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Statistically-based interaction indices derived from molecular surface electrostatic potentials: a general interaction properties function (GIPF)
Journal of Molecular Structure (Theochem), 301(1994) 55-64 0166-1280/94/%07.00 0 1994 - Elsevier Science B.V. All rights reserved
55
Statistically-based interaction indices derived from molecular surface electrostatic potentials: a general interaction properties function (GIPF) Jane S. Murray, Tore Brinck, Pat Lane, Kim Paulsen, Peter Politzer* Department of Chemistry, University of New Orleans, New Orleans, LA 70148, USA (Received 19 July 1993; accepted 14 August 1993) Abstract A number of physical properties determined primarily by non-covalent interactions can be expressed quantitatively in terms of molecular surface area plus three statistically-based quantities obtained from the surface electrostatic potential: II, a measure of local polarity; a:,,, which indicates the variability of the potential on the surface; II, a measure of the balance between positive and negative regions. In the applications discussed, these quantities and the area are obtained through ab initio computations. The various specific relationships can be summarized through a general interaction properties function (GIPF), property =f(area, II, &, v), the functional form of which depends upon the property of interest.
Introduction
A continuing focus of our computational studies is the interpretation and prediction of molecular reactive behavior [l-4]. Pursuant to this objective, we have developed several statistically-based interaction indices which are obtained by plotting the computed electrostatic potential V(r) on molecular surfaces defined by the 0.001 a.u. contour of the electronic density p(r). V(r) is defined by Eq. (1).
Z, is the charge on nucleus A located at RA,and p(r’) is the total electronic density. During the past 20 years, the electrostatic potential has been used extensively in a qualitative manner to identify molecular regions most susceptible to electrophilic and/or nucleophilic attack, and also * Corresponding
author.
XSD10166-1280(93)03572-O
to infer general patterns of positive and negative regions that promote or inhibit molecular interactions, as between drugs and receptors [l-3,5-9]. It has also been found possible to establish some quantitative relationships involving V(r) extrema: the most negative potential V&n and/or the most positive surface potential Vs,,,. For example, we have shown that within families of similar molecules, Vti, and Vs,,, correlate with hydrogen bond basicity and acidity, respectively [lO,l 11. In the course of the past two years, we have sought to develop more quantitative means for using the electrostatic potential to analyze noncovalent molecular interactions in which there is no significant polarization or charge transfer. This has led us to introduce several statisticallybased indices that reflect the entire surface potentials of molecules: (a) ll, a measure of local polarity [12], (b) CJ-&which indicates the variability of the potential on the molecular surface [13-161 and (c) V, a measure of the “balance” between positive and
