Experimental and theoretical thermochemistry of β-tetralone

J. Chem. Thermodynamics 40 (2008) 1552–1557

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Experimental and theoretical thermochemistry of b-tetralone M. Agostinha R. Matos a,*, Clara C.S. Sousa a, Victor M.F. Morais a,b a b

Centro de Investigação em Química, Departamento de Química, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre, 687, P-4169-007 Porto, Portugal Instituto de Ciências Biomédicas Abel Salazar, ICBAS, Universidade do Porto, P-4099-003 Porto, Portugal

a r t i c l e

i n f o

Article history: Received 6 June 2008 Received in revised form 27 June 2008 Accepted 30 June 2008 Available online 8 July 2008

a b s t r a c t The standard (p = 0.1 MPa) molar enthalpy of formation b-tetralone was measured, at T = 298.15 K, by static bomb calorimetry and the standard molar enthalpy of vaporization, at T = 298.15 K, was obtained using Calvet microcalorimetry. These values were used to derive the standard molar enthalpy of formation of the compound in the gaseous phase, at T = 298.15 K, (75.2 ± 2.5) kJ  mol1. Additionally, high-level density functional theory calculations using the B3LYP hybrid exchange-correlation energy function with extended basis sets and more accurate correlated computational techniques of the MCCM/3 suite have been performed. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction

2.2. Experimental determination of the enthalpy of formation in the gas phase

Tetralones are a class of aromatic ketones that are widely used.

a-tetralone is mainly used to prepare dehydro-anphthol, 18methyl norethisterone (a contraceptive), and it can also be used as solvent and softener of plastic [1]. b-tetralone is used as a precursor of many compounds in organic synthesis with a huge variety of applications [2]. In this work, we present the experimental values of the enthalpies of formation, in the condensed and gas phase, and the enthalpy of vaporization of b-tetralone. We also present the estimated enthalpy of formation in the gas phase, of b-tetralone obtained by DFT calculations and more accurate correlated computational techniques of the MCCM/3 suite (MCUT and MCQCISD). Similar calculations were made for a-tetralone and the values obtained were compared with literature data [3]. 2. Experimental 2.1. Materials and purity control b-tetralone [530-93-8] was obtained from Aldrich Chemical Co. at a stated mass fraction purity of 0.997 and was further purified by repeated distillation and its mass fraction purity evaluated as 0.9992 by (gas + liquid) chromatography (Agilent 4890 D chromatograph). The purity of the sample was also confirmed through the carbon dioxide recovery ratio. The average ratio, together with the standard deviation of the mean, of the mass of carbon dioxide recovered to that calculated from the mass of sample was (100.017 ± 0.002). The density of the sample is 1.106 g  cm1 [4]. * Corresponding author. Tel.: +351 22 0402 517; fax: +351 22 0402 522. E-mail address: [email protected] (M.A.R. Matos). 0021-9614/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2008.06.019

The enthalpy of formation in the gas phase of the compound, Df H0m ðgÞ, at T = 298.15 K, was determined from the experimental value of its standard enthalpy of formation in the condensed state, Df Hm ðlÞ, and the standard phase change enthalpy, Dgl Hm . 2.2.1. Combustion calorimetry The standard massic energy of b-tetralone in the condensed phase was obtained from combustion calorimetry with a static bomb calorimeter. The apparatus and technique have been described previously [5,6]. Benzoic acid (NBS thermochemical standard 39j) was used for calibration of the bomb. Its massic energy of combustion is Dcu = (26434 ± 3) J  g1, under certificate conditions. The calibration results were corrected to give the energy equivalent ecal corresponding to the average mass of water added to the calorimeter, 3119.6 g. From six independent calibration experiments performed ecal = (16012.8 ± 1.1) J  K1, where the uncertainty quoted is the standard deviation of the mean. The compound was enclosed in polyester bags made of MelinexÒ, using the technique described by Skinner and Snelson [7] who determined the massic energy of combustion of dry MelinexÒ as Dcu0 = (22902 ± 5) J  g1. This value was confirmed in our laboratory. The mass of Melinex used in each experiment was corrected for the mass fraction of water (0.0032) and the mass of carbon dioxide produced from it was calculated using the factor previously reported [7]. Combustion experiments were performed in oxygen at p = 3.04 MPa, with 1.00 cm3 of water added to the bomb: DUR is the correction to the standard state. For the cotton-thread fuse, empirical formula CH1.686O0.843, Dcu0 = 16250 J  g1[8]. This value has been confirmed in our laboratory. The corrections for

