Conformational stability of ethylenediamine from temperature dependent infrared spectra of liquid xenon solutions, r0 structural parameters, ab initio calculations, and vibrational assignments

Journal of Molecular Structure 984 (2010) 58–67

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Conformational stability of ethylenediamine from temperature dependent infrared spectra of liquid xenon solutions, r0 structural parameters, ab initio calculations, and vibrational assignments James R. Durig ⇑, Savitha S. Panikar 1, Takuya Iwata, Todor K. Gounev Department of Chemistry, University of Missouri-Kansas City, Kansas City, MO 64110, USA

a r t i c l e

i n f o

Article history: Received 30 June 2010 Received in revised form 9 September 2010 Accepted 9 September 2010 Available online 17 September 2010 Keywords: Conformational stability r0 Structural parameters Ab initio calculations Vibrational assignments Ethylenediamine

a b s t r a c t Variable temperature (55 to 100 °C) studies of the infrared spectra (4000–400 cm1) of ethylenediamine, NH2CH2CH2NH2, dissolved in liquid xenon and the infrared spectra in the gaseous phase have been carried out. From these data, three of the possible ten conformers have been identified, and the enthalpy differences have been determined among the most stable g0 G0 g0 conformer and the second stable conformer, g0 G0 t, to be 64 ± 6 cm1 (0.77 ± 0.07 kJ mol1) and the third conformer, gG0 g0 , to be 210 ± 19 cm1 (2.51 ± 0.23 kJ mol1). The first indicator is the lone pair of electrons on the nitrogen-1 atom with respect to the NCC angle (g = gauche or t = trans) and the second indicator is the NCCN dihedral angle (G = gauche or T = trans) and the third one similar to the first one but with respect to nitrogen-2. The percentage of each conformer at ambient temperature is estimated to be 47 ± 1% of g0 G0 g0 , 36 ± 2% of g0 G0 t and 17 ± 2% of gG0 g0 . The conformational stabilities have been predicted from ab initio calculations by utilizing several different basis sets up to aug-cc-PVTZ for both MP2(full) and density functional theory calculations by the B3LYP method. By utilizing previously reported microwave rotational constants along with ab initio MP2(full)/ 6-311+G(d,p) predicted structural values, adjusted r0 parameters have been obtained for the two most stable conformers. The determined heavy atom structural parameters for the g0 G0 g0 [ g0 G0 t] conformer are: the distances (Å) N1–C2 = 1.472(3) [1.470(3)], C2–C3 = 1.526(3) [1.532(3)], N4–C3 = 1.464(3) [1.463(3)] and the angles (°)\N1C2C3 = 109.7(5) [109.7(5)], \N4C3C2 = 109.5(5) [115.3(5)] and sN1C2C3N4 = 63.5(5) [59.7(5)]. Vibrational assignments have been provided for most of the observed bands which have been supported by MP2(full)/6-31G(d) ab initio calculations to predict harmonic force fields, frequencies and infrared intensities for all three conformers. The results are discussed and compared to the corresponding properties of some similar molecules. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction There have been many determinations of the enthalpy difference between the trans and gauche conformers of ethylamine. A multitude of techniques including electron diffraction [1], Raman spectra of the gas [2], far infrared spectra [3,4], microwave spectra [5] and infrared spectra of variable temperature vapor deposited in an argon matrix [6] were carried out. Prior to the experimental determination of the enthalpy difference, an ab initio predicted value from HF/431G basis set of the energy difference was reported [7] with the gauche conformer being more stable by 182 cm1 (2.18 kJ mol1). Two years after this predicted energy difference a far infrared spectral study was reported [3] and an enthalpy difference of 104 cm1 ⇑ Corresponding author. Tel.: +1 816 235 6038; fax: +1 816 235 2290. E-mail address: [email protected] (J.R. Durig). Taken in part from the dissertation of S.S. Panikar which will be submitted to the Department of Chemistry in partial fulfillment of the Ph.D. degree. 1

0022-2860/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2010.09.007

(1.24 kJ mol1) was determined with the gauche form the more stable conformer. However, a year later two studies were reported where data from the Raman spectrum of gas [2] gave an estimated enthalpy difference of 207 cm1 (2.48 kJ mol1) but with the trans conformer the more stable form. Similar results were also reported with DH = 230 cm1 (2.75 kJ mol1) from far infrared spectral data with a coupled two-rotor model [4]. Nearly a decade later three studies were reported with the data from the infrared spectrum of the argon matrix [6] of 100 ± 10 cm1 (1.20 ± 0.12 kJ mol1), the relative intensity of the microwave spectrum [5] 110 ± 50 cm1 (1.32 ± 0.60 kJ mol1) and the value from electron diffraction studies [1] of 107 ± 70 cm1 (1.28 ± 0.84 kJ mol1) with all of the studies giving the trans conformer the more stable form. These latter studies indicated a value of 100 cm1 but two of them had very large uncertainties. Therefore, we carried out a variable temperature infrared study of xenon solutions [8] which gave an enthalpy difference of 54 ± 4 cm1 (0.65 ± 0.05 kJ mol1) with the trans conformer the more stable form which was consistent with the

J.R. Durig et al. / Journal of Molecular Structure 984 (2010) 58–67

ab initio predicted energy differences of 52 cm1 (0.62 kJ mol1) from MP2(full)/6-311G(2df,2pd) and 62 cm1 (0.74 kJ mol1) from MP4(SQDT)/6-311G(2d,2p). However, with diffuse functions utilizing these same basis sets and level of calculations the gauche conformer was predicted to have the lower energy of 41 cm1 (0.49 kJ mol1) and 39 cm1 (0.47 kJ mol1), respectively. So calculations with diffuse functions at this level incorrectly predicted the conformational stability of ethylamine. This is in contrast with ab initio predictions for aminomethylcyclopropane [9] where MP2(full)/6-311+G(2d,2p) calculations gave correctly the gauche form as the more stable conformer by 66 cm1 (0.79 kJ mol1) with an experimental value of 109 ± 11 cm1 (1.30 ± 0.13 kJ mol1) whereas the calculations with the same basis set but without diffuse functions predicted the trans form to have the lower energy by 73 cm1 (0.87 kJ mol1). Therefore, with such small energy differences the ab initio calculations cannot be relied on to give the correct conformational stability of these organoamines. Because of the importance of the organoamines in biological activities further determinations of the conformational stabilities of these important molecules is desirable. As a continuation of our spectroscopic studies of organoamines we have chosen ethylenediamine, NH2CH2CH2NH2, which is a very important chelating agent, for the scientific purpose of determining the conformational stabilities of several of the ten possible stable conformers for this 1,2-disubstituted ethylene molecule. Although there have been numerous previously reported [10–14] vibrational studies of this important molecule, there has not been any reported enthalpy determinations of the conformers from the vibrational studies. However, from the microwave investigation [15], two of the rotamers were identified with both of them possessing an intramolecular hydrogen bond. These two conformers had gauche N–C–C–N forms with the one designated as I relatively more stable by 0.3 ± 0.2 kcal mol1 (1.25 ± 0.84 kJ mol1). Later, an extensive conformational and ab initio investigation was reported [16] from an electron diffraction study from which anti-gauche energy and entropy differences were determined. The DE = EA  EG = 0.68 ± 0.41 kcal mol1 (2.85 ± 1.71 kJ mol1) and DS = SA  (SG+R ln 2) = 0.29 ± 0.90 cal mol1 K1 (1.21 ± 3.77 J mol1 K1). At 70 °C it was estimated that the two gauche forms with the internal hydrogen bonds had 88 ± 7% abundance compared to the single anti form. Therefore, we expected to be able to identify at least three conformers from the vibrational spectra of the xenon solution. Most of the reported vibrational spectra have been for the condensed phases or in polar solutions where extensive aggregation of the molecules is expected. Therefore, our vibrational studies have been restricted to the gas phase or from very dilute (104 M) xenon solutions where limited dimerization is expected. We have also carried out ab initio calculations employing a variety of basis sets up to aug-cc-PVTZ at the Moller–Plesset (MP) level to second order with full electron correlation to obtain predicted conformational stabilities and complete equilibrium geometries. Similar calculations have also been carried out by density functional theory by using the B3LYP method. The force constants, vibrational frequencies, infrared intensities, and conformational stabilities have also been obtained from the ab initio MP2(full)/631G(d) calculations. The results of these spectroscopic and theoretical studies are reported herein and comparisons of these results to those of related molecules are made.