56
J.S. Murray et al./J. Mol. Struct. (Theochem)
Table 1 Experimentally-determined Molecule
Tbp (K)
normal boiling point?
307 (1994) 55-64
and calculated molecular properties
Surface
II
2 g+
2
area (A2)
(kcal mol-‘)
(kcal mol-1)2
2
V
$cal mol-‘)2
2 V~tot
(kcal mol-‘)2
109.2
55.5
3.15
5.4
3.5
8.9
0.238
2.1
144.2 169.5
65.5 68.9
8.32 4.06
66.9 1.2
2.9 8.3
69.8 15.5
0.040 0.249
2.8 3.9
184.6 189.2
11.5
2.42 9.01
3.4
C2H2
0.6 20.5
4.0 56.1
0.128 0.231
0.5 13.1
CHF3 CH3F
191.2 194.8
63.0 58.2
11.74
36.3 58.2 12.3
11.6 51.8
69.8
9.78
195.0 221.6 225.8
95.2 60.7
70.9 24.4
CH4 CF4 C2H4 CZH6
59.8
0.139 0.154
9.7 9.9
2.2 22.0
64.4 73.1 46.4
0.029 0.249
2.1 11.6
5.5 15.4
9.5 18.1
15.1 33.5
0.229 0.248
3.5 8.3
0.8 71.2
3.9 81.1
0.163 0.106
0.6 8.6
0.170 0.049
10.0 8.5
0.232 0.224 0.184
10.8 9.2 0.8
0.250 0.170 0.066
3.8 0.6 15.9
0.193
0.8 9.5
90.2 86.1
C3Ht7
225.9 231.1
8.30 12.55 3.83 10.84
98.5
2.38
3.1
W-W
235.5
80.7
246.1
89.4 87.3
7.80 11.48
9.8 46.0
9.12
9.0
10.46 8.08 2.52 4.50
17.2 13.9
2.37
2.9 17.0
C2F6
CH;F, C3H6
CH3CF3
CH2FCF3 (CH3)20
CH3CHF2 HCCCH3 (CHWH H2CCHCHCH2 CH3(CHhCH3 (CH,hNH
92.8 132.4
8.64 2.76
94.2
9.00
3.1 14.3
1.1 28.4
4.2 42.1
10.33 9.84
11.6 27.5
130.0 264.3
6.68 2.35 4.41
8.0 2.8
286.4 289.8 307.1 309.3
75.3 92.2 131.4 139.7
310.5 324.1
98.5 130.4
325.7 329.4
90.0
H,CCHCHO CH3COCH3 CH3COOCH3 CH30H (CH2)40 CH3(CH2)4CH,
CF3COOH CF3CH20H cc14
CH3CH20H C6H6 C6F6
cycle-CgH,2 CH3CN (CHWOH CH3CHOHCH3 CsHsF (CH,CHhS CH3N02 CsH,CH3
3.7 241.2
280.1
CH3CH2NH2
(CH3M
15.1
102.6 118.8
CH20CH2
(CH3)3CCl,
7.5 0.8 224.2
268.8 272.7
CH3CH2Cl
(CH&H2hO CH3(CHWH,
58.8 113.1 46.6 40.9 4.1
83.5 83.3 116.7
282.7 285.5
C(CH314
12.8 164.8 29.4 21.0 1.0
248.3 248.5 250.0 261.6
330.2 338.2 340.2 342.0
99.4 109.3 64.7 112.2 159.6
10.6 24.8
129.8 0.9
137.8 3.6
0.055 0.194
7.6 0.7
1.2 13.2
25.4 42.5
32.6 55.7
18.0 15.9
143.7
161.7 175.7
0.172 0.181 0.099 0.082
5.6 10.1 16.0 14.4
138.9 231.0
0.065 0.169
9.0 39.0
190.2 3.6 180.5
0.032 0.188 0.168
6.1 0.7 30.3
135.2 31.3 227.5
0.233 0.073 0.159 0.246
31.5 2.3
0.116
5.3
0.171 0.108 0.124 0.135 0.195 0.132 0.209 0.236
0.5 20.7 26.5 29.7 8.8 3.5 24.2 4.2
9.7 49.6
8.17 2.33
6.2 2.1 141.8
96.2 120.3
13.95 15.20 5.22
351.7 353.3
87.1 115.3
10.05 4.83
353.1 353.9 354.8 355.5 355.6 358.3
132.0 136.8
365.3
140.9 81.2 136.0
10.35 2.16 17.12 7.69 8.70 5.56 3.55 19.90 4.63
15.9 123.5 107.0 117.7
141.5 291.9
0.223 0.075 0.085
10.03 12.79
345.6 347.2 349.1
374.0 383.8
95.6
8.06 9.36 9.40
3.1 7.6
85.0 28.8 45.1 7.1 39.1 2.5 23.6 31.1 35.5 12.0 4.2 34.4 6.8
159.8 129.2 181.5 184.0 0.9 38.7 50.2 2.5 182.4 9.2 6.1
16.3 45.3
0.7 167.8 182.7 184.2 32.9 22.3 81.7 11.1
3.2 191.4 213.8 219.7 45.0 26.6 116.0 17.9
36.2 4.0
JS.
Murray et al./J. Mol. Strut.
