.0043 -0.0040 -0.0502 -0.0204 4.8871 0.0183 0.0163 -0.0104 -0.01 59 -0.0051 -0.0499 -0.0296 0.0055 -0.0928 0.0266 0.0042 0.0064 0.0684 -0.0782 0.5325 0.061 1 0.68 17 0.7218 -0.0624 -0.0021 0.51 I7
1 1 1 1 1
3 3 3 3 3 5 5 5 5 5 6 6 6 6 9 9 9
IO IO 11 11 12 12 12 14 14 14 16 16 18 18 20 21 22 24
3 8 13 18 23 3 8 13 18 23 5
IO 15 20 25 9 14 19 24
IO 18 27 16 25 16 25 15 20 25 16 21 26 19 24 19 24 22 23 27 27
0.097 1 0.1697 -0.2113 -0.03 13 0.0089 4.21 12 -0.0142 0.0288 -0.0278 0.0933 4.5294 -0.0084 0.0048 -0.0043 0.0058 0.0008 0.0041 -0.0067 0.0455 0.0527 -0.0105 0.0124 -0.02 17 -0.0201 -0.038 1 0.0372 -0.0029 0.0057 0.0205 0.0339 -0.027 1 0.0115 -0.0046 0.0088 -0.0072 -0.0472 0.0091 0.0505 -0.01 36 -0.1584
1 1 1 1 1
3 3 3 3 3 5 5 5 5 5 6 6 6 6 9 9
IO IO IO 11 11
12 12 I2 14 14 14 16 16 18 18 20 21 23 25
4 9 14 19 24 4 9 14 19 24 6 11
16 21 26
IO 15 20 25 11
20
IO 18 27 18 27 16 21 26 17 22 27 20 25 20 25 24 26 23 25
0.1069 -0.01 54 -0.0239 -0.0329 0.0820 0.0072 0.061 1 -0.1686 -0.0208 -0.0383 0.0720 0.0181 -0.0272 0.0118 -0.0008 0.0152 0.0020 -0.0025 0.0093 0.0009 0.0868 4.8794 0.0205 0.0072 -0.0155 0.0993 -0.0104 -0.0044 0.0014 -0.0045 -0.008 1 -0.0244 0.0073 0.0196 -0.0020 -0.0466 0.1030 0.0161 0.7004 0.1268
1 1 1 1
I 3 3 3 3 3 5 5 5 5 5 6 6 6 6 9 9
IO IO 11 11
12 12 12 12 14 14 16 16 16 18 18 20 22 23 25
5
IO 15 20 25 5 IO 15 20 25 7 12 17 22 27 11
16 21 26 12 22 11
20 11
20 12 17 22 27 18 23 16 21 26 21 26 25 22 26 27
-0.0028 -0.009 1 0.3092 0.0298 0.0132 0.0686 0.0600 -0.0172 -0.1526 -0.0362 0.0078 0.0950 0.0008 0.0168 -0,0292 -0.0006 0.0165 0.0041 0.0205 -0.0028 -0.0575 0.0005 0.0793 6.2448 -0.0042 0.721 5 0.0008 -0.0009 0.0068 0.0070 -0.0197 0.6936 -0.021 5 -0.0363 0.0067 -0.0332 0.03 15 0.4064 -0.0129 0.0005
” Units of millidyne per angstrom (stretches),millidyne angstroms (bends), and millidyne (stretch/bend interactions). Only symmetry-independent force constants are listed. and the single strong feature in the solution phase spectrum was believed initially to correspond to an apparent B contour at 91 1 cm-I in the vapor phase and hence assigned as the A” mode v26. However, this interpretation is not consistent with the calculated infrared and Raman intensities, which indicate that the A’ mode should dominate the A” mode in the infrared. In contrast, the A” mode is predicted with twice the intensity of the A’ in the Raman spectrum. These predictions can only be reconciled if the strong Raman band observed at 920 cm-l (peak no. 22) is assigned as v26, with no apparent counterpart in the infrared (in accord with the low predicted intensity) and the solution-phase infrared absorption at 903 cm-I (peak no. 23) then assigned as vI3. The complexity of the vapor-phase band shape in the 850-950-cm-I range is then attributed to strong coupling of vI3 (ring deformation) with the ring-puckering mode. The ring-inversion mode V I 6 may be described as a skewed quartic oscillator and cannot be modeled realistically by a harmonic force field, although as discussed by Pulay and co-workers in the context of ~ x e t a n ethe , ~ ~force field does probably correctly include some of the influence of harmonic coupling of the inversion with other modes of the same symmetry. The predicted position of 198-200 cm-’ is in surprisingly good agreement with the experimental s p a ~ i n g ~of* 207.2 ~ ~ ~ ’cm-I for the 0-1 transition and the Raman feature measured at 217 cm-I (peak no. 28, Figure 3). This agreement is probably fortuitous, and the observed position was used neither in assessing the accuracy of the force field predictions nor in the final stages refining the scaling factors. A” Modes. The axial (Y-CH, stretch, vI8, may be assigned assuming that the vapor-phase band contour at 2862 cm-l reflects
the presence of two overlapping fundamentals, vs (A’) and vI8 (A”), the latter giving rise to a characteristic B-type band contour with the gap occupied by the A’ fundamental. These transitions (peak no. 6 and 7, Figure 2) are resolved upon Fourier self-deconvolution (FSD)22of the solution infrared spectrum. The second A” C H stretch, vI7, is calculated at 2927 cm-’ with appreciable intensity. There is no obvious counterpart in the observed infrared spectra; however, the depolarized Raman spectrum clearly places this fundamental at 2924 cm-’ (peak no. 5 , Figure 3), 10 cm-I below the strongly polarized A’ mode v4. These two fundamentals are also resolved upon FSD of the solution infrared absorption spectrum. In the final calculated spectrum (see Figure 2), the fundamentals v4 and vI7 coincide and are not resolved even assuming a band width (10 cm-l) somewhat narrower than typical experimental values over the CH-stretching region. There remains some ambiguity in assigning the out-of-phase cu-CH2-scissoring mode ~ 1 9 .Whereas the corresponding modes in ~ x e t a n eand ~ ~thietane6 are not discernible in the infrared absorption spectra, this vibration is predicted for azetidine to dominate the two A’ scissors. The vapor-phase infrared absorption spectrum of Figure 1 shows the latter clearly at 1498.7 and 1450.1 cm-I, with no clearly defined B contour evident in the region (22) Kauppinen, J. K.; Moffatt, D. J.; Mantsch, H. H.; Cameron, D. G . Appl. Spectrosc. 1981, 35, 271-276. (23) Pople, J. A,; Schlegel, H. B.; Krishnan, R.; DeFrees, D. J.; Binkley, J. S.; Frisch, M. J.; Whiteside, R. A,; Hout, R. F.; Hehre, W. J. Int. J . Quantum Chem., Quantum Chem. Symp. 1981, 15, 269-278.
