-
The Journal of Physical Chemistry, Vol. 83, No. 21, 1979
MO Calculations for Glycine Crystals
V,, and V3of 1.15, 3.13, and 0.85 kcal/mol, respectively. As with fluoroglyoxal,the Vzterm is the dominant one but the V1 term is significantly larger, suggesting a greater degree of steric hindrance in the cis conformer of chloroglyoxal than in the trans conformer. The ordering of the highest occupied molecular orbitals in chloroglyoxal (Table VII) is significantly different from that in fluoroglyoxal (Table IV). As with fluoroglyoxal, the highest occupied orbital is a nonbonding, in-plane orbital associated primarily with the oxygen but having significant halogen p character and hydrogen 1s character. However, while the second highest occupied orbital in fluoroglyoxal is clearly of T character (aC0,aCC*, aCF), the equivalent orbital in chloroglyoxal is almost entirely chlorine 3p, and should be classified as nonbonding. The third highest occupied orbital, which is in fluoroglyoxal predominantly oxygen in-plane nonbonding, is in chloroglyoxal a chlorine 3p in-plane nonbonding orbital. The next two molecular orbitals of chloroglyoxal are, in order of increasing Koopman's theorem ionization potential, an oxygen, in-plane, nonbonding orbital and a T orbital essentially equivalent to the second highest orbital in fluoroglyoxal. These results would indicate that, unlike fluoroglyoxal, the oxalyl halide^,^ glyoxal,3 and biacety1,'O there is little likelihood of finding a a* electronic
-
transitions among the n
2785
a* transitions of chloroglyoxal.
References and Notes (1) J. C. D. Brand, Trans. Faraday Soc., 50, 431 (1954). (2) G. N. Currie and D. A. Ramsay, Can. J . Phys., 49, 317 (1971); J. R. Durig, C. C. Tong, and Y. S. Li, J. Chem. Phys., 57, 4425 (1972). (3) C. E. Dykstra and H. F. Schaefer, J. Am. Chem. Soc., 97, 7210 (1975). (4) J. R. Durig, S. C. Brown, and S. E. Hannum, J. Chem. Phys., 54, 4428 (1971). (5) J. Tyrrell, J. Am. Chem. Soc., 98, 5456 (1976). (6) J. Goubeau and M. Adelhelm, Spectrochim. Acta, Part A , 28a, 2471 (1972). (7) J. R. Durig and S. E. Hannum, J. Chem. Phys., 52, 6089 (1970). (8) K. Hagen and K. Hedberg, J. Am. Chem. Soc., 95, 1003 (1973). (9) K. Hagen and K. Hedberg, J. Am. Chem. Soc., 95, 8266 (1973). (10) J. Tyrrell, J. Am. Chem. SOC., 101, 3766 (1979). (1 1) C. E. Dyllick-Brenzinger and A. Bauder, Chem. Phys., 30, 147 (1978). (12) R. R. Lucchese and H. F. Schaefer, J. Chem. Phys., 68, 769 (1978). (13) M. J. Dewar, H. Metiu, P. J. Student, A. Brown, R. C. Bingham, D. H. Lo, C. A. Ramsden, H. Kollmar, P. Weiner, and P. K. Bischof, ~ ~ 3 1general 3 , IBM version, modified by M. L. Olson and J. F. Chiang, QCPE No. 309, Quantum Chemistry Program Exchange, Indiana University, Bloomington, Ind. (14) W. J. Hehre, W. A. Lathon, R. Ditchfield, M. D. Newton, and J. A. Pople, GAUSSIAN 70, QCPE No. 236, Quantum Chemistry Program Exchange, Indlana University, Bloomington, Ind. (15) E. Clementi, J. Mehl, and H. Popkie, "IBMOL 5A User's Guide", IBM Research Laboratory, San Jose, Calif. (16) S. Huzinaga and Y. Sakai, J . Chem. Phys., 50, 1371 (1969). (17) R. F. Miller and R. F. Curl, J. Chem. Phys., 34, 1847 (1961). (18) 0. Gropen and H. M. Seip, Chem. Phys. Lett., 11, 445 (1971).
