J. Phys. Chem. 1995,99, 12751-12758
12751
Correlated ab Initio Force Fields and Vibrational Analysis of the Spectra of Isoxazole and Isothiazole Adel A. El-Azhary**?and Hans Ulrich Suter’ Department of Chemistry, Faculty of Science, Cairo University, Giza, Egypt, and Centro Svizzero di Calcolo Scienti3co (CSCS), CH-6928 Manno, Switzerland Received: March 23, 1995; In Final Form: May 11, 1995@
Optimized geometries, harmonic force fields, and dipole derivative tensors were computed for isoxazole and isothiazole with HF, MP2, DFT,and MCSCF methods using the 6-31G** atomic orbital basis set. The ab initio force fields were scaled to form scaled quantum mechanical (SQM) force fields using the experimental fundamental frequencies for isoxazole-do and -d3 and isothiazole-do, -4-d,, -5-d,, and -4,5-d2. The calculated frequencies confirmed the experimental assignment for isothiazole and its isotopomers and showed up possible misassignments for isoxazole and its -d3 isotopomer. The computed atomic polar tensors were used to calculate the IR absorption intensities. The best agreement between the calculated optimized geometries and IR absorption intensities and the experimental results was obtained with density functional calculations, but the correlation between the scale factors determined for both molecules was worse than those calculated at the MP2 and H F levels. With MP2 the optimized geometries were slightly worse than those at the DFT level, the calculated IR absorption intensities were in excellent agreement with the experimental IR absorption intensities for the in-plane modes but in poor agreement for the out-of-plane modes, and the correlation between the scale factors determined for both molecules was excellent. The HF- and MCSCF-optimized geometries and IR absorption intensities are slightly worse than the density functional results. Although the geometry and the intensity for the in-plane modes are calculated correctly with MP2, the large disagreement of the out-of-plane modes indicates a strong static correlation. The correlation between the scale factors determined with HF was worse than that at the MP2 level but better than that of the density functional and MCSCF calculations.
Introduction Isoxazole and isothiazole are five-membered heterocyclic molecules isoconjugate with the cyclopentadienylanion and are derived from it by replacing two adjacent carbon atoms with a nitrogen atom and an oxygen atom for isoxazole and a sulfur atom for isothiazole. Both molecules are of important biological and pharmacological uses.’ Saccharin, 3-oxo-2,3-dihydrobenz[dlisothiazole, 1,1-dioxide2 is a well-known derivative of isothiazole. Sulfis~xazoles~ and sulfas~mizole~ derivatives of isoxazole and isothiazole are used as antibiotics. Analgesic, antipyretic, fungicidal, and herbicidal activities were reported for is~thiazoles?~~ The wide biological and pharmacological applications for both molecules increase the importance of understanding their vibrational spectra and vibrational modes. In our initial analysis of the vibrational spectra of isoxazole and isothiazole, only force fields calculated at the HartreeFock (HF) and M0ller-Plesset (MP2) levels of theory (using the 6-31G** basis set) were used, but in order to rationalize the poor agreement between the calculated and experimental IR absorption intensities for the out-of-plane modes at the MP2 level, our study was extended to include the force fields calculated with density functional theory (DFT) and the multiconfiguration self-consistent field (MCSCF) methods. The calculated frequencies with HF are usually overestimated by about 10-20%. This overestimation is due to the incompleteness of the atomic orbital (AO) basis set, neglect of anharmonicity, and lack of electron correlation. On the other hand, the calculated frequencies at the MP2 level of theory are +
t @
Cairo University.
cscs.
Abstract published in Advance ACS Abstracts, July 15, 1995.
0022-365419512099-12751$09.0010
overestimated by only about 5- 10%. This improvement over the HF-calculated frequencies is due to the inclusion of electron correlation, despite the rather crude estimation of correlation energy. The MP2-calculated frequencies, since they are closer to the experimental frequencies than the HF-calculated frequencies, are then more suitable in the vibrational analysis. This may aid in the assignment of the fundamental frequencies of the studied molecules.6 A systematic study of IR frequencies with density functional methods can be found in the work of Andzelm and W i m e r . ’ Although the computational expense of DFT methods is modest compared to correlated ab initio calculations and would enable us to use larger A 0 basis sets than 6-31G**, we have chosen this basis set to be consistent for all methods. However, it is not expected that the A 0 basis set dependence in the DFT methods is similar to the one in ab initio methods. The problem of the overestimationof the ab initio force fields is commonly solved by the approach developed by Fogarasi and P u l a ~ ~ in9which ~ a set of scale factors is used to empirically refine the force fields using the experimental frequencies. The optimized scale factors can then be transferred to similar molecules to calculate their vibrational spectra without prior knowledge of their experimental spectra. Our study for the two analogous molecules, isoxazole and isothiazole, allows us not only to analyze the vibrational spectra for these two biologically important molecules but also to compare the optimized geometries, force fields, IR absorption intensities, and scale factors determined with HF, MP2, DFT, and MCSCF and to compare the obtained scale factors to check their reliability for transfer to other molecules. Furthermore, it is expected that the IR absorption intensities calculated at the HFl6-31G** level atomic polar tensors are sufficiently accurate to reproduce the qualitative 0 1995 American Chemical Society
