Experimental and Computational Thermochemical Study of Barbituric

ARTICLE pubs.acs.org/JPCA

Experimental and Computational Thermochemical Study of Barbituric Acids: Structure
Energy Relationship in 1,3-Dimethylbarbituric Acid María Victoria Roux,* Rafael Notario, Concepci
on Foces-Foces, and Manuel Temprado† Instituto de Química Física “Rocasolano”, CSIC, Serrano 119, 28006 Madrid, Spain

Francisco Ros Instituto de Química M
edica, CSIC, Juan de la Cierva 3, 28006 Madrid, Spain

Vladimir N. Emel'yanenko and Sergey P. Verevkin Department of Physical Chemistry, University of Rostock, Dr-Lorenz-Weg-1, D-18059 Rostock, Germany ABSTRACT: This paper reports an experimental and computational thermochemical study on 1,3-dimethylbarbituric acid. The value of the standard (p
= 0.1 MPa) molar enthalpy of formation in the gas phase at T = 298.15 K has been determined. The energy of combustion was measured by static bomb combustion calorimetry, and from the result obtained, the standard molar enthalpy of formation in the crystalline state at T = 298.15 K was calculated as
639.6 ( 1.9 kJ 3 mol
1. The enthalpy of sublimation was determined using a transference (transpiration) method in a saturated N2 stream and a value of the enthalpy of sublimation at T = 298.15 K was derived as 92.3 ( 0.6 kJ 3 mol
1. From these results a value of
547.3 ( 2.0 kJ 3 mol
1 for the gas-phase enthalpy of formation at T = 298.15 K was determined. Theoretical calculations at the G3 and G4 levels were performed, and a study on molecular and electronic structure of the compound has been carried out. Calculated enthalpies of formation are in very good agreement with the experimental value.

1. INTRODUCTION Structure and energy are two of the most fundamental and therefore important concepts in modern chemistry.1 These are intimately related because the energy associated with a particular structure depends on the atoms, bond lengths, and bond and torsional angles that form the molecular framework. The enthalpy of formation of a molecule is the thermochemical property that permits the evaluation of the feasibility of putative reaction paths in a synthetic process, i.e., to determine the reaction’s thermodynamic viability. Enthalpies of formation are also helpful in the understanding of the structural and reactivity trends exhibited by molecules. In addition this information is also needed to estimate the amount of energy released or absorbed in a chemical reaction, in calculating other thermodynamics functions, and, more importantly, in assessing the relative stability of molecules. Over the past years, we have been involved in the thermochemical study of the energetics of nitrogen-containing compounds such as amides,2 β-lactams,3 azoles,4 and cyclic ureas.5 We are presently involved in the study of the thermochemistry of barbituric acid (2,4,6(1H,3H,5H)-pyrimidinetrione) and its derivatives with the aim of developing an understanding of the structural effects on their thermodynamic stabilities that are reflected in the gas-phase enthalpies of formation, and on the influence of steric, electrostatic, and stereoelectronic interactions r 2011 American Chemical Society

produced by substituents on the thermochemical stability of these molecules. Barbituric acid derivatives possess a rather broad spectrum of therapeutic activity. They are used as sedatives, hypnotics, soporifics, anticonvulsants, or as adjuncts in anesthesia.6 New pharmacological properties of some barbituric acid derivatives established in recent years have significantly expanded the range of application of these compounds.7 In the context of a systematic study of the thermodynamic properties of this family of compounds and despite the important uses and applications of barbituric acids derivatives, reliable experimental thermochemical studies in the literature are scarce. We have recently published thermochemical studies of the parent compound barbituric acid8 and its 5,5-dimethyl9 and 5,5-diethyl (barbital) 5,10 derivatives. The purpose of the present work is to study the energy
structure relationship of 1,3-dimethylbarbituric acid whose structure is presented in Figure 1. The approach selected is a combination of experimental measurements of the enthalpy of formation and highlevel ab initio calculations. Received: January 19, 2011 Revised: February 24, 2011 Published: March 23, 2011 3167

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Figure 1. Schematic formula of 1,3-dimethylbarbituric acid.