Molecular Orbital Calculations for Glycine Crystals Z. Latajka and H. Ratalczak" Institute of Chemistry, University of Wroclaw, F. Joliot-Curie 14, 50-383 Wroclaw, Poland (Received January 29, 1979)
The Bacon-Santry perturbation method in CNDO approximation has been employed to study three-dimensional glycine crystals in a , 0, and y forms. It is found that the a-glycine crystal is more stable by about of 6.9 kcal mol-' than the P-glycine crystal and about 8.8 kcal mol-l more stable than the y-glycine crystal. The change of molecular properties in the gas phase monomer and in crystals has been discussed.
Introduction As a simple a-amino acid, glycine has the priviledged role of a model compound in quantum biochemistry. As the very simplest molecule which will form a peptide bond, it is of great interest in terms of understanding the electronic and conformational structure of proteins. Glycine is known to exist in a variety of forms, depending on its environment. In the isolated state it exists in the canonical form, H,NCH2COOH.1-3 In solution, the glycine molecule is well known to exist as the zwitterion, H3N+CH2COO-,at biological pH, and as glycinium ion, H3N+CHzCOOH,at low pH, while in the solid state it takes on variety of structures. Glycine itself in the crystalline state exists in three polymorphic forms. The ordinary state, a, crystallizes readily by slow evaporation of neutral solution^.^^^ The P form crystallizes by adding ethyl alcohol to a concentrated aqueous solution of glycines6Crystals of the P form readily transform into the a form in moist air. The third form, y-glycine, crystallizes by slow cooling of aqueous solutions of glycine made acidic with acetic acid.' Moreover, the y form is also obtainable by appropriate treatment of the 6 form with water. The crystal of yglycine shows a marked piezoelectric property along the c axis.4 0022-365417912083-2785$01 .OO/O
Recently, Bacon and Santry8-lodeveloped a SCF perturbation theory for molecular crystals based on localized orbitals of the molecules in the unit cell. The CNDO version of this method was applied by Santry et al. to the studies of three-dimensional crystals of HF,1° ice,12-14and urea.16 The total energies of unit cells and the geometry of the molecules in the crystals were reproduced satisfactorily in these calculations. However, recently Santryl1J6 has shown that this method in the CNDO/2 approximation has a tendency to predict nonpolar lattice structures to be more stable than polar ones for simple hydrogen bonded crystals. In the present paper we have reported the studies of the three-dimensional glycine crystals in a , 0, and y forms by using the Bacon-Santry perturbation method in the CNDO approximation.
Method of Calculation A general formalism of the Bacon-Santry perturbation method for the evaluation of molecular crystals has been given in the original paper,a1o so that we mention here only a few essential points. In this method the crystal energy per molecule was expressed as the sum of five terms: Wcrys = W m o l + Welec + Wpolarizn + Wintermol + Wintramol 0 1979 American Chemical Society
2786
The Journal of Physical Chemistry, Vol. 83, No. 21, 1979
Z. Latajka and H. Ratajczak
TABLE I: Fractional Atomic Coordinates ( A ) Assumed in the Calculations on Glycine Crystals a-glycine NH,' HI H2 H, CH2 H'l
H5 CI c 2
N 01 0 2
0-glycine