El-Azhary and Suter
12752 J. Phys. Chem., Vol. 99, No. 34, 1995 TABLE 1: Equilibrium Geometry for Isoxazole coordinate" R(OI-N~) R(N-C3) R(C3-G) R(C4-Cd R(c5-01) R(C3-H6) R(C4-H7) R(C5-Hs) L(OI-N~-C~) L(N*-C3-C4) L(C~-CA-C~) L(C~-C~-OI) L(C~-OI-N~) L(N*-C3-&) L(C4-C3-H6) L(C3-C4-H7) L(C5-C4-H7) L(C~-C~-HS) L(OI-C~-H~)
iu
MNDOb
CND012'
1.301 1.351 1.449 1.387 1.373 1.082 1.077 1.083 109.2 108.4 103.4 108.5 110.5 122.6 129.0 127.6 129.0 133.8 117.7 2.73
HF/4-31Gd
HF/6-31G**d
MP2/631G**d
DFT/6-31G**d
MCSCF/6-31G**d
expt'
1.418 1.290 1.431 1.340 1.349 1.064 1.063 1.062 104.9 112.4 104.1 109.8 108.8 119.5 128.1 127.3 128.6 133.5 116.8 4.04
1.360 1.281 1.428 1.340 1.321 1.072 1.068 1.070 106.1 111.7 102.2 110.6 109.4 119.5 128.8 128.8 129.0 133.1 116.4 3.28
1.389 1.327 1.412 1.363 1.352 1.077 1.074 1.075 105.1 112.2 103.5 110.0 109.2 118.5 129.2 128.6 127.9 134.3 115.6 2.94
1.398 1.313 1.423 1.360 1.345 1.083 1.079 1.080 105.1 112.5 103.0 110.4 109.0 118.9 128.6 128.6 128.4 133.7 115.9 2.96
1.360 1.296 1.437 1.347 1.341 1.071 1.068 1.068 106.5 111.3 102.6 110.2 109.4 119.6 129.1 128.5 128.8 133.5 116.3 3.25
1.399 1.309 1.425 1.356 1.344 1.077 1.074 1.075 105.3 112.3 103.0 110.6 108.8 118.6 129.1 128.5 128.5 133.4 116.0 2.90'
1.277 1.328 1.418 1.355 1.359 1.112 1.108 1.112 109.0 110.2 101.2 111.0 108.6 120.9 128.9 128.8 130.0 134.6 114.4
Reference 33. Reference 19. This work. e Double resonance a Bond lengths are in A, angles are in deg, and p is the dipole moment in D. modulated microwave spectroscopy, ref 3 1. f Reference 30.
pattern of the IR absorption intensities.'0," It is then important to investigate the IR absorption intensities calculated with M E , DFT, and MCSCF methods using the same basis set, 6-31G**. Several authors reported the vibrational assignment of the spectra of isoxazoleI2-l6 and i s o t h i a ~ o l e ' ~and . ' ~ their isotopomers. Differences between the reported vibrational spectra for both molecules will be discussed in the Results section. Normal coordinate analysis using empirical force fields were reported for i ~ o x a z o l e 'and ~ ~ 'isothiazole20 ~ and its isotopomers. Computational Details
Cartesian coordinate force fields were calculated with HF, MP2, DFT, and MCSCF methods at the corresponding optimized geometries using the 6-31G** basis set and at the HF level using the 4-31G basis set. The force fields were calculated analytically, except for MP2 and MCSCF, where the vibrational frequencies have been obtained by numerical differentiation of the gradients. The calculations were performed for both molecules assuming a planar C, symmetry. The HF and MP2 calculations were performed using the CADPAC2' program, while for the DFT and MCSCF calculations the GAUSSIANz2
program was used. For the MCSCF calculation the n and n* orbitals of the double bonds and the free electron pair at the heteroatom were correlated (all excitations of 6 electrons in 5 orbitals). The gradient-corrected Becke3LYP density funct i ~ n a was l ~ ~used for the DFT calculation. The calculated Cartesian coordinate force fields were transferred to internal coordinate force using a program written by one of the authors.25 The internal coordinates' definition described by Pulay and co-workerss,26was adapted. The harmonic vibrational frequencies were calculated according to the GF formalism described by Wilson et a127 using the program of Schnactschneider.28 The internal coordinate force fields were scaled to form SQM force fields using the wellknown
scaled - Fijfheo(CjCj)'" IJ
where Ci and Cj are scale factors to internal coordinates 4i and e,respectively. A least-squares procedure was used to minimize the difference between the experimental and calculated frequencies, as indicated by the calculated rms deviation, by varying
TABLE 2: Equilibrium Geometry for Isothiazole coordinate"
HF/3-21G*b
HF/4-31GC
HF/6-31G**'
MPU6-3 lG**'
DIT/6-31G**'
MCSCF/6-31G**'
exptd
1.657 1.300 1.435 1.350 1.713 1.067 1.067 1.067 110.9 115.5 110.0 110.1 93.7 119.9 124.6 124.6 125.4 127.2 122.7 2.28
1.782 1.283 1.443 1.336 1.785 1.069 1.068 1.065 109.4 117.7 111.6 110.6 90.6 118.6 123.7 123.5 124.9 128.2 121.2 3.43
1.656 1.285 1.434 1.347 1.711 1.076 1.072 1.072 109.8 116.8 109.6 109.6 94.2 119.0 124.2 124.8 125.6 128.2 122.2 2.88
1.662 1.336 1.411 1.378 1.701 1.081 1.078 1.077 108.2 117.0 110.1 109.1 95.6 117.6 125.5 125.2 124.7 128.3 122.6 2.46
1.680 1.319 1.425 1.369 1.722 1.087 1.083 1.082 108.4 117.4 110.1 109.1 96.9 118.0 124.6 124.8 125.1 128.5 122.4 2.63
1.708 1.302 1.434 1.343 1.717 1.075 1.073 1.072 108.4 117.2 110.4 110.3 93.7 118.4 124.3 124.4 125.2 128.0 121.7 3.01
1.642 1.319 1.436 1.388 1.702 1.102 1.102 1.102 112.2 111.8 113.8 106.2 96.1 120.6 127.6 128.9 117.3 138.0 115.8
R(S I -Nd R(N2-Cd R(C3-Cd R(C4-G) R(C5-S 1 ) R(C3-Hc.I
R(C4-H7) R(C5-Hs) L(SI-N2-C3) L(N2-C3-C4) L(C3-C4-C5) L(C4-C5-S1) L(Cs-Si-Nz) L(N2-Cj-Hd L(C4-C3-H6) L(C~-CI-H~) L(C5-C4-H7) L(C~-C~-HE) L(SI-C5-Hs) P a
Bond lengths are in
A, angles are in deg, and p
is the dipole moment in D. Reference 32. This work. Electron diffraction, ref 32.
