J. Phys. Chem. 1993,97, 2115-2122
2715
Electrostatic Energy in Inorganic and Organic Hexahalogenoplatinate Lattices Pawel Dokurno, Jacek Lubkowski, and Jerzy Blaiejowski' Department of Chemistry, University of Gdahsk. 80-952 Gdahsk, Poland Received: July 28, 1992
The electrostatic part of the lattice energy of alkali metal and nitrogen organic base hexahalogenoplatinates, for which the complete or at least partial structures have been established, was determined by the extended Ewald method. In the case of incomplete structures, the unknown positions of atoms were found by the AM1 method. Charge distributions necessary for the lattice energy calculations were either taken from the literature, for PtX,?, arbitrarily assumed (1+ at nitrogen), or evaluated using I N D O and A M I methods, in the case of cations of nitrogen bases. The Coulombic energies decrease almost linearly with the increase of volume of the simplest structural unit. Qualitative correlations between electrostatic energies and distances reflecting interacting centers in the lattice, as well as proton affinities (calculated applying the AM1 method) of constituting base molecules are also noted. Generally, energies resulting from various approaches do not differ substantially, which can be accounted for by the fact that the electrostatic potential surrounding even complex ions assumes a very similar shape and almost spherical symmetry irrespective of the charge distribution assumed.
Introduction The crystal lattice energy is the most important quantity accounting for the structure, features and behavior (reactivity) of solids. Its values can be determined either theoretically or on this basis of Hess's law (appropriate thermochemical cycle) applying experimentallyderived values of certain physicochemical quantities.I4 Theoretical studies on lattice energy have been carried out almost since the beginning of this century.S-' The majority, however, concerned inorganic ionic substances.1-2+41 Considering a chosen such substance of a general formula K,A, thecrystal lattice energy (E,) can be defined as an energy change for the process K,A,(c)
-
mK""+(g)
+ nAUm-(g)
where a is the multiplicator accounting for the actual valence of both ions. The above understanding of lattice energy links this quantity to the magnitude of attractive and repulsive interactions in the solid phase. It is generally recognized that these are represented by four effects which are included in (2), viz.2~4J1J2 E, = -Eel
+E,-
Ed
+ E,
where E,, represents electrostatic (Coulombic) interactions between ions, E, repulsive interactions, Ed van der Waals (dispersive) interactions, and EOzero point energy. For inorganic ionic substances, the EOterm is negligible as compared with the other terms in (2).2J3J4 Furthermore, the estimated values of E, and Ed do not usually exceed 1/ 10 of the Eel value and since they have opposite signs their sum becomes negligible.2*4J3-1sIn the caseof such substances, therefore, -E,] well represents the crystal lattice energy. Knowledge of the crystal lattice energy is important in the case of both inorganic and organic salts. To our knowledge, however, with the exception of our latest effortsl6I9 no others have been undertaken in the past to determine the lattice energies of organic ionic substances. Among these latter substances the objects of particular attention are derivatives formed of cations of nitrogen organic bases and simple inorganic anions which may be considered as lying on the boundary of inorganic and organic matter. The interest shown in these compounds is due to their simplicity and common occurrence (at least cationic forms) in living organisms and environment and also the fact that some can serve as model compounds in studying physicochemical features of the solid phase. The present paper is thus devoted to the calculation of the Coulombic energy in the hexahalogenoplatinates OQ22-3654/93/2O91-2115304.00/0
of alkali metals and protonated organic bases, for which complete or at least partial crystal structures are known. The compounds containing PtX62- (X = C1, Br, 1) ions were chosen since they have been thoroughly investigated in the past and thus for many of them the solid-phase structures have been determined. They also represent relatively simple model systems in which both complementary ions exhibit a complex nature. The chosen group of compounds thus forms a convenient basis for investigatingthecrystal latticeenergy and hencenatureofcohesive forces in the solid phase.
