Article pubs.acs.org/jced
Vapor Pressures and Sublimation Thermodynamic Parameters for Novel Drug-Like Spiro-Derivatives Marina V. Ol’khovich,† Angelica V. Sharapova,† Svetlana V. Blokhina,†,* German L. Perlovich,† and Alexey N. Proshin‡ †
Institute of Solution Chemistry, Russian Academy of Sciences, 1 Akademicheskaya Street, 153045, Ivanovo, Russia Institute of Physiologically Active Compounds, Russian Academy of Sciences, 142432, Chernogolovka, Russia
‡
ABSTRACT: Temperature dependences of saturated vapor pressure for eight new molecular crystals of spiro-derivatives of 1,3-thiazine have been determined by transport method by means of an inert gas carrier. Thermodynamic functions of sublimation have been calculated. The processes of substances fusion have been examined by differential scanning calorimetry. The effect of alkyl substituents structure and introduction of halogen atoms on sublimation properties of spiro-compounds has been assessed. The correlation between thermodynamic parameters of sublimation processes and thermo-physical properties of the substances and molecular descriptors is established.
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INTRODUCTION The vapor pressure of any organic substance is a key physical property that is required for thermodynamic calculations of enthalpies of sublimation/vaporization. The sublimation enthalpy is indispensable to determine the thermodynamic properties of a substance in various states as well as to find out the relationship between thermodynamic properties, the bond energies, and the molecular structure of a substance.1 Thermodynamic characteristics of sublimation processes of molecular crystals are significant parameters determining the solubility of compounds and giving an opportunity to estimate molecular solvation properties.2 Practically, all of the processes ensuring drug transport, namely dissolution, distribution, and passive transport, are dependent on these characteristics in pharmaceutics.3 Spiro-compounds belong to a class of chemicals which are successfully used in medicine. Drugs based on these chemicals possess high biological activity and are employed as cardiotonic, antiarrhythmic, and antitumor agents. These are represented in the patent base of drug compounds as potential candidates for further preclinical study aimed at the treatment of cognitive deficits in schizophrenia and Alzheimer’s disease.4−6 The compilation of both theoretical and experimental data on the dependence between the structure and physicochemical and pharmacological activity of chemical compounds is of great value in production of novel drug substances.7 It is the purpose of the present work to study the effect of specific features of molecular structure of advanced spiro-derivatives of thiazine on thermophysical and sublimation properties.
(3); (4-isopropyl-phenyl)-(1-thia-3-aza-spiro[5.5]undec-2-en-2-yl)amine (4); (3-chloro-4-methyl-phenyl)-(1-thia-3-aza-spiro[5.5]undec2-en-2-yl)-amine (5); (1-thia-3-aza-spiro[5.5]undec-2-en-2-yl)(4-trifluoromethyl-phenyl)-amine (6), (4-chloro-phenyl)-1-thia-3aza-piro[5.5]undec-2-en-2-yl)-amine (7); and (4-bromine-phenyl)1-thia-3-aza-piro[5.5]undec-2-en-2-yl)-amine (8). These substances have been synthesized by reaction of the appropriate isothiocyanate with 2-cyclohex-2-enyl-ethylamine followed by cyclization of the intermediate thiourea under acidic conditions in the final bicyclic product. The chemical synthesis of compounds, confirmation of their structure, and the degree of purity have been described before.8 The tested substances were purified by recrystallization from propanol-2. Purity of the spiroderivates was 0.98 (mass fraction). Apparatus and Procedure. Temperatures and enthalpies of fusion of the compounds under investigation have been determined using a Perkin-Elmer Pyris 1 DSC differential scanning calorimeter (Perkin-Elmer Analytical Instruments, Norwalk, Connecticut, USA) with Pyris software for Windows NT. DSC runs were performed in an atmosphere of flowing 20 cm3·min−1 dry helium gas of high purity 0.99996 (mass fraction) using standard aluminum sample pans and a heating rate of 2 K·min−1. The accuracy of weight measurements was 0.005 mg. The DSC was calibrated with an indium sample from Perkin-Elmer (P/N 0319-0033). The value determined for the enthalpy of fusion corresponded to 28.48 J·g−1 (reference value 28.45 J·g−1). The fusion temperature was 429.5 ± 0.1 K (determined from at least ten measurements). The enthalpy of fusion at 298 K was calculated by the following equation:
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Δcrl Hmo(298.15) = Δcrl Hmo(Tfus) − Δcrl Smo(Tfus)(Tfus − 298.15)