59

trometer equipped with a Ge/CsI beamsplitter and a DTGS detector. Atmospheric water vapor was removed from the spectrometer housing by purging with dry nitrogen. The theoretical resolution used to obtain the spectrum of the gas was 0.5 cm1 and 128 interferograms were added and transformed with a boxcar truncation function. The mid-infrared spectra (3500–400 cm1) of the sample dissolved in liquefied xenon at ten different temperatures (55 °C to 100 °C) were recorded on a Bruker model IFS-66 Fourier transform spectrometer equipped with a globar source, a Ge/KBr beamsplitter and a DTGS detector. In all cases, 100 interferograms were collected at 1.0 cm1 resolution, averaged and transformed with a boxcar truncation function. For these studies, a specially designed cryostat cell was used. It consists of a copper cell with a path length of 4 cm with wedged silicon windows sealed to the cell with indium gaskets. The temperature was maintained with boiling liquid nitrogen and monitored by two Pt thermoresistors. A typical spectrum is shown in Fig. 1A and the wavenumbers of the observed bands from the spectra of the gas and xenon solutions are listed in Tables 1–3. The ab initio calculations were performed with the Gaussian-03 program [17] using Gaussian-type basis functions. The energy minima with respect to nuclear coordinates were obtained by the simultaneous relaxation of all geometric parameters using the gradient method of Pulay [18]. Several basis sets as well as the corresponding ones with diffuse functions were employed with the Møller–Plesset perturbation method [19] to the second order (MP2(full)) as well as with the density functional theory by the B3LYP method. In order to obtain a complete description of the

2. Experimental methods and theoretical calculations The ethylenediamine sample was purchased from Acros Organics, New Jersey with a stated purity of 99% and it was utilized without further purification. The mid-infrared spectrum of the gas was obtained from 4000 to 250 cm1 on a Perkin-Elmer model 2000 Fourier transform spec-

Fig. 1. Comparison of experimental and calculated infrared spectra of ethylenediamine: (A) observed infrared spectrum in xenon; (B) simulated infrared spectrum of a mixture of g0 G0 g0 , g0 G0 t and gG0 g0 conformers at 60 °C with DH = 64 and 210 cm1; (C) simulated infrared spectrum of pure gG0 g0 ; (D) simulated infrared spectrum of pure g0 G0 t; (E) simulated infrared spectrum of pure g0 G0 g0 .

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J.R. Durig et al. / Journal of Molecular Structure 984 (2010) 58–67

Table 1 Observed and calculateda frequencies (cm1) and potential energy distributions (P.E.D.s) for the g0 G0 g0 conformer of ethylenediamine. Vib. no.

Approx. description

ab initio

Fixed scaledb

IR int.

IR gas

IR liq. Xe

m1 m2 m3 m4 m5 m6 m7 m8 m9 m10 m11 m12 m13 m14 m15 m16 m17 m18 m19 m20 m21 m22 m23 m24 m25 m26 m27 m28 m29 m30

NH2 antisymmetric stretch NH2 antisymmetric stretch NH2 symmetric stretch NH2 symmetric stretch CH2 antisymmetric stretch CH2 antisymmetric stretch CH2 symmetric stretch CH2 symmetric stretch NH2 deformation NH2 deformation CH2 deformation CH2 deformation CH2 wag CH2 wag CH2 twist CH2 twist CH2 rock CN stretch CN stretch NH2 twist NH2 twist CH2 rock C–C stretch NH2 rock NH2 rock CCN bend NH2 torsion CCN bend NH2 torsion CC torsion

3621 3620 3518 3517 3169 3135 3052 3009 1721 1709 1578 1562 1487 1447 1384 1367 1268 1219 1162 1096 1050 980 944 903 867 525 371 315 261 203

3435 3434 3337 3337 2973 2941 2863 2823 1633 1621 1480 1465 1411 1373 1312 1297 1203 1156 1102 1040 996 929 896 756 725 498 352 298 247 192

5.0 0.8 0.2 5.5 24.3 40.4 70.9 78.3 35.2 43.3 2.7 3.0 7.2 9.1 2.2 2.4 11.1 7.5 2.7 5.0 18.7 62.0 143.0 31.9 77.6 15.5 39.2 56.5 27.4 4.1

3417 3417 3344 3344 2957 2923 2858 2820 1619 1613 1472 1457 1399 1371 1310 1283 1195 1130 1070 1033 971 932 867 806 772 489 331 282

3401 3401 3328 3328 2964 2918 2861 2819 – 1615 1475 1457 1399 1369 1305 1283 1198 1129 1062 1032 963 923 868 809 770 490 – –

P.E.D.c

Contour A

B

C

55 3 2 79 6 15 13 1 85 7 88 48 2 87 71 1 40 12 2 98 17 8 39 13 1 81 98 73 – 77

42 8 58 20 4 76 87 7 10 49 8 14 95 2 1 95 – 20 97 1 12 92 8 17 99 19 1 17 1 –

3 89 40 1 90 9 – 92 5 44 4 38 3 11 28 4 60 68 1 1 71 – 53 70 – – – 10 99 23

90S1, 10S2 90S2, 10S1 99S3 99S4 72S5, 27S7 65S6, 34S8 73S7, 26S5 66S8, 33S6 79S9, 13S22 79S10, 13S24 97S11 96S12 42S13, 30S14, 52S14, 37S13 68S15 59S16, 13S22, 40S17, 13S21 24S18, 20S20, 35S19, 20S18, 31S20, 37S19, 55S21, 11S22, 15S22, 24S18, 59S23, 13S22, 68S24, 11S10 64S25, 12S22, 33S26, 37S28 48S27, 27S26, 23S28, 36S27, 81S29, 10S27 89S30

