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A theoretical study of the molecular structure and vibrational spectra of methyl cyanate and its sulfur and selenium analogues
Journal of Molecular Structure (Theochem) 501–502 (2000) 277–284 www.elsevier.nl/locate/theochem
A theoretical study of the molecular structure and vibrational spectra of methyl cyanate and its sulfur and selenium analogues q P. Babinec a,b, J. Leszczynski a,* a
Department of Chemistry, The Computational Center for Molecular Structures and Interactions, Jackson State University, 1400 Lynch Street, Jackson, MS 39217, USA b Department of Biophysics and Chemical Physics, Comenius University, 842 15 Bratislava, Slovakia
Abstract Ab initio electronic structure calculations at the MP2, Becke3LYP, and CCSD levels in conjunction with 6-31111G(d,p) basis set are used for determining the structure of equilibrium and the top-of-barrier methyl conformers of CH3 –XCN (X O,S,Se) molecules. Energy minimum structures for all substituents correspond to the staggered and top-of-barrier structures to the eclipsed conformations, each having Cs point-group symmetry. At the MP2 and Becke3LYP levels vibrational analysis was performed. For methyl cyanate and methyl thiocyanate, the theoretical IR spectra are compared with the experimentally obtained values. For the structural and vibrational parameters, there is excellent agreement between the theoretical and the available experimental data. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Methyl cyanate; Methyl thiocyanate; Methyl selenocyanate; Molecular structure; Ab initio methods
1. Introduction Syntheses of covalent cyanates with organic ligands have been reported since the 1960s [1]. However, very little is known about their structures. The only crystal structure is known for 4-chloro-3,5dimethyl phenyl cyanate [2]. A reliable gas phase structure has been determined for SeF5OCN [3]. Molecules with an ambidextrous cyanato –OCN group form very diverse classes of compounds because the cyanato group is able to react at the site of either the oxygen or nitrogen atom, forming either R–OCN or R–NCO species. The simplest molecule q
Dedicated to Professor R. Ga´spa´r on the occasion of his 80th year. * Corresponding author. Tel.: 11-601-968-2171; fax: 11-601973-3674. E-mail address: [email protected] (J. Leszczynski).
from this class HNCO, isocyanic acid, exist only as the R–NCO type in the gas phase [4]. Another species from this class, methyl cyanate (CH3OCN), is known to be an unstable molecule and is expected to be an interstellar molecule. Although the first preparation of methyl cyanate has been reported long ago [5], it was difficult to characterize the synthesized compound because it rapidly isomerizes to methyl isocyanate (CH3 –NCO). Recently methyl cyanate has been generated by reacting O-methylthiocarbamate with mercury oxide. Such samples were systematically studied using microwave spectroscopy in the frequency range of 8–50 GHz [6–8]. From microwave spectroscopy are also available structural parameters for methyl thiocyanate (CH3 –SCN) [9,10] and methyl selenocyanate (CH3 –SeCN) [11,12]. At present only a very few ab initio calculations for these compounds have been reported. In Refs. [13,14],
0166-1280/00/$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(99)00439-X
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Table 1 Predicted and experimental parameters of equilibrium (staggered) and top of barrier (eclipsed) conformers of methyl cyanate Equilibrium conformation MP2
DFT
Top of barrier Exp. a
CCSD
Structural parameters (bond lengths in A˚, angles in 8) 1.091 1.090 1.093 Ho –C1 HI –C1 1.087 1.086 1.089 C1 –O 1.452 1.459 1.450 O–C2 1.293 1.287 1.295 C2 –N 1.179 1.158 1.163 Ho –C1 –O 109.62 109.53 109.68 105.14 105.04 105.21 Hi –C1 –O C1 –O–C2 113.07 115.67 113.57 O–C2 –N 178.47 177.98 178.75 Total electronic energy (a.u.) and zero-point energy (kcal/mol) E 2207.452160 2208.006483 2207.470294 ZPE 31.61094 31.38638 Dipole moment (Debye) 4.87 Rotational constants (GHz) A 38.49652 40.70193 38.74093 B 5.30114 5.23046 5.32759 C 4.80354 4.77730 4.82950 a
1.075 (25) 1.074 (25) 1.455 (1) 1.302(3) 1.146 (3) 109.4 (14) 106.5 (11) 113.8 (6) 178.4 (6)
MP2
DFT
1.079 1.080 1.439 1.269 1.132 107.25 110.24 117.57 179.18 2207.450227 31.80391
1.088 1.088 1.463 1.284 1.159 107.03 110.18 116.85 177.89 2208.004908 31.57342
4.26 (46) 39.04241 5.32289 4.81999
Ref. [8].