y -glycine
X
Y
z
X
Y
z
X
Y
z
0.2897 0.4945 0.2993 0.0769 -0.1332 0.0750 0.0647 0.3012 0.3049 -0.1472
0.1004 0.1193 0.0056 0.2344 0.1144 0.1249 0.1448 0.0898 0.0944 0.1415
-0.4541 -0.1318 -0.2261 -0.2432 -0.3572 0.0662 -0.2131 -0.2590 0.2354 0.1071
0.540 0.340 0.337 0.125 -0,091 0.1378 0.1145 0.3522 0.3772 -0.0896
0.012 -0.031 -0.203 0.241 0.008 0.0532 0.0719 -0.0440 0.0270 0.0773
-0.135 -0.449 -0.216 -0,274 -0.362 0.0633 -0.2265 - 0.2619 0.2420 0.0970
0.248 0.274 0.084 0.567 0.369 0.3929 0.4010 0.2414 0.2325 0.5425
0.013 0.183 -0.079 0.089 -0.186 0.0012 -0.0222 0.0263 0.0083 0.0011
0.686 0.458 0.441 0.446 0.427 0.1033 0.3794 0.5035 0.0139 -0.0150
TABLE I1 : Calculated and Experimental Unit Cell Dimensions for Glycine Crystals
a-glycine 0-glycine y-glycine
space group P2,/n P2, ~ 3 ;
b,
a, A
Z 4
2 3
calcd 5.126 5.099 7.076
expt 5.105 5.077 7.037
calcd 11.993 6.289 7.073
Wmolis the zero-order energy of the reference molecule, including nuclear repulsion, calculated from the molecular geometry assumed for the purpose of the crystal calculation. Welecis the energy of the electrostatic interaction between the zero order net atomic charge densities of the molecules in the lattice. Wpolarizn gives the intermolecular electrostatic interaction between the perturbed charge densities. Wintermolincludes all the terms in the crystal energy involving a lattice summation over the intermolecular density submatrices. Wintramolincludes all of the intramolecular terms for the reference molecule which are not included in Wmol. The calculations have been performed with a modified version of the CRYSMOprogram at the ZOETO Jelcz on an IBM 370/145 computer. The Coulomb and the intermolecular energy lattice sums included all molecules within spheres of 35 and 8 A, respectively.
Results of Calculations and Discussion Glycine exists in the zwitterion form in all three crystals. The bond lengths and bond angles of the molecules in crystals are nearly i d e n t i ~ a l . The ~ ~ ~differences ,~ between these three crystalline forms of glycine are primarily in the three-dimensional frameworks of their hydrogen bonds. The a-glycine crystal forms a monoclinic lattice of symmetry R 1 / n with four molecules in the unit cells4 The crystal of 0-glycine is monoclinic with space group and two molecules in the unit The y-glycine crystal has trigonal crystal symmetry and three molecules in the unit cell. The space group of this form is P32.7 The fractional atomic coordinates of these three forms of glycine crystals assumed in calculations on the basis of experimental data4i6J are presented in Table I. In the calculations lattice constants a, b, and c for a-, 0-, and y-glycine have been optimized, but the experimental values of unit cell angles were used. The results presented in Table I1 show that there exists a good agreement between calculated and experimental values for all three forms. The energies calculated for the glycine crystals are listed in Table 111. According to our calculations the crystal of the a-glycine is the more stable by about of 6.9 kcal mol-l than the crystal of &glycine and about 8.0 kcal mol-l more stable than the crystal of y-glycine. However, when we compare crystal binding energies, the appropriate relative energy difference are smaller; the crystal of the a-glycine is the more stable by about 0.85 and 1.05 kcal mol-l, respectively.