11S23

11S21 21S22, 15S16, 11S28 19S23 18S18 11S17 13S23, 11S17 11S21 11S9 15S28 16S26, 14S30

a

MP2(full)/6-31G(d) ab initio calculations, scaled frequencies, infrared intensities (km mol1) and potential energy distributions (P.E.D.s). Scaled ab initio calculations with factors of 0.88 for CH stretches and CH2 deformations, 0.70 for NH2 rocks and 0.90 for all other modes except torsions and heavy atom bends. c Symmetry coordinates with P.E.D. contribution less than 10% are omitted. b

molecular motions involved in the fundamental modes of NH2CH2CH2NH2 a normal coordinate analysis has been carried out. The force field in Cartesian coordinates was obtained with the Gaussian-03 program [17] at the MP2(full) level with the 631G(d) basis set. The internal coordinates used to calculate the G and B matrices are given in Tables 4 and 5 with the atomic numbering shown in Fig. 2. This complete set of internal coordinates was used to form the symmetry coordinates listed in Tables 1S and 2S. By using the B matrix [20], the force field in Cartesian coordinates was converted to a force field in internal coordinates. Subsequently, scaling factors of 0.88 for CH stretches, 0.70 for NH2 rocks and 0.90 for other coordinates except for the heavy atom bends and torsions which were not scaled, along with the geometric average of the scaling factors for the interaction force constants were applied, to obtain the fixed scaled force field and resultant wavenumbers. The predicted wavenumbers, infrared intensities, and band contours for the g0 G0 g0 , g0 G0 t and gG0 g0 conformers which are expected to be in the greatest abundance were predicted from the MP2(full)/6-31G(d) calculations and are listed in Tables 1–3, respectively. The first indicator is the lone pair of electrons on the first nitrogen atom with respect to the NCC angle (g = gauche or t = trans) and the second indicator is the NCCN dihedral angle (G = gauche or T = trans) and the third one similar to that for the first but with respect to the second nitrogen atom. The predicted scaled frequencies were used together with a Lorentzian function to obtain the simulated spectra. Infrared spectra of the xenon solution and the predicted infrared spectra for the pure g0 G0 g0 , g0 G0 t and gG0 g0 conformers, as well as the mixture of the three conformers with relative concentrations calculated for the equilibrium mixture at 25 °C by using, initially, the predicted

energy differences and finally the experimentally determined enthalpy differences which are shown in Fig. 1, respectively. The predicted spectrum is in satisfactory agreement with the observed spectrum which shows the utility of the scaled predicted frequencies and intensities to aid in making the vibrational assignment even though the agreement is not as good as usually found in substituted hydrocarbons. It is believed that the lone pair of electrons on the nitrogen atom contributes to the poor predictions of both frequencies and intensities of the NH2 bending modes. 3. Vibrational assignment To determine the enthalpy differences among the major conformers of ethylenediamine, it is necessary to assign the observed bands in the spectral region where the conformer pairs are going to be selected. The lower frequency region is the most desirable spectral region since it will have fewer overtones and combination bands for interference with the measured intensities of the conformer pairs which are selected for the enthalpy determinations. Also, in this lower frequency region the greatest separation is expected for the vibrational fundamentals of the various conformers. Thus, the spectral region from 700 to 1200 cm1 was selected and the infrared spectra of the gas and xenon solution are shown in Fig. 3. As can be noted, the band contours are not as definitive as normally found for a small molecule in the gas phase. However, the very strong band at 867 cm1 is clearly an A/C band type arising from the C–C stretch of the most stable conformer ( g0 G0 g0 ) with a predicted intensity of 143 km mol1. There are several other bands where the Q-branches are not as intense but still quite distinct. In the xenon solution the bands are not nearly as sharp as usually

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J.R. Durig et al. / Journal of Molecular Structure 984 (2010) 58–67 Table 2 Observed and calculateda frequencies (cm1) and potential energy distributions (P.E.D.s) for the g0 G0 t conformer of ethylenediamine.

a b c

Vib. no.

Approx. description

ab initio

Fixed scaledb

IR int.

IR gas

IR liq. Xe

m1 m2 m3 m4 m5 m6 m7 m8 m9 m10 m11 m12 m13 m14 m15 m16 m17 m18 m19 m20 m21 m22 m24 m23 m25 m26 m27 m28 m29 m30

NH2 antisymmetric stretch NH2 antisymmetric stretch NH2 symmetric stretch NH2 symmetric stretch CH2 antisymmetric stretch CH2 antisymmetric stretch CH2 symmetric stretch CH2 symmetric stretch NH2 deformation NH2 deformation CH2 deformation CH2 deformation CH2 wag CH2 wag CH2 twist CH2 twist CH2 rock CN stretch CN stretch NH2 twist NH2 twist CH2 rock NH2 rock C–C stretch NH2 rock CCN bend NH2 torsion CCN bend NH2 torsion CC torsion

3616 3599 3515 3501 3157 3135 3095 3036 1737 1722 1568 1553 1459 1436 1429 1363 1311 1197 1145 1102 1041 981 954 879 852 530 369 290 272 198

3431 3415 3335 3321 2962 2941 2903 2848 1648 1634 1471 1457 1387 1363 1357 1309 1247 1147 1087 1045 987 937 858 837 776 518 366 288 271 197

1.0 3.7 0.1 2.8 42.7 35.0 31.8 71.0 26.8 35.3 2.3 1.9 5.3 9.6 10.0 1.6 1.3 23.0 9.4 7.9 88.4 109.8 92.5 15.7 66.5 19.8 32.1 40.9 38.5 3.8

3417 3397 3344 3326 2936 2923 2908 2848 1637 1623 1463 1436 1387 1363 1352 1291 1231 1090 1060 1044 966 898 809 780 759 503 331 263

3401 3381 3328 3328 2932 2918 2907 2843 – – 1459 1440 1385 1360 1350 1291 1232 1083 1052 1040 963 897 809 784 759 503 – –

P.E.D.c

Contour A

B

C

17 47 25 53 17 – 2 13 26 72 28 38 13 93 83 15 39 72 13 92 63 95 54 87 – – 20 1 64 42

1 53 65 25 25 27 47 86 29 2 29 39 82 3 7 1 57 1 83 6 37 1 45 13 99 94 8 17 15 5

82 – 10 21 59 73 51 1 47 26 43 23 5 3 10 84 4 27 4 2 – 4 1 – 1 6 72 82 21 53

99S1 100S2 99S3 100S4 87S5 67S6, 21S8 90S7 74S8, 26S6 85S9, 13S23 84S10, 14S25 97S11 98S12 65S13 71S14, 14S13 66S15, 17S18 63S16, 12S22 28S17, 18S18, 50S18, 13S22 53S19, 19S24 32S20, 18S15, 41S21, 19S20, 12S22, 27S24, 26S24, 19S17, 23S23, 21S24, 57S25, 12S22, 35S26, 34S28 50S27, 17S26, 23S28, 32S27, 75S29, 14S27 89S30

13S21, 13S22

17S19, 15S21 17S22 23S23 15S20 21S17 11S17 17S28 22S26

MP2(full)/6-31G(d) ab initio calculations, scaled frequencies, infrared intensities (km mol1) and potential energy distributions (P.E.D.s). Scaled ab initio calculations with factors of 0.88 for CH stretches and CH2 deformations, 0.70 for NH2 rocks and 0.90 for all other modes except torsions and heavy atom bends. Symmetry coordinates with P.E.D. contribution less than 10% are omitted.

