J. Chem. Thermodynamics 50 (2012) 30–36

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J. Chem. Thermodynamics

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2,1,3-Benzothiadiazole: Study of its structure, energetics and aromaticity

Margarida S. Miranda a,b, M. Agostinha R. Matos a,⇑, Victor M.F. Morais a,c, Joel F. Liebman d

a Centro de Investigação em Química, Departamento de Química e Bioquímica, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre, s/n, P-4169-007 Porto, Portugalb Centro de Geologia da Universidade do Porto, Rua do Campo Alegre, s/n, P-4169-007 Porto, Portugalc Instituto de Ciências Biomédicas Abel Salazar, ICBAS, Universidade do Porto, P-4099-003 Porto, Portugald Department of Chemistry and Biochemistry, University of Maryland, Baltimore County, Baltimore, MD 21250, USA

a r t i c l e i n f o

Article history:Received 9 December 2011Received in revised form 20 January 2012Accepted 3 February 2012Available online 14 February 2012

Keywords:2,1,3-BenzothiadiazoleEnthalpyCombustionSublimationG3(MP2)//B3LYPStructureAromaticity

0021-9614/$ - see front matter � 2012 Elsevier Ltd. Adoi:10.1016/j.jct.2012.02.005

⇑ Corresponding author. Tel.: +351 22 0402 517; faE-mail addresses: msmirand@fc.up.pt (M.S. M

(M.A.R. Matos), vmmorais@icbas.up.pt (V.M.F. MoraLiebman).

a b s t r a c t

The present work reports an experimental study on the energetics of 2,1,3-benzothiadiazole and a com-putational study on its structure, energetics and aromaticity. In the experimental part the standard(p� = 0.1 MPa) massic energy of combustion, at T = 298.15 K, was measured by rotating bomb combustioncalorimetry, in oxygen, and allowed the calculation of the respective standard molar enthalpy of forma-tion, in the crystalline phase, at T = 298.15 K. The standard molar enthalpy of sublimation, at T = 298.15 K,was measured by high-temperature Calvet microcalorimetry. From the combination of data obtained byboth techniques we were able to calculate the respective standard molar enthalpy of formation, in the gasphase, at T = 298.15 K: (276.6 ± 2.5) kJ �mol�1. This thermochemical parameter was compared withestimates obtained from high level ab initio quantum chemical calculations using the G3(MP2)//B3LYPcomposite method and various appropriately chosen reactions. The molecular structure of 2,1,3-benzo-thiadiazole was obtained from DFT calculations with the B3LYP density functional and various basis sets:6-31G(d), 6-311(d,p), 6-311+G(3df,2p), aug-ccpVTZ and aug-ccpVQZ and its aromaticity and that of somerelated molecules were evaluated by analysis of nucleus independent chemical shifts (NICS) values.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

2,1,3-Benzothiadiazole (see figure 1) is a bicyclic compoundthat contains an unsaturated 6-membered, rather much nonbenz-enoid, ring fused to a five-membered ring with two nitrogen atomsat 1,3 position and one sulphur atom at 2 position. It has 10p-electrons and a single classical resonance structure that obeysthe octet rule with uncharged atoms. Alternatively, it may bedrawn with accompanying resonance structures that havereturned the benzene ring at the price of also having either avalence expanded sulphur as –N@S@N–, or atoms with formalcharges as –N�–S+@N–.

2,1,3-Benzothiadiazole has been incorporated in a number ofmaterials, namely electroluminescent dyes and polymers to gener-ate efficient green to red organic light-emitting diodes (OLEDs),two-photon absorbing materials and organic photovoltaics [1–5].Conjugated materials that incorporate 2,1,3-benzothiadiazolesalso include fluorescent dichroics that align in liquid crystal dis-plays (LCDs) [6], electrochromic polymers [7], and low-band-gappolymers [8]. Energy transfer to a 2,1,3-benzothiadiazole-centred

ll rights reserved.

x: +351 22 0402 522.iranda), marmatos@fc.up.ptis), jliebman@umbc.edu (J.F.

lower energy site has been utilized in the development of biosen-sors for single-strand DNA and alkaline phosphatase activity [9].

2,1,3-Benzothiadiazole derivatives have been shown to exhibitantimicrobial [10], antiviral [11], fungicidal, bactericidal andnematocidal [12], herbicidal [13], insecticidal and acaracidal [14],and radioprotective [15] activity.