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nitric acid formation DU(HNO3) were based on 59.7 kJ  mol1 [9] for the molar energy of formation of 0.1 mol  dm3 HNO3(aq) from N2, O2, and H2O(l). The mass of compound, m(compound), used in each experiment was determined from the total mass of carbon dioxide, m(CO2, total), produced after allowance for that formed from the cotton thread fuse and Melinex. An estimated pressure coefficient of specific energy: (ou/op)T = 0.2 J  g1  MPa1 at T = 298.15 K, a typical value for most organic compounds, was assumed [10]. As samples were ignited at T = 298.15 K,

DUðIBPÞ ¼ fecal þ DmðH2 OÞ  cp ðH2 O; lÞ þ ef gDT ad þ DU ign ;

ð1Þ

where DU(IBP) is the energy associated with the isothermal bomb process, ef is the energy of the bomb contents after ignition and DTad is the adiabatic temperature rise calculated using the program LABTERMO [11]. For each compound, the corrections to the standard state, DUR, to derive the standard massic energy of combustion, Dcuo, were made by the procedure given by Hubbard et al. [12]. The atomic weights of the elements were those recommended by the IUPAC commission in 2005 [13]. 2.2.2. Calvet microcalorimetry The standard molar enthalpy of vaporization was measured using the vacuum sublimation drop microcalorimetric method [14] which was adapted by Ribeiro da Silva et al. [15]. Samples about (7 to 10) mg in thin glass capillary tubes sealed at one end were dropped, at room temperature, into the hot vessel in a high-temperature Calvet microcalorimeter held at T = 363 K, and then removed from the hot zone by vacuum vaporization. The thermal corrections for the glass capillary tubes were determined in separate experiments and were minimized, as far as possible, by dropping tubes of nearly equal mass into each of the twin calorimeter cells. The microcalorimeter (Calvet High Temperature Microcalorimeter, SETARAM HT 1000) was calibrated in situ for these measurements using the reported standard molar enthalpies of vaporization of n-decane [16]. From six independent experiments, we have obtained a mean value for the observed standard molar enthalpy of vaporization, g;T  Dl;298:15 which was then corrected to T = 298.15 K, K Hm ,

Z

T

298:15 K

C p;m ðgÞ=ðJ  mol

1

 K1 Þ ¼ 0:000375ðT=KÞ2 þ 0:788ðT=KÞ  49:962:

ð3Þ

3. Computational details The geometries of all molecules have been fully optimized using density functional theory (DFT) with the Becke 3-parameter hybrid exchange [17] and the Lee et al. [18] correlation density functional (B3LYP) and the Pople’s split-valence 6-31G* [19] extended basis set. The optimum structures so obtained were further certified as true minima by constructing and diagonalizing the corresponding Cartesian Hessian matrix. This procedure provides also the harmonic vibrational frequencies which, after being properly scaled by the recommended scaling factor 0.9614 [20], allow reliable calculations of the thermal corrections to the molecular energy. We have further refined the optimum structures by re-optimizing them using the same methodology with the Pople’s split-valence 6-311G** extended basis set [21]. These final optimized structures were then used to perform single point DFT calculations with the cc-pVTZ basis set [22] and also to obtain the energy calculations based on more accurate correlated computational techniques of the MCCM/3 suite [23,24]. The latter calculations were conducted as a mean of accounting, at least in part, for the correlation energy, while still maintaining the computational cost within comfortable levels. We have thus selected two of the methods proposed in the MCCM/3 suite, one of them (MCUT) based on perturbational theoretical techniques and the other (MCQCISD) based on configuration interaction methodologies [23,24]. All the geometry optimizations, vibrational analysis and single point calculations have been performed using the UK version of program GAMESS [25,26]. The MCCM/3 series of calculations have been performed using the MLGAUSS program version 2.0 [27], which relies on the Gaussian 03 series of programs [28]. The natural bond orbital (NBO) analysis has been performed with NBO 5.0 program [29]. 4. Results