EXPERIMENTAL SECTION Materials. Use has been made of the following eight compounds: phenyl-(1-thia-3-aza-spiro[5.5]undec-2-en-2-yl)-amine (1); (4-methyl-phenyl)-(1-thia-3-aza-spiro[5.5]undec-2-en-2-yl)-amine (2); (4-ethyl-phenyl)-(1-thia-3-aza-spiro[5.5]undec-2-en-2-yl)-amine © 2012 American Chemical Society
(1)
Received: June 6, 2012 Accepted: October 24, 2012 Published: November 5, 2012 3452
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(Δcrg Hmo(T ) − Δcrg Gmo(T )) (4) T g o with ΔcrHm(T) = −RT ln(p/p0), where p0 is the standard pressure of p0 = 1.013·105 Pa. For experimental reasons sublimation data are obtained at elevated temperatures. However, in comparison with effusion methods, the temperatures are much lower, which makes extrapolation to room conditions easier. In order to further improve the extrapolation to room conditions, we estimated the heat capacities (crCop,m value) of the crystals using the additive scheme proposed by Chickos et al.12 Heat capacity was introduced as a correction for the recalculation of the sublimation enthalpy ΔgcrHom according to the equation:
where the difference between the heat capacities of the melt and solid states was approximated by the fusion entropy (as an upper estimate). This approach was used by Dannenfelser and Yalkowsky. 9 Sublimation experiments were carried out by the transport method. This method consists of passing a stream of an inert gas over a sample at the constant flow rate and temperature, the rate being low enough to achieve practically the saturation state of the gas with the substance vapor. Then the vapor is condensed and the sublimated quantity is determined. The vapor pressure over the sample at this temperature can be calculated from the amount of sublimated material and the volume of the inert gas used. Details of the technique are given in the literature.10 The inert gas (nitrogen) from the tank flows through a column packed with silica to adsorb a humidity from the gas. The stabilization of the gas temperature occurs in a water thermostat. The stability of the gas flow with precision better than 0.01% is realized by use of mass flow controller MKS type 1259CC-00050SU. The inert gas of constant temperature and velocity passes then to the glass tube, which is placed in the air thermostat. Three zones of the glass tube can be distinguished to perform: the starting zone for stabilizing of the inert gas; the transitional zone in which sublimation process occurs; ensuring slow sublimation of the investigated substance; the finishing zone in which the inert gas together with the sublimated substance is overheated by (4 to 5) K, controlled by platinum resistance thermometer. The determined temperature of the air thermostat is kept constant with a precision of 0.01 K by means of the temperature controller PID type 650 H UNIPAN equipped with a resistance thermometer. The finishing zone is coupled with the condenser built from glass helix, placed (outside the thermostat) located in a Dewar vessel filled with a liquid nitrogen. To avoid a humidity adsorption from the air, a condenser is connected to a vessel filled with CaCl2. The equipment was calibrated using benzoic acid. The standard value of the sublimation enthalpy obtained was ΔgcrHom = 90.5 ± 0.3 kJ·mol−1.This is in good agreement with the value recommended by IUPAC (ΔgcrHom = 89.7 ± 0.5 kJ·mol−1).11 From the experimentally determined pressure−flow rate relationship, the optimal flow rate of 1.2 to 1.8 dm3·h−1 has been revealed. Under this flow rate, the saturated vapor pressure is independent of the flow rate and, thus, the thermodynamic equilibrium is realized. The saturated vapor pressures were measured five times at each temperature with the standard deviation no more than 5 %. Because the saturated vapor pressure of the investigated compounds is low, it may be assumed that the heat capacity change of the vapor with temperature is so small that it can be neglected. The experimentally determined vapor pressure data may be described in the following way: ln(p) = A + B /T
Δcrg Smo(T ) =
Δcrg Hmo(298.15) = Δcrg Hmo(T ) + ΔHcor o = Δcrg Hmo(T ) + (0.75 + 0.15cr Cp,m )
(T − 298.15)
The enthalpy of vaporization was calculated as Δgl Hmo(298.15) = Δcrg Hmo(298.15) − Δcrl Hmo(298.15)
(6)
where enthalpy of fusion at 298.15 was calculated by the following equation Δcrl Hmo(298.15) = Δcrl Hmo(Tfus) − Δcrl Smo(Tfus)· (Tfus − 298.15)
(7)
Physico-chemical descriptors polarizability α and sum of all H-bond acceptor factors ΣCa are calculated by program HYBOT.13
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RESULTS AND DISCUSSION The objects of the investigation are eight compounds of spiroderivatives of 1,3-thiazine (Figure 1). Formulas of radical struc-
Figure 1. Molecular structure of spiro-compounds.
