J. Phys. Chem. 1991,952311-2316 charge-iterative models is 1.18 eV. No quantitative improvement is observed for the Koopmans IP’s of the model compounds for the two parameterizations. Both models maintain correct qualitative ordering for the orbital energies except for pyridine. In this case, both models place the nonbonding orbital lower in energy than is observed relative to the occupied ?r orbitals. This order is corrected in AE(SCF) calculations or through a CI treatment of the positive ion. We are currently examining the use of electron propagator35methods to correct for such disarrangement by including low-order correlation and orbital relaxation effects associated with ionization. VI. Conclusions This study has demonstrated that improvement over existing model spectroscopic Hamiltonians is possible with charge-dependent parameters. While the quality of r-r* transitions is maintained, the simple and physically intuitive strategy for improving n-?r* excitation energies for carbonyls is possible. In addition to improving agreement with molecular electronic spectra, the information content of atomic parameters is increased while their structures are simplified. By fitting for a whole row a t once for all available charges, both the one-center Coulomb integrals and one-electron core integrals are easily obtained with (35) Linderberg, J.; Ohm, N. Y. Propagators in Quanrum Chemistry; Academic: New York, 1973.
2311
total atomic energies or total energies and ionization potentials. It is not necessary to obtain orbital electron affinities as is necessary for the use of Pariser’s approximation for Coulomb integrals. Since the parameters are constrained to be at most quadratic in atomic number, interpolation for sparse atomic data occurs naturally, as does extrapolation to atomic anions. The extension of the form of the one-center core terms to the one-center resonance terms greatly simplifies the parametrization at the molecular level. Much smaller data bases of molecular data can be employed to obtain parameters. If no charge dependence for the resonance integrals is needed, one can define the resonance integrals for a whole row by specifying only three values (preferably for the atoms at the ends of the row and one in the middle). The analysis of the atomic parameters in terms of the chemically useful concepts of orbital hardness and electronegativity provides a connection to the areas of density functional theory.36 This type of analysis allows the probing of forces within molecules necessary for the description of chemical activity and in this case orbital energies and electronic spectra. Acknowledgment. J.D.B. acknowledges support through a Tennessee Eastman Postgraduate Fellowship. This work was supported in part through a grant from Eastman Kodak Co. and from the Office of Naval Research. (36) Gizquez, J. L.; Ortiz, E. J. Chem. Phys. 1984,81, 2741-2748.
Electrostatic Energy In Chloride Salts of Mononltrogen Organic Bases Jacek Lubkowski and Jerzy Blaiejowski* Institute of Chemistry, University of Gdatisk, 80-952 GdaAsk, Poland (Received: June 26, 1990)
The electrostatic part of the lattice energy in chloride salts of mononitrogen organic bases was determined by adopting the Ewald method. The calculations were performed for compounds for which complete, or at least partial, crystal structures are known. In the case of incomplete structures, the MNDO geometry optimization procedure was used to find the unknown positions of atoms. The electrostatic energy calculations were performed on the assumption that a negative (-1) charge is attached to the chlorine atom and a positive (+I) charge either is located on the N atom or is distributed among all the atoms in the cation. The charge distribution in the isolated cation was evaluated by applying CNDO/2, INDO, and MNDO methods. The electrostatic energy in an NH4Cl crystal was also evaluated by considering the influence of neighboring ions on the charge distribution in the lattice. The electrostatic energy values derived were compared with the published values of the crystal lattice energy determined either theoretically or experimentally. The agreement appeared to be satisfactory, which implies that, in the case of the compounds studied, the main contribution to the cohesive forces is made by the Coulombic interactions.
Introduction Crystal lattice energy determines the magnitude of cohesive forces in the solid phase. In the case of an ionic substance of general formula K,,,A,, the crystal lattice energy (E,) is defined as an energy change for the process where a is the multiplicator accounting for the actual valences of both ions. It is generally recognized that four effects contribute to the crystal lattice energy.’” These effects are expressed by eq 2, where Eelrepresents the electrostatic interactions between E, = -Eel + E, - E d + Eo (2) ions; E,, the repulsive interactions; Ed, the van der Waals inter(1) Thakur. K. P. Ausr. J . Phys. 1976. 29, 39. (2) Jenkins, H. D. B.; Pratt, K. F. Adu. Inorg. Chem. Radiochem. 1979, 22, 1. ( 3 ) Raghurama, G.;Narayan, R. J . Phys. Chem. Solids 1983, 44, 633.