the structure of methyl cyanate has been predicted at HF/STO-3G level and later in Ref. [15] at the correlated MP2/6-31G pp theoretical level. For sulfur and selenium analogues, no ab initio results have been reported. As has been shown recently on related C2H5 –XCN (X O,S,Se) molecules [16–18], close agreement between the theoretical and experimental values is obtained using at least a basis set of triplezeta quality in conjunction with the MP2 correlation level. Such a conclusion is supported also by the results of various molecules containing sulfur, selenium, and other heavier atoms studied recently in our laboratory [19–24] and also in related studies from other laboratories [25–27]. Our aim in this study is to perform ab initio MO calculations for the CH3 –XCN (X O,S,Se) molecular systems using an accurate, post Hartree–Fock levels of theory up to the coupled cluster level using high quality basis set which is the highest possible level for molecules of these sizes. Moreover, to characterize these molecules using the density functional method, which represents substantially less computational effort expensive alternative capable of producing very reliable results. Our study
is dedicated to Professor Rezso¨ Ga´spar whose landmark paper [28] was of tremendous significance as a link between the simple Thomas–Fermi theory [29,30] and the Kohn–Sham computational scheme [31] adapted for quantum chemical studies today [32]. 2. Computational details The molecular structures of studied molecules have been optimized without any symmetry constraints using the second-order Moller–Plesset theory (MP2), the coupled cluster theory with single and double excitations (CCSD), and the density functional theory (DFT) where we have used a hybrid functional of the form [33] 1 2 AEXSlater 1 AEXHF 1 BEXBecke 1 CECLYP 1 1 2 CECVWN where EXSlater is the Slater exchange, EXHF is the Hartree–Fock exchange, EXBecke is the gradient part of the exchange functional of Becke [34], ECLYP is the correlation functional of Lee et al. [35], ECVWN is
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Table 2 Predicted and experimental parameters of equilibrium (staggered) and top of barrier (eclipsed) conformers of methyl thiocyanate Equilibrium conformation MP2
DFT
Top of barrier CCSD
Structural parameters (bond lengths in A˚, angles in 8) 1.089 1.088 1.087 Ho –C1 Hi –C1 1.092 1.090 1.091 C1 –S 1.816 1.841 1.833 S–C2 1.693 1.698 1.691 C2 –N 1.181 1.159 1.179 Ho –C1 –S 110.74 110.31 110.42 105.67 105.07 105.61 Hi –C1 –S C1 –S–C2 98.28 99.78 99.02 S–C2 –N 178.84 177.85 178.92 Total electronic energy (a.u.) and zero-point energy (kcal/mol) E 2530.064567 2530.998441 2530.083724 ZPE 29.40412 29.25151 Dipole moment (Debye) 4.45 Rotational constants (GHz) A 15.58781 15.77811 15.78237 B 4.13564 4.06808 4.04581 C 3.33852 3.30285 3.34192 a
Exp. a
1.086 (3) 1.094 (4) 1.824 (2) 1.683 (3) 1.170 (2) 109.7 (1) 105.4 (3) 179.8 (13)
MP2
1.089 1.088 1.827 1.691 1.181 109.03 109.50 99.04 178.35 2530.062207 29.26676
DFT
1.088 1.087 1.852 1.695 1.159 108.31 109.30 100.46 177.51 2530.996309 29.06779
4.12 15.78691 3.80793 3.35413
Ref. [10].
Table 3 Predicted and experimental parameters of equilibrium (staggered) and top of barrier (eclipsed) conformers of methyl selenocyanate Equilibrium conformation MP2
DFT
Top of barrier CCSD
Structural parameters (bond lengths in A˚, angles in 8) Ho –C1 1.089 1.087 1.086 Hi –C1 1.091 1.090 1.090 1.958 1.981 1.957 C1 –Se Se–C2 1.843 1.848 1.844 C2 –N 1.182 1.159 1.736 Ho –C1 –Se 109.77 109.55 109.58 105.53 104.97 105.38 HI –C1 –Se C1 –Se–C2 95.60 96.92 95.77 Se–C2 –N 178.94 178.11 179.22 Total electronic energy (a.u.) and zero-point energy (kcal/mol) E 22532.315394 22534.331705 22533.214856 ZPE 28.58881 28.48443 Dipole moment (Debye) 4.69 Rotational constants (GHz) A 10.05151 10.05765 10.06321 B 3.44201 3.41982 3.46306 C 2.60708 2.59478 2.61192 a
Ref. [12].
Exp. a
1.083 (6) 1.073 (4) 1.954 (7) 1.836 (11) 1.162 (9) 109.3 (6) 105.4 (5) 179.3 (15)
4.42 (5) 10.14393 3.48367 2.63162
MP2
DFT
1.089 1.088 1.968 1.841 1.181 108.54 108.33 96.45 178.65
1.087 1.086 1.992 1.846 1.159 108.04 108.15 97.54 177.88
22532.313372 28.44350
22543.329997 28.31820
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Fig. 1. General molecular structures of eclipsed (top-of-barrier) and staggered (equilibrium) conformers of CH3 –XCN molecules.
the correlation potential of Vosko et al. [36], and A, B, and C are the coefficients determined by Becke [34] using his three-parameter fit to the experimental heats of formation for different choices of correlation potential. This modification of the original Becke hybrid functional [33] is described in Ref. [37] and is commonly denoted as Becke3LYP. Vibrational spectra were calculated at the MP2 and DFT levels for both equilibrium and transition state structures. The standard 6-31111G(d,p) Gaussian basis set was employed for all studied atoms. All calculations were performed using the Gaussian 94
program package [38]. The errors arising from numerical integration were reduced by the “finegrid” option which corresponds roughly to 7000 gridpoints/atom.