DT298:15 K Hm ðgÞ, using the equation:

DT298:15 K Hm ðgÞ ¼

tional frequencies obtained from the DFT calculations with the B3LYP functional and the 6-31G* basis set,

4.1. Experimental

C p;m ðgÞdT;

ð2Þ

where T is the temperature (363 K) of the hot reaction vessel, C p;m ðgÞ is the molar heat capacity of the compound in the gas phase and was obtained from statistical thermodynamics using the vibra-

Results for the combustion experiments of the compound are given in table 1. The standard massic energy values, Dcu0, are referred to the combustion reaction according to equation (4):

C10 H10 OðlÞ þ 12O2 ðgÞ ! 10CO2 ðgÞ þ 5H2 OðlÞ:

ð4Þ

TABLE 1 Standard (p = 0.1 MPa) massic energy of combustion of b-tetralone, at T = 298.15 K Experiment No. m (CO2)/g m (compound)/g m (cotton)/g m (melinex)/g ef/(J  K1) Dm (H2O)/g DTad/K DU (PBI)/J DU (HNO3)/J DU (ignition)/J DU (cotton)/J DU (melinex)/J DUR/J Dcu0 (compound)/(J  g1)

1

2

3

4

0.55806 0.00256 0.05206 16.12 0.0 1.3192 21144.36 9.42 0.99 41.57 1192.27 11.97 35639.77

1.94841 0.60164 0.00261 0.05805 16.25 0.0 1.4247 22835.63 9.90 0.96 42.39 1329.56 13.06 35637.13

1.95748 0.60721 0.00254 0.05474 16.04 0.0 1.4325 22960.48 9.39 0.83 41.25 1253.72 13.12 35643.35

1.96819 0.61379 0.00261 0.05072 16.28 0.0 1.4417 23108.42 9.70 0.70 42.39 1161.66 13.18 35649.80

Dcu0 (compound) = (35646.3 ± 3.6) J  g1

5

6

7

0.60180 0.00226 0.05743 16.02 0.0 1.4246 22833.65 10.44 1.01 36.70 1315.17 13.05 35656.85

2.06299 0.64897 0.00252 0.04593 16.13 0.0 1.5126 24244.35 10.42 1.01 40.92 1052.00 13.87 35636.69

0.59070 0.00259 0.05092 15.98 0.0 1.3910 22295.09 9.47 0.94 42.06 1166.22 12.67 35660.52

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TABLE 2 Standard (p = 0.1 MPa) molar enthalpies of vaporization, at T = 298.15 K determined by Calvet microcalorimetry for b-tetralone RT K K 1 Exp. m/mg T/K Dg;T H /(kJ  mol1) 298:15 K C p ðgÞ dT/(kJ  mol ) l;298:15K m

2 3 4 5 6

Dgl Hm ð298:15 KÞ/(kJ  mol1)

5.679

363

79.1

6.9

72.2

5.235 7.115 4.751 5.976 5.658

363 363 363 363 363

78.0 81.2 81.2 80.6 79.5

6.9 6.9 6.9 6.9 6.9

71.1 74.3 74.3 73.7 72.6

Dgl Hm ð298:15 KÞ ¼ ð73:0  1:1Þ kJ  mol1

The mean value and its standard deviation are given at the end of table 1. From this value, we have derived for the standard 1 molar energy of combustion, Dc U m ðlÞ ¼ ð5211:1  1:4Þ kJ  mol and for the standard molar enthalpy of combustion, Dc Hm ðlÞ ¼ 1 ð5216:1  1:4Þ kJ  mol . In accordance with customary thermochemical practice [30], the uncertainty assigned to the standard molar enthalpy of combustion, is twice the overall standard deviation of the mean and includes the uncertainty in calibration and auxiliary materials. In 1 order to derive Df Hm ðlÞ ¼ ð148:2  1:9Þ kJ  mol from Dc Hm ðlÞ, the standard molar enthalpies of formation of H2O(l) and CO2(g), at T = 298.15 K, (285.830 ± 0.042) kJ  mol1 [31] and (393.51 ± 0.13) kJ  mol1 [31], respectively, were used. The standard molar enthalpy of vaporization, Dgl Hm (298.15 K), was determined from six independent experiments (the uncertainty is twice the standard deviation of the mean). To obtain the standard molar enthalpy of vaporization, at T = 298.15 K, the observed enthalpy in each experiment, at T/K, were corrected using equation (2). Values are reported in table 2. The standard molar enthalpy of formation in the gaseous state, 1 at T = 298.15 K, Df Hm ðgÞ ¼ ð75:2  2:5Þ kJ  mol , was obtained by combining the derived standard molar enthalpy of formation in the liquid state and the standard molar enthalpy of vaporization.