0022-3654/91/2095-2311$02.50/0
actions; and Eo, the zero-point energy. Knowledge of the charge distribution in the lattice enables a precise evaluation to be made of the E,, term on the basis of the Coulomb law. For lattices composed on K,A, units, one can assume that point charges of values an+ and am-, for cation and anion, respectively, are located at the centers of given atom^.^^^ For simple ionic substances containing symmetrical ions, for example octahedral ions, the charge distribution between atoms can sometimes be guessed.2.6 In the case of compounds composed of unsymmetrical ions, the charge distribution is not easily predictable. For the latter substances, therefore, theoretical calculations of the lattice energy have not so far been carried out. To this group belong chloride salts of mononitrogen organic bases. A somewhat more difficult problem is posed by the evaluation of the remaining three terms on the right-hand side of eq 2. The (4) Weenk, J. W.; Harwig, H. A. J. Phys. Chem. Solids 1977, 38, 1047. ( 5 ) Atkins, P. W. Physical Chemistry, 3rd ed.;Freeman: New York, 1986; p 595. (6) Jenkins, H. D. B.; Pratt, K, F. Prog. Solid Stare Chem. 1979,12, 125.
0 1991 American Chemical Society
2312 The Journal of Physical Chemistry, Vol. 95, No. 6, 1991
relationships proposed for the determination of E, contain constants that can be derived only from a knowledge of certain experimental In some cases, the approximate values of Ed and Eo can also be obtained the~retically.~,'~ For these reasons, the complete calculations of the lattice energy have so far been carried out only for simple inorganic, ionic ~ubstances,'~,''for compounds composed of complex but symmetrical ions,a6 and for very simple organic ionic substances.l5-l6 The four terms of the right-hand side of eq 2 do not contribute equally to the E, values. For the ionic compounds, for which complete lattice energy calculations have been carried out, the main contribution is always made by the E,, term. This results from the facts that the E, and Ed terms are usually equal in magnitude but opposite in sign and that the E,, term is negligible in comparison with the values of the other terms in eq 2.2 Therefore, in the case of ionic substances, -EeIwell represents the crystal lattice energy. Such simplification also seems to be justifiable in the cases of the compounds studied. This paper deals with the theoretical evaluation of the electrostatic energy in chloride salts of mononitrogen organic bases for which structural data are available. Most of the compounds examined contain highly unsymmetrical cations. Thus, the study reveals the influence of the size and structure of the cation on the lattice energy. Further, it reveals how the cohesive energy changes on moving from inorganic to organic solid substances. Last, the study should shed more light on the nature of the hydrogen bonding, +N-H.-CI, which is present in the majority of the compounds examined. It is perhaps worth mentioning that a hydrogen bond of similar origin occurs when organically bound nitrogen interacts with Brijnsted acids. Such bonding also occurs in numerous biological systems. For some of the compounds examined, the basic thermochemical characteristics and thus the crystal lattice energies have been determined by other methods. The present study, therefore, enables a comparison to be made of values determined in various, independent ways. Electrostatic Lattice Energy Calculations General Problems. The electrostatic energy of 1 mol of an ionic substance composed of structural units (Ka"+),(Aa"), is given by the equation5 E,! 1 / 2 N ~ ( m E y+) REP")) (3) where NA is Avogadro's number and the factor eliminates the duplication of electrostatic interactions. E:"') and E$-) express the potential energy of a single cation and anion, respectively, as a result of their interactions with all other ions. Therefore, the problem of the evaluation of the electrostatic energy comes down to the calculation of the and E:-) terms. Among several approaches to this p r ~ b l e m , ' ~the - ~ most ~ often recommended seems to be the Ewald method.'* This method has been adopted in the present study. Principles ofthe Ewald Method. This method utilizes the effect of a periodic location of atoms in the lattice. Further, it is based on the assumption that the density of a charge localized at the center of a given atom is well represented by the three-dimensional Gaussian distribution function. The relationship for the potential (7) Tosi, M. P. Solid Slate Phys. 1964, 16. 1 . (8) Boswarva, 1. M.; Lidiard, A. B. Philos. Mag. 1967, 16 (42), 805. (9) Lowndes, R. P.; Rastogi. A. Phys. Reo. 1976, B14, 3598. (IO) Singh, A. V.;Sharma, J. C.;Shanker, J. Physica 1977, B+C94, 331. (1 1) Singh, A. V.; Shanker, J. Indian J . Phys. 1981, ASS, 58.