2. EXPERIMENTAL PROCEDURES 2.1. Material and Purity Control. 1,3-Dimethylbarbituric acid [CAS 769-42-6] was commercially available from Fluka. The sample was carefully dried under vacuum, and no further purification needed to be performed. Determination of purity, assessed by HPLC and differential scanning calorimetry (DSC), using the fractional fusion technique,11 indicated that the mole fraction of impurities in the compound was less than 0.0001. 2.2. Procedure for Thermochemical Measurements. 2.2.1. Differential Scanning Calorimetry. The behavior of the sample as a function of temperature was studied by differential scanning calorimetry. A Pyris 1 instrument from Perkin-Elmer equipped with an intracooler unit was used to monitor purity, the possible existence of phase transitions in the solid sample in the interval of temperatures where the thermochemical measurements were done, and its heat capacity at T = 298.15 K. The apparatus, technique, and procedure have been described.12 The apparatus was previously calibrated in temperature and energy with reference materials.13 Thermograms of samples hermetically sealed in aluminum pans were recorded in a nitrogen atmosphere. All the pans with the samples were weighed on a Mettler AT21 microbalance with a detection limit of 1  10
6 g, before and after the experiments to confirm that no product had volatilized. After calibration, several runs with high-purity benzoic acid and indium as reference materials13 were performed under the same conditions as the experimental determinations. The accuracies associated with measurements of temperature and enthalpy were calculated as the percentage deviation of the experimental data with respect to the values given in the literature;13 in all cases the deviations were lower than 0.2 and 2.0% for temperature and enthalpy determinations, respectively.12 Different scans at heating rates of 0.04 and 0.17 K 3 s
1 were performed to determine the possible existence of phase transitions in the sample over the temperature range from T = 268 K to T = 400 K. 2.2.2. Combustion Calorimetry. An isoperibol calorimeter equipped with a static bomb was used for the measurements of the energy of combustion. The apparatus, technique, and procedure have been described.14 Calorimetric temperatures were measured within (1  10
4 K by means of a 100 Ω platinum resistance thermometer, using a calibrated resistence bridge (model F300, Automatic System Laboratories Ltd.) interfaced to a microcomputer programmed to calculate the adiabatic temperature change. The energy equivalent of the calorimeter, ε (calor), was determined from the combustion of benzoic acid, NIST standard reference sample 39j, having a specific energy of combustion, Δcu =
26434 ( 3 J 3 g
1, under certificate conditions. From eight calibration experiments, ε (calor) = 14262.6 ( 2.5 J 3 K
1, where the uncertainty quoted is the standard deviation of the mean. Frequent calibration experiments were made throughout the series of combustion experiments. The energy of

