Lattice-energy calculations in the atom-atom potential
approach have been performed for observed and
isostructurally derived hypothetical forms of phenothiazine and phenoselenazine compounds. Energy
minimizations with respect to cell constants and
molecular rigid-body coordinates lead to absolute
minima of energy surfaces in all cases. The experimental
values of cell constants for the three observed structures are reproduced to better than 5%
and the shifts of positional and orientational molecular
parameters are lower than 0.1 A and 2 °, respectivel

Conde Amiano, Alejandro

Estrada de Oya, María Dolores

Márquez Delgado, Rafael

idUS. Depósito de Investigación Universidad de Sevilla

T. M. KRYGOWSKI, R. ANULEWICZ AND J. KRUSZEWSKI 739 BOER, J. L. DE & VOS, A. (1968b). Acta Cryst. B24, 720-725. BOER, J. L. DE & VOS, A. (1972a). Acta Cryst. B28, 835-839. BOER, J. L. DE & VOS, A. (1972b). Acta Cryst. B28, 839-848. BOLHUIS, F. VAN & KIERS, C. T. (1978). Acta Cryst. B34, 1015-1016. BRESLOW, R. (1964). Mechanisms of Organic Reactions. New York: John Wiley. BURNS, D. M. & IBALL, J. (1960). Proc. R. Soc. London Set. A, 257, 491-514. CAMERMAN, A. & TROTTER, J. (1964). Proc. R. Soc. London Ser. A, 279, 129-146. CHARBONNEAU, G. P. & DELUGEARD, Y. (1977). Acta Cryst. B33, 1586-1588. COULSON, C. A. (1961). Valence, 2nd ed., ch. 7. Oxford Univ. Press. Cox, E. G., CRUICKSHANK, D. W. J. & SMITH, J. A. S. (1958). Proc. Soc. London Ser. A, 247, 1-2 I. DEWAR, M. J. S. (1969). The Molecular Orbital Theory of Organic Chemistry. New York: McGraw-Hill. ELVIDGE, J. A. & JACKMAN, L. M. (1961). J. Chem. Soc. 8, 859-866. FALLON, L., AMMON, H. L., ANDERSON, A. G. JR, CURRIE, J. O. & LABAR, R. A. (1974). Acta Cryst. B30, 531-533. FERRARIS, G., JONES, D. W. & YERKESS, J. (1973). Z. Kristallogr. 138, 113-128. FLANDROIS, S. & CHASSEAU, D. (1977). Acta Cryst. B33, 2744-2750. FmTCHm, CH. & ARTHUR, R. (1966). Acta Cryst. 21, 139-145. HANSON, A. W. (1965). Acta Cryst. 19, 610-613. HANSON, A. W. (1968). Acta Cryst. B24, 768-778. HAZELL, A. C., LARSEN, F. K. & LEHMANN, M. S. (1972). Acta Cryst. B28, 2977-2984. HAZELL, A. C. & PAWLEY, G. S. (1973). Z. Kristallogr. 137, 159-172. HESS, B. A. & SCHAAD, L. J. (1971a). J. Am. Chem. Soc. 93, 305-310. HEss, B. A. & SCHAAD, L. J. (1971b). J. Org. Chem. 36, 3418-3423. IKEMOTO, I. (1979). A cta Cryst. B35, 2264-2265. JULG, A. (1971). Aromaticity, Pseudoaromaticity and Anti- aromatic#y, edited by E. D. BERGMANN & B. PULLMAN, pp. 383--385. New York: Academic Press. JULG, A. & FRAN(~OIS, P. (1967). Theor. Chim. Acta, 7, 249-259. KAI, Y., HAMA, F., YASUOKA, N. & KASAI, N. (1978). Acta Cryst. B34, 1263-1270. KAY, M., OKAYA, Y. & Cox, D. E. (1971). Acta Cryst. B27, 26- 33. KIMMA, K. & KUBO, M. (1959). J. Chem. Phys. 30, 151-158. Kot, rso, M., ISHn, T. & SAn'O, Y. (1977). Acta Cryst. 1333, 763-770. KRUSZEWSKI, J. & KRYGOWSKI, T. M. (1972). Tetrahedron Left. pp. 3839-3842. KRUSZEWSKI, J. & KRYGOWSKI, T. M. (1975). Can. J. Chem. pp. 945-951. KRYGOWSKI, T. M. & WII~CKOWSKI, T. (1981). Croat. Chim. Acta, 54, 193-202. KUCHITSU, K. (1968). J. Chem. Phys. 49, 4456-4462. KUCHITSU, K., FUKUYAMA, T. & MORIMO, Y. (1969). J. Mol. Struct. 4, 41-50. KVESETH, K., SLIP, R. & KOHL, D. A. (1980). Acta Chem. Scand. Ser. A, 34, 31-42. LEHMANN, M. S. & PAWLEY, G. S. (1972). Acta Chem. Scand. 26, 1996-2004. LONG, R. E., SPARKS, R. A. & TRUEBLOOD, K. N. (1965). Acta Cryst. 18, 932-939. MAARTMANN-MOE, K. (1966). A cta Cryst. 21, 979-982. MORSSINK, H. & VAN BODEGOM, 13. (1981). Acta Cryst. B37, 107-114. OHASm, Y., IWASAKI, H. & SAITO, Y. (1967). Bull. Chem. Soe. Jpn, 40, 1789-1796. PENN, R. E. (1978). J. Mol. Speetrosc. 69, 373-382. PONOMAREV, V. I., FmIPENKO, O. S. & ATOVMVAN, L. O. (1976). Kristallografiya, 21,392-394. PULAY, P. & T6R6K, F. (1975). J. Mol. Struct. 