a
c,
expt
calcd
11.969 6.268 7.037
5.499 5.411 5.517
a
expt
a , deg
(expt)
0,deg (expt)
Y,deg (expt)
5.465 5.380 5.483
90.0 90.0 90.0
111.7 113.2 90.0
90.0 90.0 120.0
TABLE 111: Calculated Contributions to the Crystal Energies (au) for Glycine Crystals a-glycine
0-glycine
y-glycine
-66.310021 0.027765 -0.006376 -0.124232 0.060411 - 66.3 5 24 5 3
-66.308538 0.025845 -0.006393 -0.122819 0.061266 - 66.3 5 0 64 0
~~
-66.319674 W,I, 0.027696 U&,o~n -0.006632 **mol -0.124789 W i , . , ~ ~ ~ 0.059944 l - 66.3 6 34 5 5 Wcryst Wmol
~
To our knowledge, in the literature there are no accurate experimental values for the stability of these crystals. However, some indication of the expected reliability of these results may be obtained. As Scheraga et al. noted,17 y-glycine crystals change irreversibly into a-glycine crystals upon heating to about 165 "C. The experimentally estimated heat of transition is about 600 cal mol-l. The crystals of 0-glycine changes into the a form by heating to about 100 "C or by grinding or mechanical shock, and may change into the y form in the presence of water vapor. Scheraga et al.,l' using their method based on the empirical potential function, have made calculations of the binding energies of the three forms of glycine crystals. They found a difference of 1.5 kcal mol-l between the lattice energies of a- and 0-glycine, and a difference of 13 kcal mol-l between 0-and y-glycine crystals. This large difference arises from the calculated electrostatic energy since other contributions are nearly equal for these three forms. Recently, Derissen and co-workersla have shown that the unexpected results obtained by Scheraga et al. were caused by poor convergence of the electrostatic lattice sum. Using convergence acceleration methods, Derissen et al. obtained, for all three glycine forms, very similar values for the electrostatic energy. On the basis of experimental estimations as well as the above-mentioned calculated values, our results correctly predict the relative stability order as a-glycine > @-glycine > y-glycine. This relative stabilization order is due to differences in all energy contributions. It is also interesting to note that the electrostatic energy contributions presented in Table I11 are similar in all three forms. This result is in agreement with the conclusions obtained by Derissen et al.18 Moreover, the electrostatic energy contribution for three forms are positive. Similar results have been previously obtained by Santry for other hydrogen-bonded ~rysta1s.ll-l~Positive values for this term result largely from the neglect of penetration effects in the CNDOIB methods. Santry suggested that Welecmay be considered
Sorption and Permeation in Linear Laminated Media
TABLE IV: Calculated Changes of A t o m i c Charges (e) uuon Crvstal F o r m a t i o n a
a-glycine
NH3+H, H 2 H3
CH, H.) H 5
Cl
c2
N 0, 0 2
0.1024 0.1091 0.1053 0.0022 0.0031 0.0027 -0.0214 0.0098 -0,1543 -0.1595
0-glycine
y-glycine
0.1078
0.1059 0.1038 0.1028 0.0017 0.0026 0.0036 -0.0247 0.0069 -0.1507 -0.1519
0.1005 0.1032 0.0020 0.0029 0.0034 -0.0233 0.0078 -0.1511
-0.1531
a A positive value corresponds to a decrease in electron density .
to include the closed-shell overlap-dependent repulsion energy. For all three forms of glycine crystals, we observed relatively large inter- and intramolecular energy contributions. This has been observed for all hydrogen-bonded molecular crystals studied to date,11-16 and seems to be a characteristic feature of hydrogen-bonded crystals. In Table IV the calculated changes of the atomic charge upon crystal formation for all three forms of glycine are presented. The increase in polarity for the atoms participate directly in the hydrogen bond, e.g., oxygen atoms
The Journal of Physical Chemistry, Vol. 83, No. 27, 1979 2787
of the COO- groups and hydrogen atoms of the NH3+ groups have been observed. For the a-glycine crystal greater changes in atomic charges are observed than for the 0 and y forms.
Acknowledgment. The authors thank the Polish Academy of Sciences for support (MR-1-9).