3. Results and discussion The results of geometry optimization at the MP2, DFT, and CCSD levels as well as available experimental values, are summarized in Tables 1–3. The equilibrium geometry for all O, S, Se substituted methyl cyanates is characterized by a Cs point-group
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Table 4 Predicted harmonic vibrational frequencies in cm 21 and IR intensities in km/mol (in parentheses) and experimental frequencies of CH3OCN and CH3SCN CH3OCN Mode
CH3SCN MP2
143.7 (0) Methyl torsion (a 0 ) CXC in-plane def. (a 0 ) 222.3 (7.3) XCN out-of-plane def. (a 00 ) 481.6 (6.4) XCN in-plane def. (a 0 ) 600.1 (2.0) X–C1 sym. str. (a 0 ) 920.9 (27.3) X–CN str. (a 0 ) 1141.5 (130) 1189.7 (1.1) CH3 asym. rock (a 00 ) CH3 sym. rock (a 0 ) 1243.4 (47) CH3 sym. def. (a 0 ) 1498.4 (1.7) CH3 asym. def. (a 00 ) 1510.1 (10) CH3 asym. def. (a 0 ) 1523.9 (15) 2231.4 (144) CyN str. (a 0 ) C–H sym. str. (a 0 ) 3100.2 (26) C–H asym. str. (a 00 ) 3201.6 (11) C–H asym. str. (a 0 ) 3238.4 (5.1) a b
DFT 136.4 (0) 228.9 (7.8) 524.4 (9.2) 614.1 (3.6) 883.7 (39.4) 1135.9 (103) 1163.3 (0.5) 1226.8 (62) 1472.0 (0.9) 1488.0 (12) 1493.7 (16) 2352.9 (208) 3054.3 (25) 3138.4 (13) 3176.8 (5.5)
Exp.
a
893 1112 1152 1213 1462 1470 2263 2968 3017 3042
CH3SeCN b
MP2
DFT
Exp.
143.9 (0) 168.3 (5.4) 330.6 (1) 449.6 (0.6) 698.8 (0) 745.0 (1.6) 1006.8 (3.7) 1028.0 (10) 1402.5 (3.7) 1461.5 (9.0) 1498.1 (11) 2113.1 (7) 3100.8 (12) 3205.0 (1.6) 3216.3 (1.3)
134.8 (0) 147.8 (4) 360.9 (0.9) 401.3 (0.1) 531.7 (2.9) 564.9 (0.7) 922.8 (5.3) 944.1 (10.3) 1315.5 (8.1) 1460.0 (8.5) 1475.6 (9.8) 2255.1 (1.7) 3066.0 (9) 3162.7 (1.4) 3181.6 (0.4)
153.0 190.0 405.0 546.0 673.0 698.0 967.0 974.0 1333.0 1436.0 1436.0 2171.0 2945.0 3029.0 3029.0
MP2
DFT
149.7 (0) 173.0 (5.5) 393.2 (1.9) 456.6 (0.5) 660.03 (1.4) 692.7 (0.8) 981.3 (3.9) 1010.6 (10) 1363.0 (4.5) 1464.1 (10) 1480.1 (11) 2259.4 (32) 3060.8 (11) 3152.8 (1.8) 3164.1 (1.7)
136.7 (0) 144.1 (4.1) 327.9 (0.7) 391.5 (0.3) 544.8 (2.2) 607.4 (0.3) 941.5 (4.8) 955.8 (10.3) 1344.1 (7.2) 1474.6 (7.4) 1495.9 (9.0) 2090.0 (0.2) 3102.5 (8) 3212.4 (1) 3228.6 (0.1)
Ref. [43]. Ref. [39].
symmetry staggered conformation (Fig. 1). The topof-barrier structure corresponds to the eclipsed conformation which also possesses Cs symmetry. The structural parameters of the methyl group in methyl cyanate are quite similar to those of methyl thiocyanate and methyl selenocyanate within a limit of errors. The experimental parameters are in good agreement with those obtained from ab initio calculations. Experimental values are best reproduced at the CCSD level. The bond length of C1 –X is almost the same as that for a normal single bond of CH3XCH3. On the contrary, the bond length X–C2 is between that of a single bond and a double bond and has a value ˚ than a normal single which is shorter by about 0.1 A ˚ than a normal bond and is longer by about 0.1 A double bond in, e.g. CH3 –C(H) Se. This intermediate bond arises from back donation of electrons from the X atom to a cyano group. C1 –Hi and C1 –Ho bond lengths are at all levels slightly larger than the experimental values (especially for methyl cyanate) even though well within the range of experimental ˚ ) obtained for these parameters. uncertainty (^0.025 A The mutual influences of experiment and theory are more illustrated on the development of data for the
cyanate group and in particular for the O–C2 –N angle. In the first experimental study this bond has been found to be linear [6]. In the first ab initio study [13], the O–C2 –N group of methyl cyanate was found to be bent by almost 48, and finally the series of very precise experiments on a number of isotopic species [7,8] yielded a value for this angle of 178:4 ^ 68: Our theoretical values of 178.47 and 178.758 at the MP2 and CCSD levels, respectively, are essentially identical with the experiment. This is another example of the reliability of the results obtained at the CCSD level with a basis set of triple zeta quality. The DFT level lead to a slightly more bent bond but is also very close to the experimental value. For methyl thiocyanate and methyl selenocyanate, the X–C2 –N angles are predicted at CCSD level to be 178.92 and 179.228, respectively. For X Se we again have excellent agreement with the experimental value of 179:3 ^ 0:158 (it should be noted that the experimental values found in Ref. [11] have been substantially improved in Ref. [12] using more isotopic species in microwave study). The X S predicted value suggests that this chain bond may be slightly bent similar to the X O case, and represents
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Table 5 Comparison of theoretical and experimental barrier heights (cal/mol)
Experiment MP2 MP2 (ZPE corrected) DFT DFT (ZPE corrected) a b c
CH3OCN
CH3SCN
CH3SeCN
1140 (50) a 1213 1406 988 1175
1570 (10) b 1481 1343 1338 1154
1240 (50) c 1269 1123 1072 927
Ref. [8]. Ref. [10], in Ref. [43] 1200 cal/mol has been found. Refs. [11,12].