(12) Born, M.; Huang, K. Dynamical Theory ojCrystal Lattices; Oxford University Press: Oxford, U.K., 1954. (13) Ladd, M. F. C.; Lee, W. H. Trans. Faraday SOC.1958, 54, 34. (14) Waddington, T. C. Ado. Inorg. Chem. Radiwhem. 1959, I , 157. ( I S ) Boyd, R. H. J . Chem. Phys. 1969, 51, 1470. (16) Ladd, M. F. C. Z . Phys. Chem. (Munich) 1970, 72.91. (17) Madelung, E. Phys. 2.1918, 19, 524. (18) Ewald, P. P. Ann. Phys. (Leiprig) 1921, 64, 253. (19) Born, M . Z . Phys. 1921, 7 , 124. (20) Evjen, H. M. Phys. Reo. 1932, 39, 675. (21) Frank, F. C. Philos. Mag. 1950, 41, 1287. (22) Bertaut, E. F. J . Phys. Radium 1953, 13, 499. (23) Boganov, A. G.; Cheremisin, 1. I.; Rudenko, V. S.Fir. Tuerd. Tela (Leningrad) 1966, 8, 1910.
Lubkowski and Blatejowski (V)at a site ri in an ionic lattice, taken as an origin of the coordinate system, due to the monopoles at sites rj, can then be derived. If the points against which the electrostatic potential is considered correspond to the location centers of a cation and anion, then the relationship resulting from the Ewald approach admits of the forms given in eqs 4 and 5 , respectively. In eqs 4 pan+)
= (f/4*€o)[(l/*u) C F t h ) / h 2 exp(-*h2/P) h=O
+
~ ( a n + ) e Cz,e/rij erfc (dI2Krij)] (4) j#i
Pam)= ( y ~ r t o ) [ ( l / ~ u ) C F ( h ) /exp(-rh2/KZ) h~ h=O
2 ~ ( a m - ) e + Cz,e/rij erfc (d2Kri,)] ( 5 ) j#i
and 5 , u represents the volume of a unit cell; h is the length of a vector in the reciprocal space; F(h) = Egg cos (2rhri,) represents the Coulombic structure factor, with s running over a unit cell with its origin at site ri; K is the convergence parameter to obtain the optimal convergence of the series (in this work we have assumed that K = u'/~);rij(ris) is the length of the distance vector between the origin site ri = 0 and the site rj (rs), with charge z,e ( ~ 8and ) ; erfc ( x ) = 2/7r'/2J,"e4 dt represents the complementary error function. In eqs 4 and 5 , the symbol Ch=Oindicates sumindicates mation over the reciprocal space, whereas Zj+i(E,) summation over the real lattice, omitting ri, = 0. The potential energy of a charge (4)in an electrostatic potential (V) is equal to qV.s Therefore, the electrostatic lattice energy of an ionic substance (K,A,) can easily be determined by substituting into eq 3 the expressions (an+)eV&) and (am-)eV(-) for E T ) and respectively. The Ewald method was originally developed for lattices composed of monoatomic ions. For such lattices, the author assumed isotropic Gaussian distributions of charge density around the ions. The substances we examined form lattices containing polyatomic and highly unsymmetrical ions. The application of the Ewald method in such a case requires, therefore, some adaptation and information on the charge distribution between atoms in the cation. It may be assumed that a negative (-1) charge is centered on the chloride ion, whereas a positive (+1) charge either is located on an N atom or is distributed among all the atoms in the cation. These charge distributions were derived on the basis of the solid-phase structures of cations by applying semiempirical CND0/2,24,2SIND0,24-27and MND02*methods. Further, it seems justifiable to assume that charges located on atoms in polyatomic ions exhibit isotropic density distributions. This is revealed by the crystallographic electron density maps of several complex ionic substance^.^^-^' There is a certain freedom in the choice of function describing the density of charge around an atom. Bertaut has shown that various mathematical functions can be used for this purpose.22 Different functions always lead to very similar values of so-called lattice sum^,'^,^* which occur in expressions for the electrostatic lattice energy. However, Jenkins at al.32have demonstrated that a Gaussian three-dimensional distribution function characterizes a high convergence of the lattice sum series. We have, therefore, assumed this type of function in our lattice energy calculations. For simple monoatomic ionic lattices, the potential created by all surrounding ions at the cation site is negative, whereas the potential at the anion site is positive. This means that Ed"") and E?") are negative and both afford stabilization of the lattice. (24) Pople, J. A.; Segal, G . A. J . Chem. Phys. 1965,43, 136; 1966,44, 3289. (25) Pople, J. A,; Beveridge, D. L. Approximate Molecular Orbital T h e ory; McGraw-Hill: New York, 1970. (26) Pople, J. A,; Beveridge, D. L.; Dobosh, P. A. J . Chem. Phys. 1967, 47, 2026. (27) Dixon, R. N . Mol. Phys. 1967, 12, 83. (28) Dewar, M. J . S.;Thiel, W. J. Am. Chem. Soc. 1977,99,4899,4907. (29) Brown, C. J. Acta Crystallogr. 1949, 2, 228. (30) Shimada, A. Acta Crystallogr. 1955, 8, 819. (31) Sakanoue, S.;Kai, Y.; Yasuoka, N.; Kakudo, M. Bull. Chem. Sw. Jpn. 1970, 43, 1306. (32) Jenkins, H. D. B.; Pratt, K. F. Chem. Phys. Lett. 1979, 62, 416.