We additionally note that despite the long-term importanceand thermochemical interest of compounds of sulphur and ofnitrogen there are surprisingly few other organic species contain-ing sulphur–nitrogen bonds that are not sulphonamides for whichthe enthalpy of formation is known. Such species include diethyl-amine sulphoxide and its corresponding disulphide [16], thedipiperidinyl mono and disulphide [17], and ‘‘dideoxysaccharin’’,more properly named 1,2-benzoisothiazol-3(2H)-one [18].

In the present work we report an experimental and computa-tional study on the energetics of 2,1,3-benzothiadiazole. In theexperimental part of this study we have determined the standardmassic energy of combustion, of the title compound, in oxygen,at T = 298.15 K, using a rotating-bomb combustion calorimetry,from which we have derived the standard molar enthalpy of for-mation, in the crystalline phase, at T = 298.15 K. The standard mo-lar enthalpy of sublimation, at T = 298.15 K, was determined usingCalvet microcalorimetry. The combination of these two thermody-namic parameters allowed us to calculate the standard molarenthalpy of formation in the gas phase, at T = 298.15 K. In addition,

FIGURE 1. Resonance structures of 2,1,3-benzothiadiazole.

M.S. Miranda et al. / J. Chem. Thermodynamics 50 (2012) 30–36 31

a computational study was performed using the G3(MP2)//B3LYPcomposite method. The standard molar enthalpy of formation inthe gas phase, at T = 298.15 K, was estimated using various appro-priate reactions. The geometry of 2,1,3-benzothiadiazole was fullyoptimized using DFT with the B3LYP density functional and variousbasis sets. The calculation of the nucleus independent chemicalshifts (NICS) allowed us to evaluate the aromaticity of 2,1,3-benzo-thiadiazole in comparison with that of related molecules.

2. Experimental

2.1. Material and purity control

2,1,3-Benzothiadiazole, molecular formula C6H4N2S, CAS Regis-try No. [273-13-2], was bought from Aldrich Chemical Co. assignedmass fraction purity of 0.98 (m.p. = (317 to 319) K). Prior to thecalorimetric experiments we have further purified this compoundby repeated sublimation under reduced pressure. The final puritywas assessed by differential scanning calorimetry (DSC) analysisusing a fractional fusion technique [19]. The DSC experiments wereperformed with a Setaram DSC 141 apparatus. The crystalline sam-ples were hermetically sealed in stainless steel crucibles and theheating rate used was of 1.67 � 10�2 K � s�1. The power scale ofthe calorimeter was calibrated with high purity indium (molarfraction > 0.99999) and its temperature scale was calibrated bymeasuring the melting temperatures of the following high purityreference materials [20]: naphthalene, benzoic acid and indium.

2.2. Rotating-bomb combustion calorimetry

The standard massic energy of combustion of 2,1,3-benzothia-diazole was measured by rotating-bomb combustion calorimetry.The apparatus and the technique have already been reported[21,22] so, only a brief description will be given here. The combus-tion experiments were performed with an isoperibol rotatingbomb calorimeter equipped with a twin valve bomb of stainlesssteel lined with platinum, whose internal volume is 0.258 dm3.

The energy equivalent of the calorimeter, ecal, was determinedusing the combustion of benzoic acid, NBS standard reference mate-rial 39j, with a massic energy of combustion of�(26,434 ± 3) J � g�1,under certificate conditions. Calibration experiments were carriedout in oxygen at a pressure of 3.04 MPa with 1.00 cm3 of deionisedwater added to the bomb. From a set of six calibration experimentswe obtained ecal = (25145.0 ± 1.3) J � K�1, where the uncertaintyquoted is the standard deviation of the mean.

The procedure followed for the combustion of 2,1,3-benzothia-diazole was the one described by Waddington et al. [23] for thecombustion of organosulphur compounds. The compound wasburnt, in the pellet form, with 15.00 cm3 of deionised water inthe bomb. As 2,1,3-benzothiadiazole is volatile at room tempera-ture, the pellets were enclosed into polyester bags made from Mel-inex, using the technique described by Skinner and Snelson [24].

The bomb was charged to a pressure of 3.04 MPa with oxygenwithout previously flushing, ensuring the formation of sufficientamounts of nitrogen oxides to oxidize the sulphur quantitativelyto sulphur trioxide.

Water was added to the calorimeter from a weighted perspexvessel and for each experiment a correction to the energy

equivalent was made for the deviation in the mass of water from5222.5 g.