J. Phys. Chem., Vol. 99, No. 34, 1995 12753
Analysis of Spectra of Isoxazole and Isothiazole
TABLE 3: Internal Coordinates for Isoxazole and
Results
Isothiazole"
The optimized geometries at the HF level using the 4-31G basis set and at the HF, MP2, DFT, and MCSCF levels using rl X-N stretch the 6-31G** basis set for isoxazole and isothiazole are shown r2 C=N stretch in Tables 1 and 2, respectively. The optimized geometries were r3 C-C stretch calculated assuming a planar C, geometry for both molecules r4 C=C stretch as indicated by microwave30 and double resonance modulated r5 C-X stretch microwave3' (DRM)spectroscopy for isoxazole and electron i-6 C-H stretch r7 C-H stretch d i f f r a ~ t i o nfor ~ ~isothiazole. The optimized geometries using rs C-H stretch other ab initio basis sets32 and semiempirical method^,'^.^^ a1 + a(a2 + as) + b(a3 + ad ring deformation available from the literature, are also shown in Tables 1 and 2. (a - b)(a2 - as) (1 - a)(a3 - &) ring deformation The computed ab initio Cartesian coordinate force fields were PI -P2 CH rocking transferred to intemal coordinate force fields using a nonreP3 -8 4 CH rocking P5 -P6 CH rocking dundant set of intemal coordinate definitions given in Table 3. 569 51, 58 CH wagging The atom numbering employed for both molecules is shown in b(5l + 55) + a(5z + t4) + 5 3 ring torsion Figure 1. The internal coordinate force fields and the dipole ( a - b)(r4 - 52) (1 - a)(t5 - 51) ring torsion moment derivative tensors were used to calculate the harmonic a See Figure 1 for definitions of r, a , P, and t coordinates. a = vibrational frequencies and IR absorption intensities. cos 144" and b = cos 72". Values of normalization constants are not For isoxazole, the experimental assignments reported for the given. X = 0 for isoxazole and X = S for isothiazole. isotopomer in ref 16 and for the d3 isotopomer reported in ref 15 were adopted. The experimental assignments for both isotopomers were compared to the unscaled and scaled MP2 frequencies using a one-scale-factor (1SF) scaling of 0.9. From this comparison, it was evident that the assignment of the 1260 and 1030 cm-I bands to the do and d3 isotopomers, respectively, is problematic. Furthermore, both bands are very weak bands, not observed in the gas phase spectra, and their assignment as fundamentals by the reported authorsI2-l6 is doubtful. Both bands were then excluded from the fit, the other in-plane modes were assigned accordingly, and v12 for the do and v13for the d3 isotopomers were left unassigned. Bands at 3086, 889, and 792 cm-I for the do isotopomer and at 2368,719, and 669 cm-' for the d3 isotopomer had large deviation from the corresponding unscaled or scaled HF or MP2 frequencies and were excluded from the final scaling step. The other frequencies are sufficient to accurately determine the scaled force fields. The band at Figure 1. Atom numbering and internal coordinates for isoxazole (X 1260 cm-' for the isotopomer may correspond to a combina= 0) and isothiazole (X = S). tion band, VI6 Y17. The band at 2368 cm-' for the d3 isotopomer may also correspond to a combination band, v5 the scaling constants. The dipole strengths were calculated as vs or v6 -k v7. Furthermore, it was noticed that the 889 and described elsewhere.29 TABLE 4: Calculated Vibrational Frequencies and Dipole Strengths Using the MW6-31G** Force Field for Isoxazoldb no.
modeb
descriDtion'
+
+
+
+
Q expt sym A'
no. 1 2 3 4 5 6 7
8
A"
rmS
9 10 11 12 13 14 15 16 17 18
d3
calcd
freq
int
freq
3160 3128 (3086) 1560 1432 1373 1217 1128 1089 1021 917
8 10 5 40 85 34 19 75 28 21 49
856 (889) (792) 764 632 595
71 30
3164 3140 3128 1564 1439 1365 1212 1136 1093 1031 918 900 854 841 806 757 632 592 6
215 19 66
expt
D
0 0 1 17 67 14 10 63 13 26 50 4 89 67 291 1 62 18
PED
freq
68q7+27qs 70@+22q7 8896 60q4+ 11q2-t llqi3 35q2+21q3+21qil 28qi2+27q13+ 19@+ 17qz 36qii +34q2+ 12q13 42q13+23q5+ 12q4+ llqlz 42q5+24q3+21qll 42q12+30q3+ 13q5 82ql0 80q9 87q1 93q14 5541~+41q16 51q16 + 41ql5 67qis+31q17 58417+29qi8
2381 (2368) 2325 1504 1403 1272 1109 957 930 892 880 763 (719) (669) 606 565 498
calcd intC
freq
D
PED
w
2370 2327 2315 1498 1408 1261 1107 955 933 890 878 763 733 684 663 609 570 503 6
1 2 1 24 60 18 28 21 24 22 31 88 1 0 19 249 0 38
53q7+36@ 47q6 38q8 1lq7 45q6 31q7 2iq8 62q4+ 15q2 53q2+21@ 37q3+ 19qs-t 12q12 55q5 llq3 48q9+21q13 52q1 15q3 llqio 35q11 24qi2 7Oqlo+ 15q9 37ql +31qi3+23qii 58q12+ 14qii + 12q13 60qi7+36414 50q18 + 34q16 34q18+3oq14+23q15 67qi5 16q16 46qi6+21q17+ llq18
w
m vs m vs m m m s
vs m w VS
s VS
+ +
+ +
+
+
+
Experimental data are from ref 16 for the Q isotopomer and ref 17 for the d3 isotopomer. Frequencies are in cm-'. Int is the relative absorption em2 cm2. PED is the potential energy distribution. intensities of solution IR spectra unless otherwise indicated. D is the dipole strength in Bands in parentheses are not included in the fit. Relative absorption intensities of liquid IR spectra: vs, very strong: s, strong: m, medium: w, weak.