Energy in Chloride Salts of Mononitrogen Organic Bases
TABLE I:
The Journal of Physical Chemistry, Vol. 95, No. 6, 1991 2313
Structural Data for Chloride Salts of Mononitrogen Organic Bases
substance
no. I 2 3
4 5 6 7
8 9 10 11 12 13
14 15 16 17 18 19 20 21 22
space
name of amine (cation)
formula
group
ammonia methanamine N-methylmethanamine N,N-dimeth ylmethanamine
(N,N,N-trimethylmethanaminium) N,N-diethylethanamine 2-methyl-2-propanamine cyclohexanamine N-( I , 1-dimethylethyl)-cu-methyl-y-phenylbenzenepropanamine
(S)-a-methyl-N-(phenylmethy1)benzenepropanamine tricyclo[3.3. I . 13*']decan-l -amine piperidine 1-( 1-phenylcyclohexyl)pipridine trans- 1 [4-( 1,1 -dimethylethyl)- I -phenylcyclohexyl]piperidine
-
1-azabicyclo[2.2.2]octane 1-azabicyclo[3.3.3]undecane
benzenamine 2-methylbenzenamine 4-methyl benzenamine pyridine 1,2,5,6-tetrahydro- 1 -methyl-4-phenylpyridine
2,3,4,4aa,9/3,9aa-hexahydro-2-methyl-9-phenyl-
no. of struc units in eIem cell 1 2 8 2 2 2 8 4 4 2 8 4 4 4 2 2 4 4 4 2 2 8
N-CI min dist in lattice, A 3.35 3.1812 2.8351 3.0042 4.2830 3.1069 3.1624 3.1410 3.1281 2.8106 3.1629 3.1158 3.0863 3.0887 4.3 199 2.9784 3.1580 3.1842 3.1174 2.9551 3.0189 4.531 1
ref 3, 34, 35 36 37 38 39, 40, 41 42 43 30 44 45 46 47 48 49 50 51 29 52 53 54 55 56
1 H-indeno[Z, I-clpyridine a
For structures, see Figures 1 and 2.
Assuming the location of +1 and -1 charges at the N and C1 atoms, respectively, one notices regularities similar to those discussed above. On the basis that a +1 charge is distributed among all the atoms in the cation, a value of the potential at a chosen C1- site was evaluated by assuming that it is created by -1 charges attached to all other C1 atoms and charges located at all atoms of the cations in the lattice. The appropriate participation in the potential energy gives the multiplication of the above value by -e. The potential a t the chosen atomic site of the cation was assumed to be created by charges located at all C1 atoms and charges attached to all atoms of the cations in the lattice, excluding atoms that are part of the cation under consideration. Such an approach results from the fact that a cation as a whole is transferred, according to reaction 1, to the gaseous phase. In this way, the potential at each atom of the cation was established. Subsequently, the participation of each atomic site of the cation in the electrostatic energy was found by multiplying the appropriate value of the potential by the actual charge at this site. When we applied such a procedure, the product was not always negative. The values of E,, determined in this work are the sums of values, with respect to the sign, brought by all charged sites of the simplest ion pair. All known programs for the E,, calculation have been written for simple lattices composed of monoatomic ions. One such program was modified to make possible its use in the case of salts containing polyatomic and unsymmetrical ions. This program was further adapted for an IBM PC computer on which all the calculations were carried out. Structural Information. The electrostatic energy calculations require a knowledge of the location of the interacting charges in the lattice. The crystallographic electron density data indicate that the most adequate method is to localize charges a t points corresponding to the centers of appropriate This information is available from diffraction measurements. The search for the crystal structures of chloride salts of mononitrogen bases has been carried out by using the Cambridge Structural Database System33and other sources. During this search we found (33) Cambridge Structural Database Sysrem; Cambridge Crystallographic Data Centre: Cambridge, U.K., 1988. (34) Plumb, R. C.; Hornig, D. F. J. Chem. Phys. 1953, 21, 366. (35) Press, W. Acra Crysrallogr. 3973, A29, 257. (36) Hughes, E. W.; Lipscomb. W. N. J. Am. Chem. SOC.1946.68, 1970. (37) Lindgren, J.; Olovsson, 1. Acta Crysrallogr. 1968, BZI, 549. (38) Lindgren, J.; Olovsson, I. Acta Crystallogr. 1968, B24, 554.