For all experiments, the temperature of the water inside the cal-orimeter was measured to ±(1 � 10�4) K, at time intervals of 10 s,with a quartz crystal thermometer (Hewlett Packard HP 2804A),interfaced to a PC. The ignition of the samples was made by the dis-charge of a 1400 lF capacitor through a platinum ignition wire.The program LABTERMO [25] was used for control of the experi-ment and for data acquisition: at least 100 temperature readingswere taken for the initial period and 200 readings were taken forthe main and final periods. For each experiment, the ignition tem-perature was chosen so that the final temperature would be closeto T = 298.15 K.

Rotation of the bomb was started when the temperature rise inthe main period reached about 63% of its total value and was thencontinued throughout the rest of the experiment ensuring a homo-geneous solution of sulphuric acid in the bomb. By adopting thisprocedure, the frictional work due to the rotation of the bomb isautomatically included in the temperature corrections for the workof water stirring and for the heat exchanged with the thermostatedjacket [26]. The nitric acid formed was determined using the De-varda’s-alloy [27] method.

2.3. Microcalorimetry Calvet

The standard molar enthalpy of sublimation of 2,1,3-benzothia-diazole was measured using the ‘‘vacuum sublimation’’ drop micro-calorimetric method [28]. Samples, about (3 to 4) mg contained ina thin glass capillary tube sealed at one end, were dropped, at roomtemperature, into the hot reaction vessel, in a high temperatureCalvet microcalorimeter (SETARAM HT 1000D) held at a convenienttemperature T = 365 K and then removed from the hot zone by vac-uum sublimation. An empty capillary tube was dropped in the refer-ence calorimetric cell, simultaneously. The thermal corrections forthe glass capillary tubes were determined in separate experimentsand were minimized, as far as possible, by dropping tubes of nearlyequal mass, to within ±10 lg, into each of the twin calorimeter cells.The microcalorimeter was calibrated in situ for these measurementsusing the reported standard molar enthalpy of sublimation of naph-thalene Dg

crH�mð298:15 KÞ = (72.600 ± 0.600) kJ �mol�1 [29] a pri-

mary reference material. Accuracy tests were performed withbenzoic acid Dg

crH�mð298:15 KÞ = (89.700 ± 1.000) kJ �mol�1 [29].

3. Computational details

The geometry of 2,1,3-benzothiadiazole was fully optimizedusing density functional theory (DFT) with the hybrid functionalB3LYP and various basis sets: 6-31G(d), 6-311G(d,p),6-311+G(3df,2p), aug-cc-pVTZ and aug-cc-pVQZ. The B3LYP/6-31G(d) geometries were certified as true minima by constructionand diagonalization of the hessian matrices at the same level of the-ory. This procedure also provides the harmonic vibrational frequen-cies which after scaling by an appropriate factor of 0.9613 [30] allowthe calculation of heat capacity values at different temperatures. Inorder to obtain better estimates of the molecular energies calcula-tions were carried out using the G3(MP2)//B3LYP method [31]. Inthis method the geometries are fully optimized at the B3LYP/6-31G(d) level and the obtained stationary points are characterizedas minima through frequency calculations at the same level. Thensingle point energy calculations are performed at higher levels oftheory: QCISD(T)/6-31G(d) and MP2/GTMP2Large. The final abso-lute G3(MP2)//B3LYP enthalpies, at T = 298.15 K, are obtained cor-recting the electronic energies by introducing the vibrational,translational, rotational and the pV terms computed at the B3LYP/6-31G(d) level. From these calculations and using appropriate

32 M.S. Miranda et al. / J. Chem. Thermodynamics 50 (2012) 30–36

reactions, the standard molar enthalpy of formation of 2,1,3-benzo-thiadiazole, at T = 298.15 K, was derived.

The aromatic behaviour of molecules can be assessed on the ba-sis of the analysis of their magnetic properties, viz. the observableeffects of the circular ring current induced by applied externalmagnetic fields. For aromatic systems such current produce an in-duced magnetic field opposing the external one, a phenomenonwhich can be experimentally probed by the nuclear magnetic res-onance (NMR) chemical shifts measured at each nucleus. This con-cept has been generalized and converted into an useful aromaticityindex by Schleyer et al. [32] who developed a methodology involv-ing the calculation of the chemical shifts, not just at every nucleus,but at any point in the space in the vicinity of molecules, leading to

TABLE 1Combustion experiments performed for 2,1,3-benzothiadiazole.