Methods and Complementary Information Electrostatic Lattice Energy. The electrostatic energy of 1 mol of an ionic substance composed of structural units (Kun+),(AUm-),,is defined by (3),j where N A is the Avogadro
number, whereas factor 1/2 eliminates the duplication of electrostatic interactions. The terms E P + ) and E?,-) in (3) express the potential energies which result from interactions of a single cation and anion, respectively, with all other ions in the lattice. Taking into account, that the potential energy is determined by the product of the actual charge of an ion and the potential (V,) created at the site of its l o c a t i ~ n ,eq~ 3 can be written in the form
+
E,, = '/2NA[m(an+)eVp(a"+)n(am-)eV,(am-)]
(4)
where e denotes the elementary charge. The problem of evaluating the Coulombic energy thus boils down to the calculation of the electrostatic potential. The most "accurate" value of the electrostatic potential would presumably be obtained by applying the SCF procedure to the electronic wave function and combining the result with the core potential. At distances greater than 4 A, however, it is well approximated by a potential created by point charges located at atoms.20.2'In the crystal, constituting fragments are usually more than 4 A away and thus electrostatic potential ( VzJ)is manifested mainly through the long range interactions. This potential at site i (at which a net charge Ziis situated), taken as the origin of the coordinate system, can therefore, be expressed with the 0 1993 American Chemical Society
Dokurno et al.
2116 The Journal of Physical Chemistry. Vol. 97, No. 11, 1993
formula
HI421
nim
where €0denotes the permittivity of free space and Z, a net charge at site j removed from site i by rv, The summation extends over all positive and negative ionic centres (n)exluding, of course, site i. The crystal presents an infinite lattice of periodically located charges. Thus, ( 5 ) is, in reality, a series which is always poorly converged. Of several approaches to the calculation, of the lattice potential (lattice sums)proposed in the past5-7.22-24 the most widely used in the Ewald method.6 Below is only the final equation resulting from this method, namely
n
13
I
H
erfc ( d K r i j ) ] (6) j + i rij
Hllll
16
The electrostatic potential in (6) is expressed as three term dependence (the meanings of these terms have been given elsewhere4J9), in which the meanings of the symbols are as follows: u, the volume of a unit cell; h, a vector in reciprocal space; F(h), the Coulombic structure factor F(h) = C z s ecos(2~hr,)
IZI
H
with s running over a unit cell with its origin a t site i ; K, the convergence parameter (it was assumed K = v1I3); ri,(ri,), the distance vector between the original site i (ri, = 0; ri, = 0) and sitej(s) with charges Zj = zje (Z, = zse) (where zj and z, denote relative charges); and
HI921
24 Figure 1. Structures of cationic fragments of substances 13.16, and 24.
L
erfc(x) = -Jmexp(-rz) /-x
HI21
dt
t/*
represents the complementary error function. In (6)the symbol r h = o indicates summation over reciprocal space, whereas indicates summation over the real lattice, omitting tij(ris)= 0. The Ewald method was originally developed to evaluate the lattice energy of monoatomic ionic substances. The application of this method for crystals composed of complex and polyatomic ions requires certain assumptions,4~’6-’9namely: (i) in species constituting the simplest formula unit of the molecule positively and negatively charged fragments are distinguished; (ii) to each such fragment are ascribed charges which in the first approximation are whole multiplicities of e; (iii) it is assumed that within each such fragment a charge is located on certain chosen atoms, or is distributed between the atoms of which it is formed; (iv) it is assumed that each partial charge contributes to the electrostatic potential (i.e. is considered separately in the calculations); (v) the electrostatic potential is determined a t the sites of location of each partial charge (atom) of a given fragment, excluding partial charges ascribed to the remaining atoms constituting this fragment. For calculations the electrostatic energy of one of the basic programs for the Ewald method was appropriately extended and modified. StructuralInformation. The electrostatic energy calculations require a knowledge of the location of the interacting charges in the lattice. If one assumes that charges are centered at atoms then this information is available from crystallographic data. The search for the solid phase structures has been carried out in the Cambridge Structural Database System25 and Chemical Abstracts. In effect the group comprising 10 inorganic hexahalogenoplatinates (all known structures) and 14saltsof relatively
&zi(xs)
simple nitrogen organic bases (containing, apart from nitrogen, also chlorine or oxygen atom(s)) were selected for lattice energy calculations. Structural information for thesecompounds is given in Table I. The complete crystal structures have been established for all inorganic (compounds 1-10) and some organic (compounds 14, 15, 19, 21, and 23) hexahalogenoplatinates. Crystallographic studies on the remaining compounds listed in Table I did not provide information on the location of all the hydrogen atoms attached to both carbon and nitrogen atoms (compounds 12,13, 16, 17, 18, 20,22, and 24) or only to carbon atoms (compound 11). To enable crystal lattice energy calculations the structures of the corresponding cations (the cationic fragments for compounds 18, 21, and 22 were assumed to be composed of two (compound 18) or one singly (compounds 21 and 22) protonated base molecules and one H20 molecule) were completed by placing the H atoms at a standard distance from C, N, or 0 atoms46and determining the most probable location of these atoms by the optimisation of bond lengths and relevant valence and torsion angles by the AM1 method,47installed under MOPAC$* together with the minimum energy criterion. Several structures of the cations of the compounds examined are presented in Figures 1 and 2. Figure 1 demonstrates three fairly simple ions for which the calculated charge distributions are listed in Table 11, whereas Figure 2 shows eight complex cationic fragments that are rather difficult to reproduce either on the basis of the formulas or names of the compounds. MO Calculations. The charge distributions between the atoms in the cations were determined using the structures of these ions in the lattice and employing semiempirical I N D O / S ~and ~~~ AM 14’ quantum chemistry methods. For the compounds which form hydrates, the H 2 0molecule was arbitrarily attached to the
The Journal of Physical Chemistry, Vol. 97, No. 11, 1993 2111
Hexahalogenoplatinate Lattices
TABLE I: Structural Data for Hexabalogenoplatinates substance" no.