that only certain limited structural data are sufficient to enable lattice energy calculations to be performed. The compounds for which calculations could be performed, together with appropriate structural information, are listed in Table I. For compounds 6-12, 15, 16, 19, 21, and 22, the complete crystal structures are known. In the case of ammonium chloride, the locations of all H atoms were assumed by following the work of Raghurama and Narayan (ref 3 and references cited therein). In compounds 2-5,17, and 20, the locations of none of the hydrogen atoms have been established. Therefore, the structures of corresponding cations were completed by placing the H atoms at the standard distance from the C atoms (1.1 1 A in the case of aliphatic C-H bonds and 1.08 A for aromatic C-H bonds)." The most probable locations of H atoms were subsequently determined by the optimization of appropriate valence and torsion angles, applying the MNDO method together with the minimum energy criterion.28 Similarly, the structure of compound 18 was completed with a CH3 group. The H atom involved in the (39) Vegard, L.; Sollesnes, K. Philos. Mag. 1927, 4 (7), 985. (40) Wyckoff, R. W. G., Z.Kristallogr., Krislallgeom., Kristallphys., Kristallchem. 1928, 67, 9 1. (41) Bottger, G. L.; Geddes, A. L. Specrrochim. Acta 1965, 21, 1701. (42) James, M. A.; Cameron, T. S.;Knop, 0.;Neuman, M.; Falk M. Can. J . Chem. 1985,63, 1750. (43) Trueblood, K. N. Acta Crystallogr. 1987, C43, 71 1. (44) Carlstroem, D.; Hacksell, I. Acta Crystallogr. 1983, C39, 1 130. (45) Murray-Rust, P.; Murray-Rust, J.; Hartley, D.; Clifton, J. Acta Crystallogr. 1982,838, 306. (46) Belanger-Gariepy, F.; Brisse, F.; Harvey, P. D.; Butler, 1. S.;Gilson, D. F. R. Acta Crystallogr. 1987, C43, 756. (47) Rerat, C. Acta Crysrallogr. 1960, 13, 72. (48) Argos, P.; Barr, R. E.; Weber, A. H. Acra Crystallogr. 1970, 826, 53. (49) Briard, P.; Roques, R.; Kamenka, J. M.; Geneste, P.; Declerq, J. P.; Germain, G. Cryst. Struc?. Commun.1982, 11, 231. (50) Kurahashi, M.; Engel, P.; Nowacki, W. Z. Kristallogr. 1980, 152, 147. (51) Wang, A. H. J.; Missavage, R. J.; Byrn, S.R.; Paul, I. C. J . Am. Chem. Soc. 1972, 94, 7100. (52) Cameron, T.S.; Duftin, M.; Singh, E. B. Cryst. Strucr. Commun. 1976, 5, 927. (53) Colapietro, M.; Domenicano, A.; Portalone, G. Acra Crystallogr. 1982, B38, 2825. (54) Rerat, R. Acta Crystallogr. 1962, 15, 427. (55) Flippen-Anderson, J. L.; Gilardi, R.; George, C. Acta Crystallogr. 1985, A42, 1185. (56) Mathew, M.; Palenik, G. J. J . Crysr. Mol. Strucr. 1981, 11, 79. (57) Newton, H. D.; Lathan, W. A.; Hehre, W. J.; Pople, J. A. J . Chem. Phys. 1970, 52, 4064.
2314 The Journal of Physical Chemistry, Vol. 95, No. 6, 1991
Lubkowski and Blaiejowski m.
m.