References and Notes (1) K. Biemann, J. Seibl, and F. Gapp, J . Am. Chem. Soc., 83, 3795 (196 1). 12) G. Junk and H. Svec. J . Am. Chem. Soc.. 85, 839 (1963). (3) Y. Grenie, J.-C. Lassegues, and C. Garrigou-Lagrange, J . Chem. Phys., 53, 1827 (1972). (4) P.-G. Jonsson and A. Kvick, Acta Crysfallogr., Sect. 8 , 28, 1827 (1972). (5) R. E. Marsh, Acta Crysfallogr., 11, 654 (1958). (6) Y. Iitaka, Acta Crystallogr., 13, 35 (1960). (7) Y. Iitaka, Acta Crystallogr., 14, 1 (1961). (8) J. Bacon and D. P. Santry, J . Chem. Phys., 55, 3743 (1971). (9) J. Bacon and D. P. Santry, J. Chem. Phys., 56, 2011 (1972). (10) S.F. O'Shea and D. P. Santry, Theor. Chim. Acta, 37, 1 (1975). (11) R. W. Crowe and D. P. Santry, Chem. Phys. Lett., 45, 44 (1977). (12) D. P. Santry, J. Am. Chem. SOC.,94, 8311 (1972). (13) R. W. Crowe and D. P. Santry, Chem. Phys., 2, 304 (1973). (14) D. P. Santry, Chem. Phys. Lett., 27, 464 (1974). (15) K. Middlemiss and D. P. Santry, Chem. Phys., 1, 128 (1973). (16) D. P. Santry, Chem. Phys. Lett., 52, 500 (1977). (17) F.A. Momany, L. M. Carruthers, and H. A. Scheraga, J. Phys. Chem., 78, 1621 (1974). (18) J. L. Derissen, P. H. Smit, and J. Voogd, J. Phys. Chem., 81, 1474 (1977).
Time Moment Analysis of Sorption and Permeation in Linear Laminated Media H. L. Frisch," G. Forgacs,+ and S. T. C h d Department of Chemistry and Center for Biological Macromolecules, and Department of Physics, State University of New York at Albany, Albany, New York 12222 (Received January 22, 1979) Publicatlon costs assisted by the National Science Foundation and the US.Army Research Office
The time moments of the amount of penetrant (per unit area) in a desorbing membrane or the difference between the instantaneous and asymptotic flow (per unit area) up to a given time through a membrane in a permeation cell can be obtained by numerical integration of experimental data. We show that for membranes composed of a linear laminated medium these time moments can be exactly, recursively calculated without solving the diffusion equation. We then obtain novel, exact functional constraints on the local permeability and distribution coefficients which characterize such a linear laminated medium. We can relate the precursor functions of these time moments to the asymptotic long time behavior of penetrant sorption and permeation.
1. Introduction Considerable interest exists in sorption and permeation studies of dilute penetrants in films of simple inhomogeneous materials which form a linear laminated medium.1-8 Such a medium is characterized by a partition coefficient, k, diffusion coefficient, D , and local permeability coefficient, P, whose spatial dependence arises solely from a dependence on the distance in the direction of penetrant flow, x k = k(x) D = D ( x ) P = Dk = P(x) (1.1) The penetrant activity must be sufficiently low so that both k (Henry's law) and D are independent of the penetrant activity. At ordinary pressures this restricts one Central Research Institute for Physics, 1525 Budapest, 114 P.O. Box 49, Hungary. t Departmentof Physics, State University of New York at Albany. 0022-365417912083-2787$0 1.0010
to gases or vapors whose critical temperatures are considerably lower than the ambient temperature of the transport measurement. Examples of such linear inhomogeneous media are (1)composite membranes which are laminates of films of different composition,4 (2) microporous powder compacts (e.g., graphite powder compacts),G8and (3) crystalline polymer films with effectively linear gradients in crystallinity or orientation of the spherulites as in the case of surface-nucleated transcrystalline films,g etc. The aim of the sorption and permeation studies in such films is t~ obtain some information concerning k , D, or P which characterize the medium and its diffusion properties; one is thus dealing with an inverse problem in diffusion theory. In this paper we obtain exact constraints, as functionals of k and P, on k and P from time moments of entities which can be expressed in the routinely measured weight change of the penetrant in sorption balance experiments3 and the penetrant flow up to time 0 1979 American
Chemical Society