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combustion of 1,3-dimethylbarbituric acid was determined by burning the solid samples in pellet form in oxygen. The combustion bomb was flushed and filled with oxygen, previously freed from combustible impurities, and an initial pressure of oxygen of 3.04 MPa was used. Details of the characterization and physical properties of 1,3-dimethylbarbituric acid and the cotton used as fuse in this work are collected in Table 1. After disassembly of the calorimeter, the bomb gases were slowly let out and the absence of CO was confirmed with Dr€ager tubes (sensitivity level ≈1  10
6 mass fraction). No traces of carbon residue (soot) were observed in any of the experiments. The absence of NO2
was checked by calibrated ionic chromatography using a Dionex DX-120-chromathographic apparatus with a sensitivity level of 0.1 ppm for the measurements of NO2
. The nitric acid content in the bomb liquid was determined by titration with 0.1 mol 3 dm
3 NaOH(aq). The corrections for nitric acid formation17 were based on the value of
59.7 kJ 3 mol
1 for the standard molar energy of formation of 0.1 mol 3 dm
3 HNO3(aq) from N2(g), O2(g), and H2O(l). All samples were weighed with a Mettler AT-21 microbalance, sensitivity (1  10
6 g, and corrections of apparent mass to mass were made. For these corrections, conversion of the energy of the actual bomb process to that of the isothermal process, and for the correction to standard states, the values given in Table 1 were used. Corrections to the standard states were made according to Hubbard et al.18 The atomic weights of the elements were those recommended by IUPAC in 2006.19 The energy of solution of carbon dioxide in water at 298.15 K, ΔsolU(CO2), was taken as
17.09 kJ 3 mol
1, and the solubility constant, K(CO2), as 0.03440 mol 3 dm
3 3 atm
1 at T = 298.15 K.20 From the combustion energy, Δcuo, the enthalpy of formation in the condensed state, ΔfHm
(cr), at T = 298.15 K was calculated. 2.2.3. Vapor Pressure Measurements. Vapor pressures and enthalpies of sublimation, ΔgcrHm, of 1,3-dimethylbarbituric acid were determined by using the method of transference in a saturated stream of nitrogen. The method has been described before21 and has proven to give results in agreement with other established techniques for determining vapor pressures of pure substances and enthalpies of vaporization from the temperature dependence of the vapor pressure.22 About 0.5 g of the sample was mixed with glass beads and placed in a thermostated U-tube of length 10 cm and diameter 0.5 cm. A preheated nitrogen stream was passed through the U-tube at constant temperature ((0.1 K). The flow rate of the nitrogen stream was measured using a soap bubble flow meter ((0.2
0.3%) and optimized in order to reach the saturation equilibrium of the transporting gas at each temperature under study. We tested our apparatus at different flow rates of the carrier gas in order to check the lower boundary of the flow below which the contribution of the vapor condensed in the trap by diffusion becomes comparable to the transpired one. In our apparatus the contribution due to diffusion was negligible at a flow rate down to 0.5 dm3 3 h
1. The upper limit for our apparatus where the flow of nitrogen could disturb the equilibration was at a flow rate of 12.5 dm3 3 h
1. Thus, we carried out the experiments in the flow rate interval from 4 to 9 dm3 3 h
1 which ensured that the transporting gas was in saturated equilibrium with the coexisting solid phase in the saturation tube. The transported amount of material was condensed in a cooled trap. The amount of condensed product was determined by weighing ((0.0001 g). The saturated vapor pressure pisat at each temperature Ti was calculated from the amount of product collected within a definite period of time. Assuming that Dalton’s law of partial pressures is 3168

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Table 1. Properties at T = 298.15 K (the Value in Brackets was Estimated) compound cotton 1,3-dimethylbarbituric acid

M, g 3 mol
1

F, g 3 cm
3

27.700a,b

10
7(δV/δT)P, dm3 3 g
1 3 K
1 9.69c

1.5

156.1393

1.395

d

cP, J 3 K
1 3 g
1


17410 ( 37a

1.48

[3.354]

1.208

Δcu
m(cr), J 3 g
1

a,e

a

Determined in our laboratory. b Corresponding to an empirical formula of C1.000H1.740O0.871. c Value taken from ref 15. d Value taken from ref 16. e Determined by DSC.

Table 2. Temperature and Enthalpy and Entropy of Fusion for the Compound Studied

1,3-dimethylbarbituric acid

Tfus, K

ΔfusH(Tfus), kJ 3 mol
1

ΔfusS(Tfus)expt, J 3 K
1 3 mol
1

396.1 ( 0.3

17.7 ( 0.1

44.6 ( 0.3

Table 3. Results of the Combustion Experiments on 1,3-Dimethylbarbituric Acida m0 (compound)/gb m00 (fuse)/gb ΔTc/K = (Tf
Ti þ ΔTcorr)/K ε(calor) (
ΔTc)/kJc ε(cont.) (
ΔTc)/kJd ΔUign/kJe ΔUdec(HNO3)/kJf ΔU(corr to std states)/kJg
m00 Δcu0(fuse)/kJ Δcu0(compound)/kJ g
1 ÆΔcu0(298.15 K)æ/kJ g
1