TABLE 5: Calculated Vibrational Frequencies and Dipole Strengths Using the MP2/6-31G** Force Field for Isothiazole"~ do 4-d I 5-dl ~
expt_
calcd _
_
expt
_
sym no. freq int freq D PED A' 1 3105 8 3109 1 74qx+24q7 5 3089 1 69q7+25q~ 2 3086 3 3056 9 3063 8 93q6 4 1484 17 1489 7 52q4+ l8q12+ 12qll 5 1390 105 1390 43 36q3+21qli 13q2
+
rmS
PED
14 1270 53 1215
7 1236
57 1230
8 1066
24 1069
31 51q1,+23q12+2Oq4 1046
1040
9 1034
3 56q1+26q12+ 12q11 878
calcd int
freq
869 815
41 82
873 817
12 13 14
758 44 639 4 908 12 858 24 728 365 587 31 474 35
755 639 896 863 749 581 473 7
31 65qio+21qs 88 35q~+2Oq9+19ql 19qio 28 64qi +26qs 5 72qs-t l6q1 18 82414+ 12q17 254 6Oq1s+33q16 1 66416+31q15 18 83q17 345 98q1x
expt PED
D
2 3094 6 3063 2300 8 1476 85 1383
1268
4 1273
94q7 94q6 96qs 47q4 22q2 14qll 36q3+22q11 14q2 + 1% 5 42q2+22q4+ 18q12
34 48q11+25q13+ llq2
1224
68 1220
41 48q11 l9qi2+ 18q2
37 1048
21 35q,+31q13+ 1844
1040
6 1034
57
SO 43q5
8 0 4 37
+
+
+ 17q10+16412
+
20 44qio+22ql-r+ 16qs
825 761
155
53 36ql0+23qs l6q1 60 45ql + 2 0 q l 3 + 16qy + 15qio 25 38qs+31q13+24ql 3 64qy+ 15qs+ 14qi 24 84414+ 12q17 174 8841s 1 71q16+ 1 6 4 1 7 23 67qI7+ l2qI6+ l l q l x 346 85q18+ 14q16
61
819 763
731 629 891 809
30
725 19 37qr+31qi2+2391 737 46 636 4 72q9+ 15qi llqs 626 9 893 70 91q14 904 15 799 126 88ql6 (858) 639 32 52q1~+33q17 606 82 557 16 47qI7 38qIs+ l l q l x 575 160 463 365 91q18 450 10 6
742 627 896 834 600 579 454 7
~
+
calcd int
freq
3058 2318 2295 1465 1365
10 3065 2314 2280 10 1454 75 1373
1254
23 1250
1171
45 1167
D
PED
8 1 0 5 39
99% 56qx+38q7 57q7+40qs 44q4+ 27q2+ 1 7 q i l 34q3+25q3+20q11 + 13q2 4 56q2+26qll
16
943
850
54
844
34 32q11+28q3+ 12q13 + Ilq12 9 26qlo+20q3+2Oqs + 17q13 53 5Oqlo+ l8q12 12q3
780 740
39 42
782 748
45 65q1 +21q12 40 57q13+ 15q9+ 15q10
4 SOq3+34q12+ 12q11 943
921
842 784
+
+ +
38
49 61
+
+
922
849 782
57 59 644 279 (576) 16 462 44
40 65qlo+ 13qi2+ llq, 54 61ql + 2 2 q i 2 + 12q9
2 7 1 9 41
freq
3085 3058 2320 1479 1380
885
1 99qs
freq
+ llq13
10 11
16 17 18
expt
D
99q6 96q7 50q4+ 22q2+ 14qll 33q3+22q4 22q1I 16q2 1 47q2+26q13
7 32q2+28q13+ 19qiz 1268 + 15q4 30 52qll+33q2 1215
15
freq
4 3104 8 3065 2294 9 1466 65 1379
1 1305
9
calcd int
3105 3060 2305 1468 1372
1296
6
A"
freq
~~
4,S-d~
728 31 624 5 890 48 (707) 18 576 162 (541) 29 441 15
+
723 20 624 3 892 58 677 88 585 15 553 5 446 372 7
43qs+29412+2Oql 64qy+ 13g1 13qs 91q14 49qls+30q17+ 19q16 60q16+ 18q17 15qlg 47qIs+ 38qI7 84q18+ l l q 1 6
+
+
" Experimental data are from ref 18. See corresponding footnote in Table 4.
Ba
J. Phys. Chem., Vol. 99, No. 34, I995 12155
Analysis of Spectra of Isoxazole and Isothiazole TABLE 6: Scaled MW6-31G** Force Field for Isoxazold 1 2 3 4 5 6 7 8 9 10 11 12 13 qi a
3.81 1 0.380 0.002 0.199 0.319 -0.043 -0.056 -0.032 0.137 -0.572 0.019 0.005 -0.035 1
14 0.247 7.691 0.667 -0.230 0.179 0.077 -0.004 -0.041 -0.474 0.310 0.179 -0.021 -0.020 2
5.979 0.509 -0.193 0.057 0.032 0.000 0.488 -0.111 -0.089 0.111 0.009
3
8.125 0.417 0.003 0.005 0.025 -0.438 -0.296 0.027 -0.124 -0.058 4
5.755 -0.063 -0.017 0.057 0.091 0.513 -0.032 0.005 0.232
5
5.356 0.005 0.001 -0.043 -0.110 0.012 0.004 -0.007
5.423 0.007 -0.025 0.101 0.002 -0.009 0.003
6
7
5.393 0.072 -0.057 -0.002 O.Oo0 O.Oo0 8
1.927 0.075 -0.089 0.076 0.095 9
15 0.011 0.225
1.723 -0.026 0.025 0.020 10
16
17
18
qi
-0.006 -0.017 0.176
-0.006 -0.005 0.018 0.271
-0.064 0.057 -0.035 -0.017 0.339
14 15 16 17 18
0.460 0.007 0.013 11
0.406 -0.006 12
0.462 13
Force constants in mdynlA.