tures, temperatures, enthalpies, and entropies of fusion of the compound concerned are given in Table 1. All spiro-compounds have a central fragment in common and different substituents. Compound 1 with phenyl as a substituent can be used as a model compound to assess the contribution of individual groups to physicochemical properties of the substances being investigated. Compounds 2 to 4 of group I have been obtained by substituting hydrogen atom in para-position of phenyl ring by alkyl radical. Halogen atoms are introduced in the structure of compounds 6 to 8 of group II. Substituents which are available in the above two groups, namely methyl radical and chlorine atom are present in compound 5 as well. Stability and the absence of phase transitions in the compounds involved in the temperature range studied have been proved by means of DSC experiment. While making calculations, it was assumed that the molecules of the substances being investigated in a gas phase are in a monomolecular state. The experimental values saturated vapor pressure of the compounds are given in Table 2. Correlation equations describing these dependences are presented in Table 3. It is known that the nature and position of substituents in a benzene ring are critical for architecture and energy content of a crystal lattice.14
(2)
The value of the sublimation enthalpy is calculated by the Clausius−Clapeyron equation ⎛ ∂(ln p) ⎞ Δcrg Hmo(T ) = −R ⎜ ⎟ ⎝ ∂(1/T ) ⎠
(5)
(3)
whereas the sublimation entropy at the given temperature T was calculated from the following relation: 3453
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374.15 375.15 378.15 380.15 385.15 388.15 391.15 393.15 395.15 397.15 399.15 401.15 403.15 405.15 406.15 409.15 411.15 0.0108 0.0128 0.0130 0.0200 0.0279 0.0358 0.0541 0.0705 0.0769 0.0896 0.1171 0.1487 0.1855 0.2176 0.2803 0.3898 370.15 372.15 373.15 376.15 377.15 380.15 383.15 384.15 387.15 389.15 391.15 393.15 395.15 398.15 400.15 403.15 0.0495 0.0532 0.0553 0.0620 0.0735 0.0850 0.0941 0.1076 0.1185 0.1376 0.1497 0.1884 0.2215 0.2241 0.2762 0.2858 384.15 385.15 386.15 387.15 389.15 390.15 392.15 393.15 394.15 395.15 397.15 398.15 399.15 401.15 402.15 403.15 365.15 366.15 369.15 371.15 373.15 375.15 376.15 379.15 381.15 383.15 385.15 386.15 388.15 390.15 393.15 0.0345 0.0416 0.0531 0.0708 0.0822 0.1151 0.1434 0.1583 0.2134 0.2567 0.3270 0.3632 0.4631 0.6420 0.7981 366.15 367.15 370.15 372.15 374.15 376.15 377.15 380.15 382.15 384.15 386.15 387.15 390.15 392.15 394.15 0.0094 0.0129 0.0158 0.0224 0.0302 0.0366 0.0454 0.0673 0.0976 0.1314 0.1366 0.1547 0.1852 0.2336 0.3508 353.15 355.15 356.15 360.15 363.15 365.15 366.15 369.15 372.15 375.15 376.15 377.15 378.15 380.15 384.15 0.0069 0.0082 0.0101 0.0132 0.0147 0.0180 0.0239 0.0314 0.0442 0.0622 0.0634 0.0910 0.1035 0.1298 0.1351 0.1541 342.15 343.15 345.15 347.15 349.15 350.15 352.15 355.15 357.15 360.15 361.15 362.15 365.15 367.15 368.15 369.15
a
Standard uncertainty for temperature u(T) = 0.01 K; and relative standard uncertainty for pressure ur(p) = 0.05.