formula
space erouo
name of cation (amine)
Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m Pnnm N,N,N-trimethylmethanaminium Fm3m Pna2 I (1,3-propanediamine) (N,N,N',N'-tetramethyl- 1,2-ethanediamine) P 2 1 l a N-[(dimethylamino)methylene]-N-methyl- c 2 / c methanaminium piperazinium C2/m C2/m piridinium (6,7-dihydro-SH-pyrazino[2,3-c]carbazole) P 2 1 l m N-[ (dimethylamino)methoxymethylene]-N- c 2 / c methylmethanaminium (2-[ 2-(dimethylamino)ethyl]- 1H-benz[de]P21Ic isoquinoline- 1,3(2H)-dione) (2-amino-] ,7-dihydro-9-methyl-6H-purin- PI 6-one) (alkaloid derived from Senecio kirkii) c2 N- [chloro(dimethylamino)methylene]-N- P 2 d n methylmethanaminium (L-lysine) p 2 I212 I potassium rubidium caesium thallium potassium rubidium caesium caesium ammonium ammonium N-methylmethanaminium
1 2 3
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Zh
M(N)-Pt dist." A
ref
4 4 4 4 4 4 4 4 4 4 2 4 4 4 4
4.2 1 4.28 4.4 1 4.23 4.45 4.51 4.60 4.92 4.26' 4.49. 4.25* 5.51* 2 X 4.16* 4.75*; 4.07' 5.56**: 5.27**
26,27 28,29 28,29 2 28,30 28 28 31 28,29 28 32,33 34 35 36 37
2 2 2 4
2 X 4.16* 5.08* 5.14; 5.34**; 4.62** 4.97**; 5.30''
38 39 40 41
2
6.65; 4.55*
42
1
4.56; 4.71; 4.83'*; 3.92**; 4.18
43
2 2
5.40' 5.12**: 3.92"
44 41
4
4.32.; 4.17*
45
*
For structures, see Figures 1 and 2. Number of structural units in elementary cell. Minimum distance(s) between alkali metal cation (M) or nitrogen atom(s) ( N ) and Pt in the lattice (values occur in such an order as numbering of nitrogen atoms increases); single asterisk indicates protonation site in nitrogen bases, whereas double asterisks indicate sites of location of formal charge 1 resulting from the consideration of mesomeric structures.
+
one (compounds 21 and 22) or two (compound 18) base cations and distribution of a charge as well as subsequent crystal lattice energies were calculated considering both conglomerates. Proton affinities (PA) of molecules constituting organic cations, corresponding to protonation at nitrogen atoms, were determined as heats of reaction (7)50
-.
14
15
18
19
20
21
22
23
BH+ B + H+
(7) using the experimentally derived value of the heat of formation of the proton (equal to 1536.7 kJ/mo150) and obtained by AM1 heats of formation of neutral (B) and protonated (BH+) molecules. The latter were derived by complete geometry optimisation of neutral and singly or doubly protonated base molecules starting from their relevant solid phase structures.