TABLE 7: Scaled MPU6-31G** Force Field for Isothiazol@ 1 3.735 2 0.340 3 -0.084 4 0.297 5 -0.045 6 -0.018 7 -0.059 8 0.001 9 -0.012 10 -0.578 11 0.032 12 -0.020 13 -0.014 41 a
1
7.320 0.716 -0.199 0.235 0.165 0.004 -0.049 -0.570 0.155 0.259 0.004 0.010 2
5.735 0.559 -0.244 0.054 0.03 1 0.001 0.465 -0.095 -0.112 0.105 0.0 15 3
7.406 0.456 0.006 0.044 0.025 -0.395 -0.203 -0.001 -0.146 -0.115 4
4.078 -0.045 0.001 0.024 0.026 0.408 -0.015 0.014 0.127 5
5.142 0.004 0.001 -0.039 -0.108 -0.008 0.002 -0.005
5.224 0.004 -0.038 0.1 16 0.001 -0.001 0.005
6
7
5.261 0.082 -0.069 -0.004 0.004 0.002
8
14
15
0.305
-0.016 0.276
1.780 0.026 -0.077 0.070 0.048 9
1.482 -0.009 0.034 0.061 10
16 -0.006 -0.038 0.228
0.493 0.007 0.012 11
17 -0.047 -0.043 -0.034 0.236
0.422 -0.010 12
18 -0.077 0.069 -0.037 -0.015 0.352
qi
14 15 16 17 18
0.402 13
Force constants in mdyn/A.
719 cm-I bands for the Q and d3 isotopomers, respectively, assigned as V I 4 could correspond to v12 and VI3 for the do and d3 isotopomers, respectively. For isothiazole, the experimental assignment for the Q, 4-d1, 5-dl, and 4,5-d2 isotopomers was reported by Meyer et a1.I" Contrary to that of isoxazole, the assignment for isothiazole was straightforwardexcept for bands at 576 cm-' for 4-d1,858 cm-I for 5-d1, and 541 and 707 cm-' for 4,5-d2 isotopomers which had large deviation from their corresponding scaled frequencies at the MP2 or HF levels and were excluded from the fit. The band at 576 cm-I for 4-dl could be due to an isotopic impurity of the 5-dl (VI,) or 4,s-d~(vl6) isotopomers. For the band at 858 cm-' for 5-dl, its assignment as fundamental is doubtful.IE In all, 30 and 68 fundamental vibrations for isoxazole and isothiazole, respectively, and their isotopomers were used in the refinement of the 10 scale factors. The calculated vibrational frequencies and IR absorption intensities using the MP2/631G** force field for isoxazole-6 and -d3 are given in Table 4 and those for isothiazole-do, -4-dl, -5-dl, and -4,5-d2 are given in Table 5. Scaled MP2/6-31G** force fields using lOSF scaling for isoxazole and isothiazole are given in Tables 6 and 7, respectively. The final scale factors and rms deviation using lSF, 3SF, 7SF, and lOSF scaling are given in Table 8.
Discussion The calculated optimized geometries for isoxazole, Table 1, indicate that the optimized geometry calculated with DFT is in excellent agreement with the experimentalgeometry determined by microwave spectro~copy,~' and the agreement is better than that determined at the MP2 level. The difference between the
DFT-optimized and the experimental bond lengths is less than 0.005 8, (except for the C-H bond distances) and less than 0.6" for bond angles. The agreement at the HF and MCSCF levels is worse than that at the MP2 level. The C-H bond distances are exactly predicted at the MP2 level, while they are overestimated by about 0.005 8, at the DFT level and underestimated by about 0.005 and 0.006 8, at the HF and MCSCF levels, respectively. For isothiazole, the calculated optimized geometries with HF, MP2, DIT, and MCSCF are in poor agreement with the experimental geometry determined by electron d i f f r a ~ t i o n .The ~ ~ calculated optimized geometries for similar sulfur-containing molecules, 1,3,4-thiadia~ole,~~ 1,2,5t h i a d i a z ~ l e and , ~ ~ thiazole3' at the MP2 level indicate that the MPZoptimized geometries predict the S-C bond lengths by a difference of less than 0.004 A, the S-N bond length by less than 0.013 A, the C-H bond length by less than 0.002 A, the CSN, NSN, and CSC bond angles by less than 0.3", and most of the other bond angles by a difference of less than 0.6" and 1.0" at most. For isothiazole, the optimized geometry at the MP2 level predicts the C-H bond length to be 0.022 8, too short, and most of the bond angles predicted by the four methods differ by more than 3.0" from the experimental bond angles. The C ~ - C ~ - H Ebond angle is underestimated by about 10" by the four methods, HF, MP2, DFT, and MCSCF. The accuracy of the experimental geometry determined for isothiazole by electron diffraction is then doubtful. The scaled MP2/6-31G** force fields for both molecules (Tables 6 and 7) show that the diagonal force constants corresponding to the stretching modes, ql-qs, for isoxazole are bigger than those for isothiazole, in agreement with the bond
El-Azhary and Suter
12756 J. Phys. Chem., Vol. 99,No. 34, 1995 TABLE 8: Scale Factors for Isoxazole and IsothiazoW isoxazole
isothiazole
coordinate
1SF
3SF
7SF
lOSF
1SF
3SF
7SF
lOSF
41
0.802 0.892 0.927 0.821
0.814 0.880 0.919 0.824
0.776 0.859 0.926 0.788
0.669 0.808 0.932 0.648
0.804 0.884 0.9 18 0.814
0.813 0.866 0.907 0.815
0.875 0.883 1.057 1.Ooo
0.837 0.927 1.075 1.105
43
0.891 0.883 0.955 0.945
0.900 0.853 1.094 0.887
45
0.75 1 0.869 0.902 0.789
0.874 0.885 1.114 0.955
0.743 0.95 1 0.929 0.798
0.678 0.946 0.9 18 0.75 1
0.692 0.943 0.880 0.714
0.79 1 0.947 0.937 0.833
0.754 0.952 0.966 0.791
0.790 0.943 0.949 0.905
tltlS
30 22 11 25
27 15 6 20
0.832 0.875 0.917 0.832
0.835 0.874 0.917 0.83 1
0.779 0.947 0.969 0.798
0.824 0.964 0.970 0.845
0.800 0.927 0.95 1 0.826
0.794 0.923 0.950 0.803
0.762 0.935 0.944 0.742
0.762 0.935 0.944 0.742
0.826 0.954 0.950 0.926
0.827 0.954 0.950 0.926
14 8 5 17
9 6 5 6
0.678 0.942 0.947 0.702 0.716 0.947 0.760 0.750
0.774 0.965 0.975 0.814
0.745 0.994 0.959 0.791
35 29 35 41
31 12 31 41
0.824 0.864 0.905 0.821
0.823 0.864 0.905 0.821
0.827 0.955 0.900 0.802
0.832 0.947 0.885 0.808
0.795 0.900 0.948 0.791
0.787 0.906 0.954 0.786
0.697 1.013 0.966 0.745
0.697 1.013 0.966 0.745
0.864 0.946 0.941 0.926
0.864 0.946. 0.941 0.926
9
8 26 27
8 7 25 20