I
ia
A
7
"m
n12
I
K
B II
n
II
n
n
n
C Figure 1. Structures of [CH3NH3]+ (A), [CSHloNH2]' (B), [CsHsNH]+ (C) in chloride salt lattices.
and
TABLE 11: Charge Distribution in Cationic Forms of Simple Mononitrogen Bases Calculated by Quantum Chemistry Methods
cation" formula atom(s) (CH,NH,]'
N C
HI H2 H3 H4 H5 H6 [CSHIONH~]' N c1, c 5 C2, C4 c3 H1 H2 H3, HI1 H4, H I 2 H5, H9 H6, H I 0 H7 H8 [CSHSNH]' N c1, c 5 C2, C4 c3 H1 H2, H6 H3, H5 H4
method CNDO/2 -0.3235 -0.0506 0.3145 0.3 I69 0.3176 0.1425 0.1429 0.1399 -0.2935 0.01 19 -0.1061 -0.0385 0.2847 0.2693 0.1158 0.0953 0.0759 0.1349 0.0183 0.1016 -0.2560 0.1446 -0.0164 0.0617 0.3185 0.1249 0.1365 0.0965
INDO -0.2456 0.0274 0.2953 0.297 1 0.2978 0.1099 0.1 103 0.1078 -0.2285 0.0709 -0.0540 0.0086 0.2699 0.2572 0.0855 0.0646 0.0442 0.1057 -0.0134 0.0723 -0.2092 0.1724 -0.0050 0.0916 0.2990 0.0964 0.1114 0.068 1
" For structures and numbering of atoms, see Figure 1
MNDO 0.0258 0.0603 0.2213 0.2267 0.2277 0.0794 0.0801 0.0788 0.0486 0.0530 0.0102 -0.0452 0.198 1 0.1620 0.0613 0.0754 -0.0078 0.0893 -0.0076 0.0814 -0.0140 0.0861 -0.0313 0.0327 0.1802 0.1489 0.1398 0.1 141
Figure 2. Geometries of cations of substances 9, 10, 11, 15, 16, 21, and 22 (cf. Table I) in crystal lattices used in E,, calculations.
+N-H-CI bond in compounds 2-4,17, and 20 was located in the direction of N-CI such that the N-H distance was equal to 1.03 8, in methanaminium, N-methylmethanaminium, and N,Ndimethylmethanaminium chloride^,^-'^^^ 0.91 5 8, in benzenaminium ~hloride:~,~~ and 0.905 8, in pyridinium chloride.58 The remaining H atoms attached to nitrogen in compounds 2,3, and 17 were located as follows: In methanaminium chloride, two H atoms were moved 1.03 8, apart on the N atom and their valences and torsion angles were optimized by the MNDO method. The crystallographic data revealed that, in N-methylmethanaminium chloride and benzenaminium chloride, two H atoms attached to nitrogen, in fact, participate in +N-H..CI bonding and their locations were assumed as described above. The location of the third H atom in the amino group of benzenaminium chloride was established by MNDO geometry optimization. The structure determinations of compounds 13 and 14 have not been completed and electrostatic energy calculations for them were carried out only on the basis of the known locations of N and CI atoms. To enable better visualization of structures of the cations for the compounds examined, some of them are presented in Figures 1 and 2. Figure 1 shows structures of three fairly simple cations for which the charge distributions are listed in Table 11. Figure 2 shows seven complex cation structures that are rather difficult to reproduce either on the basis of the formulas or the names of the compounds. (58) Sherfinski, J. S.; Marsh, R. E. Acra Crysrallogr. 1975, A31, 1073.
Energy in Chloride Salts of Mononitrogen Organic Bases
The Journal of Physical Chemistry, Vol. 95, No. 6, 1991 2315
TABLE 111: Influence of Surroundings on Charge Distribution in the NHXI Lattice (Calculated bv tbe MNDO Method)
species formula NH4+ NHd+** *C1(Nl-i4+. (NH4+-..6NH4+)'+ (NH4+*.-8CI-,6NH4+)-
-
figure 3A 3B 3C 3D
atom N 0.0672 0.0518 0.0869 0.0397 0.0405
H 0.2332 0.2201 0.2178 0.2400 0.2220
CI' -1 .OOOO*
-0.9322 -0.9581' -0.9997' -0.9285*
Values marked with an asterisk denote the complementary negative charge to the total positive charge evaluated for NH4+. They do not result from the calculations.