124 The Journal of Physical Chemistry, Vol. 94, No. I, 1990
between these bands (the A” scissor is indicated to lie in the range 1468-1477 cm-I). It appears that the predicted infrared intensity for this mode is in error, and our preferred assignment is to a weak shoulder in the Raman spectrum at 1458 cm-’ (see Figure 3, peak no. 9). Finally, both uZ3 (calculated, 1176-1 188 cm-l) and ~ 2 (cal7 culated 803-8 l l cm-l) are predicted to be extremely weak in the infrared. The latter is assigned to a weak Raman transition at 81 5 cm-‘. As discussed above, v23 is suggested to give rise to the shoulder on v i 7 (1 194 cm-l) at 1180 cm-l in the depolarized Raman spectrum. This completes the vibrational assignments. In the A’ species, only three of the assignments differ from those reported by Gunther et a1.,I0 those being v4, ug, and u I 3(see Table I), although in many cases the mode descriptions differ substantially. Several of the A” modes are evident only in the solution infrared and Raman spectra, not reported in ref 10, and so within this symmetry species the assignments have been completely revised (see Table 1). Scaling factor refinements were then pursued so as to determine the optimum force field within the constraint of a limited set of data. Initially, six scaling factors (a-CH, P-CH, N H , CC, and CN stretches and one factor for all bends) of run 1 were optimized to fit only the boldfaced assignments of Table IV. This is designated as “run 5” in Tables 111 and IV. The average error relative to those assignments diminished from 6.5 cm-I before optimization-with values from run 1 for the bends, CN, and CC stretches and of run 4 for the C H and N H stretches-to 4.8 cm-I after reoptimization. The overall fit, including all assigned frequencies, is then 7.0 cm-I. Only minor alterations from the transferred oxetane factors were encountered (see Table III), and the C N stretch factor, which had been set at 0.8 for all predictions, also assumes a reasonable value upon refinement. There are two modes for which the calculated position is in error by over 20 cm-l, those being vg (a-CH2 wag) and vu) (NH in-plane bend). Optimization of separate scaling factors for each of these coordinates does improve the fit in both cases, the overall average error dropping from 7.0 to 5.3 cm-I, with new values of 0.764 and 0.752 for the two scaling factors, respectively. These deviations might appear insignificant relative to the average bending factor of 0.785, but are undoubtedly worth recognizing in transferring the scaling factors to predict the spectra of related molecules. Including apparently subtle variations among the scaling factors may play a crucial role in resolving assignments for closely spaced
-
Dutler et al. transition^.^,^ These adjustments were pursued here only as a means of fine tuning the values for transfer and are only cosmetic once the assignments are complete. For this reason, we adopt run 5, which reproduces all fundamentals reasonably well and for which the scaling factors may be justified by comparison with the oxetane results, as a reasonable compromise, balancing the number of scaling factors against the available experimental data. Final confirmation is found in the fact that reoptimization of the six factors including all assigned frequencies of Table IV alters neither the values of the scaling factors nor the fit (average error, 7.0 cm-’) to the twenty-fiveobserved positions included in the average. (Both ut and V I 6 were excluded in assessing the accuracy of the predicted positions. For the sake of comparison, they are also excluded in reporting the average deviation for the refined force field.) The scaled force constants are listed in Table V and the scaling factors and calculated frequencies in Tables I11 and IV, respectively. The absorption spectrum synthesized with the calculated frequencies and intensities for the final force field is cc npared with the experimental solution spectra in Figures 1 and 2.
Conclusion
The vibrational spectra of azetidine have been measured and assigned with the guidance of a scaled 6-31G* force field and calculated infrared absorption and Raman intensities. The previously reported assignments of Gunther et a1.I0 are generally confirmed in the A‘ species; however, the A” assignments have been revised completely. The overall tit is significantly better than that for oxetane despite using less than half the number of scaling factors. This suggests that the conformational flexibility and resultant uncertainties in the appropriate reference geometry, features that are important considerations for oxetane, are less so in the case of azetidine. This observation, combined with the success of the force field in accounting for all prominent infrared and Raman bands, confirms that only a single conformer, with the N H assuming the equatorial position, contributes to the observed spectra.
Acknowledgment. This research was supported by a grant from the Natural Sciences and Engineering Research Council of Canada. R.A.S. gratefully acknowledges the receipt of a University of Calgary research fellowship. We also thank Supercomputer Services of the University of Calgary for a generous grant of computer time. Registry No. Azetidine, 503-29-7.