Experiment no. 1 2

m(compound)/g 0.72856 0.55794m(cotton fuse)/g 0.00352 0.00370m(Melinex)/g 0.03800 0.03619DTad/K 0.83232 0.64476ei/(J � K�1) 72.02 71.85ef/(J � K�1) 71.29 71.06Dm(H2O)/g �3.0 �1.2�DU(IBP)/J 20977.84 16255.10�DU(cotton fuse)/J 57.16 60.09�DU(Melinex)/J 870.38 828.81�DU(HNO3)/J 60.42 49.73DU(ign.)/J 0.36 0.57�DU(carbon)/J 3.30 0.00�DUR/J 38.62 32.22�Dcu

�/(J � g�1) 27389.04 27394.07�Dcu

�/(J � g�1) = 27402.8 ± 4.4 (0.016 %)

m(cpd) is the mass of compound burnt in the experiment; m(fuse) is the mass of fuseexperiment; DTad is the corrected temperature rise; ei is the energy equivalent of conDm(H2O) is the deviation of the mass of water added to the calorimeter from 5222.5 g;bomb conditions; DU(IBP) includes DU(ign.); DU(fuse) is the energy of combustion of thethe energy correction for the nitric acid formation; DU(carbon) is the energy correctionenergy correction to the standard state; Dcu

� is the standard massic energy of combusti

TABLE 2Most relevant geometric parameters obtained using the B3LYP functional and the basis se

6-31G(d) 6-311G(d,p) 6-311+G(3df,2p) aug

R1,2 0.1645 0.1640 0.1615 0.1R2,3 0.1646 0.1640 0.1615 0.1R3,4 0.1339 0.1336 0.1341 0.1R4,5 0.1426 0.1424 0.1417 0.1R5,6 0.1371 0.1367 0.1367 0.1R6,7 0.1434 0.1432 0.1426 0.1R7,8 0.1370 0.1367 0.1367 0.1R8,9 0.1426 0.1424 0.1417 0.1R4,9 0.1452 0.1450 0.1443 0.1R1,9 0.1339 0.1336 0.1341 0.1H1,2,3 100.4 100.1 101.0 100H2,3,4 106.1 106.4 106.4 106H3,4,5 126.3 126.5 126.8 126H4,5,6 118.1 118.2 118.0 118H5,6,7 121.9 121.8 121.8 121H6,7,8 121.8 121.8 121.8 121H7,8,9 118.1 118.2 118.0 118H8,9,1 126.3 126.5 126.8 126H9,1,2 106.1 106.4 106.4 106H3,4,9 113.7 113.5 113.0 113H4,9,1 113.7 113.5 113.0 113H9,4,5 120.0 120.0 120.2 120H8,9,4 120.1 120.0 120.2 120

a Bond lengths in nm and bond angles in degrees.b Experimental parameters taken from the crystal structure of 2,1,3-benzothiadiazole [4c Experimental parameters taken from the crystal structure of 4,7-diiodo-2,1,3-benzothd Experimental parameters taken from the crystal structure of (1,3-butadiyne-1,4-diyl)-e Parameters not available in the experimental crystal structure.

what is now described as Nucleus Independent Chemical Shifts(NICS); these are just the negative of the isotropic component(the trace) of the chemical shielding tensor evaluated at the spe-cific points. Aromaticity has then been very often assessed by cal-culating the NICS at the geometric centre of the rings and also, toavoid the shielding effects of the framework of r electrons, at an-other point somewhat (generally 0.10 nm) above the geometriccentre of the ring [33,34].

Significantly negative (shielded) NICS values inside rings aredue to induced diatropic ring currents and denote aromaticity,whereas positive (deshielded) values denote paratropic ring cur-rents associated with anti-aromatic behaviour. Additionally, ithas also been recognized that, since ring currents resulting from

3 4 5 6

0.65024 0.61977 0.60487 0.545250.00394 0.00397 0.00360 0.004120.03500 0.03371 0.03950 0.036340.74441 0.71060 0.69870 0.6317171.94 71.91 71.90 71.8471.19 71.14 71.13 71.05�0.4 �1.5 �0.7 �2.018770.11 17914.45 17616.58 15924.1863.99 64.47 58.46 66.91801.62 771.92 904.65 832.2353.55 54.51 50.75 48.180.37 0.35 0.35 0.300.00 0.00 9.90 3.3035.68 34.46 34.21 31.7527397.99 27411.93 27408.22 27415.70