0.899994 0.002542 1.1655
16.6223
0.0192 0.0008 0.0661 0.0131 0.0443
18.3525

0.895695 0.002365 1.1590
16.5302
0.0191 0.0008 0.0638 0.0131 0.0412
18.3437

0.893759 0.002447 1.1578
16.5131
0.0190 0.0008 0.0618 0.0131 0.0427
18.3649
18.3552 ( 0.0035

0.899271 0.002789 1.1650
16.6156
0.0192 0.0008 0.0646 0.0131 0.0486
18.3566

0.903382 0.002524 1.1701
16.6887
0.0193 0.0008 0.0654 0.0132 0.0440
18.3583

a For a definition of the symbols see refs 18 and 32. Tth = 298.15 K; Vbomb = 0.380 dm3; pigas = 3.04 MPa; miwater = 1.00 g. b Masses obtained from apparent mass. c ε(calor), energy equivalent of the whole system less the content of the bomb. d ε(cont.), energy equivalent of the contents of the bomb. ε(cont.)(
ΔTc) = εi(cont.)(Ti
298.15 K) þ εi(cont.)(298.15 K
Tf þ ΔTcorr.). e Experimental energy of ignition. f Experimental energy of formation of nitric acid. g Energy of correction to standard states.

valid as applied to the nitrogen stream saturated with the substance, i, of interest, values of pisat were calculated pi sat ¼ mi RTa =VMi ;

V ¼ VN2 þ Vi ;

ðVN2 . Vi Þ

ð1Þ

where R = 8.31451 J 3 K
1 3 mol
1; mi is the mass of transported compound, Mi is the molar mass of the compound, and Vi its volume contribution to the gaseous phase. VN2 is the volume of transporting gas and Ta is the temperature of the soap bubble meter. The volume of transporting gas VN2 was determined from the flow rate and time measurements. 2.3. Computational Details. Standard ab initio molecular orbital calculations23 were performed with the Gaussian 0324 and Gaussian 0925 series of programs. The energy of the compound studied was calculated26 using Gaussian-n theory, at the G327 and G428 levels. G3 corresponds effectively to calculations at the QCISD(T)/ G3large level, G3large being a modification of the 6-311þG(3df,2p) basis set, including more polarization functions for the second row (3d2f), less on the first row (2df), and other changes to improve uniformity. In addition, some core polarization functions are added. Single-point energy calculations are carried out on MP2(full)/6-31G(d) optimized geometries, incorporating scaled HF/6-31G(d) zero-point vibrational energies, a socalled higher-level correction to accommodate remaining deficiencies, and spin
orbit correction for atomic species only.27 G4 is the more recent29 theory developed in the Gaussian-n theories. The G4 theory modifies the G3 theory in five ways, including (a) an extrapolation procedure to obtain the Hartree
Fock limit for inclusion in the total energy calculation, (b) increase of the d-polarization sets to 3d on the first-row atoms and to 4d on the second-row atoms, with reoptimization of the exponents for the 4d

set, (c) the replacement of the QCISD(T) method by CCSD(T), (d) geometries and zero-point energies obtained at the B3LYP/631G(2df,p) level, and (e) two new higher level correction parameters to account for deficiencies in radicals and in species having only one electron pair in the valence space.28 We have also reoptimized the geometry at the MP2(full)/ 6-31G(3df,2p) level to obtain a more reliable molecular structure for the compound studied. The charge distribution has been analyzed using a population partition technique, the natural bond orbital (NBO) analysis of Reed and Weinhold.29 The NBO analysis has been performed using the NBO program30 implemented in the Gaussian 03 package.24 3. Results and Discussion 3.1. Experimental Results. 3.1.1. Phase Transitions. DSC was used to study the possible existence of phase transitions in the solid sample of 1,3-dimethylbarbituric acid. No phase transitions were observed in the temperature interval between T = 268 K to T = 396 K, the melting temperature. Fusion temperature, enthalpy, and experimental entropy of fusion are given in Table 2.31 The uncertainties were taken as the standard deviation of the mean. Tfus values are reported as DSC onset temperatures. 3.1.2. Experimental Enthalpy of Formation. Results for the combustion experiments on 1,3-dimethylbarbituric acid are given in Table 3 and correspond to the reaction C6 H8 O3 N2 ðcrÞ þ 13 =2 O2 ðgÞ f 6CO2 ðgÞ þ 4H2 OðlÞ þ N2 ðgÞ ð2Þ Table 4 lists the derived standard molar enthalpies of combustion and formation in the crystalline state at T = 298.15 K. In 3169