Table 3 Observed and calculateda frequencies (cm1) and potential energy distributions (P.E.D.s) for the gG0 g0 conformer of ethylenediamine. Sym. block

Vib. no.

Approx. description

ab initio

Fixed scaledb

A

m1 m2 m3 m4 m5 m6 m7 m8 m9 m10 m11 m12 m13 m14 m15 m16

NH2 antisymmetric stretch NH2 symmetric stretch CH2 antisymmetric stretch CH2 symmetric stretch NH2 deformation CH2 deformation CH2 wag CH2 twist CH2 rock CN stretch NH2 twist C–C stretch NH2 rock NH2 torsion CCN bend CC torsion

3618 3520 3147 3060 1736 1565 1484 1398 1229 1169 1098 938 905 397 342 175

3433 3339 2953 2870 1647 1468 1409 1326 1170 1108 1042 890 817 396 338 174

1.4 0.1 32.4 30.4 24.1 0.3 10.0 2.6 2.3 3.6 11.1 93.5 11.7 7.5 7.7 2.6

m17 m18 m19 m20 m21 m22 m23 m24 m25 m26 m27 m28 m29 m30

NH2 antisymmetric stretch NH2 symmetric stretch CH2 antisymmetric stretch CH2 symmetric stretch NH2 deformation CH2 deformation CH2 wag CH2 twist NH2 twist CN stretch NH2 rock CH2 rock CCN bend NH2 torsion

3616 3518 3151 3065 1708 1558 1445 1376 1256 1087 957 874 518 216

3430 3337 2956 2875 1620 1461 1371 1307 1191 1031 837 831 505 216

1.6 0.7 48.6 75.5 55.5 2.7 8.6 3.1 11.8 15.2 188.6 2.8 18.5 124.9

B

a b c

IR int.

IR gas

IR liq. Xe

2942 2867 1637

2943 2873 –

1394

1399

1036 839 810

–

2948 2867 1613 – 1378 – 1155 1024 780 803 500

837 809

2943 2873 1615 – 1380 – 1152 1024 784 – 500

P.E.D.c

Contour A

B

C

– – – – – – – – – – – – – – – –

100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

– – – – – – – – – – – – – – – –

100S1 100S2 74S3, 26S4 74S4, 26S3 87S5, 12S13 98S6 72S7, 10S12 79S8, 12S11 49S9, 17S12, 11S13 53S10, 17S9, 15S7, 13S12 55S11, 14S10, 11S8 44S12, 25S10, 16S11, 14S9 74S13, 10S9, 10S5 99S14 79S15, 13S16 88S16, 12S15

66 32 26 2 40 95 95 29 2 96 8 – 56 92

– – – – – – – – – – – – – –

34 68 74 98 60 5 5 71 98 4 92 100 44 8

100S17 100S18 87S19, 13S20 87S20, 13S19 85S21, 13S27 98S22 89S23 67S24, 13S25, 12S28 37S25, 20S29, 17S26, 17S24 68S26, 20S25 64S27, 11S21 60S28, 23S25, 11S27 75S29, 12S28 98S30

MP2(full)/6-31G(d) ab initio calculations, scaled frequencies, infrared intensities (km mol1) and potential energy distributions (P.E.D.s). Scaled ab initio calculations with factors of 0.88 for CH stretches and CH2 deformations, 0.70 for NH2 rocks and 0.90 for all other modes except torsions and heavy atom bends. Symmetry coordinates with P.E.D. contribution less than 10% are omitted.

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J.R. Durig et al. / Journal of Molecular Structure 984 (2010) 58–67

Table 4 Structural parameters (Å and degree) and rotational constants (MHz) for g0 G0 g0 form of ethylenediamine.

a b c d

Structural parameters

Internal coordinates

RHF/631G(d)

MP2(full)/631G(d)

MP2(full)/6311+G(d,p)

B3LYP/6311+G(d,p)

EDa

EDb

Microwavec

Adjusted r0

r (N1–C2) r (C2–C3) r (C3–N4) r (N1–H5) r (N1–H6) r (C2–H7) r (C2–H8) r (C3–H9) r (C3–H10) r (N4–H11) r (N4–H12) \N1C2C3 \N4C3C2 \H5N1C2 \H6N1C2 \H7C2N1 \H8C2N1 \H7C2C3 \H8C2C3 \H9C3C2 \H10C3C2 \H9C3N4 \H10C3N4 \H11N4C3 \H12N4C3 \H5N1H6 \H7C2H8 \H9C3H10 \H11N4H12 sN1C2C3N4 A B C

R1 R2 R3 r1 r2 r3 r4 r5 r6 r7 r8

1.458 1.522 1.451 1.002 1.001 1.091 1.084 1.086 1.095 1.001 1.002 110.2 110.0 110.6 111.1 113.0 111.1 109.4 108.4 109.0 108.7 108.7 113.5 111.1 109.3 107.0 107.6 106.8 107.8 64.8 14,880 5209 4422

1.468 1.519 1.460 1.019 1.018 1.101 1.093 1.096 1.105 1.018 1.019 109.1 108.8 109.4 110.2 113.9 107.9 109.8 108.1 109.3 108.4 109.1 114.3 110.3 107.1 106.2 107.9 106.9 107.3 63.4 14,419 5337 4484

1.467 1.520 1.460 1.015 1.014 1.099 1.093 1.095 1.103 1.014 1.015 109.4 109.2 110.1 110.9 113.5 108.0 109.4 108.2 109.2 108.3 109.0 113.8 111.0 107.9 107.0 108.2 107.3 107.9 63.9 14,501 5288 4455

1.471 1.526 1.463 1.015 1.013 1.100 1.093 1.095 1.105 1.014 1.016 110.2 109.9 111.1 111.5 113.4 107.8 109.2 108.4 108.9 108.4 108.9 113.7 111.6 109.1 107.4 107.7 106.8 108.2 63.5 14,521 5184 4374

1.469(4) 1.545(8) 1.469(4) 1.030d 1.030d 1.109(10) 1.109(10) 1.109(10) 1.109(10) 1.030d 1.030d 110.2(7) 110.2(7) 112.1d 112.1d 111.6 105.9 111.9(46) 111.9(46) 111.9(46) 111.9(46) 107.0 111.4 112.1d 112.1d 105.9d 112.7(85) 112.7(85) 105.9d 64.0(45) 14,455 5050 4286

1.472(5) 1.520(14) 1.465(5) 0.995(4) 0.995(4) 1.125(6) 1.125(6) 1.125(6) 1.125(6) 0.995(4) 0.995(4) 110.2(4) 110.1(4) 103.5(22) 103.5(22) 113.9 106.9 108.7(20) 108.7(20) 108.7(20) 108.7(20) 109.2 112.7 117.8(44) 117.8(44) 113.1 108.3 107.3 98.8 63.3(9) 14,403 5202 4383