Results and Discussion Charge Distribution. In alkali metal salts the 1+ charge was always centered at metal atoms. In the organic base cations the positive charge was assumed to be located either, as a whole, on one (for monovalent) or two (in the case of divalent) nitrogen atoms, or on all the atoms of these ions. In the latter case charge distributions were, as mentioned, evaluated employing the IND049 and AM14' methods, and the examples for three cations of structures shown in Figure 1, are demonstrated in Table 11. In the case of pyridinium cation (compound 17) the location of the nitrogen atom has not been elucidated. Thus, the charge was averaged over both all ring and separately all hydrogen atoms. The distributions of charge in PtX6*-were taken from the literature (footnotes to Table III).2.14.51-55 Examination of the results of quantum chemistry calculations in this and our previous reveals that the charge is diffused throughout the whole molecule. The excess of a negative charge is usually predicted at more electronegative atoms, Le. on nitrogen and carbon atoms, whereas the deficiency of a negative charge at hydrogen atoms. This does not correspond to our
Figure 2. Geometries of cationic fragments of substances 14, 15, and 18-23 (cf. Table I ) in crystal lattices used in E,I calculations.
Dokurno et al.
2718 The Journal of Physical Chemistry, Vol. 97, No. 11, 1993
TABLE II: Net Atomic Charges in Cationic Forms of Simple Nitrogen Bases Calculated bv Ouantum Chemistry Methods cation" ~
13 atom(s)
24
16
INDO
AM1
-0.063 0.171 -0.038 0.179 -0.050 0.257 0.264 0.257 0.025 0.030 0.064 0.039 0.038 0.064 0.255 0.236 0.272
-0.082 -0.085 -0.172 -0.055 -0.069 0.279 0.292 0.280 0.115 0.123 0.140 0.118 0.132 0.154 0.277 0.259 0.295
atom(s)
INDO
AMI
0.016 0.085 0.085 0.260 0.231 0.099 0.063 0.099 0.063
0.047 -0.151 -0.144 0.224 0.220 0.214 0.186 0.206 0.193
atom(s)
INDO
AMI
-0.624 -0.449 0.800 0.187 -0.106 -0.030 0.015 -0.009 0.163 -0.049 0.364 0.05 1 0.250 0.240 0.245 0.023 0.018 0.000 0.026 0.047 0.016 0.047 0.053 0.240 0.235 0.250
-0.352 -0.248 0.252 -0.034 -0.087 -0.197 -0.165 -0.202 -0.127 -0.070 0.341 0.212 0.28 1 0.265 0.270 0.129 0.124 0.095 0.121 0.148 0.117 0.166 0.175 0.261 0.257 0.272
For structures of cations and numbering of atoms, see Figure I .
traditional belief that deficiency of a charge imparted to the proton is shared by the nitrogen atom of the base molecule upon its attachment. Molecular orbital calculations predict charge distributions for isolated molecules. In the solid phase a given ion is surrounded by negative and positive ions which may influence charge distributions and subsequently evaluated Coulombic interaction energies. The effect of surroundings has, indeed, been predicted in NH4Cli6and NH4Br4lattices. It may, thus, be expected also in the compounds studied. Unfortunately, the objects examined are too large to enable such an analysis. The question arises as to how realistic are charge distributions derived by quantum chemistry methods? In general, the INDO method better reproduces electrostatic features of molecules than does AMle60 Both methods assign partial charges somewhat artificially to atoms in ions and molecules. Such an assignment forms, however, a necessary basis for lattice energy calculations. Ability of OrganicBasesTo Protonate. Organic bases forming hexahalogenoplatinate salts liseted in Table I contain up to five nitrogen atoms able to participate in the formation of crystal lattices. To reveal the abilities of individual nitrogen atoms to protonate and thus the most probable protonation sites, as well as correlations between the formerquantitiesand the electrostatic interaction energies, the proton affinities which are compiled in Table IV were derived. Theoretical PAS deviate from experimentally found values by +20, for pyridine, to -87 kJ/mol in the case of 1,3-propanediamine. To account for such discrepancies we should note that the AM 1 method, although considered very useful for examining this feature, often provides values which differ from the experi m e n t a l ~ n e s . On ~ ~ the . ~ ~other hand, experimental PASare usually affected by the conditions of measurements or reference compounds used and the proton affinities assumed for Reviewing data in Table IV, it can be seen that the PA value for ammonia is generally lower than that resulting from the attachment of the proton to any nitrogen atom participating in the hydrogen bonding interactions in the lattice (the exception is compound 24). Moreover, PASvary from 785 to 956 kJ/mol. This may imply that proton affinity is related to some features
C1700
0 t
1
bb16 13
I
i-
.O 1300 Y
ll
0 e v)
2
15
Y
21
U
17612 D19
u 1100 W
0
20
22
9001 200
'
'
23 I
500
D
'
'
'
800
'
'
I
1100
'
'
v/z ( A 3 ) Figure 3. Lattice energy (compound numbers are given at points) versus volume of a basic stoichiometric unit (V,volume of elementary cell; 2, number of structural units in elementary cell). The electrostatic energies are the mean values from six columns listed under INDO and AM1 (Table HI), in the case of organic base salts, or three columns shown under (2)K(+)-PtX6(2-) (Table Ill), for alkali metal hexahalogenoplatinates.