Top scale factor is a scale factor for subsequent internal coordinates. For each intemal coordinate, the scale factor in the first line is for the HF/6-31G** force field. the second line is for the MP2/6-31G** force field, the third line is for the DFT'/6-31G** force field, and the fourth line is for the MCSCF/6-31G** force field.
distances for isoxazole being shorter than those for isothiazole (determined at the MP2 or DFT level). Also, the fact that the diagonal force constants corresponding to the ring deformation modes q 9 and 410 are bigger for isoxazole than for isothiazole may be rationalized as being due to the bond angles for isoxazole being smaller than those for isothiazole except for, and as a consequence of, the smaller CSN bond angle in isothiazole than the CON bond angle in isoxazole. The difference between the CCO and CCS bond angles is small compared to the difference between the other bond angles. For comparison between the calculated and experimental IR absorption intensities, the experimental and calculated IR absorption intensities for isoxazole-do and isothiazole-do with HF, MP2, DFT,and MCSCF are shown in Table 9. The best agreement with the experimental intensities is obtained at the DFT level. The worst agreement is at the HF and MCSCF
levels, although both are in good qualitative agreement with the experimental intensities. The calculated IR absorption intensities at the MP2 level are in excellent agreement with the experimental IR absorption intensities for the in-plane modes, although the agreement is slightly worse than for those at the DFT level, but for the out-of-planemodes the agreement is very poor. Since the n and n* orbitals and therefore the out-ofplane p-orbitals are mainly correlated with the MCSCF method, it seems to be clear that the out-of-plane vibrations need a multireference treatment. The coefficient of the Hartree-Fock configurations in this rather small active space is around 0.95 for both compounds. The rest of the important configurations are double excitations in the n orbitals. The large coefficient seems at first to indicate a Hartree-Fock-dominated case, which may also be underlined by the small deviation of the geometries between Hartree-Fock and MCSCF. However, it is obvious
J. Phys. Chem., Vol. 99, No. 34, 1995 12757
Analysis of Spectra of Isoxazole and Isothiazole that the out-of-plane movement includes the breaking of the double bonds, and it seems necessary for the IR intensity to be explained by a reasonable description of this movement. That density functional theory is also able to give reasonable results in such cases is surprising, but it has been observed at other times, for example, in the case of allyl and polyene radicalsS3* Similar behavior at the MP2 level was found for oxazole and thiazole,37although for 1,3,4-0xadiazole and t h i a d i a z ~ l eand ~~ 1,2,5-0xadiazole and t h i a d i a ~ o l e(notice ~ ~ that the oxadiazoles and thiadiazoles are of C2” symmetry and oxazole, isoxazole, thiazole, and isothiazole are of C, symmetry) the agreement at the MP2 level for the in-plane and out-of-plane modes was excellent. The calculated IR absorption intensities for the other isoxazole and isothiazole isotopomers behave similarly to those of the do isotopomers. The determined scale factors using lSF, 3SF, 7SF, and lOSF scalings for isoxazole and isothiazole at the MP2 level, Table 8, are well correlated for the same intemal coordinate except for the N-0 and N-S stretch and the CH wagging coordinates. This correlation is less observed at the HF level. In addition, the scale factors determined at the MP2 level are less divergent than those determined at the HF level. The values of the scale factors determined using 1SF scaling at the MP2 and HF levels have been of interest before. Pople et reported a value of 0.9427(0.8929) at the MP2(HF)/6-3 lG* level with a corresponding r m s deviation of 61(50) cm-I. Since these values were determined as an average value for a wide range of small organic and inorganic molecules, they are significantly different from ours, 0.885(0.806). On the other hand, according to our best knowledge, there are no values of scale factors determined at the DFT level. The average difference between the unscaled calculated frequencies and the experimental frequencies, for both isoxazole and isothiazole and their isotopomers, was about 55 cm-I with a corresponding rms deviation of about 70 cm-I. The determined scale factors using 1SF and 3SF scaling for isoxazole and isothiazole are well correlated, with the rms deviation for isoxazole exceptionally low. In going to 7SF and then to lOSF scaling, the correlation between the scale factors becomes worse, without a significant improvement of the rms deviation for isothiazole. It was noticed that, using 7SF and lOSF scaling, only a few bands had high contributions to the rms deviation for isothiazole. In a trial to improve the rms deviation for isothiazole, these bands were excluded from the assignment,
and in a second trial the scale factors were optimized for isoxazole-do or isothiazole-do isotopomers only, but the correlation between the scale factors was poor without significant improvement of the rms deviation for isothiazole. Similar results were obtained at the MCSCF level. It is important to notice that although the rms deviation for isothiazole using 1SF and 3SF scaling seems reasonable, few calculated frequencies had large deviation from their corresponding experimental frequencies. The worst is for v7 for the 4-dl isotopomer, which is observed at 1215 cm-I and is calculated at 1085 cm-’ using 3SF scaling. One reason for the large rms values for both MCSCF and DFT methods seems to be the unbalanced treatment of the electron correlation, which naturally arises from the small active space in the MCSCF calculation. For DFT this effect is not so well known but may be observed for example in the calculation of the spin densites with We feel that the scaling with DFT requires a further deliberate study which includes a greater number of molecules. Conclusion