385.15 386.15 387.15 388.15 389.15 391.15 393.15 395.15 396.15 397.15 399.15 401.15 402.15 404.15 405.7 406.4 407.3 0.0198 0.0234 0.0321 0.0370 0.0474 0.0594 0.0714 0.0830 0.1048 0.1249 0.1533 0.1933 0.1988 0.2603 0.3364
p/Pa 4 T/K p/Pa 3 T/K p/Pa 2 T/K p/Pa 1 T/K
Table 2. Experimental Values of Sublimation Vapor Pressures for the Spiro-Compoundsa
T/K
5
p/Pa
The dependence of saturated vapor pressure on substance molecular structure was determined by the sublimation experiment. Saturated vapor pressure of spiro-compounds at 393 K diminishes and is arranged in a row 1 > 2 to 4 > 6 to 8 > 5 (Figure 2). Thermodynamic functions of sublimation: Gibbs energies, enthalpies and entropies (Table 4) have been calculated in terms of experimental data. Of special importance is the thermodynamic parameter ΔgcrGom(298.15) because it can be used to characterize the equilibrium crystal state−vapor, to estimate the nonideal character of the system, as well as to elucidate solvation effects. It has been found out that compensation effect with domination of enthalpy contributions to Gibbs energies is realized for the compounds examined. Thermodynamic functions analysis shows that it is a model compound 1 that has the lowest ΔgcrGom(298.15). Introducing alkyl substituents into benzene ring of compound 1 increases Gibbs energy values of compounds 2 to 4 as compared to number 1. Lower saturated vapor pressure values and higher Gibbs energy values of sublimation respectively seem to be associated with the growth in a molecular mass of a substance. The highest values of ΔgcrGom(298.15) are characteristic for 6 to 8 compounds with atom of halogens. Linear dependence between Gibbs energies of sublimation and fusion temperature of the substances examined ln ΔgcrGom(298.15) = 19.98 − 0.20Tfus (R = 0.9450) is demonstrated in Figure 3. Use can be made of the equation to evaluate ΔgcrGom(298.15) for the compounds with similar chemical structures in terms of fusion temperatures known. On the basis of close-to-linear correlation between enthalpies sublimation and evaporation of the compounds the conclusion can be drawn as to the similar character of intermolecular interactions both in crystal and in liquid states (Figure 4). Compounds with sterically branched substituents that do not ensure close packing of the molecule possess lower energies of intermolecular interactions. These are compounds with isopropyl radical 4, methyl group and chlorine atom 5, trifluoro-methyl radical 6 in their structure. As enthalpies of sublimation and evaporation are to a greater extent determined by intermolecular distances, higher values of the thermodynamic functions
0.0079 0.0088 0.0113 0.0122 0.0129 0.0159 0.0179 0.0205 0.0229 0.0295 0.0331 0.0340 0.0375 0.0455 0.0509 0.0534 0.0609
T/K
6
p/Pa
T/K
7
p/Pa
T/K
8
p/Pa
Table 1. Structural Formula of the Radical, Thermophysical Parameters of Fusion and the Polarizability for the Spiro-Compounds
0.0057 0.0076 0.0105 0.0135 0.0192 0.0320 0.0417 0.0550 0.0674 0.0799 0.0950 0.1235 0.1454 0.1813 0.2145 0.2770 0.3482
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Table 3. Coefficients of the Clausius−Clapeyron Equation ln p = A − B/T (R ≥ 0.9980) compound
temperature range, K
1 2 3 4 5 6 7 8
342.15−369.15 353.15−384.15 366.15−394.15 365.15−393.15 385.15−407.15 384.15−403.15 369.15−403.15 374.15−411.15
A 38.3 40.2 40.6 34.9 31.0 35.3 40.1 38.9
± ± ± ± ± ± ± ±
B 0.6 0.6 0.6 0.3 0.6 0.4 0.4 0.5
14821 15834 16098 14164 13767 14746 16512 16463
± ± ± ± ± ± ± ±
226 230 225 128 224 176 175 196
Figure 3. Correlation between the sublimation Gibbs energies ΔgcrGom(298.15) and fusion temperature Tfus..