a challenging task for experimentalists to verify this theoretical hypothesis using a more precise study with more isotopic species than in relatively old studies [9,10] of this molecule. Another theoretical quantity which is in an excellent agreement with the experimental values is a dipole moment calculated at the MP2 level for all three cyanate analogues. At the MP2 and DFT levels we have also performed vibrational analysis for both equilibrium (Table 4) and top-of-barrier structures (not shown). For X S, relevant experimental data are also available. In Table 4 we have shown the frequencies revealed in Ref. [39] which are more reliable than older studies [40,41]. Overall theoretical IR spectra at the both MP2 and DFT levels fit well with the experimental values. The frequency of methyl torsion was not used in the experimental normal mode analysis in Ref. [39] and has been determined independently (153 cm 21). Also this value is in good agreement with the predicted methyl torsion frequency of CH3 –SCN. The general appearance of the CH3OCN infrared spectra is studied in Ref. [42]. Because of rapid decomposition (lifetime few minutes), the performed analysis is not very exhaustive. The experimentally resolved spectrum showed CH stretching vibrations near 3000 cm 21, CN stretching vibration at ca. 2250 cm 21, CH3 deformations near 1100 cm 21, and some vibrations near 500 cm 21. As can be seen from Table 4, these values correspond to our theoretical frequencies with the strongest IR intensities. In Table 4 we have compared our theoretical frequencies with IR spectra obtained in a recent study [43]. Again the theoretical values fit well with the experimental.
As we mentioned in Section 1, similar to isocyanic acid detected in emissions from a galactic radio source SgrB2 [44] methyl cyanate is another candidate for an interstellar molecule. Because the search for the spectral lines of methyl cyanate obtained in Ref. [6] by the 45 m radiotelescope at the Nobeyama Radio Observatory was not successful, we hope that our theoretical spectra furnished in this study could be of importance in the search and characterization of this molecule. Finally, we have compared the experimental and theoretical values of barrier height of internal rotation of the methyl group (Table 5). The skeletal flexing which accompanies torsional rotation of the methyl group implies changes in the normal modes of the molecule even those, which do not involve methyl torsional, motion, per se. In the framework of the Born–Oppenheimer approximation, the influence of these changes can be obtained by considering the alteration in the zero-point energy of all normal modes without including methyl torsional vibration. Therefore, an effective barrier energy can be written as DEbarrier DE 1 D ZPE where DE is the ab initio electronic energy difference between the global minimum staggered and top-ofbarrier eclipsed conformers. The D(ZPE) is the zeropoint energy difference between these two conformers, summed over the 14 high-frequency modes (torsion not included). The predicted harmonic contributions to D(ZPE) are shown in Table 5. Although the anharmonicities have not been included, these relatively small harmonic values (13, 10, and 12% at the MP2 level for O, S, and Se cyanates, respectively) indicate that the rotational barriers in the studied cyanates is almost entirely electronic in nature as in cases of acetaldehyde [43] and propene [45] and unlike ethane [46].