Results and Discussion Charge Distribution. The examples of charge distributions in chosen cations are listed in Tables I1 and 111. Examining these, as well as data for other ions, one notices that charge distribution is a characteristic feature of a given ion. The numerical values of charges a t certain atoms depend on the quantum chemistry method applied (Table 11), as well as on consideration of the surroundings of the ion (Table 111). These methods usually predict an excess of charge at the N and C atoms and a deficiency at the H atoms. The density of charge at atoms is qualitatively related to their electronegativity. The examination of charge distributions gives the impression shown in Table 11 and those for other that N and C atoms form the core of the cation, which gathers an excess of charge, surrounded by a layer of H atoms, which exhibits a deficiency of charge. The calculations in this work reveal that a +1 charge supplied to the base molecule upon protonation or alkylation (during formation of quaternary cations) does not remain at the N atom but is delocalized throughout the whole molecule. It is rather difficult to ascertain to what extent the calculated values give an accurate representation of charge distribution in these cations. These characteristics, however, form a necessary basis for the lattice energy calculations. As was mentioned above, the charge distributions in this work were calculated for isolated cations by assuming that they preserve the geometry characteristic of a solid phase. In the lattice, cations are surrounded by other ions that may influence the density of charge at ions as a whole and at certain atoms in complex ions. We have examined this problem in the case of the simple NH4Cl lattice. The calculations concerned the NH4+-.C1- pair and the conglomerates shown in Figure 3. These conglomerates were constructed by surrounding the NH4+ unit with neighboring C1and NH4+ ions placed exactly in the positions they occupy in the lattice. The calculations for the supermolecules thus created were performed on the MNDO level. The results are presented in Table 111. As may be noticed, the density of charge a t the atoms in NH4+ is apparently affected by the neighboring ions. This effect presumably occurs in lattices containing more complex cations than NH4+. One may also expect such an effect to influence the energy of electrostatic interactions. Coulombic Energy. The calculated values of the electrostatic energy together with the literature values of the crystal lattice energy are compiled in Table IV. Assuming the charge distribution for an isolated cation (Table HI),one obtains the Coulombic energy of an NH4Cl lattice, which is usually higher than the literature values of the lattice energy. The surroundings influence the charge distribution in the NH4Cl lattice (Table 111) and the values of -EeI. These values are lower than the ones obtained in the cases of isolated ions (seeTable IV under MNDO). It is, perhaps, worth noting that, using charge distributions for
(60)
press. (61) (62) (63) (64) (65) (66)
D Figure 3. Geometries of conglomerates of NH4+-CI- (A), (NH4+-. 8C1-)7- (B), (NH4+*-6NH4+)'+ (C), and (NH4+-.8C1-,6NH4+)- (D).
'C
Lubkowski, J.; Blazejowski, J. J . Chem. Soc., Furaday Trans., in
the NH4+-C1- supermolecule, one obtains a value of -EeIalmost 100 kJ/mol lower than that characteristic of isolated ions. Similarly, the low value of -Ee1 was found on the basis of the charge distribution for the (NH4+-8C1-,6NH4+)- supermolecule. The above discussion reveals that the method of evaluation of the charge distribution affects the -Eel values subsequently obtained. A similar problem may be faced in the case of lattices composed of more complex ions. Due to the complexity of the other systems studied, we were not able to consider this effect in our calculations. It is rather difficult to judge at present which values of -EeI for NH4Cl are more realistic. The answer to this question could, perhaps, come from calculations of the Coulombic energy on the basis of the electrostatic potential data resulting from X-ray measurements. We intend to consider this problem in the future. The values of -EeI calculated on the basis of the charge distributions obtained from three different quantum chemistry methods usually differ from each other insignificantly. Greater discrepancies are seen in the cases of compounds 11 and 21. Table IV also lists the values of -Ee, obtained by assuming that +1 and -1 charges are attached to N and C1 atoms, respectively. For simple derivatives, these values correlate well with those obtained by using charge distributions determined by quantum chemistry methods (see -Ee1 for compounds 1-5). This simple method requires only a knowledge of the location of the N and C1 atoms in the lattice. Since in the latter case the number of charged points is drastically reduced, calculation by the Ewald method is much shorter. Therefore, this approach can be applied for a rough estimation of -EeI values. One should remember, however, that the location of charges only on N and C1 atoms is unrealistic in view of the discussion in the previous section. This regularity, observed also for other similar derivative^,^^" may be considered as purely phenomenological. The values of -Eel decrease with an increase in the size and number of substituents attached to the nitrogen atom. This is particularly pronounced in the series of methanaminium chlorides. The calculated values of the Coulombic energy for these latter derivatives decrease almost linearly with the number of methyl groups in the cation. This tendency has also been noticed in The regularity examining the experimental values of Ec.67,73,76
Grimm, H. Handb. Phys. 1927, 24, 518. Ladd, M.F. C.; Lee, W. H. J . Inorg. Nucl. Chem. 1960, 13, 218. Ladd. M . F. C. Trans. Faraday SOC.1970.66, 1592. Sharma, M . N. Indian J . Phys. 1969, 43, 358. Bleick, W. E. J. Chem. Phys. 1934, 2, 160. May, A. Phys. Rev. 1937, 52, 339.