29, 239-246. RANDI6, M. (1977). Tetrahedron, 33, 1905-1920. SEHERS, H. & BOGGS, J. F. (1981). J. Mol. Struct. 74, 137-142. SHIMANOUCHI, H., ASHIDA, T., SASADA, Y., MURATA, I. & KITAHARA, Y. (1966). Bull. Chem. Soc. Jpn, 39, 2322-2331. SHIMANOUCHI, H., SASADA, Y., KABUTO, C. & KITAHARA, Y. (1974). Acta Cryst. B30, 1273-1277. SONDHEIMER, F. (1964). Pure Appl. Chem. 7, 363-407. STOICHEFF, B. P. (1958). Can. J. Phys. 36, 218. TAMAGAWA, K., hJIMg, T. & KIMMA, K. (1976). J. Mol. Struct. 30, 243-253. THOMAS, R. & COPPENS, P. (1972). Acta Cryst. B28, 1800-1806. TROTTER, J. (1960). Acta Cryst. 13, 86-95. WAL, R. VAN DER & VAN BODEGOM, B. (1979). Acta Cryst. B35, 2003-2008. WII~CKOWSKI, T. & KRYGOWSKI, T. M. (1981). Can. J. Chem. 59, 1622-1629. WINTER, W. & BUTTERS, T. (1981). Acta Cryst. B37, 1524-1527. Acta Cryst. (1983). B39, 739-742 Lattice-Energy Calculations on Phenothiazine and Phenoselenazine Modifications BY M. D. ESTRADA, A. CONDE AND R. MARQUEZ Departamento de Optica, Facultad de Ffsica, Universidad e Sevilla, Spain (Received 18 April 1983; accepted 13 July 1983) Abstract Lattice-energy calculations in the atom-atom potential approach have been performed for observed and isostructurally derived hypothetical forms of pheno- 0108-7681/83/060739-04501.50 thiazine and phenoselenazine compounds. Energy minimizations with respect to cell constants and molecular rigid-body coordinates lead to absolute minima of energy surfaces in all cases. The ex- perimental values of cell constants for the three © 1983 International Union of Crystallography 740 PHENOTHIAZINE AND PHENOSELENAZINE MODIFICATIONS observed structures are reproduced to better than 5% and the shifts of positional and orientational molecular parameters are lower than 0.1 A and 2 °, respectively. Introduction Packing analyses within the atom-atom approach ave been carried out for a number of hydrocarbons with largely satisfying results but the method is also reasonably valid, as shown in the literature, for other organic molecules containing atoms other than C and H, especially when these atoms are partially screened by C and H. In a previous work (Villares, Jim+nez-Garay, Conde & Mhrquez, 1976) we successfully applied molec- ular-packing analysis for the determination of the then unknown crystal structure of phenoselenazine. We also modeled (Benavente, Conde & M/trquez, 1975) the crystal packing of 3,7-dichlorophenoselenazine - the cell constants and molecular position and orientation, which had been found experimentally (Bernier, Conde & M~.rquez, 1974), were well reproduced after energy minimization. In this paper we discuss the results of the van der Waals energy calculations performed for pheno- thiazine and phenoselenazine crystals. Molecules with a 'hollow' in the middle are not, as a consequence, very convenient for packing and several polymorphous modifications are encountered. For example, five acridine modifications (Phillips, 1954; Herbstein & Schmidt, 1955) and two polymorphous phenazines (Herbstein & Schmidt, 1955) have been reported. For phenothiazine a monoclinic (space group P21) form was studied (Bell, Blount, Briscoe & Freeman, 1968; Freeman, 1979) and then an orthorhombic (space group Pnma) modification was reported (McDowell, 1976). For phenoselenazine only an orthorhombic (space group P212121) form is known (Villares, Jim~nez-Garay, Conde & M/lrquez, 1976). In view of molecular similarities lattice-energy calculations were carried out for the observed and also for the iso- structural derived forms of both compounds. From the calculations it should be possible to establish whether or not hypothetical polymorphous varieties could be formed. Comparison between lattice energies calculated for the two compounds