4. Conclusions This study is a further demonstration that experimental and theoretical results should complement each other, inspiring investigations using the complementary technique, until the “convergence” of results is achieved. This is true especially for the
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particular example of O–C2 –N chain bond angle where an initial experimental study (leading to linear bond) has stimulated a theoretical analysis (which leads to an extremely bent bond) followed by very precise experimental work, furnishing results confirmed in this study by high level ab initio predictions. In order to be a guide possible for further experimental study, we have furnished the vibrational spectra and geometrical structural parameters for all species. The most challenging task seems to us as an experimental study of methyl thiocyanate for which we have predicted slightly bent S–C2 –N bond in contradiction with the experimentally obtained linear structure. Acknowledgements This work was facilitated by NSF Grant OSR9452857 and by contract (DAAL 03-89-0038) between the Army Research Office and the University of Minnesota for the Army High Performance Computing Research Center under the auspices of the Department of the Army, Army Research Laboratory Cooperative Agreement Number DAAH04-95-20003/Contract Number DAAH04-95-C-008. The policy of the government and no official endorsement should be inferred. References [1] K.A. Jensen, K. Holm, in: S. Patai (Ed.), The Chemistry of Cyanates and Their Thio Derivatives, Wiley, New York, 1977, chap. 16. [2] L. Kutschabsky, H. Schrauber, Krist. Tech. 3 (1973) 217. [3] K. Seppelt, H. Oberhammer, Inorg. Chem. 24 (1985) 1227. [4] K. Yamada, J. Mol. Spectrosc. 79 (1965) 438. [5] K. Jensen, M. Due, A. Holm, Acta Chem. Scand. 19 (1965) 438. [6] T. Sakaizumi, H. More, O. Ohashi, I. Yamaguchi, J. Mol. Spectrosc. 140 (1990) 62. [7] T. Sakaizumi, K. Sekishita, K. Furuya, Y. Tetsuda, K. Kaneko, O. Osashi, I. Yamaguchi, J. Mol. Spectrosc. 161 (1993) 114. [8] T. Sakaizumi, M. Namikawa, O. Ohashi, J. Mol. Struct. 345 (1995) 189. [9] H. Dreizler, A.M. Mirri, Z. Naturforsch A 23 (1968) 1313. [10] H. Dreizler, H.D. Rudolph, H. Schleser, Z. Naturforsch A 25 (1970) 1643. [11] T. Sakaizumi, Y. Hohri, O. Ohashi, I. Yamaguchi, Bull. Chem. Soc. Jpn 51 (1978) 3411.
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A theoretical study of the molecular structure and vibrational spectra of methyl cyanate and its sulfur and selenium analogues q P. Babinec a,b, J. Leszczynski a,* a
Department of Chemistry, The Computational Center for Molecular Structures and Interactions, Jackson State University, 1400 Lynch Street, Jackson, MS 39217, USA b Department of Biophysics and Chemical Physics, Comenius University, 842 15 Bratislava, Slovakia
Abstract Ab initio electronic structure calculations at the MP2, Becke3LYP, and CCSD levels in conjunction with 6-31111G(d,p) basis set are used for determining the structure of equilibrium and the top-of-barrier methyl conformers of CH3 –XCN (X O,S,Se) molecules. Energy minimum structures for all substituents correspond to the staggered and top-of-barrier structures to the eclipsed conformations, each having Cs point-group symmetry. At the MP2 and Becke3LYP levels vibrational analysis was performed. For methyl cyanate and methyl thiocyanate, the theoretical IR spectra are compared with the experimentally obtained values. For the structural and vibrational parameters, there is excellent agreement between the theoretical and the available experimental data. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Methyl cyanate; Methyl thiocyanate; Methyl selenocyanate; Molecular structure; Ab initio methods
1. Introduction Syntheses of covalent cyanates with organic ligands have been reported since the 1960s [1]. However, very little is known about their structures. The only crystal structure is known for 4-chloro-3,5dimethyl phenyl cyanate [2]. A reliable gas phase structure has been determined for SeF5OCN [3]. Molecules with an ambidextrous cyanato –OCN group form very diverse classes of compounds because the cyanato group is able to react at the site of either the oxygen or nitrogen atom, forming either R–OCN or R–NCO species. The simplest molecule q
Dedicated to Professor R. Ga´spa´r on the occasion of his 80th year. * Corresponding author. Tel.: 11-601-968-2171; fax: 11-601973-3674. E-mail address: [email protected] (J. Leszczynski).
from this class HNCO, isocyanic acid, exist only as the R–NCO type in the gas phase [4]. Another species from this class, methyl cyanate (CH3OCN), is known to be an unstable molecule and is expected to be an interstellar molecule. Although the first preparation of methyl cyanate has been reported long ago [5], it was difficult to characterize the synthesized compound because it rapidly isomerizes to methyl isocyanate (CH3 –NCO). Recently methyl cyanate has been generated by reacting O-methylthiocarbamate with mercury oxide. Such samples were systematically studied using microwave spectroscopy in the frequency range of 8–50 GHz [6–8]. From microwave spectroscopy are also available structural parameters for methyl thiocyanate (CH3 –SCN) [9,10] and methyl selenocyanate (CH3 –SeCN) [11,12]. At present only a very few ab initio calculations for these compounds have been reported. In Refs. [13,14],
0166-1280/00/$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(99)00439-X
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Table 1 Predicted and experimental parameters of equilibrium (staggered) and top of barrier (eclipsed) conformers of methyl cyanate Equilibrium conformation MP2
DFT
Top of barrier Exp. a
CCSD
Structural parameters (bond lengths in A˚, angles in 8) 1.091 1.090 1.093 Ho –C1 HI –C1 1.087 1.086 1.089 C1 –O 1.452 1.459 1.450 O–C2 1.293 1.287 1.295 C2 –N 1.179 1.158 1.163 Ho –C1 –O 109.62 109.53 109.68 105.14 105.04 105.21 Hi –C1 –O C1 –O–C2 113.07 115.67 113.57 O–C2 –N 178.47 177.98 178.75 Total electronic energy (a.u.) and zero-point energy (kcal/mol) E 2207.452160 2208.006483 2207.470294 ZPE 31.61094 31.38638 Dipole moment (Debye) 4.87 Rotational constants (GHz) A 38.49652 40.70193 38.74093 B 5.30114 5.23046 5.32759 C 4.80354 4.77730 4.82950 a
1.075 (25) 1.074 (25) 1.455 (1) 1.302(3) 1.146 (3) 109.4 (14) 106.5 (11) 113.8 (6) 178.4 (6)
MP2
DFT
1.079 1.080 1.439 1.269 1.132 107.25 110.24 117.57 179.18 2207.450227 31.80391
1.088 1.088 1.463 1.284 1.159 107.03 110.18 116.85 177.89 2208.004908 31.57342
4.26 (46) 39.04241 5.32289 4.81999
Ref. [8].