Figure 2. Plot of vapor pressure ln(p/Pa) against reciprocal temperature for the spiro-compounds.
of substances with methyl 2, ethyl 3 groups, atoms of chlorine 7 and bromine 8 make it possible to form a more packed crystal lattice with less volume structure of the substitutes. A model compound with its unsubstituted phenyl radical stands midway between these two groups. This latter fact means the possibility of altering intermolecular interactions of the compound under investigation by introducing substituents of a definite structure. While searching for the relation between the structure of spiro-compounds and energy of sublimation, we used physicochemical descriptors. The Gibbs energy of sublimation correlates with molecular polarizability of alkyl- and halogen-substituted spiro-compounds given in Figure 5, polarizability mainly acting as a surrogate for molecular size.15 Energy of dispersion interaction is known to be determined in terms of the values of electron polarizability and van der Waals’ radii of contacting molecules. In view of this fact, one can arrive to the conclusion that it is
Figure 4. Enthalpy of vaporization Δgl Hom(298.15) versus enthalpy of sublimation ΔgcrHom(298.15).
dispersion interaction which makes the greatest contribution to Gibbs energy of sublimation. Branching of the substituents chain of compounds 4 and 6 causes ΔgcrGom(298.15) values to drop because of the decrease in the intermolecular distance. Compound 5 with methyl radical and chlorine atom as the second substituent in benzene ring naturally stands midway between correlation straight lines of the first and second group of compounds. Figure 6 shows correlations between Gibbs energies of sublimation and total indexes of acceptor capability of all the atoms present in the molecules of the substances under study to form
Table 4. Thermodynamic Characteristics of Sublimation for Spiro-Compounds compound 1 2 3 4 5 6 7 8 a
ΔgcrGom(298.15)
ΔgcrHom(T)
o crCp,m
ΔgcrGom(298.15)
ΔgcrSom(298.15)
Δgl Hom(298.15)
kJ·mol−1
kJ·mol−1
J·mol−1
kJ·mol−1
J·mol−1·K−1
kJ·mol−1
56.8 60.6 61.7 59.7 66.2 62.5 66.4 68.9
± ± ± ± ± ± ± ±
1.9 1.7 1.8 0.6 0.9 1.1 0.7 0.8
123.2 131.6 138.3 117.8 114.5 122.6 137.3 136.8
± ± ± ± ± ± ± ±
1.9 1.9 1.8 1.1 1.8 1.4 1.4 1.6
307.7 344.3 371.2 408.2 373.0 409.5 336.4 340.1
125.9 136.8 138.3 122.8 120.1 128.5 141.7 141.6
± ± ± ± ± ± ± ±
1.9 1.9 1.8 1.1 1.8 1.4 1.4 1.6
231.7 255.7 257.0 211.6 180.9 221.4 252.6 243.7
± ± ± ± ± ± ± ±
8 9 9 6 6 7 8 7
109.2 114.8 120.2 101.7 96.6 105.3 113.0 112.1
ςH/%a ςTS/%b 64.5 64.2 64.4 66.1 70.9 66.1 65.2 66.1
35.5 35.8 35.6 33.9 29.1 33.9 34.7 33.9
ςH = (ΔgcrGom(298.15)/(ΔgcrHom(298.15) + TΔgcrSom(298.15))·100%. bςTS = TΔgcrSom(298.15)/(ΔgcrHom(298.15) + TΔgcrSom(298.15))·100%. 3455
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pressure and fusion temperature of these compounds was obtained. The sublimation thermodynamic functions of the studied spiro-derivatives were calculated. The influence of both alkyl substituents (methyl-, ethyl-, and isopropyl ones) and halogen atoms (chlorine, bromine, and fluorine) on the sublimation behavior of these compounds was investigated. The compensation effect for the sublimation process is stated, the enthalpy factor being a main contribution into the Gibbs energy. Correlations between the Gibbs energy and the polarizability as well as the Gibbs energy and the spiro-compounds ability to form hydrogen bonds were revealed.
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AUTHOR INFORMATION
Corresponding Author
*Phone: 7 (4932)351545. Fax: 7(4932)336246. E-mail: svb@ isc-ras.ru. Figure 5. Correlation between the sublimation Gibbs energies ΔgcrGom(298.15) and the polarizability α.