O11

8

6

9

2 3

5 10

4

8

2

6

9

3

5 10

O 11

1

7

1

7

4

FIGURE 1. Atom numbering scheme for the geometric results of a- and b-tetralone, respectively.

4.2. Computational results and discussion At their optimum structures, both a-tetralone and b-tetralone show a non-benzenoid ring considerably distorted from planarity, presumably as a consequence of the repulsions between proximate –CH2– groups. Even though the departures from the planarity are difficult to quantify unambiguously, the behaviour of each isomer deserves some thoughts. The C–C(@O)–C fragment in each compound is always constrained to remain in a plane, an observation which is a direct consequence of the sp2 hybridization of the carbonyl group (C@O) carbon atom. On the other hand, the carbon atoms directly bonded to the benzene ring are also constrained to be coplanar with the plane of that ring. The conjugation of both restriction results, in the case of a-tetralone, in a conformation with just one of its non-hydrogen atoms (atom 3, see figure 1) displaced away from the plane containing the remaining atoms. This particular conformation is favoured since it guarantees the optimum conditions for extended electronic delocalization involving the C@O group and the aromatic ring to occur effectively. In the case of b-tetralone, the co-planarity between the aromatic ring and the carbonyl group (C@O) is no longer useful, since both moieties are separated by a large distance which inhibits the extended electronic significant delocalization to occur. Thus, the non-aromatic ring is now free to respond more significantly to the vicinal –CH2– group repulsions, becoming severely distorted: both the C2 and C3 atoms (see figure 1) are now found outside the plane defined by the remaining non-hydrogen atoms. The importance of the vicinal –CH2– group repulsions is stressed by the observation that at the optimized structures of both isomers, the vicinal –CH2– groups adopt almost perfect mutual staggered conformations. This difference in conformational behaviour between the two isomers is reflected in the relative energetics, as we will see later. In table 3, we report the total energies, identified by the subscripts EB3LYP/6-311G**, EB3LYP/cc-pVTZ, EMCUT and EMCQCISD, and thermal

TABLE 3 DFT electronic energies and thermal corrections to T = 298.15 K Compound

EB3LYP/6-311G**

EB3LYP/cc-pVTZ

EMCUT

EMCQCISD

TCEB3LYP/6-31G*

b-tetralone a-tetralone Tetralin Indane 1-indanone 2-indanone Benzene Cyclohexanone Pentane 3-Pentanone Ethane Cyclohexane

462.440538 462.447184 388.407099 349.078178 423.119415 423.112926 232.311529 309.979678 197.831677 271.867069 79.857272 235.947115

462.489121 462.494829 388.447653 349.115138 423.163942 423.157718 232.337565 310.010501 197.851403 271.894214 79.865585 235.969805

461.681082 461.685403 387.736796 348.472252 422.421829 422.417592 231.899673 309.487651 197.487013 271.433487 79.713344 235.543802

461.685189 461.689668 387.739867 348.475258 422.426039 422.421543 231.902529 309.489479 197.488019 271.435648 79.714008 235.544528

0.176749 0.177571 0.195113 0.165800 0.148134 0.147330 0.101394 0.152520 0.162415 0.144374 0.075856 0.170406

a

All energies are in a.u. (1 EH = 2625.50184 kJ  mol1). K TCEB3LYP=6-31G ¼ Etrans þ Erot þ Ezp þ D298:15 Evib . 0K

b

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corrections, TCE/6-31G* for b-tetralone and for all the auxiliary molecules needed to estimate the enthalpy of formation of the compound. In order to obtain estimates of that parameter from DFT and MCCM/3 calculations, we have used the following set of isodesmic/homodesmic reactions and the experimental molar enthalpies of formation taken from the literature of all the compounds (table 4):

The resulting estimated values of the molar enthalpy of formation of both, a- and b-tetralone, shown in table 4 for every reaction used, compare well or at least reasonably well with the experimental available data. Indeed, the deviations of our computational estimates are not larger than (6 and 13.6) kJ  mol1, respectively, for a-tetralone [3] and b-tetralone (see table 5).