(cotton) used in the experiment; m(Melinex) is the mass of Melinex used in thetents in the initial state; ef is the energy equivalent of contents in the final state;DU(IBP) is the energy change for the isothermal combustion reaction under actualfuse (cotton); DU(Melinex) is the energy of combustion of the Melinex; DU(HNO3) isfor carbon formation; DU(ign.) is the energy of combustion of the fuse; DUR is theon.

ts: 6-31G(d), 6-311G(d,p), 6-311 + G(3df,2p), aug-cc-pVTZ, aug-cc-pVQZ.a

-cc-pVTZ aug-cc-pVQZ Exp.b Exp.c Exp.d

629 0.1620 0.160 0.1615 0.1613629 0.1620 0.160 0.1616 0.1616338 0.1340 0.134 0.1347 0.1344418 0.1418 0.146 0.1415 0.1429366 0.1366 0.129 0.1363 0.1373427 0.1426 0.146 0.1421 0.1414366 0.1366 0.129 0.1355 0.1380418 0.1418 0.146 0.1427 0.1433444 0.1443 0.141 0.1439 0.1435338 0.1334 0.134 0.1342 0.1343.6 100.9 102 101.0 101.5.3 106.4 105 106.5 105.9.5 126.7 e 127.8 e

.1 118.1 120 118.7 116.8

.8 121.8 121 121.9 123.0

.8 121.8 121 121.5 122.3

.1 118.1 120 118.4 116.4

.5 126.7 e 126.6 e

.3 106.4 105 106.4 105.9

.4 113.2 114 112.8 113.2

.4 113.2 114 113.3 113.5

.1 120.1 119 119.4 120.3

.1 120.1 119 120.1 121.2

9].iadiazole [50].4,40-bis[7-(3-n-hexyl-2-ethynyl-2,1,3-benzothiadiazole] [51].

N1

N3

S2

C4

C5

C6

C7

C8

C9

FIGURE 2. Fully optimized molecular structure of 2,1,3-benzothiadiazole.

M.S. Miranda et al. / J. Chem. Thermodynamics 50 (2012) 30–36 33

cyclic p-electron delocalization are induced primarily by the exter-nal magnetic field applied perpendicularly to the ring (convention-ally the ZZ direction), the out-of-plane (ZZ) component of themagnetic shielding tensor should contain the most relevant infor-mation for the aromaticity evaluation [35]. We thus have chosen tocalculate both the isotropic and the out-of-plane components ofthe chemical shielding tensor, denoted respectively as riso andrZZ, evaluated at the ring centres and 0.10 nm above, using theB3LYP/6-311G(d,p) wavefunctions and the GIAO [36–39] method,as a convenient way of characterizing aromaticity.

All calculations were performed with the Gaussian 03 series ofprograms (Gaussian Inc., Wallingford, CT, USA) [40].

TABLE 3Computed G3(MP2)//B3LYP standard molar enthalpy of formation, Df H

�m(g)comp., of

2,1,3-benzothiadiazole, in the gaseous phase, at T = 298.15 K.

Reaction Df H�mðgÞcomp:/(kJ �mol�1) Da/(kJ �mol�1)

(5) 268.1 8.5(6) 269.5 7.1(7) 279.8 �3.2(8) 272.5 4.1(9) 264.4 12.2(10) 262.6 14.0

a D represents the enthalpic difference between the experimental and computedvalue (D ¼ Df H�mðgÞexp : - Df H�mðgÞcomp:Þ.

4. Experimental results

The molar fraction of the 2,1,3-benzothiadiazole samples wereobtained from the DSC experiments and computed by means of afractional fusion technique as [19]: (0.9996 ± 0.0001) where the as-signed uncertainty corresponds to the standard deviation of themean of six independent runs. No phase transitions were observedbetween room temperature and the fusion temperature of the com-pound (observed at the onset of the calorimetric peaks),Tfus = (316.96 ± 0.04) K. From the DSC experiments we were alsoable to obtain the enthalpy of fusion Dl

crH�m(Tfus) = (16.30 ±

0.04) kJ �mol�1. The assigned uncertainties are twice the standarddeviation of the mean of six independent runs (level of confidence95%).