the structure of methyl cyanate has been predicted at HF/STO-3G level and later in Ref. [15] at the correlated MP2/6-31G pp theoretical level. For sulfur and selenium analogues, no ab initio results have been reported. As has been shown recently on related C2H5 –XCN (X O,S,Se) molecules [16–18], close agreement between the theoretical and experimental values is obtained using at least a basis set of triplezeta quality in conjunction with the MP2 correlation level. Such a conclusion is supported also by the results of various molecules containing sulfur, selenium, and other heavier atoms studied recently in our laboratory [19–24] and also in related studies from other laboratories [25–27]. Our aim in this study is to perform ab initio MO calculations for the CH3 –XCN (X O,S,Se) molecular systems using an accurate, post Hartree–Fock levels of theory up to the coupled cluster level using high quality basis set which is the highest possible level for molecules of these sizes. Moreover, to characterize these molecules using the density functional method, which represents substantially less computational effort expensive alternative capable of producing very reliable results. Our study
is dedicated to Professor Rezso¨ Ga´spar whose landmark paper [28] was of tremendous significance as a link between the simple Thomas–Fermi theory [29,30] and the Kohn–Sham computational scheme [31] adapted for quantum chemical studies today [32]. 2. Computational details The molecular structures of studied molecules have been optimized without any symmetry constraints using the second-order Moller–Plesset theory (MP2), the coupled cluster theory with single and double excitations (CCSD), and the density functional theory (DFT) where we have used a hybrid functional of the form [33] 1 2 AEXSlater 1 AEXHF 1 BEXBecke 1 CECLYP 1 1 2 CECVWN where EXSlater is the Slater exchange, EXHF is the Hartree–Fock exchange, EXBecke is the gradient part of the exchange functional of Becke [34], ECLYP is the correlation functional of Lee et al. [35], ECVWN is
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Table 2 Predicted and experimental parameters of equilibrium (staggered) and top of barrier (eclipsed) conformers of methyl thiocyanate Equilibrium conformation MP2
DFT
Top of barrier CCSD
Structural parameters (bond lengths in A˚, angles in 8) 1.089 1.088 1.087 Ho –C1 Hi –C1 1.092 1.090 1.091 C1 –S 1.816 1.841 1.833 S–C2 1.693 1.698 1.691 C2 –N 1.181 1.159 1.179 Ho –C1 –S 110.74 110.31 110.42 105.67 105.07 105.61 Hi –C1 –S C1 –S–C2 98.28 99.78 99.02 S–C2 –N 178.84 177.85 178.92 Total electronic energy (a.u.) and zero-point energy (kcal/mol) E 2530.064567 2530.998441 2530.083724 ZPE 29.40412 29.25151 Dipole moment (Debye) 4.45 Rotational constants (GHz) A 15.58781 15.77811 15.78237 B 4.13564 4.06808 4.04581 C 3.33852 3.30285 3.34192 a
Exp. a
1.086 (3) 1.094 (4) 1.824 (2) 1.683 (3) 1.170 (2) 109.7 (1) 105.4 (3) 179.8 (13)
MP2
1.089 1.088 1.827 1.691 1.181 109.03 109.50 99.04 178.35 2530.062207 29.26676
DFT
1.088 1.087 1.852 1.695 1.159 108.31 109.30 100.46 177.51 2530.996309 29.06779
4.12 15.78691 3.80793 3.35413
Ref. [10].
Table 3 Predicted and experimental parameters of equilibrium (staggered) and top of barrier (eclipsed) conformers of methyl selenocyanate Equilibrium conformation MP2
DFT
Top of barrier CCSD
Structural parameters (bond lengths in A˚, angles in 8) Ho –C1 1.089 1.087 1.086 Hi –C1 1.091 1.090 1.090 1.958 1.981 1.957 C1 –Se Se–C2 1.843 1.848 1.844 C2 –N 1.182 1.159 1.736 Ho –C1 –Se 109.77 109.55 109.58 105.53 104.97 105.38 HI –C1 –Se C1 –Se–C2 95.60 96.92 95.77 Se–C2 –N 178.94 178.11 179.22 Total electronic energy (a.u.) and zero-point energy (kcal/mol) E 22532.315394 22534.331705 22533.214856 ZPE 28.58881 28.48443 Dipole moment (Debye) 4.69 Rotational constants (GHz) A 10.05151 10.05765 10.06321 B 3.44201 3.41982 3.46306 C 2.60708 2.59478 2.61192 a
Ref. [12].