Funding
This work was supported by Grant No. 12-03-00019-a, BioSol Project No. 2010-1.1-234-069, and the Federal Programme for Science and Innovation No. 02.740.11.0857. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Kitaigorodski, A. I. Molecular Crystals and Molecules; Academic Press: New York, 1973. (2) Handbook of thermal analysis and calorimetry; Brown, M. E., Gallagher, P. K., Eds.; Elsevier: Amsterdam, 2008. (3) Solid State Characterization of Pharmaceuticals; Storey, R. A., Ymen, I., Eds.; Wiley, Blackwell: London, 2011. (4) Ali, M. A.; Ismail, R.; Choon, T. S.; Yoon, Y. K.; Wei, A. C.; Pandian, S.; Kumar, R. S.; Osman, H.; Manogaran, E. Substituted spiro [2.3′] oxindolespiro [3.2″]-5,6-dimethoxy-indane-1″-one-pyrrolidine analogue as inhibitors of acetylcholinesterase. Bioorg. Med. Chem. Lett. 2010, 20, 7064−7066. (5) Ito, Y.; Takuma, K.; Mizoguchi, H.; Nagai, T.; Yamada, K. A novel azaindolizinone derivative ZSET1446 (spiro[imidazo[1,2-a]pyridine-3,2-indan]-2(3H)-one) improves methamphetamine-induced impairment of recognition memory in mice by activating extracellular signal-regulated kinase 1/2. J. Pharmacol. Exp. Ther. 2007, 320, 819− 827. (6) Yamagishi, M.; Yamada, Y.; Ozaki, K.; Asao, M.; Shimizu, R.; Suzuki, M.; Matsumoto, M.; Matsuoka, Y.; Matsumoto, K. Biological activities and quantitative structure-activity relationships of spiro[imidazolidine-4,4′(1′H)-quinazoline]-2,2′,5(3′H)-triones as aldose reductase inhibitors. J. Med. Chem. 1992, 35, 2085−2094. (7) Rama, R. N. Principles of Organic Medicinal Chemistry; New Age International: New Delhi, 2005; pp 3−31. (8) Proshin, A. N.; Serkov, I. V.; Petrova, L. N.; Bachurin, S. O. New isothiourea spiro-derivatives in a number of the 1,3-thiazine. Russ. Chem. Bull. 2011, 11, 1−2. (9) Dannenfelser, R. M.; Yalkowsky, S. H. Predicting the Total Entropy of Melting: Application to Pharmaceuticals and Environmentally Relevant Compounds. J. Pharm. Sci. 1999, 88, 722−724. (10) Zielenkiewicz, W.; Perlovich, G.; Wszelaka-Rylik, M. The vapor pressure and the enthalpy of sublimation. Determination by inert gas flow method. Therm. Anal. Calorim 1999, 57, 225−234. (11) Cox, J. D.; Pilcher, G. Thermochemistry of organic and organometallic compounds; Academic Press: London, 1970. (12) Chickos, J. S.; Acree, W. E. Enthalpies of Sublimation of Organic and Organometallic Compounds. J. Phys. Chem. Ref. Data 2002, 2, 537−698. (13) Raevsky, O. A.; Grigor’ev, V. J.; Trepalin, S. V. HYBOT program package, Registration by Russian State Patent Agency No. 990090 of 26.02.99.
Figure 6. Correlation between the sublimation Gibbs energies ΔgcrGom(298.15) and the sum of H-bond acceptor factors ΣCa.
hydrogen bonds ΣCa. The first curve of those presented in Figure 6 represents an increment in Gibbs energy as a function of a change in alkyl radical structure; the second one, as a function of adding halogen atom. Compound 5 stands midway between these two curves and hence indicates the additive character of contributions of energies of intermolecular interaction of individual functional groups. The experiment showed that the substitution of the hydrogen atom by an alkyl radical in the benzene ring of compound 1 results in increasing the Gibbs energy of sublimation within the limits of one correlation dependence. Electronegative halogen atoms of the second group of compounds initiate greater hydrogen bond basicity and, as a rule, greater dipole moment of the molecules At close descriptor values ΣCa Gibbs energies of sublimation of these compounds are considerably higher as compared to a model analogue 1 and alkylderivatives. This fact shows the possibility of forming specific intermolecular bonds.
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CONCLUSIONS The saturated vapor pressure of eight new drug-like 1,3-thiazine spiro-derivatives was measured by the transport method with an inert gas as a carrier within in the temperature range of (342.15 to 411.15) K. The fusion was studied by the DSC technique. The linear correlation between the saturated vapor 3456
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(14) Stephenson, R. M., Malanowski, S. Handbook of the Thermodynamics of Organic Compounds; Elsevier: New York, 1987. (15) Perlovich, G. L.; Raevsky, O. A. Sublimation of Molecular Crystals: Prediction of Sublimation Functions of on Basis on HYBOT Physicochemical Descriptors and Structural Clusterisation. Cryst. Growth Des. 2010, 10, 2707−2712.
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