1.469 1.546 1.469 1.017 1.017 1.093 1.093 1.093 1.093 1.017 1.017 109.0(10) 109.0(10) 109.48 109.48 114.4 106.9 109.48 109.48 109.48 109.48 109.6 112.6 109.48 109.48 109.48 109.48 109.48 109.48 63(2) 14449.45 5223.59 4402.32

1.472(3) 1.526(3) 1.464(3) 1.015(2) 1.014(2) 1.099(2) 1.093(2) 1.095(2) 1.103(2) 1.014(2) 1.015(2) 109.7(5) 109.5(5) 110.1(5) 110.9(5) 113.6(5) 107.7(5) 109.4(5) 108.2(5) 109.2(5) 108.3(5) 108.7(5) 113.8(5) 111.0(5) 108.3(5) 105.5(5) 108.1(5) 107.2(5) 105.8(5) 63.5(5) 14471.4 5228.6 4406.5

e1 e2 b1 b2

r1 r2 p1 p u1 u2 h1 h2 b3 b4

a1 c1 c2 a2

Ref. [21], experimental rg values. Ref. [16]. Ref. [15]. Assumed parameters.

found in rare gas solutions but the breadth is believed, in many cases, to be due to association of the molecules although the presence of significant amounts of three conformers can give rise to the breadth since the corresponding fundamentals have similar frequencies for many cases. Nevertheless, by utilizing the predicted frequencies, infrared intensities, and band contours it has been possible to assign most of the fundamentals for the two most stable forms as well as many of the fundamentals for the third conformer. In the previous investigations [10–12] of the infrared spectra of the gas, the resolution utilized did not permit the observation of the multiple fundamentals of the three conformers. For example, in the 1000–1100 cm1 region we observed at least five bands which could be assigned as fundamentals whereas in the two previous studies [10,11] only two bands were reported in this region. In Tables 1 and 2 complete assignments are proposed for the fundamentals of the g0 G0 g0 and g0 G0 t conformers along with their approximate descriptions. For the third conformer the more intense predicted bands could be assigned but no attempt was made to assign the weaker fundamentals. With the proposed assignments we then proceeded to utilize bands, which were believed to be relatively pure fundamentals of the indicated conformers, for the enthalpy determinations. 4. Conformational stability With complete assignments of the predicted fundamentals for the two most stable conformers in the 700–1200 cm1 region, the task was to choose bands for the enthalpy determination which

were not expected to have fundamentals for the third conformer in near coincidence with those selected for the g0 G0 g0 and g0 G0 t forms. Additionally, bands arising from the NH2 bends particularly the NH2 rocks can not usually be chosen since they associate to form dimers or other associated species and very large intensity changes are observed when the temperature of the xenon solutions is lowered. For the g0 G0 t conformer the pronounced band at 1083 cm1 which is a CN stretch was chosen as well as the other weaker CN stretch at 1052 cm1. The selection of the bands for the g0 G0 g0 conformer for the enthalpy determination is significantly more difficult since the higher frequency CN stretch is observed at 1129 cm1 which is a region of the spectrum where the signalto-noise is poor due to absorption by the cell windows so the band intensities can not be as accurately measured. The other CN stretch at 1062 cm1 is much weaker and it is difficult to obtain meaningful intensity variations by lowering the temperature. Therefore, we used the 923 cm1 band which was relatively sharp and the P.E.D. indicates that the largest contribution of any symmetry coordinate is 24% and it is from the CN stretch and the predicted intensity is quite large. For the third conformer, gG0 g0 , the band assigned as the CN stretch (t26) at 1024 cm1 was selected for the enthalpy determination. Its intensity could be measured rather accurately since it was not significantly overlapped by fundamentals of the other conformers. This band was used in combination with the 923 cm1 band of the g0 G0 g0 form and the 1040 cm1 band of the g0 G0 t conformer. Initially, the relative intensities of two pairs for the two most stable conformers were measured as a function of the temperature and their ratios were determined. Ten sets of spectral data were

63

J.R. Durig et al. / Journal of Molecular Structure 984 (2010) 58–67 Table 5 Structural parameters (Å and degree) and rotational constants (MHz) for g0 G0 t form of ethylenediamine.

a b c d

Structural parameters

Internal Coordinates

RHF/631G(d)

MP2(full)/631G(d)

MP2(full)/6311+G(d,p)

B3LYP/6311+G(d,p)

EDa

EDb

Microwavec

Adjusted r0

r (N1–C2) r (C2–C3) r (C3–N4) r (N1–H5) r (N1–H6) r (C2–H7) r (C2–H8) r (C3–H9) r (C3–H10) r (N4–H11) r (N4–H12) \N1C2C3 \N4C3C2 \H5N1C2 \H6N1C2 \H7C2N1 \H8C2N1 \H7C2C3 \H8C2C3 \H9C3C2 \H10C3C2 \H9C3N4 \H10C3N4 \H11N4C3 \H12N4C3 \H5N1H6 \H7C2H8 \H9C3H10 \H11N4H12 sN1C2C3N4 A B C

R1 R2 R3 r1 r2 r3 r4 r5 r6 r7 r8

1.457 1.529 1.451 1.003 1.001 1.092 1.086 1.086 1.088 1.002 1.003 110.3 115.3 110.5 111.1 113.2 107.8 109.3 109.2 109.3 108.9 108.6 108.0 109.1 110.2 106.9 106.9 106.4 106.5 60.2 14,653 5140 4385

1.467 1.526 1.460 1.019 1.018 1.103 1.096 1.095 1.098 1.020 1.020 109.1 114.8 109.3 110.3 114.0 107.7 109.8 109.0 109.8 108.8 108.0 108.8 107.0 108.7 106.1 107.1 106.5 105.4 58.1 14,232 5248 4428

1.465 1.528 1.459 1.015 1.014 1.101 1.095 1.095 1.097 1.016 1.015 109.4 115.0 110.0 111.1 113.7 107.8 109.3 109.0 109.4 108.6 108.7 108.1 108.4 109.7 106.9 107.6 106.7 106.4 60.3 14,406 5163 4393

1.469 1.536 1.462 1.015 1.014 1.102 1.095 1.095 1.097 1.016 1.016 110.1 115.7 111.0 111.7 113.5 107.7 109.1 109.1 109.2 108.6 108.7 108.0 109.1 110.6 107.3 107.1 106.2 106.8 60.0 14,415 5063 4314

1.469(4) 1.545(8) 1.469(4) 1.030d 1.030d 1.109(10) 1.109(10) 1.109(10) 1.109(10) 1.030d 1.030d 110.2(7) 110.2(7) 112.1d 112.1d 108.9 108.9 111.9(46) 111.9(46) 111.9(46) 111.9(46) 107.0 111.8 112.1d 112.1d 105.9d 112.7(85) 112.7(85) 105.9d 64.0(45) 14,062 5131 4399

1.471(5) 1.526(14) 1.464(5) 0.995(4) 0.995(4) 1.124(6) 1.124(6) 1.124(6) 1.124(6) 0.995(4) 0.995(4) 110.3(4) 115.3(4) 103.5(22) 103.5(22) 114.0 106.8 108.8(20) 108.8(20) 108.8(20) 108.8(20) 109.5 107.3 111.4(27) 111.4(27) 113.1 107.9 106.8 104.1 59.5(10) 14,358 5125 4359