The standard molar enthalpy of formation of 2,1,3-benzothiadi-azole, in the crystalline phase, at T = 298.15 K, was determinedfrom the rotating bomb combustion calorimetry experiments.The detailed results of six the combustion experiments performedare given in table 1. The symbols in this table have the same mean-ing as previously described [41]. The internal energy for theisothermal bomb process, DU(IBP), was calculated according tothe following equation,

DUðIBPÞ ¼ �ecal þ DmðH2OÞcpðH2O; lÞ þ efDTad þ eiðT i

� 298:15Þ þ efð298:15� T i � DTadÞ þ DUðign:Þ; ð1Þ

where ecal is the energetic equivalent of the calorimeter, Dm(H2O) isthe deviation of the mass of water added to the calorimeter from5222.5 g, cp(H2O, l) is the specific heat capacity of liquid water, ei

is the energy of the bomb contents before ignition, ef is the energyof the bomb contents after ignition, DTad is the adiabatic tempera-ture raise, Ti is the initial temperature of the experiment and

DU(ign.) is the energy of ignition. The energy for ignition DU(ign.)was determined from the change in potential difference across acapacitor when discharged through the platinum ignition wire.For the cotton-thread fuse, empirical formula CH1.686O0.843, themassic energy of combustion is Dcu

� = �16,240 J�g�1 [42] and fordry Melinex the massic energy of combustion is hDcu

�i = �(22,902 ±5) J � g�1 [24]. Both these values have been confirmed in our labora-tory. The corrections for nitric acid formation were based on�59.7 kJ �mol�1, for the molar energy of formation of0.1 mol � dm�3 HNO3(aq) from 1/2 N2(g), 5/4 O2(g), and 1/2 H2O(l)[43]. To calculate the standard massic energy of combustion, Dcu

�,corrections to the standard state were made by the procedure givenby Hubbard et al. [41]. An estimated pressure coefficient of specificenergy: (ou/op)T = �0.2 J � g�1�MPa�1 at T = 298.15 K, a typical valuefor most organic compounds, was assumed [44]. The specific den-sity of the samples was estimated from the mass and the dimensionof the pellets as q = 1.30 g � cm�3.

The relative atomic masses of the elements used throughoutthis paper were those recommended by the IUPAC Commissionin 2009 [45] yielding for 2,1,3-benzothiadiazole the following mo-lar mass: 136.1744 g �mol�1.

The massic energy of combustion Dcu� was calculated by the pro-

cedure given by Hubbard et al. [41]. The obtained mean value of thestandard massic energy of combustion hDcu

�i = �(27402.8 ±4.4) J � g�1, at T = 298.15 K, is referred to the following combustionreaction:

C6H4N2SðcrÞ þ 9:25O2ðgÞ þ 113:5H2OðlÞ! 6CO2ðgÞ þH2SO4 � 115H2OðlÞ þ N2ðgÞ: ð2Þ

The assigned uncertainty corresponds to the standard deviation ofthe six experiments performed. The derived standard molar energyand enthalpy of combustion and the standard molar enthalpy offormation, in the crystalline phase, are respectively, DcU

�

m(cr)= �(3731.6 ± 1.6) kJ �mol�1, DcH�m(cr) = �(3735.3 ± 1.6) kJ �mol�1

and Df H�m(cr) = (200.6 ± 1.8) kJ �mol�1. In accordance with normal

thermochemical practice [46], the uncertainties assigned to thestandard molar enthalpies of combustion and formation are twicethe overall standard deviation of the mean and include the uncer-tainties in calibration and in the auxiliary quantities used (level ofconfidence 95%). To derive Df H

�m(cr) from DcH�m(cr) the standard mo-

lar enthalpies of formation, at T = 298.15 K, of H2O(l), CO2(g), andH2SO4 in 115H2O(l), respectively, �(285.830 ± 0.042) kJ �mol�1

[47], �(393.51 ± 0.13) kJ �mol�1 [47] and �(887.81 ± 0.01) kJ �mol�1

[43] were used.The standard molar enthalpy of sublimation, at T = 298.15 K,

DgcrH

�mð298:15 KÞ = (76.0 ± 1.8) kJ �mol�1, was determined from six

independent microcalorimetric experiments and the uncertaintyis twice the standard deviation of the mean (level of confidence95%). In each experiment, the observed enthalpy, Dg;T

cr;298:15 KH�m =(84.0 ± 1.8) kJ �mol�1, was corrected to T = 298.15 K using the cor-rection enthalpy DT

298:15KH�mðgÞ = 8.0 kJ �mol�1. This correction wasobtained from the equation:

TABLE 4Isotropic (riso) and out-of-plane (rZZ) components of the chemical shielding tensor measured at the centre (0) and 0.10 nm above the centre (+1) of the benzene and theheterocyclic rings (all values in ppm).