in the different space groups should also give information about the extent o which homologous molecules within a family of the Periodic Table can be expected to form isostructural crystals. Description of the calculation Lattice-energy calculations in the atom-atom potential approach were performed using the computer program PCK6 (Williams, 1972b). In this program the energy is taken as the sum of pairwise interactions between non-bonded atoms, using a Buckingham form ~0 = -A i r  6 + B exp[-Cr] for the potential functions describing interactions between pairs. Truncation er- rors in the van der Waals contributions are virtually eliminated by use of the Ewald-Bertaut-Williams technique for accelerated convergence (Bertaut, 1952; Williams, 1971). A limit of 6 A was set to ensure convergence to 0.1 kJ mo1-1 and some attempts with a larger sphere of interactions showed no influence on the location of energy minima. The program allows for minimization of the energy with respect to the structural parameters, that is, the cell constants and rigid-body positions and orientations. Potential-function parameters assuming the atoms to be electrically neutral were used. Coefficients fitted by Williams (1972a) for the C and H atoms and by Govers (1975) for the N atom were selected. For the S. . .S  interactions potential parameters were taken from Rinaldi & Pawley (1973), and for the Se.. .Se interactions parameters proposed by Govers (1979) were used. For mixed interactions the geometric-mean combining law was used for coefficients A and C, while B was fitted to give the minimum of the potential function at the sum of the respective van der Waals radii. All parameters used are listed in Table 1. Lattice-energy calculations were made for all three (P21, P21212 ~ and Pnma) forms, either observed or hypothetical structures, of phenothiazine and pheno- selenazine compounds. Intermolecular-energy minimi- zations were performed with respect to the cell constants and molecular rigid-body parameters. In P21, the position of the origin along the y axis being undetermined, there are nine independent variables to be minimized while in Pnma, because of the special positions of the molecules in the cell, only two translational nd one rotational degree of freedom exist and, therefore, there are only six independent variables for this space group. Table 1. Non-bonded potential-function parameters The energy is in kJ too l -  z if r is in A. Interact ion A B (× 103) C H . . .H  101.95 9.07 3.74 C . . .H  467.41 35.54 3-67 C. • • C 2143.04 300.05 3.60 N . . .H  569.10 25.73 3.67 N. • • C 2609.20 217.29 3.60 N . . .  N 3176.80 440.57 3.60 S . . .H  712.42 12.22 3.24 S . . .  C 3266.32 86.22 3.17 S . . .N  3976.85 86.83 3.17 S . . .  S 4978.38 42.22 2-80 Se. . -  H 1083.93 50.59 3-54 Se. . .  C 4969.60 434.38 3-47 Se. . .  N 6050.64 415.07 3-47 Se. . .  Se 11524.26 345.40 3.34 M. D. ESTRADA, A. CONDE AND R. M,~RQUEZ 741 Of the six structures for which calculations were made, only three are known experimentally. For the known structures the initial cell constants and molec- ular position and orientation were those experi- mentally found; published coordinates for non-hydro- gen atoms were used but H-atom positions were calculated for the expected geometry (Williams, 1965). For the hypothetical crystals, initial cell constants were the experimental values for the respective isostructural crystal and starting models were generated by using a grid for molecular translations and rotations according to the Cheshire group (Hirshfeld, 1968). The atomic coordinates of the trial model were calculated from values of bond lengths and angles, the dihedral angle value being that observed for experimental structures. There seems (Marsau, 1972) to be no