1.469 1.546 1.469 1.017 1.017 1.093 1.093 1.093 1.093 1.017 1.017 111.5(10) 111.5(10) 109.48 109.48 110.3 108.7 109.48 109.48 109.48 109.48 108.4 111.6 109.48 109.48 109.48 109.48 109.48 109.48 63(2) 14362.77 5091.65 4373.18

1.470(3) 1.532(3) 1.463(3) 1.015(2) 1.014(2) 1.101(2) 1.095(2) 1.095(2) 1.097(2) 1.016(2) 1.015(2) 109.7(5) 115.3(5) 110.0(5) 111.1(5) 114.0(5) 107.2(5) 109.3(5) 109.0(5) 109.4(5) 108.6(5) 109.0(5) 107.6(5) 108.4(5) 109.7(5) 106.9(5) 107.6(5) 106.7(5) 106.4(5) 59.7(5) 14355.8 5125.4 4356.3

e1 e2 b1 b2

r1 r2 p1 p2 u1 u2 h1 h2 b3 b4

a1 c1 c2 a2

Ref. [21], experimental rg values. Ref. [16]. Ref. [15]. Assumed parameters.

obtained for these pairs and by application of the van’t Hoff equation, ln K = DH/(RT)  DS/R, the enthalpy difference was determined from a plot of ln K versus 1/T, where DH/R is the slope of the line and K is substituted with the appropriate intensity ratios, i.e. Iconf-1/Iconf-2. It was assumed that DH, DS and the ratio of the molar absorption coefficients econf-1/econf-2 are not a function of temperature in the temperature range studied. The conformational enthalpy differences (Table 6) were determined to be 81 ± 9 cm1 (0.97 ± 0.11 kJ mol1) and 53 ± 9 cm1

Fig. 2. g0 G0 g0 form of ethylenediamine showing atom numbering and internal coordinates.

(0.63 ± 0.11 kJ mol1) from the xenon solution for the 923/1083 and 923/1052 pairs, respectively. Another band at 1040 cm1 (conformer-2) was combined with the 923 cm1 (conformer-1) band

Fig. 3. Mid-infrared spectra (700–1150 cm1) of ethylenediamine: (A) gas in transmittance; (B) liquid xenon solution at 100 °C in absorbance; (C) liquid xenon solution at 60 °C in absorbance.

64

J.R. Durig et al. / Journal of Molecular Structure 984 (2010) 58–67 Table 6 Temperature and intensity ratios of the conformational bands of ethylenediamine from the infrared spectra of the liquid xenon solution phase. T (°C)

1/T (103 K1)

55.0 60.0 65.0 70.0 75.0 80.0 85.0 90.0 95.0 100.0

4.584 4.692 4.804 4.923 5.047 5.177 5.315 4.460 5.613 5.775

DH (cm1) a

g0 G 0 g0 ? g0 G 0 t

Average value: DH = 64 ± 6 cm

g0 G0 t ? gG0 g0

g0 G0 g0 ? gG0 g0

I923/I1083

I923/I1052

I923/I1040

I1040/I1024

I923/I1024

0.2800 0.2857 0.2931 0.3000 0.3065 0.3077 0.3134 0.3143 0.3194 0.3243

1.2730 1.7368 1.7561 1.7619 1.7727 1.7917 1.7692 1.8214 1.8095 1.8965

1.4783 1.5000 1.5000 1.4783 1.5833 1.6154 1.6071 1.5937 1.6286 1.6000

– 1.5000 1.5714 1.5556 1.5417 1.6000 1.7857 1.8750 1.7500 1.8085

– – 0.2386 0.2500 0.2609 0.2631 0.2845 0.2909 – –

53 ± 9

58 ± 13

136 ± 28

210 ± 19

81 ± 9 1

a

(0.77 ± 0.07 kJ mol

1

) and the statistical uncertainty (r) obtained by utilizing all of the data as a single set.

from which an additional DH value of 58 ± 13 cm1 (0.69 ± 0.16 kJ mol1) was obtained. An average value was obtained by utilizing all the data as a single set which gave a DH value of 64 ± 6 cm1 (0.77 ± 0.07 kJ mol1) with the g0 G0 g0 form the more stable conformer. These error limits were derived from the statistical standard deviation of one sigma of the measured intensity data where the data from the three pairs were taken as a single set. These error limits do not take into account associations with the liquid xenon or the interference of overtones and combination bands in near coincidence with the measured fundamentals. For the enthalpy determination between the second most stable conformer ( g0 G0 t) and the third most stable conformer ( gG0 g0 ) only the conformer pair of 1040/1024 cm1 provided a consistent plot of the intensity ratios from 60 to 100 °C. This pair gave an enthalpy of 136 ± 28 cm1 (1.63 ± 0.33 kJ mol1) (Table 6). Similarly, only one conformer pair of 923/1024 cm1 was found for the determination of the enthalpy difference between the most stable conformer ( g0 G0 g0 ) and the third most stable conformer and a value of 210 ± 19 cm1 (2.51 ± 0.23 kJ mol1) was obtained (Table 6). This value is consistent with the values obtained for the other two enthalpy differences. 5. Structural parameters In the initial microwave study [15] only two of the structural parameters (\CCN and the dihedral angle sNCCN) were determined for each of the two identified conformers whereas the remaining structural parameters were taken from the initial electron diffraction study [21]. Since the earlier determined electron diffraction parameters are significantly different from the most recent determined values by the same technique, it is expected that the reported parameters from the microwave study are not very reliable. Therefore, we have again determined the structural parameters for the two conformers by utilizing the rotational constants previously reported from the microwave study [15]. We have found that good structural parameters for hydrocarbons and many substituted ones can be determined by adjusting the structural parameters obtained from the ab initio MP2/6311+G(d,p) calculations to fit the rotational constants obtained from microwave experimental data by using a computer program ‘‘A&M” (Ab initio and Microwave) developed [22] in our laboratory. In order to reduce the number of independent variables, the structural parameters are separated into sets according to their types where bond distances in the same set keep their relative ratio, and bond angles and torsional angles in the same set keep their difference in degrees. This assumption is based on the fact that errors from ab initio calculations are systematic. Additionally, we have also shown that the differences in predicted distances and angles

Table 7 Comparison of rotational constants (MHz) obtained from modified ab initio MP2(full)/ 6-311+G(d,p) predictions, experimental valuesa from microwave spectra, and the adjusted r0 structural parameters for ethylenediamine.

a

Isotopomer

Rotational constant

MP2(full)/6311+G(d,p)

Experimentala

Adjusted r0

| D|

g0 G0 g0

A B C

14500.6 5288.4 4455.5

14472.0 5229.2 4405.5

14471.4 5228.6 4406.5

0.6 0.6 1.0

g0 G0 t

A B C

14405.9 5163.4 4392.5

14355.5 5125.3 4356.3

14355.8 5125.4 4356.3

0.3 0.1 0.0

Ref. [15].