O

O

IA +

C2H6

+

O O

IB C2 H6

O

+ CH3CH2COCH2CH3

+

CH3CH2CH2CH2CH3

+

CH3CH2CH2CH2CH3

IIA

O + CH3CH2COCH2CH3

IIB

O

O

+

+

IIIA

+

IIIB

O +

O

O

O

IVA

+

+

O O

+

+

IVB

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TABLE 4 Standard molar enthalpies of formation in the gas phase, at T = 298.15 K taken from the literature [35] Compound

Df Hm ðgÞ/(kJ  mol1)

Pentane 3-Pentanone Cyclohexane Cyclohexanone Indane 1-Indanone 2-Indanone Benzene Ethane Tetralin

147.1 ± 1.0 253.4 ± 0.9 123.1 ± 0.79 227.7 ± 1.9 60.3 ± 1.7 64.0 ± 3.834 56.6 ± 4.834 82.6 ± 0.7 83.8 ± 0.3 26.0 ± 1.9

TABLE 5 Theoretical estimates of the standard enthalpy of formation in the gas phase at T = 298.15 K of a- and b-tetralone Compound

R

Df Hm ðgÞ=ðkJ  mol1 Þ 6-311G**

cc-pVTZ

MC-UT

MCQCISD

a-Tetralone

IA IIA IIIA IVA

97.4 96.0 94.9 97.2

95.0 95.2 93.7 94.5

92.6 89.3 95.4 90.0

93.2 89.4 95.4 90.2

b-Tetralone

IB IIB IIIB IVB

82.1 80.7 87.5 82.0

82.2 82.3 89.3 81.7

83.4 80.1 88.1 80.8

83.6 79.8 88.4 80.6

On the basis of a comparison of our measurement of the enthalpy of formation of b-tetralone with the available experimental data for a-tetralone, a conclusion can be drawn: a-tetralone is energetically more stable than b-tetralone by about 20 kJ  mol1. This result is also supported by our computational estimates of the energetics of both isomers, even though a less pronounced difference, of only (10 to 15) kJ  mol1, is now found. As stated earlier in this paper, we suggest that this additional stability arises from the electronic delocalization involving the C@O group and the benzene ring of a-tetralone, a stabilizing effect which is absent in the b-isomer. In order to further support the above conclusion, we have performed an energetic analysis of the main donor-acceptor type interactions occurring in both isomers, within the framework of the NBO theory [32]. This analysis reveals that the interactions which can be considered as responsible for the different stability of the two isomers involve the p-bonding natural bond orbital (NBO) of the C@O group and the p anti-bonding NBO involving carbon atoms 5 and 6 of the benzene ring. The interactions involving these two NBOs only show measurable effect for the a-isomer, as was expected from the above reasoning. Also, an energy calculation performed with the elimination of the two referred NBOs from the Fock matrix, results in an increase of about 18 kJ  mol1 in the energy of a-tetralone, while for the other isomer no measurable rising can be observed. This result clearly supports the above explanation of the different stabilities of the two tetralone isomers. Finally a further corroboration of the validity of our findings can be obtained on the basis of oxidation potential data reported nearly 60 years ago [33]. Adopting the same assumptions we have used elsewhere [34], we can thus obtain from the oxidation potential data a difference of about 14.5 kJ  mol1 in the stability of the two isomers. This figure clearly represents a good consensus value between our experimentally findings obtained and the computationally derived energetics for these compounds.

Acknowledgements Thanks are due to Fundação para a Ciência e a Tecnologia, F.C.T., Lisbon, Portugal, and to FEDER for financial support to Centro de Investigação em Química of the University of Porto (CIQ-UP). Clara C. S. Sousa thanks the F.C.T. for the award of her doctoral scholarship (BD/19650/2004).

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JCT 08-206