(Theochem)
307 (1994) 55-64
51
Table 1 (continued) Molecule
H2NCH0 CSNHS CH,(CH,)@H CH2
W2)2
CH,COOH CH,(CH&CH, C6H,Cl (CH3)2NCH0 C6HSOCH3 C6H& CH3CH2S(CH2)2Cl (CH3)2NCOCH3 ,?‘&jHz,Cl2 @6H4C12 o-C6H4C10H
C1(CH2)&l &5H4Cl2 ChH,OH CsH,NH, C2Cl6 (CH3)2S0 CbH,CN m-C6H4C10CH3 m-C6H4BrCl p-C6H4BrCl HOCH2CH20H p-C6H.&lOCH3 o-C6H&lOCH3 a-CbH$rCl 1,3,5-C,5H,Cl, 2,4-C12C6H30H 1,2,4-C(jH3C13 m-C6H&10H (ClCH2CH2)2S Naphthalene 1,2,3C6H,C13 pC,H,ClCN o-C6H4ClCN m-C6H4ClN02 p-C6H4ClN&
5-OCH3-indole o-C,H,ClN& C6HsCOOH Indole C6(CH3)6 3-CH,-indole m-C6H4(N02)2 2-Naphthol Anthracene
W
Surface II area (A)2 (kcalmol-‘)
384.2 388.7 390.4 390.4 391.1 398.9 405.2 426.2 428.2 429.2 429.2 438.2 446.2 447.2 448.1 453.2 453.7 454.9 457.2 459.2 462.2 463.9 466.7 469.2 469.2 470.6 470.7 471.7 477.2 481.2 483.2 486.7 487.2 490.2 491.2 491.7 496.2 505.2 508.7 515.2 519.2 519.2 522.2 526.2 538.2 538.2 564.2 568.2 613.2
110.4 127.9 106.8 86.4 200.6 132.2 112.2 144.2 137.0 163.8 130.8 148.3 148.5 137.7 170.3 146.3 124.7 129.5 161.8 107.8 135.6 160.8 152.0 152.6 96.4 160.8 159.9 150.1 164.6 153.9 160.5 139.7 172.4 159.9 160.9 152.1 150.3 154.1 154.2 179.3 152.8 143.3 149.1 221.9 169.1 160.4 169.8 207.1
Tb
68.9
17.31 8.55 7.54 14.82 12.89 2.32 6.25 11.07 7.43 5.94 6.66 10.08 6.31 6.24 6.75 9.51 7.62 8.63 9.28 5.42 15.39 9.98 8.52 6.12 6.06 13.52 8.32 9.60 7.34 6.00 7.18 7.14 8.61 9.55 5.12 8.27 10.33 11.69 11.85 11.57 9.56 13.44 8.24 8.39 3.89 7.55 17.08 8.14 5.30
2 g+
(kcal mol-1)2 85.5 18.5 35.0 39.0 41.2 2.6 14.4 18.6 15.9 13.4 11.3 17.3 19.7 18.1 23.9 17.9 22.4 63.8 50.4 28.0 24.3 18.4 26.0 18.9 17.5 68.5 26.0 23.7 21.7 11.9 29.2 18.0 80.1 21.1 8.1 22.5 18.9 21.8 23.0 20.1 58.4 22.9 41.0 76.0 3.8 63.9 35.3 56.5 8.8
0! (kcalmol-‘)2 233.6 212.3 165.9 234.6 112.1 1.0 22.9 158.8 61.3 18.8 28.9 169.6 10.5 10.1 69.7 23.3 23.2 73.7 95.5 3.4 271.7 176.9 47.4 9.8 9.3 157.2 47.8 89.9 21.6 5.4 46.5 12.5 53.6 22.4 7.8 18.5 157.7 154.8 119.0 126.0 59.2 125.9 106.8 20.7 15.9 22.5 67.9 57.4 6.8
2 gtot
u
(kcal mol-‘)2 319.1 230.8 201.0 273.7 153.3 3.6 37.4 177.4 77.2 32.2 40.2 186.9 30.2 28.3 93.6 41.5 45.6 137.4 145.8 31.4 296.0 195.3 73.4 28.7 26.8 225.7 73.8 113.6 43.3 17.3 75.7 30.5 133.7 43.5 15.9 40.9 176.5 176.5 142.0 146.1 117.6 148.9 147.9 96.6 19.7 86.4 103.2 113.9 15.6
2 VUt0t
(kcal mol-‘)2 0.196 0.074 0.144 0.122 0.197 0.201 0.236 0.094 0.164 0.243 0.202 0.084 0.227 0.228 0.190 0.242 0.250 0.249 0.226 0.097 0.075 0.085 0.229 0.225 0.227 0.211 0.228 0.165 0.250 0.215 0.237 0.242 0.240 0.250 0.250 0.249 0.096 0.108 0.136 0.119 0.250 0.130 0.200 0.169 0.156 0.193 0.225 0.250 0.246
62.5 17.1 28.9 33.4 30.2 0.7 8.8 16.7 12.7 7.8 8.1 15.7 6.9 6.5 17.8 10.0 11.4 34.2 33.0 3.0 22.2 16.6 16.8 6.5 6.1 47.6 16.8 18.7 10.8 3.7 17.9 7.4 32.1 10.9 4.0 10.2 16.9 19.1 19.3 17.4 29.4 19.4 29.6 16.3 3.1 16.7 23.2 28.5 3.8
58
J.S. Murray et al./J. Mol. Struct. (Theochem)
307 (1994) 55-64
Table 1 (contined) Molecule
Phenanthrene Acridine
Surface area (A*) 613.2 618.2
aExperimentally-determined
203.0 204.3 properties