of parent base molecules most probably electronic in origin. As proton affinity is believed to describe the ability of certain basic sites to protonate, it could therefore be expected that it is in someway dependent on the electron density a t nitrogen atoms. Actually, no correlation could be found between PAS and net atomiccharges, which reflect densities ofvalenceelectrons relative to core charges.48 Thus determined were densities of the lonepair electrons at nitrogen atom(s) by careful analysis of localized orbitals obtained by applying the procedure "localized orbitals" incorporated in the MOPAC.69 The values found originally, multiplied by 2 in order to reflect the density of the lone-pair, are demonstrated in Table IV. Generally, no correlation is seen between PAS and the latter quantity. It can, however, be noticed that nitrogen atoms in compounds 20 and 21 to which the highest
Hexahalogenoplatinate Lattices
The Journal of Physical Chemistry, Vol. 97, No. 11, 1993 2719
TABLE 111: Crystal Lattice Energies of Hexahrlogenoplatinates (in kJ/mol) this work (Coulombic energy) INDOh
Id
(2)K(+) - PtXb(2-)'
AMIh
IIY
IIV
I I'
1
1481
1461
1424
2 3
1471 1439
1454 1423
1420 1399
4
1490 1450
1472 1415
1438 1361
1438 1417 1320 1464
I405 1387
1355 1342
1445
1407
1422 1366 1219 1701 1612 1120 1 I75 1732
1376 1351 1210 1679 1601 1116N(I) 1174 N(2) 1713
1116 983 1120 1 I44 1206 1029 994 1057 850 947 1569
11 12 N(2) 977 N(3) 1 1 17 N(1) 1140 N(2) 1200 N(2) 1028 N(3) 993 N(4) 1052 847 N(1) 944 N(2) 1552
11'
Id
IIP
5
6 7
8 9
1474
1461
1436
1474
1461
1435
1442 1 I94 1070 1695 1577 1168
1422 1191 1077 1683 1571 1167
1392 1186 1088 1659 1560 1164
1442 1309 1163 1693 1561 1181
1422 1303 1162 1680 1555 1179
1391 1291 1 I59 1656 1544 1176
1720 1115 985
1710
1691
1680
983
979
1706 1 I40 956
1697
17 18h
954
949
19h
1125
1 I24
1121
1095
1093
1090
20h 2lh
1 I98
1195 1 I49
1190 1 I43
1 I24
1 I51
1152
1123 1149
1120 1 I44
22 23h
1016 924
1013 923
1008 920
998 906
985 904
979 900
24
1496
1487
1469
1481
1472
1455
10 11 12 13 14 lSh
16
1453 1374 1224 1713 1618 1122 1 I76 1742 1 I61 1118 986 1122 1146 1209 1029 995 1060 851 948 1579
11t.8
IIY
Id
no."