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accordance with normal thermochemical practice, the uncertainty assigned is twice the overall standard deviation of the mean and includes the uncertainties in calibration and in the auxiliary quantities used.33 To derive ΔfHm
(cr) from ΔcHm
(cr), the CODATA values of the standard molar enthalpies of formation at T = 298.15 K of H2O(l) and CO2(g),
285.830 ( 0.042 and
393.51 ( 0.13 kJ 3 mol
1 were used.34 3.1.3. Enthalpy of Sublimation. Vapor pressures of 1,3dimethylbarbituric acid have been measured between 340 and 390 K (see Table 5). The following equation   b T g þ Δ ¼ a þ C ln ð3Þ R ln psat cr p i T T0 was fit to the experimental p, T data using a and b as adjustable parameters. T0 appearing in eq 3 is an arbitrarily chosen reference temperature (which has been chosen to be 298.15 K). Consequently, from eq 3 the expression for the vaporization enthalpy at temperature T is derived (eq 4). Δgcr Hm ðTÞ ¼
b þ Δgcr Cp T

ð4Þ

A value of ΔgcrCp =
29.0 J 3 mol
1 3 K
1 has been derived according to the procedure developed by Chickos35 using the experimental isobaric molar heat capacities of solid 1,3-dimethylbarbituric acid, Cpcr(298.15 K) = 188.5 J 3 mol
1 3 K
1, measured by DSC.31 In order to assess the uncertainty of the sublimation enthalpy, the experimental data were approximated with the linear equation ln(pisat) = f (T
1) using the method of least squares. The uncertainty in the enthalpy of sublimation was assumed to be identical to the average deviation of experimental ln(pisat) values from this linear correlation and uncertainties in values of ΔgcrCp were not taken into account. Experimental results, and parameters a and b are listed in Table 5. Table 4. Experimentally Determined Standard (p
= 0.1 MPa) Molar Energy of Combustion and Standard Molar Enthalpies of Combustion and Formation in the Crystalline State at T = 298.15 K for 1,3-Dimethylbarbituric Acida

a

ΔcUm
(cr)

ΔcHm
(cr)

ΔfHm
(cr)


2866.0 ( 1.8


2864.8 ( 1.8


639.6 ( 1.9

Values in kJ 3 mol
1.

Table 6 summarizes the values of the standard molar enthalpy of combustion, ΔcHm
, sublimation, ΔgcrHm, and formation in the crystalline, ΔfHm
(cr), and gaseous state, ΔfHm
(g) at T = 298.15 K. No experimental results for the energies and enthalpies of combustion, sublimation, and formation have been found in the literature for comparison with our results. 3.2. Molecular and Electronic Structure. 1,3-Dimethylbarbituric acid contains only one enolizable hydrogen atom, and so it may exist in two tautomeric forms differing by the position of the hydrogen, which may be bound to a carbon or an oxygen atom. Calculations at the B3LYP/6-31G(d) level show the triketo tautomer to be more stable in the gas phase than the enolized form, 2,4diketo-6-hydroxy, with the OH group in syn conformation with respect to the CdC bond, by 59.5 kJ 3 mol
1. Bertolasi et al.16 have calculated a value of 45.9 kJ 3 mol
1 at the B3LYP/6-31G(d,p) level. The higher stability of the triketo form is associated with the much stronger double bond of CdO compared with the strength of the CdC bond. This high energy difference suggests that the gas phase of 1,3-dimethylbarbituric acid consists of a single molecular species. The crystal structure of 1,3-dimethylbarbituric acid was reported by Bertolasi et al.16 The structure is orthorhombic of the space group Fdd2, a = 15.642(3), b = 29.006(6), c = 6.5560(11) Å, with Z = 16. 1,3-Dimethylbarbituric acid does not enolize in crystals. In contrast to barbituric acid, the crystal structure of 1,3dimethylbarbituric acid does not contain any traditional H-donor group that would enable formation of strong hydrogen bonding interactions. It forms crystals whose packing is dominated by perpendicular donor
acceptor CδþdOδ
3 3 3 CδþdOδ
interactions and C—H 3 3 3 OdC hydrogen bonds.16 Besides the DFT study of Bertolasi et al.,16 to our knowledge, there is only one previous theoretical study on 1,3-dimethylbarbituric acid. Chandra et al.36 have recently carried out quantum chemical calculations, at the B3LYP/6-31G(d,p) level, of energies, geometrical structure, and vibrational wavenumbers along with experimental Table 6. Experimentally Determined Thermodynamic Quantities at T = 298.15 K for 1,3-Dimethylbarbituric Acida