In this paper we presented the vibrational analysis of two five-membered heterocyclic molecules containing two different heteroatoms, isoxazole and isothiazole. The calculations were carried out at four different levels of theory, HF, MP2, DFT, and MCSCF. Every effort has been made to include in our force field calculations only those bands for which their assignments as fundamental were, to the best estimate, certain. This effort was mainly dependent on the unscaled and scaled MPZcalculated frequencies. The calculated frequencies generally confirmed the experimental assignment for isothiazole and its isotopomers and revealed possible misassignments for isoxazole and its d3 isotopomer. The optimized geometries and IR absorption intensities calculated with DFT are better than those calculated at the MP2 level, and both are significantly better than those calculated with HF and MCSCF methods, except for the calculated IR absorption intensities for the out-of-plane modes at the MP2 level, which are in poor agreement with the experimental IR absorption intensities. The reason for this behavior was explained. The scale factors determined at the MP2 level are better correlated and less divergent than those calculated with HF. Although the scale factors determined using 1SF and 3SF scaling at the DFT and MCSCF levels are well correlated, problems arise
TABLE 9: Comparison between the Experimental IR Absorption Intensities and the Calculated Dipole Strengths for Isoxazole-do and Isothiazole-do Using Unscaled Force Fields” isoxazole sym A‘
mode VI
v2 v3 v4 v5
v6 v7
vs v9 VI0 VI I VI2
A”
VI 3 VI4
HF
MP2
DFT
MCSCF
expt
HF
MP2
DFT
MCSCF
8 10 5 40 85 34 19 75 28 21 49
1 1 6 39 123 47 29 66 41 9 240 29 5 10 1 254 22 123
0 0 1
0 0 2 21 84 16 21 65 28 20 42 5 117 18 0 233 17 80
1 0 5 9 53 37 6 48 36 7 75 23 121 28 4 254 9 111
8 5 9 17 105 1 57 24 9 41 82 44 4 12 24 365 31 35
1 3 18 19 109 9 18 35 20 52 173 30 3 3
1 1 7 6 44 7 27 29 3 38 71 33
1 2 11 10 54 2 34 31 3 29 102 46 1 9 5 335 29 45
2 3 14 25 66 15 17 25 12 41 107 50 3 1 5 337 19 36
71 30
vi5 VI6
VI7 VI8 a
Dipole strengths in
isothiazole
expt
215 19 66
esu2 cm2.
15 71 8 15 51 15 21 98 7 32 70 227 1 61 17
1
37 1 41 40
5
11 263 1 18 335
12758 J. Phys. Chem., Vol. 99, No. 34, 1995
using 7SF and lOSF scaling, which leads to poorly correlated scale factors. Acknowledgment. I would like to thank Prof. Timothy A. Keiderling of the University of Illinois at Chicago for the use of the CADPAC program installed on the Department of Chemistry Titan minisupercomputer. Note Added in Proof: Unlike the calculated frequencies with the other density functionals, e.g. LDA, LSD, and BLYP, where some of the calculated frequencies are overestimated and some are underestimated:' which may limit the application of the DFT method for the vibrational analysis, the calculated frequencies by the DFT/B3LYP method are generally overestimated, Table 8. For this reason the analysis of the vibrational spectra for 1,2,5-oxadiazole, 1,2,5-thiadia~ole,~~ 1,3,4-oxadiazole, 1,3,4t h i a d i a ~ o l eoxazole, ,~~ and thiazole37previously reported at the MP2 and HF levels were recently calculated by the DFT/ B3LYP.42,43The results indicated that the rms deviations with the DFTB3LYP are about half those at the MP2 or HF levels for the oxygen-containing molecules. For the sulfur-containing molecules the rms deviations are similar to those at the MP2 level, and both are about half those calculated at the HF level. This was explained as due to the poorer prediction of the DFT method for the C-S and N-S bond lengths and CSC and NSN bond angles than those where the sulfur atom is replaced by the oxygen atom. This provides a partial explanation for the high rms deviation for isothiazole by the DFT method, although a full explanation is not possible in absence of a reliable experimental geometry for isothiazole. In view of the excellent accuracy to computational effort ratio obtained by the DFT/ B3LYP force fields, it was concluded that, although for the rather small number of five-membered heterocyclic molecules, it is preferred to use the DFTh33LYP force field than the MP2 or HF force field for the vibrational a n a l y s i ~ . ~ * - ~ ~ References and Notes (1) Barton, D.; Ollis, W. D. Comprehensive Organic Chemistry, The Synthesis and Reactions of Organic Compounds; Pergamon Press: New York, 1979; Vol. 4, Heterocyclic Compounds. (2) Lawson, A.; Tinkler, R. B. Chem. Rev. 1970, 70, 593. (3) Wilson, C. 0.; Gisvold, 0.;Doerge, R. F. Textbook of Medicinal and Pharmaceutical Chemistry; Pitman: London, 1966. (4) Slack, R.; Wooldridge, K. R. H. Adv. Heterocycl. Chem. 1965.4, 107. ( 5 ) Davis, M. Adv. Heterocycl. Chem. 1972, 14, 43. (6) See, for example: Simandiras, E. D.; Handy, N. C.; Amos, R. D. J . Phys. Chem. 1988. 92, 1739. Tomkvist, C.; Bergman, J.; Liedberg, B. J . Phys. Chem. 1991, 95, 3119. Murphy, W. F.; Zerbetto, F.; Duncan, J. L.; McKean, D. C. J . Phys. Chem. 1993, 97, 581. Tang, W.; Bally, T. J . Phys. Chem. 1993, 97,4365. Gejji, S. P.; Hermansoon, K.; Lindgren, J. J . Phys. Chem. 1993, 97, 6986. (7) Andzelm, J.; Wimmer, E. J . Chem. Phys. 1992, 96, 1280. (8) Fogarasi, G.; Pulay, P. Vibrational Spectra and Structure; Dung, J. R., Ed.; Elsevier: New York, 1985; Vol. 14, p 125.