Compound Benzene ring Heterocyclic ring

0 +1 0 +1

riso rZZ riso rZZ riso rZZ riso rZZ

Benzene �8.90 �14.52 �11.13 �29.322,1,3-Benzothiadiazole �5.97 �5.93 �9.02 �22.16 �16.31 �22.74 �14.93 �37.94Imidazole �14.02 �13.80 �11.21 �31.79Thiophene �13.85 �9.25 �11.28 �28.15

34 M.S. Miranda et al. / J. Chem. Thermodynamics 50 (2012) 30–36

DT298:15KH�mðgÞ ¼

Z T

298:15KC�p;mðgÞdT; ð3Þ

where T is the temperature of the hot reaction vessel (T was set at365 K) and C�p;mðgÞ is the molar heat capacity of the compound inthe gaseous phase. The heat capacity and its temperaturedependence

C�p;mðgÞðJ �mol�1 � K�1Þ ¼ 0:000347ðT=KÞ2 þ 0:588ðT=KÞ � 37:606

ð4Þ

were derived from statistical thermodynamics using the vibrationalfrequencies obtained from the DFT calculations with the B3LYPfunctional and the 6-31G(d) basis set after scaling by an appropriatefactor, 0.9613 [30].

The standard molar enthalpy of formation, in the crystallinephase, at T = 298.15 K, Df H

�m(cr) = (200.6 ± 1.8) kJ �mol�1, together

with the standard molar enthalpy of sublimation, at T = 298.15 K,Dg

crH�mð298:15 KÞ = (76.0 ± 1.8) kJ �mol�1, yields the standard molar

enthalpy of formation in the gaseous phase, at T = 298.15 K,Df H

�m(g) = (276.6 ± 2.5) kJ �mol�1.

In 1998, Sabbah et al. [48] performed a thermodynamic study of2,1,3-benzothiadiazole using three techniques: differential thermalanalysis, sublimation calorimetry and combustion calorimetry. Theauthors reported the enthalpy of fusion, Dl

crHm = (16.62 ± 0.43)kJ �mol�1, the enthalpy of sublimation, Dg

crH�mð298:15 KÞ = (70.73

± 0.22) kJ �mol�1, and the enthalpy of formation, in the crystallinephase, Df H

�m(cr) = (111.8 ± 4.1) kJ �mol�1, and in the gas phase,

Df H�m(g) = (182.5 ± 4.1) kJ �mol�1. The enthalpies of fusion and

sublimation reported by Sabbah et al. [48] are in good agreementwith the values determined in this work but the enthalpy of forma-tion in the crystalline phase is very different from the value re-ported in this work: Df H

�m(cr) = (200.6 ± 1.8) kJ �mol�1. We

cannot think of any reason for the observed discrepancy.

5. Computational results and discussion

We have fully optimized the molecular structure of 2,1,3-benzo-thiadiazole using DFT with the B3LYP functional and the following

Benzofurazan

Tetrahydrofuran

basis sets: 6-31G(d), 6-311G(d,p), 6-311+G(3df,2p), aug-cc-pVTZand aug-cc-pVQZ. Various basis sets were evaluated in order toestablish their accuracy in providing geometrical parameters forthis molecule. In table 2 we have collected the most relevant geo-metric parameters obtained using the different basis sets (see figure2 for the numbering of the atoms). In this molecule all atoms arefound to be in the same plane. The molecule belongs to the C2v pointsymmetry group, as it has a plane bisecting the molecule throughthe sulphur atom. It can be observed that there is a considerableshortening of the C5–C6 and C7–C8 bonds compared to the otherCC bonds which suggests a quinonoid character of the six mem-bered ring of 2,1,3-benzothiadiazole. Comparing the bond lengthsand angles obtained with the different basis sets we may concludethat they do not differ significantly. The bond lengths obtaineddiffer at most by 0.0031 nm while for the bond angles differencesof at most 0.9� are observed. The largest differences were observedfor the N–S bonds and the N–S–N bond angle.

In table 2 we also present literature experimental data on thecrystal structure of 2,1,3-benzothiadiazole [49] for comparisonwith our computational values. This study is from 1951 and theauthor assigned an error of ±0.003 nm to the interatomic distances.So, we also present in table 2 some more recent experimental databut on the crystal structure of two molecules that contain the2,1,3-benzothiadiazole unit: 4,7-diiodo-2,1,3-benzothiadiazole[50] and (1,3-butadiyne-1,4-diyl)-4,40-bis[7-(3-n-hexyl-2-ethy-nyl-2,1,3-benzothiadiazole] [51]. The 6-311+G(3df,2p), aug-cc-pVTZ and aug-cc-pVQZ basis sets give bond lengths in better agree-ment with experiment, whereas in the case of the bond angles allbasis sets used give similar deviations from the experimentalresults.