a

ΔcHm


ΔfHm
(cr)

ΔgcrHm

ΔfHm
(g)


2864.8 ( 1.8


639.6 ( 1.9

92.3 ( 0.6


547.3 ( 2.0

Values in kJ 3 mol
1.

Table 5. Results from Measurements of the Vapor Pressure p of 1,3-Dimethylbarbituric Acid Using the Transpiration Method T,a K

m,b mg

V(N2),c dm3

p,d Pa

(pexp
pcalc), Pa

ΔgcrHm, kJ 3 mol
1

ΔgcrHm(298.15 K) = 92.29 ( 0.57 kJ 3 mol
1 339.7 343.7 345.8 348.8 354.0 359.3 364.2 369.1 374.6 380.1 382.7 384.8 390.1

13.2 19.3 16.5 18.0 27.3 9.6 20.4 11.1 10.8 12.4 15.9 11.7 11.5

ln(p/Pa) = (306.15/R)
(100932.75/R(T, K))
(29.0/R) ln((T, K)/298.15) 113.77 4.15 1.85
0.02 106.44 4.15 2.81 0.09 81.28 4.15 3.23
0.07 68.36 4.15 4.12
0.21 62.55 4.15 6.88 0.02 13.41 4.15 11.24 0.43 18.87 4.15 16.95 0.71 7.40 4.15 23.52
0.61 4.49 4.15 37.67 0.37 3.39 4.15 57.36 0.92 3.66 4.15 68.00
0.47 2.28 4.15 80.36 0.49 1.59 4.15 113.33
3.59

91.08 90.97 90.91 90.82 90.67 90.51 90.37 90.23 90.07 89.91 89.84 89.78 89.62

a

Temperature of saturation b mass of transferred sample, condensed at T = 293 K c volume of nitrogen, used to transfer mass m of sample, gas-flow 4.15 dm3/h was constant through the all measurements d vapor pressure at temperature T, calculated from m and the residual vapor pressure at the cooling temperature T = 299 K. 3170

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Table 7. Experimental and Calculated Geometric Parameters for 1,3-Dimethylbarbituric Acid (Bond Distances in Ångstroms, and Bond Angles in degrees).

N1
C2 C2
N3 N3
C4 C4
C5 C5
C6 C6
N1 C2
O C4
O C6
O N1
C N3
C C6N1C2 N1C2N3 C2N3C4 N3C4C5 C4C5C6 C5C6N1 OC2N1 OC2N3 OC4N3 OC4C5 OC6C5 OC6N1 C6N1C C2N1C C4N3C C2N3C N1C2N3C4 N3C2N1C6 N1C6C5C4 N3C4C5C6 C2N1C6C5 C2N3C4C5 CN1C2N3 CN3C2N1 CN1C2O CN3C2O C2N1C6O C2N3C4O C6N1C2O C4N3C2O CN1C6C5 CN3C4C5

Figure 2. Front and side view of the molecular structure of 1,3dimethylbarbituric acid optimized: (a) at the B3LYP/6-31G(2df,p) level; (b) at the MP2(Full)/6-31G(3df,2p) level.