El-Azhary and Suter (9) Fogarasi, G.; Pulay, P. Ann5 Rev. Phys. Chem. 1984, 35, 191. (IO) Hess, B. A.; Schaad, L. J.; C h k y , P.; Zahradnk, R. Chem. Rev. 1986, 86, 709. (11) Amos, R. D. Adv. Chem. Phys. 1987, 67, 99. (12) Califano, S.; Piacenti, F.; Speroni, G. Spectrochim. Acta 1959, 15, 86. (13) Borello, E. Gazz. Chim. ltal. 1959, 89, 1437. (14) Katritzky, A. R.; Boulton, A. J. Spectrochim. Acta 1961, 17, 238. (15) Adembri, G.; Speroni, G. Spectrochim. Acta 1963, 19, 1145. (16) Pouchan, C.; Senez, S.; Raymond, J.; Sauvaitre, H. J . Chim. Phys. 1974, 71, 525. (17) Califano, S.; Piacenti, F.;.Sbrana, G. Spectrochim. Acta 1964, 20, 339. (18) Meyer, J. L.; Davidovics, G.; Chouteau, J. Can. J . Chem. 1971, 49, 2254. (19) Pouchan, C.; Dargelos, A.; Chaillet, M.; Ford, G.; Katritzky, A. R. J . Mol. Struct. 1976, 33, 39. (20) Mille, G.; Metzger, J. Spectrochim. Acta 1975, 31A, 1115. (21) Amos, R. D. CADPAC - The Cambridge Analytical Derivatives Package; SERC: Daresbury, U.K., 1984. (22) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A,; Head-Gordon, M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; DeFrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92/DFT, Revision 6.1;GAUSSIAN, Inc.: Pittsburgh, PA, 1993. (23) Pulay, P. Modern Theoretical Chemistry, Schaefer, H. F., 111, Eds.; Plenum Press: New York, 1977; Vol. 4. (24) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. J . Phys. Chem. 1994, 98, 11623 and references therein. (25) El-Azhary, A. A. Unpublished. (26) Pulay, P.; Fogarasi, G.; Pang, F.; Boggs, J. E. J . Am. Chem. SOC. 1979, 101, 2550. (27) Wilson, E. B.; Decius, J. C.; Cross, P. C. Molecular Vibrations; Dover Publications: New York, 1980. (28) Schnachtschneider, J. H. Technical Reports No. 231-64, 1964; Technical Reports No. 57-65, 1965; Shell Development Co.: CA, 1965. (29) Jalkanen, K. J.; Stephens, P. J. J . Phys. Chem. 1991, 95, 5446. (30) Stiefvater, 0. L.; Nosberger, P.; Sheridan, J. Chem. Phys. 1975,9, 435. Mackrodt, W. C.; Wardley, A.; Cumuck, P. A,; Owen, N. L.; Sheridan, J. Chem. Commun. 1966, 19, 692. (31) Stiefvater, 0. L. J. Chem. Phys. 1975, 63, 2560. (32) Schultz, G.; Hargittai, I. J . Mol. Struct. 1988, 176, 61. (33) Olivella, S.; Vilarrasa, J. J . Heterocycl. Chem. 1981, 18, 1189. (34) Herzberg, G. Molecular Spectra and Molecular Structure 11. Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand: Princeton, 1945; Chapter 4. (35) El-Azhary, A. A. Spectrochim. Acta. In press. (36) El-Azhary, A. A. Acta Chim. Scand. 1995.49, 11. (37) El-Azhary, A. A. J . Chem. Res. 1995, 174, 1149. (38) Sim, F.; Salahub, D. R.; Chin, S.; Dupuis, M. J . Chem. Phys. 1991, 95, 4317. (39) Pople, J. A.; Scott, A. P.; Wong, M. W.; Radom, L. Isr. J . Chem. 1993, 33, 345. (40) Suter, H. U.; Pless, V.; Emzerhof, M.; Engels, B. Chem. Phys. Lett. (41) See for example: Handy, N. C.; Murray, C. W.; Amos, R. D. J. Phys. Chem. 1993, 97,4392. Fan, L.; Ziegler, T. J. Chem. Phys. 1991, 96, 9005. Fan, L.; Ziegler, T. J. Chem. Phys. 1991, 94, 6057. (42) El-Azhary, A. A.; El-Shakre, M. E.; Ghoneim, A. A. J. Chem. Res., in press. (43) El-Azhary, A. A. Spectrochim. Acta, submitted for publication.
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