Wilson, J. W. J . Chem. SOC.,Dalton Trans. 1976, 890. Blazejowski, J. Thermochim. Acta 1983, 68, 233. Sharma, M.N.; Madan, M. P. Indian J . Phys. 1964, 38, 305. Goodlife, A. L.; Jenkins, H. D. B.; Martin, S. V.;Waddington, T. C. Mol. Phys. 1972, 21, 761.
(59) Lubkowski, J.;
press.
B
A
Dokurno, P.; Blazejowski, J. Thermochim. Acta, in
(67) (68) (69) (70)
2316 The Journal of Physical Chemistry, Vol. 95, No. 6, 1991
Lubkowski and BIatejowski
TABLE 1V: Crystal Lattice Enemies (kJ/mol) for Chloride Salts of Mononitrogen Organic Bases
lit. no.’ 1
CNDO/Zb 747
this work (Coulombic energy) _. IND@ MND@& N(+)C1(-)d 747 742 731 645 681** 74l*** 640****
2
686
688
688
704
3
637
639
640
652
4 5
587 534
590 533
593 533
614 536
6
518
524
531
593
7 8
606 600
613 609
565 581
576 588
623 61 1 492 512 590 588
535 496 603 573 580 570 493
543 505 602 574 581 568 499
667 660 592 676 636 636 546 539 580 573 646 663 665 60 1 600 534
9 10 11 12 13 14 1s 16 17 18 19 20 21 22
554 520 613 582 596 564 532 499
theof
exptl
value 640 653 658 638,670 676 688, 720 697, 700 688, 698 708 (735)
ref 61 62 63 64 14, 65 66 69 70 71 72
502, (544) 523 (538) 535,553
16 74 75 15
value 692 697
ref 67 68
639 656 624 627 596 566 576
68 67 73 67 67,73 67 73
597 607, 660 62 1 636
73 76 73 73
626
73
612
73
661
77
603
78
‘For names and formulas of the compounds, see Table I. bMethod of evaluation of the distribution of the + I charge among atoms in the cation. cValues marked with asterisks denote Coulombic energies of ammonium chloride calculated by using the charge distributions listed in Table 111: *, NH,+...CI-; **, (NH4+...8CI-)’-; ***, (NH,+-..6NH4+)’+; ****, (NH4+...8C1-,6NH,f)- . dLOcations of + I and -1 charges at N and CI atoms, respectively. e Values in parentheses indicate calculated energies of Coulombic interactions.
discussed above seems to su port the idea of the additive character of the lattice energy.67*73*7B The -E,, values derived in this work generally correlate well with the experimentally determined values of the lattice energy. This means that in chloride salts of mononitrogen organic bases the main contribution to the cohesive forces is made by the (71) Jenkins, H. D. B.; Morris, D.F. C. Mol. Phys. 1976, 32, 231. (72) Singh, R. K.; Rana, J. P. S. Nuwo Cimento Soc. Ital. Fis. 1981,857, 177. (73) Blazejowski, J.; Kowalewska, E. Thermochim. Acta 1986, 105,257. (74) Johnson, D. A.; Martin, J. F. J . Chem. Soc., Dalton Trans. 1973, 1586. ..._ (75) Nagano. Y.; Sakiyama, M.;Fujiwara, T.; Kondo, Y. J . Phys. Chem. 1988. 92. 5823; 1989, 93,6882. (76) Derakhshan, B. M.; Finch, A.; Gates, P. N.; Stephens, M. J . Chem. Soc., Dalton Trans. 1984, 601. (77) Lubkowski, J.; Blazejowski, J. Thermochim. Acta 1987, 121, 413. (78) Lubkowski, J.; Blazejowski J. J. Chem. Sa.,Faraday Trans. I 1986, 82, 3069.
Coulombic interactions. It is rather difficult to answer the question of how well the calculations in this work account for the participation of the >N-H...CI bond in the cohesive forces. It seems that the hydrogen bonding mentioned above is a part of the overall bonding system that holds molecules in the rigid solid phase mainly through electrostatic interactions. A complete description of the energetics of crystals of halide salts of nitrogen organic bases also requires some consideration of the other interactions included in eq 1. This is a rather difficult task in the case of the compounds examined in this work, if one intends to obtain such information on a purely theoretical basis. We are attempting to solve this problem. Acknowledgment. We express our gratitude to Dr. Dieter Schmitz of the Technischen Hochschule, Aachen, Germany, for providing the basic program for the electrostatic energy calculations. Financial support for this work from the Polish Ministry of National Education is also acknowledged.