Exp. a
1.083 (6) 1.073 (4) 1.954 (7) 1.836 (11) 1.162 (9) 109.3 (6) 105.4 (5) 179.3 (15)
4.42 (5) 10.14393 3.48367 2.63162
MP2
DFT
1.089 1.088 1.968 1.841 1.181 108.54 108.33 96.45 178.65
1.087 1.086 1.992 1.846 1.159 108.04 108.15 97.54 177.88
22532.313372 28.44350
22543.329997 28.31820
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Fig. 1. General molecular structures of eclipsed (top-of-barrier) and staggered (equilibrium) conformers of CH3 –XCN molecules.
the correlation potential of Vosko et al. [36], and A, B, and C are the coefficients determined by Becke [34] using his three-parameter fit to the experimental heats of formation for different choices of correlation potential. This modification of the original Becke hybrid functional [33] is described in Ref. [37] and is commonly denoted as Becke3LYP. Vibrational spectra were calculated at the MP2 and DFT levels for both equilibrium and transition state structures. The standard 6-31111G(d,p) Gaussian basis set was employed for all studied atoms. All calculations were performed using the Gaussian 94
program package [38]. The errors arising from numerical integration were reduced by the “finegrid” option which corresponds roughly to 7000 gridpoints/atom.
3. Results and discussion The results of geometry optimization at the MP2, DFT, and CCSD levels as well as available experimental values, are summarized in Tables 1–3. The equilibrium geometry for all O, S, Se substituted methyl cyanates is characterized by a Cs point-group
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Table 4 Predicted harmonic vibrational frequencies in cm 21 and IR intensities in km/mol (in parentheses) and experimental frequencies of CH3OCN and CH3SCN CH3OCN Mode
CH3SCN MP2
143.7 (0) Methyl torsion (a 0 ) CXC in-plane def. (a 0 ) 222.3 (7.3) XCN out-of-plane def. (a 00 ) 481.6 (6.4) XCN in-plane def. (a 0 ) 600.1 (2.0) X–C1 sym. str. (a 0 ) 920.9 (27.3) X–CN str. (a 0 ) 1141.5 (130) 1189.7 (1.1) CH3 asym. rock (a 00 ) CH3 sym. rock (a 0 ) 1243.4 (47) CH3 sym. def. (a 0 ) 1498.4 (1.7) CH3 asym. def. (a 00 ) 1510.1 (10) CH3 asym. def. (a 0 ) 1523.9 (15) 2231.4 (144) CyN str. (a 0 ) C–H sym. str. (a 0 ) 3100.2 (26) C–H asym. str. (a 00 ) 3201.6 (11) C–H asym. str. (a 0 ) 3238.4 (5.1) a b
DFT 136.4 (0) 228.9 (7.8) 524.4 (9.2) 614.1 (3.6) 883.7 (39.4) 1135.9 (103) 1163.3 (0.5) 1226.8 (62) 1472.0 (0.9) 1488.0 (12) 1493.7 (16) 2352.9 (208) 3054.3 (25) 3138.4 (13) 3176.8 (5.5)
Exp.
a
893 1112 1152 1213 1462 1470 2263 2968 3017 3042
CH3SeCN b
MP2
DFT
Exp.
143.9 (0) 168.3 (5.4) 330.6 (1) 449.6 (0.6) 698.8 (0) 745.0 (1.6) 1006.8 (3.7) 1028.0 (10) 1402.5 (3.7) 1461.5 (9.0) 1498.1 (11) 2113.1 (7) 3100.8 (12) 3205.0 (1.6) 3216.3 (1.3)
134.8 (0) 147.8 (4) 360.9 (0.9) 401.3 (0.1) 531.7 (2.9) 564.9 (0.7) 922.8 (5.3) 944.1 (10.3) 1315.5 (8.1) 1460.0 (8.5) 1475.6 (9.8) 2255.1 (1.7) 3066.0 (9) 3162.7 (1.4) 3181.6 (0.4)
153.0 190.0 405.0 546.0 673.0 698.0 967.0 974.0 1333.0 1436.0 1436.0 2171.0 2945.0 3029.0 3029.0
MP2
DFT
149.7 (0) 173.0 (5.5) 393.2 (1.9) 456.6 (0.5) 660.03 (1.4) 692.7 (0.8) 981.3 (3.9) 1010.6 (10) 1363.0 (4.5) 1464.1 (10) 1480.1 (11) 2259.4 (32) 3060.8 (11) 3152.8 (1.8) 3164.1 (1.7)
136.7 (0) 144.1 (4.1) 327.9 (0.7) 391.5 (0.3) 544.8 (2.2) 607.4 (0.3) 941.5 (4.8) 955.8 (10.3) 1344.1 (7.2) 1474.6 (7.4) 1495.9 (9.0) 2090.0 (0.2) 3102.5 (8) 3212.4 (1) 3228.6 (0.1)
Ref. [43]. Ref. [39].