value
ref
1274. 1327. 1450. 1461. 1521.1572 1327 1468 (1461) 1521 1540, I598 1464 (1455) 1444 ( 1424) 1459 1546 (1473) 1300 1301, 1377, 1388, 1445, 1498 1423 (1414) 1451 1452,1506
56 14 2, 57 58 59 2
1468 (1446) 1507 1439
2 58 58
2
58 2 14 56 2 58 59
For names and formulas of the compounds, see Table I. Method of evaluation of charge distribution between the atoms in the complex cations. Location of (+1) charge at nitrogen atom(s) in salts of nitrogen bases, or at centers of alkali metal cations. dCharge distribution in PtCh2- taken from ref 51: Pt, +0.40; C1, -0.40. Charge distribution in PtBrk2- taken from ref 51: Pt, -0.20; Br, -0.30. Charge distribution in PtIb2- taken from refs 52-54: Pt, -0.20; I, -0.30. e Charge distribution in PtC1b2- taken from refs 2, 14, 52-54: Pt, +0.64; CI, -0.44. Charge distribution in PtB+ taken from refs 2, 14, 52-54: Pt, +0.28; Br, -0.38.fCharge distribution in PtCIe2- taken from ref 55: Pt, +1.09; CI, -0.515. Charge distribution in PtBrb2 taken from ref 55: Pt, +0.982; Br, -0.497. g Values in parentheses indicate the calculated energies of the Coulombic interactions. Values in columns 9-1 1 correspond to the location of I + charge at nitrogen atom indicated in parentheses. These nitrogen atoms were chosen considering boundary mesomeric structures (in the case of compounds 15, 18, 19, 21, and 23) or protonation site (for compound 20). L
PA and lone-pair density is imparted, are directly engaged in the
hydrogen bonds in the crystal. In these cases crystal formation must be preceded by protonation of the base molecules. A different situation occurs in the case of compound 18 where, according to MO calculations, the lowest energy monoprotonated form should be such that hydrogens are attached to N ( l ) and N(3) (AHr = 978.6 kJ/mol) and the relevant most thermodynamically stable base molecule such that H is bound to N(3) (AHl = 397.9 kJ/mol). It must, therefore, be that upon crystal formation, H is attached to N(2) instead of N ( l ) (Figure 2) which does not exhibit the highest PA or density of the lone-pair electrons, but the highest excess of a negative charge. The cation thus obtained interacts in the solid phase with the oxygen atom of H20, through the hydrogen bonding involving N(2),40which probably creates the most favorable conditions for the crystal formation. Coulombic Energy. Electrostatic lattice energies determined here together with the literature data are given in Table 111. Values of -EeI for inorganic hexahalogenoplatinates can be compared with literature values of crystal lattice energies. Conformity is quite good, particularly as regards energies of electrostatic interactions reported in ref 2. Such a comparison
is not feasible in the caseof organic salts due to the lack of pertinent experimental data. For hexachlorostannate salts, however, where comparison was made,19 the conformity appeared to be satisfactory, which confirms the soundness of the approach applied. Values of -Eel generally decrease with increase in the size of the constituting ionic fragments, which remains in accord with well-known empirical rules.s6 This is clearly demonstrated in Figure 3 where, with few exceptions (compounds 20,22, and 23), electrostatic energies show almost linear dependence on thevolume of the elementary cell, both for K2A and K A type salts. The above-mentioned compounds 20, 22, and 23 are somewhat untypical since the base molecules of which they are constituted contain chlorine or several oxygen atoms (in the carbonyl group). The electrostatic energies further decrease with the increase of distances between interacting fragments (Table I) and thedecrease of proton affinity of parent base molecules (Table 111). Since formation of the compounds studied can be considered as resulting from hydrogen bonding interactions it must, therefore, be that these become weaker if the tendency of a given basic site, located at nitrogen atom(s) for proton attachment is weaker and when interacting atoms are more removed from each other. This may appear to be a general feature of salts of nitrogen organic bases.
2720 The Journal of Physical Chemistry, Vol. 97, No. 11, 1993
Dokurno et al.
A
B
C
D
Figure 4. Three-dimensional views of equipotential surfaces of the electrostatic potential around ions in [H3N(CH2)3NH3]PtCI6 which correspond to the interaction energy with a unit charge equal to 130 kJ/mol. The 2+ charge was located either arbitrarily on two nitrogen atoms (1+ on each) (A) or on all the atoms of the cation, using charge distributions originating from I N D O (B) and AMI (C); the distribution of the charge in PtCI62was taken according to refs 2, 14, and 52-54 (Table Ill) (D).
c
P c
c c
7
A
B
c
3 3
C
D
Figure 5. Three-dimensional views of equipotential surfaces of the electrostatic potential around ions in ( ( ( C H J ) ~ N ~ ~ C O C H ~ ]which ~ P ~ Ccorrespond I, to the interaction energy with a unit charge equal to 75 kJ/mol (A, B, C ) or 150 kJ/mol (D). The 1+ charge was located either arbitrarily on one nitrogen atom (the nearest to Pt) (A) or on all the atoms of the cation, using charge distributions originating from lNDO (E)and AM1 (C); the distribution of the charge in PtCL2- was taken from refs. 2,14,52-54 (Table Ill) (D).