from the ab initio calculations for different conformers of the same molecule can usually be used as one parameter with the ab initio predicted differences except for some dihedral angles. Therefore, it should be possible to obtain ‘‘adjusted r0” structural parameters for both conformers of ethylenediamine by utilizing the previously reported six rotational constants from the earlier microwave study [15], since, excluding the dihedral angles, there are five heavy atom parameters to be determined. We [23] have also shown that ab initio MP2(full)/6-311+G(d,p) calculations predict the r0 structural parameters for more than fifty carbon-hydrogen distances to at least 0.002 Å compared to the experimentally determined values from isolated CH stretching frequencies which were compared [24] to previously determined values from earlier microwave studies. Therefore, all of the carbon-hydrogen distances can be taken from the MP2(full)/ 6-311+G(d,p) predicted values for g0 G0 g0 and g0 G0 t conformers of ethylenediamine. The resulting adjusted parameters are listed in Tables 4 and 5, where it is believed that the N–C and C–C distances should be accurate to ±0.003 Å, the C–H and N–H distances should be accurate to ±0.002 Å, and the angles should be within ±0.5°. The fit of the six determined rotational constants (Table 7) by the structural parameters for the g0 G0 g0 and g0 G0 t conformer is remarkably good with differences of 0.6, 0.6, 1.0, 0.3, 0.1 and 0.0 MHz. Therefore, it is believed that the suggested uncertainties are realistic values and the determined structural parameters are probably as accurate as can be obtained for the molecule in the gas phase. 6. Discussion The predicted frequencies from the MP2(full)/6-31G(d) calculations with the three scaling factors as well as the infrared intensities are in reasonable agreement with the observed spectra (Fig. 1)

65

J.R. Durig et al. / Journal of Molecular Structure 984 (2010) 58–67

in the xenon solutions. However, the fundamental frequencies for the three conformers do not differ significantly which makes it difficult to obtain pairs without interference from the third conformer. Additionally, there is a problem of molecular association as the xenon solution temperature is lowered from 55 °C to 100 °C where some bands dramatically increased in intensity with decreased temperature such as the 1010 cm1 band which we believe arises from a ‘‘dimer” or associate molecules. We determined the enthalpy difference of this band with several of the other bands, which we believe are due to vibrations of the monomer, and obtained enthalpy values in the 600–700 cm1 range which is too large for any of the three most stable conformers. It could not be due to the less stable conformers since the intensity should decrease with decreasing temperature. There were several bands where the intensity drastically decreased with decrease in temperature which could be due to additional conformers or bands from the three most stable conformers where their intensities are significantly altered by molecular association. No attempt was made to assign them to other conformers since the ab initio predicted energy differences for the anti forms compared to the two most stable conformers indicated that their abundances would only be 1%. The predicted P.E.D.s do not indicate significant mixing except for a few modes between 900 and 1100 cm1 where the mode approximately described as the CN stretch (24%) has major contributions from four other symmetry coordinates which include mixing with the NH2 twist and CH2 rock for the g0 G0 g0 form. There are two other vibrations (m22 and m28) for this conformer where there is extensive mixing with contributions from three other symmetry coordinates. However, for most of the other vibrations there is usually at least 50% of the symmetry coordinate for the approximate description given. Comparable mixing is also predicted for the g0 G0 t conformer in the same spectral region. However, since the mixing of the CN stretch differs somewhat with the NH2 motions for the two forms the predicted intensities of similar frequency bands for the two conformers are quite different. These differences in some cases makes the assignments difficult to make. In the initial microwave study [15] the enthalpy difference between the two conformers where the microwave spectrum was assigned was determined to be 105 ± 70 cm1 (1.26 ± 0.59 kJ mol1) which is in agreement with the value of 64 ± 6 cm1 (0.77 ± 0.07 kJ mol1) from the current study. This experimental enthalpy difference is consistent with the ab initio predicted energy difference between these two most stable conformers with the average value of 85 ± 43 cm1 (1.02 ± 0.51 kJ mol1) obtained from the five MP2(full) calculations with the largest basis sets (Table 8). However, the predicted energy difference between the most stable con-

former ( g0 G0 g0 ) and the third most stable conformer ( gG0 g0 ) the average value of the energy difference of 181 cm1 (2.16 kJ mol1) (Table 8) is consistent with the experimental enthalpy value difference but the standard error derivation value of 64 cm1 (0.76 kJ mol1) indicates that much larger basis sets need to be utilized such as calculations MP2(full)aug-cc-pVTZ to obtain predicted energy difference which seem to be more consistent with experimentally determined enthalpy differences among multiple conformers of a molecule [25]. In the initial electron diffraction investigation [21] of ethylenediamine the investigators reported only one conformer present for the heavy atoms and it was the gauche form with NCCN dihedral angle of 64 ± 4° from the cis position and they concluded that if another isomer was present it would be less than 5%. This implies that the enthalpy difference between the gauche and the anti (trans) would be at least 450 cm1 (5.38 kJ mol1). This result is consistent with the results of the initial microwave study where two NCCN gauche conformations were concluded to be giving rise to the observed rotational transitions and it was concluded [15] that ‘‘the existence of large fractions of further conformations is ruled out”. However, in the later electron diffraction study [16] it was concluded that at approximately 70 °C there was 12 ± 7% of the anti forms where the lower limit is consistent with the earlier microwave study [15]. In this electron diffraction study the energy difference was obtained from the relative intensities at three different temperatures which gave a value of 238 ± 143 cm1 (2.85 ± 1.71 kJ mol1). This energy difference was in agreement with the predicted value from HF/6-31G(d) calculations which gave a value of 371 cm1 (4.43 kJ mol1). However, from our ab initio calculations of MP2(full) with the 6-311G(d,p) and 6311+G(d,p) basis sets the average values for the four anti forms is predicted (Table 9) to be 626 cm1 (7.49 kJ mol1) and 600 cm1 (7.16 kJ mol1), respectively. These values indicate that the lower basis sets at the HF level provide predictions much lower than the MP2 calculations. These results indicate that the percent of the anti conformers is much smaller than the value proposed from the electron diffraction study. In a more recent microwave study [26] of ethylenediamine ab initio calculations were carried out at a much higher level and the presence of only three conformers was suggested. These three conformers are consistent with those proposed in the current study. We have searched the infrared spectrum of the gas to see if any evidence could be found for the presence of any anti forms. We predicted the vibrational frequencies and intensities of all four anti forms. The most intense bands were predicted in the 750–900 cm1 region with the most intense band predicted at

Table 8 Calculated electronic energiesa (hartree) and energy differencesb (cm1) for ethylenediamine. Basis set

6-31G(d) 6-31+G(d) 6-311G(d,p) 6-311+G(d,p) 6-311G(2d,2p) 6-311+G(2d,2p) 6-311G(2df,2pd) 6-311+G(2df,2pd) aug-cc-pVTZ Average (cm1)c a b c

MP2(full)

B3LYP

g0 G0 g0

g0 G0 t

gG0 g0

g0 G 0 g0

g0 G0 t

gG0 g0

0.874783 0.893608 1.079535 1.091212 1.138088 1.147696 1.212317 1.221286 1.228740

49 135 24 120 36 122 39 115 113

175 85 216 136 246 146 251 156 106

1.511913 1.526605 1.578796 1.587798 1.587621 1.595797 1.592265 1.600299 1.605476

130 34 59 55 49 40 34 43 43

233 153 269 194 246 151 253 157 151

91 ± 41

173 ± 60

Energy of g0 G0 g0 conformer is given as – (E+189) H. Energy differences of g0 G0 t and gG0 g0 conformers are relative to g0 G0 g0 form. Average value from the six largest basis sets.