measurements of FT-IR (solid and gas phase) and FT-Raman spectra, to completely study the vibrational spectra of this molecule and to identify the various normal modes with greater wavenumber accuracy for the first time. Also, HOMO and LUMO analyses were used to elucidate the information regarding charge transfer within the molecule. The MP2(Full)/6-31G(d) and B3LYP/6-31G(2df,p)-optimized structures (obtained at the G3 and G4 levels, respectively) are nonplanar but predict an envelope conformation with the C5 atom out of planarity, in agreement with the crystal structure reported by Bertolasi et al.16 However, the MP2(Full)/6-31G(3df,2p)optimized structure predicted a planar six-membered ring. This behavior was previously observed in our study on 5,5-dimethylbarbituric acid.9 B3LYP/6-31G(2df,p) and MP2(Full)/6-31G(3df,2p)optimized structures of 1,3-dimethylbarbituric acid are shown in Figure 2, and the calculated bond distances and angles are collected in Table 7 for their comparison with the X-ray results. Atomic charges have been calculated by the natural bond orbital (NBO) population analysis scheme at the MP2(Full)/6-31G(3df,2p) level of theory. Positive charge is located at C atoms of the carbonyl groups (1.019 at C2 and 0.858 at C4 and C6 atoms), whereas negative charge is located at N atoms (
0.622), O atoms (
0.705 at O atom bonded at C2, and
0.686 at O atoms bonded at C4 and C6 atoms), at C5 atom (
0.625), and the C atom of the two methyl groups bonded at N atoms (
0.410). It is observed that the charge separation between the C2 and O carbonyl group is larger than those on the other two carbonyl groups (1.724 versus 1.544). 3.3. Theoretical Determination of the Enthalpy of Formation. The standard procedure to obtain enthalpies of formation in Gaussian-n theories is through atomization reactions.37 Several authors38 have shown that more accurate heats of formation can be derived using isodesmic or homodesmotic39 reactions rather than atomization energies. In this work we have calculated the enthalpy of formation of 1,3-dimethylbarbituric acid, C6H8N2O3, using the atomization reaction, and two isodesmic reactions using barbituric acid,

a

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

B3LYP/ 6-31G(2df,p)

MP2(Full)/ 6-31G(3df,2p)

experimentala

1.397 1.397 1.390 1.505 1.505 1.390 1.223 1.224 1.224 1.464 1.464 124.7 117.7 124.7 115.0 116.9 115.0 121.1 121.1 122.5 122.3 122.3 122.5 119.2 115.7 119.2 115.7
1.1 1.1 26.8
26.8
14.2 14.2
173.9 173.9 4.7
4.7 170.0
170.0
177.6 177.6 173.1
173.1

1.398 1.398 1.390 1.511 1.511 1.390 1.210 1.210 1.210 1.467 1.467 125.1 118.1 125.1 115.9 118.6 115.9 120.9 120.9 122.4 121.6 121.6 122.4 119.1 115.8 119.1 115.8
1.4 1.4 12.9
12.9
5.8 5.8
176.8 176.8 2.0
2.0 175.9
175.9
179.7 179.7 176.0
176.0

1.386 1.386 1.379 1.497 1.497 1.379 1 212 1.212 1.212 1.454 1.454 125.3 118.0 125.3 116.2 119.1 116.2 121.0 121.0 122.5 121.3 121.3 122.5 119.3 115.5 119.3 115.5 0.0 0.0 0.0 0.0 0.0 0.0
180.0 180.0 0.0 0.0 180.0
180.0
180.0 180.0 180.0
180.0

1.377(3) 1.383(3) 1.366(4) 1.484(4) 1.481(4) 1.376(4) 1.204(4) 1.215(3) 1.211(3) 1.465(4) 1.469(3) 124.0(2) 118.6(2) 124.2(2) 117.1(2) 118.2(3) 117.2(2) 120.5(2) 120.9(2) 121.1(3) 121.7(3) 121.8(3) 121.0(3) 118.7(3) 117.2(3) 118.9(3) 116.6(3)
7.3(4) 6.8(4) 6.8(4)
7.2(4)
6.7(4) 7.6(4)
178.0(3) 179.0(3) 2.6(4)
1.6(4) 173.9(3)
173.1(3)
172.6(3) 172.1(3) 178.1(3)
178.9(3)

X-Ray data taken from ref 16.