packing influence to force the dihedral angle between the two halves of the molecule to differ from its intrinsic value, resulting from intramolecular interactions, o it seems that the degree of molecular folding in the crystals is close to that of the free molecules. Results and discussion Results of energy minimization for the observed structures are compared with the experimental data in Table 2. The molecular position and orientation are described by the centre-of-mass coordinates (x,y,z) and by Euler angles (0,~0,~) which move (except for translation) the internal Cartesian coordinate system (inertia axes of the molecule) with respect o the fixed external Cartesian coordinate system based on the crystal axes. The difference between the experimental and calculated atomic coordinates i expressed as ~ = (Y,I,N "-'i,N" ~A2/aAron/2, J , where A i is the difference in the ith Cartesian coordinate of each of the N atoms of the molecule (Zugenmaier & Sarko, 1972). Experimental values of the cell constants for the three observed structures are reproduced to better than 5%. Only the c parameter in the Pnma form of phenothiazine shows a shift of 8%. In all cases calculated parameters are smaller than those observed. Since vibrational effects are ignored in the calculations reported herein, the unit cells measured at room temperature should contract during energy minimi- zation. Agreement between the observed and cal- culated structure can be expressed by the shifts of the positional and orientational molecular parameters which are lower than 0.1 ,/k and 2 °, respectively, in all cases. As a function of observed and calculated atomic coordinates, the agreement factor ~ is in the range 1-2%. Another measurement of the agreement be- tween the observed structure and the minimum of the potential-energy surface is based on an examination of the second derivatives of the energy evaluated at the point, on the energy surface, corresponding to the experimentally determined crystal structure. If the fit is good, all the eigenvalues of the matrix of the second derivatives will be positive (Williams, 1972a); that is, the experimental structure will be within the range of curvature of the calculated minimum. Such was the case for all the minimizations reported in this work. For the hypothetical modifications, tarting from the structural model described above, the energy was minimized by varying simultaneously the cell con- stants and the molecular degrees of freedom. The results are summarized in Table 3 in a way similar to that used for the observed forms. Lattice-energy maps show that the calculated structures correspond to real minima of the multidimensional energy surface. Table 2. Results of the energy minimization for observed structures Phenothiazine Phenoselenazine P21 Pnma P21212 l obs. calc. obs. calc. obs. calc. Cell a (~,) 7.82 (3) 7.57 b (A) 5.93 (1) 5.59 c (A) 10.70 (8) 10.58 #(o)  105.99" 106.6 V (,~3) 470.0 429.0 ¢ 0.017 K , 0.67 0.73 Molecular coordinates x -0.25 -0.29 y x 1.82 1.84 3.11 3.09 z 8( ° ) 97.0 98.4 to (o) 146.7 145.6 ~,(o) 25-3 22.3 E (kJ tool -l) -96.1 7.916 (10) 7-77 20.974 (10) 20.39 5.894 (10) 5.43 978.6 860.3 0.015 0.64 0.73 2.33 2.19 5.24 5.10 0.04 0.08 146.5 146.5 -94-8 7.829 (5) 7.62 20.909 (4) 20.55 5.927 (7) 5.93 970.2 928.6 0.006 0-68 0.71 2.23 2.14 3.14 3.09 2-29 2-30 142-5 143.6 93-8 92.3 108.2 110.0 -96.4 * In the paper of Bell et al. (1968) fl = 74.01 ° is given. 