symmetry staggered conformation (Fig. 1). The topof-barrier structure corresponds to the eclipsed conformation which also possesses Cs symmetry. The structural parameters of the methyl group in methyl cyanate are quite similar to those of methyl thiocyanate and methyl selenocyanate within a limit of errors. The experimental parameters are in good agreement with those obtained from ab initio calculations. Experimental values are best reproduced at the CCSD level. The bond length of C1 –X is almost the same as that for a normal single bond of CH3XCH3. On the contrary, the bond length X–C2 is between that of a single bond and a double bond and has a value ˚ than a normal single which is shorter by about 0.1 A ˚ than a normal bond and is longer by about 0.1 A double bond in, e.g. CH3 –C(H) Se. This intermediate bond arises from back donation of electrons from the X atom to a cyano group. C1 –Hi and C1 –Ho bond lengths are at all levels slightly larger than the experimental values (especially for methyl cyanate) even though well within the range of experimental ˚ ) obtained for these parameters. uncertainty (^0.025 A The mutual influences of experiment and theory are more illustrated on the development of data for the
cyanate group and in particular for the O–C2 –N angle. In the first experimental study this bond has been found to be linear [6]. In the first ab initio study [13], the O–C2 –N group of methyl cyanate was found to be bent by almost 48, and finally the series of very precise experiments on a number of isotopic species [7,8] yielded a value for this angle of 178:4 ^ 68: Our theoretical values of 178.47 and 178.758 at the MP2 and CCSD levels, respectively, are essentially identical with the experiment. This is another example of the reliability of the results obtained at the CCSD level with a basis set of triple zeta quality. The DFT level lead to a slightly more bent bond but is also very close to the experimental value. For methyl thiocyanate and methyl selenocyanate, the X–C2 –N angles are predicted at CCSD level to be 178.92 and 179.228, respectively. For X Se we again have excellent agreement with the experimental value of 179:3 ^ 0:158 (it should be noted that the experimental values found in Ref. [11] have been substantially improved in Ref. [12] using more isotopic species in microwave study). The X S predicted value suggests that this chain bond may be slightly bent similar to the X O case, and represents
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Table 5 Comparison of theoretical and experimental barrier heights (cal/mol)
Experiment MP2 MP2 (ZPE corrected) DFT DFT (ZPE corrected) a b c
CH3OCN
CH3SCN
CH3SeCN
1140 (50) a 1213 1406 988 1175
1570 (10) b 1481 1343 1338 1154
1240 (50) c 1269 1123 1072 927
Ref. [8]. Ref. [10], in Ref. [43] 1200 cal/mol has been found. Refs. [11,12].
a challenging task for experimentalists to verify this theoretical hypothesis using a more precise study with more isotopic species than in relatively old studies [9,10] of this molecule. Another theoretical quantity which is in an excellent agreement with the experimental values is a dipole moment calculated at the MP2 level for all three cyanate analogues. At the MP2 and DFT levels we have also performed vibrational analysis for both equilibrium (Table 4) and top-of-barrier structures (not shown). For X S, relevant experimental data are also available. In Table 4 we have shown the frequencies revealed in Ref. [39] which are more reliable than older studies [40,41]. Overall theoretical IR spectra at the both MP2 and DFT levels fit well with the experimental values. The frequency of methyl torsion was not used in the experimental normal mode analysis in Ref. [39] and has been determined independently (153 cm 21). Also this value is in good agreement with the predicted methyl torsion frequency of CH3 –SCN. The general appearance of the CH3OCN infrared spectra is studied in Ref. [42]. Because of rapid decomposition (lifetime few minutes), the performed analysis is not very exhaustive. The experimentally resolved spectrum showed CH stretching vibrations near 3000 cm 21, CN stretching vibration at ca. 2250 cm 21, CH3 deformations near 1100 cm 21, and some vibrations near 500 cm 21. As can be seen from Table 4, these values correspond to our theoretical frequencies with the strongest IR intensities. In Table 4 we have compared our theoretical frequencies with IR spectra obtained in a recent study [43]. Again the theoretical values fit well with the experimental.
As we mentioned in Section 1, similar to isocyanic acid detected in emissions from a galactic radio source SgrB2 [44] methyl cyanate is another candidate for an interstellar molecule. Because the search for the spectral lines of methyl cyanate obtained in Ref. [6] by the 45 m radiotelescope at the Nobeyama Radio Observatory was not successful, we hope that our theoretical spectra furnished in this study could be of importance in the search and characterization of this molecule. Finally, we have compared the experimental and theoretical values of barrier height of internal rotation of the methyl group (Table 5). The skeletal flexing which accompanies torsional rotation of the methyl group implies changes in the normal modes of the molecule even those, which do not involve methyl torsional, motion, per se. In the framework of the Born–Oppenheimer approximation, the influence of these changes can be obtained by considering the alteration in the zero-point energy of all normal modes without including methyl torsional vibration. Therefore, an effective barrier energy can be written as DEbarrier DE 1 D ZPE where DE is the ab initio electronic energy difference between the global minimum staggered and top-ofbarrier eclipsed conformers. The D(ZPE) is the zeropoint energy difference between these two conformers, summed over the 14 high-frequency modes (torsion not included). The predicted harmonic contributions to D(ZPE) are shown in Table 5. Although the anharmonicities have not been included, these relatively small harmonic values (13, 10, and 12% at the MP2 level for O, S, and Se cyanates, respectively) indicate that the rotational barriers in the studied cyanates is almost entirely electronic in nature as in cases of acetaldehyde [43] and propene [45] and unlike ethane [46].
4. Conclusions This study is a further demonstration that experimental and theoretical results should complement each other, inspiring investigations using the complementary technique, until the “convergence” of results is achieved. This is true especially for the
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