C4H4N2O3, (reaction 5) and urea and pentane-2,4-dione (reaction 6) as references C6 H8 N2 O3 ðgÞ þ 2NH3 ðgÞ f C4 H4 N2 O3 ðgÞ þ 2CH3 NH2 ðgÞ ð5Þ C6 H8 N2 O3 ðgÞ þ 2CH4 ðgÞ þ 2NH3 ðgÞ f ðNH2 Þ2 COðgÞ ð6Þ þ CH3 COCH2 COCH3 ðgÞ þ 2CH3 NH2 ðgÞ The G3-calculated enthalpies of formation obtained40 from the atomization reaction,
552.0 kJ 3 mol
1, from the isodesmic reaction 5,
556.5 kJ 3 mol
1, and from isodesmic reaction 6,
553.3 kJ 3 mol
1, give an average value of
553.9 kJ 3 mol
1, in reasonable agreement with the experimental value determined in this work,
547.3 ( 2.0 kJ 3 mol
1. A significant improvement is obtained when the enthalpies of formation are obtained from G4 calculations. The G4-calculated enthalpies of formation obtained 3171

dx.doi.org/10.1021/jp200562m |J. Phys. Chem. A 2011, 115, 3167–3173

The Journal of Physical Chemistry A Scheme 1

from the atomization reaction,
548.2 kJ 3 mol
1, from isodesmic reaction 5,
552.5 kJ 3 mol
1, and from isodesmic reaction 6,
545.4 kJ 3 mol
1, give an average value of
548.7 kJ 3 mol
1, in very good agreement with the experimental value determined in this work. From the values of the enthalpies of formation in the gas phase of barbituric acid,8 its 5,5-dimethyl derivative,9 and the values reported in this work, we can calculate the enthalpic increments for the introduction of two methyl groups in positions 1,3- and 5,5- of the barbituric acid ring (see Scheme 1), the values being
13.0 ( 2.6 and
56.6 ( 2.9 kJ 3 mol
1, respectively. Substitution of the two hydrogen atoms in the barbituric acid ring by two methyl groups is more exothermic at the 5,5-position than at the 1,3-position of the ring. The isomerization enthalpy is calculated as 43.6 ( 3.0 kJ 3 mol
1. The G3-calculated value, 46.9 kJ 3 mol
1, is in good agreement with the experimental difference.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Present Addresses †

Departamento de Química Física, Universidad de Alcal
a, 28871 Alcal
a de Henares (Madrid), Spain.

’ ACKNOWLEDGMENT This article is dedicated to the memory of Concepci
on FocesFoces, recently deceased. The support of the Spanish Ministry of Science and Innovation under Projects CTQ2007-60895/BQU and CTQ2010-16402 is gratefully acknowledged. M.T. acknowledges the Spanish Ministry of Science and Innovation for a “Juan de la Cierva” contract. ’ REFERENCES (1) Molecular Structure and Energetics; Liebman, J. F., Greenberg, A., Eds.; VCH Publishers: New York, 1986; Vol. 1.

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m values for the reference compounds used in isodesmic reactions (5) and (6): methane,
74.6 ( 0.3 kJ 3 mol
1, has been taken from Manion, J. A. J. Phys. Chem. Ref. Data 2002, 31, 123. methylamine,
23.4 ( 1.0 kJ 3 mol
1, has been taken from Pedley, J. B. Thermochemical Data and Structures of Organic Compounds; TRC Data Series; Thermodynamics Research Center: College Station, TX, 1994; Vol. 1; ammonia,
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358.9 ( 2.5 kJ 3 mol
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534.3 ( 1.7 kJ 3 mol
1, has been taken from ref 8.

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