742 PHENOTHIAZINE AND PHENOSELENAZINE MODIFICATIONS Table 3. Results of the energy minimization for hypo- thetical structures Phenothiazine Phenoselenazine P21212 ! P21 Pnma Cell a (A) 7-30 7.87 8.59 b (/k) 20.91 6.07 19.65 c (/k) 5.69 10.33 5.85 fl (o) 105.99 V(,~, 3) 868.5 474.4 987.4 K 0-72 0.69 0.66 Molecular coordinates x 2.50 -1.06 2.22 y 3.18 1.97 4.91 z 1.96 1.74 0.02 O(°) 149.6 93.6 144.5 ~(o) 88.2 159.2 ~(o) 109.2 27.9 E (kJ mol -l) -93.3 -90.3 -81.2 In terms of the 'coefficient of molecular packing' (Kitaigorodsky, 1961): K = ZVo/V, where V is the cell volume and Z the number of molecules of V o volume in the cell, values obtained in all cases - observed and hypothetical forms - are in the range 0.6 to 0.8, characteristic of aromatics. If we consider calculated structures resulting from the minimization process, for phenothiazine the value of K = 0.73 is the same for the two observed forms; this result agrees with the hypothesis of close packing (Kitaigorodsky, 196 I) and indicates that the packing density has major effects on the energy of the crystal structure. On the other hand, the value K = 0.72 for the hypothetical P21212 l structure shows no significant difference with respect to the value for the observed forms. For phenoselenazine a value K = 0.71 for the observed form is found, similar to the K value obtained for phenothiazine, ascorresponds to similar molecules. In this case, smaller values of K are found for hypothetical forms (K = 0.69 for P21 and K = 0.66 for Pnma), in agreement with the rule that the densest mode of packing is that which actually occurs. Within the limits of the approximate nature of the atom-atom approach and the validity of the potential functions used to describe the pair interactions, we think that the results obtained for density-packing coefficients and estimated lattice energies could indi- cate a higher probability of existence for the P212121 form of phenothiazine and for the P21 form of phenoselenazine. In spite of the errors in E introduced by the summation limits which amount o several per cent (Williams, 1971), the energy calculated for the Pnma form of phenoselenazine is higher than that for the other forms. However, these calculations cannot imply, in our opinion, the non-existence of this form of phenoselenazine. On the other hand, the form Pnma is that experimentally found for dichlorophenoselena- zine. References BELL, J. D., BLOUNT, J. F., BRISCOE, O. V. & FREEMAN, H. C. (1968). Chem. Commun. pp. 1656-1657. BENAVENTE, J., CONDE, A. & MARQUEZ, R. (1975). Unpublished work. Univ. de SeviUa. BERNIER, F., CONDE, A. & MARQUEZ, R. (1974). Acta Cryst. B30, 1332-1335. BERTAUT, F. (1952). J. Phys. Radium, 13, 499-505. FREEMAN, H. C. (I 979). Private communication. GOVERS, H. A. J. (1975). Acta Cryst. A31, 380-385. GOVERS, H. A. J. (1979). Acta Cryst. A35, 236-239. HERBSTEIN, F. H. & SCHMIDT, G. M. J. (1955). Acta Cryst. 8, 399-405. HIRSHFELD, F. L. (1968). Acta Cryst. A24, 301-311. KITAIGORODSKY, A. I. ( 1961). Organic Chemical Crystallography. New York: Consultants Bureau. McDOWELL, J. J. H. (1976). Acta Cryst. B32, 5-10. MARSAtJ, P. (1972). Thesis. Univ. de Bordeaux I. PHILLIPS, D. C. (1954). Acta Cryst. 7, 649. RINALDt, R. P. & PAWLEY, G. S. (1973). Nuovo Cimento B, 16, 55-62. VILLARES, P., JIMI~NEZ-GARAY, R., CONDE, A. & MARQUEZ, R. (1976). Acta Cryst. B32, 2293-2296. WILLIAMS, D. E. (1965). J. Chem. Phys. 43, 4424-4426. WILLIAMS, D. E. (1971). Acta Cryst. A27, 452-455. WILLIAMS, D. E. (1972a). Acta Cryst. A28, 84-88. WILLIAMS, D. E. (1972b). Acta Cryst. A28, 629-635. ZUGENMAIER, P. • SARKO, A. (1972). Acta Cryst. B28, 3158- 3166. 

Acta Crystallographica Section B Structural Science

Lattice-Energy Calculations on Phenothiazine and Phenoselenazine Modifications

https://idus.us.es/xmlui/bitstream/handle/11441/67705/Lattice-Energy%20Calculations%20on%20Phenothiazine.pdf?sequence=1&isAllowed=y

Lattice-Energy Calculations on Phenothiazine and Phenoselenazine Modifications

Abstract

Similar works

Full text

Available Versions

idUS. Depósito de Investigación Universidad de Sevilla