192 ± 47

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J.R. Durig et al. / Journal of Molecular Structure 984 (2010) 58–67

Table 9 Calculate energies (hartree) and energy differencesa (cm1) for the fourth to the tenth stable conformer of ethylenediamine.

a

Method/basis set

g0 G0 g0

g0 Gt

gTg0

tTg0

tGt

tTt

g0 Tg0

g0 G 0 g

RHF/6-31G(d) RHF/6-31+G(d) MP2(full)/6-31G(d) MP2(full)/6-31+G(d) MP2(full)/6-311G(d,p) MP2(full)/6-311+G(d,p) B3LYP/6-31G(d) B3LYP/6-31+G(d) B3LYP/6-311G(d,p) B3LYP/6-311+G(d,p)

189.268533 189.276723 189.874783 189.893608 190.079535 190.091212 190.511913 190.526605 190.578796 190.587798

483 443 490 492 467 481 340 377 379 371

371 341 696 664 712 610 549 505 573 478

456 428 658 668 608 610 416 447 455 433

596 593 482 647 427 554 193 398 266 375

443 462 484 641 424 558 182 352 278 357

421 353 756 676 762 623 602 507 610 472

1333 1301 1460 1443 1437 1354 1364 1313 1429 1287

Energy differences of the seven conformers are relative to g0 G0 g0 .

888 cm1 with an intensity of 436 km mol1 for the tTt conformer. A pronounced band was observed at 883 cm1 in the spectrum of the xenon solution at 60 °C which rapidly disappeared as the temperature was lowered. This band is also quite evident in the spectrum of the gas and was not assigned as a fundamental for any of the three most stable gauche conformers. The tTt conformer has the lowest predicted DE value from the MP2(full)/6-311+G(d,p) calculations of the four anti forms. The next most intense bands for the anti forms are at 750 (221 km mol1) and 755 cm1 (241 km mol1) for the tTg0 and g0 Tg0 conformers, respectively. There is a distinct Q-branch at 737 cm1 in the spectrum of the gas with a corresponding band at 738 cm1 in the spectrum of the xenon solution. This band could be due to either of these anti conformers or possibly from both of them. Thus we believe there is significant evidence for the presence of at least two of the anti conformers in the infrared spectrum which is consistent with the electron diffraction study [16]. The determined structural parameters for the C2–C3 distance for both conformers are significantly different from the value reported in the earlier microwave investigation which was assumed to have the same value which was taken from the first electron diffraction study. As can be seen from the data in Tables 4 and 5 the C2–C3 distance is 0.006 Å longer for the g0 G0 t form than the corresponding parameter of the g0 G0 g0 conformer. This similar difference was reported from the second electron diffraction study but the uncertainty of this parameter for the electron diffraction results was ±0.014 Å. The other heavy atom distances as well as the angles reported in the most recent electron diffraction study are in excellent agreement with the values reported in this study. In the recent microwave study [26] of ethylenediamine where the hyperfine patterns were analyzed as well as the rotational

dependence of the tunneling splitting, the centrifugal distortion constants were determined which were much more accurately determined than the earlier ones [15] determined with a relatively small number of measured transitions. Both sets of distortion constants are listed in Table 10 and both values have been predicted from MP2 and B3LYP calculations and the B3LYP calculations predict the centrifugal distortion constants more accurately than the MP2 calculations. The experimentally reported DJK values for the two conformers have differences much larger than expected for these two similar conformers and the DJK values which were much more accurately determined have very small differences as expected. However, the d1 values are predicted to be negative whereas the experimental values are positive. However, it should be noted that the d1 constants were obtained while also determining the higher order centrifugal distortion constants whereas the experimental values of DJ are positive when only the five distortion constants were determined from the microwave data. Nevertheless, very good centrifugal distortion constants can be predicted from ab initio calculations and can be used to predict higher J level energies which can aid their assignments. From the conformational study of ethylamine the enthalpy difference between the more stable trans form and the gauche conformer was determined to be 54 ± 4 cm1 (0.65 ± 0.05 kJ mol1) which is quite small and the replacement of a hydrogen atom on the methyl group is expected to have an effect on the NH2 conformational stability. When the atom is fluorine the most stable NH2 form is the gauche conformer but the enthalpy difference is only 62 ± 8 cm1 (0.74 ± 0.10 kJ mol1). This is consistent with what was found for the ethylenediamine where the gauche form for NH2 was more stable than the trans form by 64 ± 6 cm1

Table 10 Quadratic centrifugal distortion constants (kHz) and dipole moments (debye) for g0 G0 g0 and g0 G0 t conformers of ethylenediamine. g0 G0 g0

a

g 0 G0 t a

MP2(full)/ 6-311+G(d,p)

B3LYP/ 6-311+G(d,p)

Expa

4.68 18.88 50.5 1.2270 8.66

5.02 22.32 60.0 1.3565 10.00

3.85(32) 19.73(41) 51.0(51) 1.3271(95) 9.14(45)

42.372 15.502 4.246 1.1683 0.08598

49.648 17.844 4.507 1.2270 0.08666

58.998 21.162 4.828 1.3565 0.09636

55.520(211) 19.535(8) 4.745(2) 1.3289(4) 0.09632(9)

2.493 1.129 0.635 2.809

2.290 1.157 0.656 2.648

2.145 1.023 0.670 2.467

MP2(full)/ 6-31G(d)

MP2(full)/ 6-311+G(d,p)

B3LYP/ 6-311+G(d,p)

Exp

DJ DJK DK dJ dK

4.47 16.78 44.4 1.2144 8.26

4.73 18.70 49.7 1.2948 8.96

5.10 22.36 59.7 1.4329 10.14

4.85(11) 22.52(14) 80.1(16) 1.3666(30) 11.42(21)

4.42 6.53 43.2 1.1683 7.88

DK DJK DJ d1 d2

43.430 15.669 4.2827 1.2144 0.09263

48.778 17.536 4.5383 1.2948 0.09684

58.694 21.094 4.8934 1.4329 0.10536

55.322(9) 19.424(5) 4.7998(3) 1.3972(2) 0.10422(7)

|la| |lb| |lc| |lt|

1.412 0.834 1.534 2.246

1.254 0.892 1.436 2.123

1.170 0.800 1.347 1.955

1.059(7) 0.787(32) 1.179(23) 1.770(33)

Values taken from Ref. [15] except DK, DJK, DJ, d1, d2 which are from Ref. [25].

MP2(full)/ 6-31G(d)

1.952(2) 0.867(6) 0.538(6) 2.203(6)

J.R. Durig et al. / Journal of Molecular Structure 984 (2010) 58–67

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