The Coulombic energies of hexahalogenoplatinates constituted of doubly charged cations (compounds 13, 14, 16, and 24) are generally much higher than those of salts containing monovalent cations. Such a regularity has also been noticed for hexahalo-
genostannate salts. I 9-70Among compounds composed of divalent cations, a relatively low value of -EeIwas obtained for L-lysine hexachloroplatinate. This may bedue to the relatively low proton affinity of the parent molecule, particularly the amino group
Hexahalogenoplatinate Lattices
The Journal of Physical Chemistry, Vol. 97, No. 11, 1993 2721
TABLE IV: Proton Affinity (PA), Lone-Pair Electron Density, and Net Atomic Charges Imparted to Nitrogen Atom(s) of Organic Bases PAh (kJ/mol) n0.O
this work‘
9,10 876.0 11 888.6 13 14
16 17 18 20 21
22 24
lone-pair net Mulliken lit.d electron atomic net atomic value ref densityb chargeb chargeb 860 934 977
2 X 889.8 (594.9) 2 X 903.5 (559.8) 2 X 901.8 (492.7) 939 942.1 922 956.0 939.4 856.3 813.4 926.1 785.5 (953)‘ 898.1 945.8 808.9 806.4 926.8 940.3 (609.0) 1023 860.9 (688.4)
61 62 63 62 64
65
66
2.000 1.958 1.976 1.938 1.964 1.974 I .960 1.692 1.980 1.682 1.942 1.690 1.966 1.970 1.578 1.880 1.958 1.968 1.980
-0.396 -0.309 -0.338 -0.263 -0.274 -0.138 -0.174 -0.289 -0.117 -0.321 -0.269 -0.349 -0.245 -0.057 -0.155 -0.330 -0.235 -0.369 -0.356
-0.528 -0.4 IO -0.452 -0.341 -0.364 -0.189 -0.219 -0,440
-0.150 -0.437 -0.349 -0.491 -0.278 -0.090 -0,277 -0.473 -0.288 -0.448 -0.472
For names and formulasof the cations (amines), see Table I. Values follow the order of increasing numbers of nitrogen atoms (Figures 1 and 2). For compounds 13, 14, 16, and 24 values corresponding to the attachment of a second proton a r e given in parentheses. All proton affinities taken from literature were of experimental origin and corrected relative to a P A for ammonia equal to 860 kJ/mol.6’ Value for 2-amino1,7-dihydro-6H-purin-6-one (guanine).
removed from the carboxyl group (Table IV), and relatively large distance between interacting fragments. Features of Electrostatic Potential Surrounding Ions. The results of this and our latest p a p e r ~ l ~ - ~reveal ~ - ~ Othat the distribution of a charge in ionic fragments has a rather minor effect on the derived electrostatic energies. Values of -E,, determined by assuming the location of the 1+(2+) charge on nitrogen atom@) are generally somewhat higher than those obtained using charge distributions derived by quantum chemistry methods. This means that the former simple approach can tentatively be applied to estimate Coulombic energies of complex ionic substances. The question, however, arises as to what causes the above mentioned regularities. To explain this, we have drawn maps of the molecular electrostatic potential around chosen charged species employing eq 5 and using a program written for this purpose. The examples are shown in Figures 4 and 5. As is seen, the electrostatic potential exhibits almost spherical symmetry around even very complex monovalent cations at distances where other ions in the lattice occur, irrespective of the assumed charge distribution (Figure 4). The same concerns the potential around highsymmetry octahedral PtC16*- ions (Figures 4 and 5 ) . This spherical symmetry of the potential is, however, somewhat disturbed around divalent cations in which basic centers are markedly removed (Figure 5). The above findings lead to the conclusion that a given complex ion is “seen” by surrounding ions to be similar to a monoatomic ion (around which the electrostatic potential is spherical). Therefore, the electrostatic potential can be well approximated by one resulting from the point charge located at a site being a certain center of a charge. It appears that this center roughly correlates with the location of the N atom.
Concluding Remarks The extended Ewald method which uses charges determined by quantum chemistry methods appears to be very useful in examining lattice energetics of complex organic ionic substances, and thus their cohesive energy. For the complete description of
this feature all four terms in (2) should, however, be taken into account, This could be done by adopting semiempirical functions of a potential for the description of repulsive and van der Waals interactions. Despite some shortcomings mentioned above the present paper extends our understanding of the nature of cohesive forces in the solid phase and contributes further towards the development of a general method of evaluating the crystal lattice energy. Such a method would be the first step towards a model enabling prediction of physicochemical features and reactivity of solid phase systems.
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