In order to obtain reliable computational estimates of the en-thalpy of formation of 2,1,3-benzothiadiazole, in the gas phase,we have conducted G3(MP2)//B3LYP calculations for this moleculeand for all the other molecules present in reactions (5) to (10):

ð5Þ

ð6Þ

Tetrahydrothiophene

ð7Þ

Benzofuran Benzothiophene

ð8Þ

Benzoxazole Benzothiazole

ð9Þ

ð10Þ

M.S. Miranda et al. / J. Chem. Thermodynamics 50 (2012) 30–36 35

These reactions have been chosen on the basis of the availableexperimental thermochemical data for the compounds there usedand except for the atomization reactions, all the other reactionswere chosen to be almost isodesmic thus presumably leading tothe cancellation of most of the correlation energy errors inherentin quantum chemical calculations. Using the absolute enthalpy val-ues obtained for each molecule from the G3(MP2)//B3LYP calcula-tions we have calculated the enthalpies of each reaction. Thesewere then combined with the experimental standard molar enthal-pies of formation of all the intervening atoms/molecules, with theexception of 2,1,3-benzothiadiazole, to obtain the standard molarenthalpy of formation of 2,1,3-benzothiadiazole in the gaseousphase at T = 298.15 K. All the experimental standard molar enthal-pies of formation in the gaseous phase, at T = 298.15 K, were takenfrom Pedley’s compendium [52] except for the atoms [53], benzofu-ran [54], benzoxazole [55], benzothiazole [55], benzofurazan [56],ozone [53] and sulphur dioxide [53]. The calculated G3(MP2)//B3LYP absolute enthalpies at T = 298.15 K for 2,1,3-benzothiadiaz-ole and all the auxiliary atoms and molecules used in this studyare presented in supplementary material in table S1. In the same ta-ble we also show the corresponding experimental standard molarenthalpies of formation in the gaseous phase, at T = 298.15 K.

The G3(MP2)//B3LYP estimates for the enthalpy of formation of2,1,3-benzothiadiazole using the above reactions are shown in ta-ble 3. The computational estimates are, in general, in good agree-ment with the experimental values, the largest deviation being ofonly 14 kJ �mol�1. This largest deviation was given by reaction(10) which involves ozone as reactant but it should be noted thatozone is a difficult molecule to compute reliably using DFT meth-ods [57]. This good agreement supports our experimental standardmolar enthalpy of formation in the crystalline phase for 2,1,3-ben-zothiadiazole relative to that reported by Sabbah et al. [48].

The calculated components of the chemical shielding tensorsare collected in table 4 for 2,1,3-benzothiadiazole and some mono-cyclic related molecules: benzene, imidazole and thiophene. As canbe seen from this table there is a significant increase in the compo-nents of the benzene ring of 2,1,3-benzothiadiazole relative tothose of the benzene molecule, which indicates a significant dropin the aromatic character of the benzenic ring of 2,1,3-benzothiadi-azole relative to that of benzene. On the other hand, there is a de-crease in the components of the five membered heterocyclic ringrelative to those of imidazole and thiophene which reveals an in-creased aromatic character of this ring relative to the aromaticmolecules imidazole and thiophene. Similar findings were ob-served for anthranil [58].

6. Conclusions

A combined experimental and computational thermochemicalstudy was performed for 2,1,3-benzothiadiazole and a more reli-able value for its enthalpy of formation in the gas phase, atT = 298.15 K, is reported in this work. Experimentally this valuewas derived from the standard molar enthalpy of combustionand sublimation, at T = 298.15 K, measured by static bomb com-bustion calorimetry and Calvet microcalorimetry, and computa-tionally was derived from G3(MP2)//B3LYP calculations usingvarious appropriate reactions. The molecular structure of 2,1,3-benzothiadiazole was obtained from DFT calculations with theB3LYP functional and several basis sets and its aromaticity wasstudied from Nucleus Independent Chemical Shifts calculations.

Acknowledgements

Thanks are due to Fundação para a Ciência e a Tecnologia, FCT,Lisbon, Portugal, and to FEDER for financial support to Centro deInvestigação em Química, University of Porto. M. S. Miranda thanksFCT for the award of the postdoctoral scholarship (BPD/5594/2001)and for the financial support under the frame of the Ciência 2008program.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.jct.2012.02.005.

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