II (kcal mol-‘) 5.28 6.49
2 u+
UT
2 ~tot
(kcal mol-‘)’
(kcal mol-‘)’
(kcal mol-‘)’
9.7 16.1
7.1 82.7
16.8 98.8
2)
2 U~tot
(kcal mol-‘) 0.244 0.136
4.1 13.4
are taken from Ref. 37.
negative extrema [ 15,163.II, a:,, and ware defined in terms of the surface electrostatic potential by Eqs. (2)-(4).
(4) l’(ri) is the value of V(r) at point i on the surface, and Vs is the average value of the potential on the surface. In a similar fashion, V+(rJ and V-(ri) are the positive and negative values of V(r) on the surface, and Vs.+and Vs- are their averages:
II, as given by Eq. (2), is the average deviation of the electrostatic potential on the molecular surface. We have shown that II is an effective measure of local polarity (or charge separation), which may be quite significant even in a molecule having zero dipole moment, e.g. CO2 and @Z6H4(N02)z [12]. The total variance, a2tot, given by Eq. (3), is a measure of the spread of the surface potential, and is particularly sensitive to variations in its magnitude, emphasizing positive and negative extrema [13,14]. We interpret it as indicative of a molecule’s tendency for electrostatic interactions The “balance” parameter u (Eq. (4)) helps to more accurately represent the manner in which & affects electrostatic interactive tendencies [15,16]. The closer that w is to its maximum value of
0.250, the more likely it is that the molecule interacts to a similar extent (whether strongly OI weakly) through both its positive and negative regions. We have demonstrated the usefulness of II, o&,: v and ~a:,, in a number of applications [12-191. Our purpose in this article is to discuss these in the context of a generalized approach for understanding and predicting properties that are based on non-covalent molecular interactions. We also include a tabulation of calculated surface areas, II, d,,,, w and UC& values for one hundred molecules, arranged in order of increasing normal boiling point. Methods and procedure The optimized geometries of the molecules in Table 1 were computed at the ab initio SCF/STO3G* level using GAUSSIAN 88 [20]; these were used to calculate the SCF/STO-5G* electron density and electrostatic potential V(r). We computed V(r) on 0.28 bohr grids on 0.001 a.u. molecular surfaces, and used these values to obtain II, & and V, as given by Eqs. (2)-(4). The number of points on the molecular surface grids have been converted to surface areas (W2). & v and the surface area have been reported for nearly all of these molecules in earlier work [13-161, as has II for about 30 of them [12,13]. Relationships between our computed quantities and experimentally-determined physical properties [14-16,18,19] have been investigated using the SAS statistical analysis program [21]. l7, a measure of local polarity
II ranges from 0.0 for neutral
ground
state
J.S. Murray et a/./J. Mol. Struct. (Theochem) 307 (1994) 55-64 Tabie 2 Calculated II values and Abraham’s ~2” values’ for some mono-, di- and TV-substituted benzene derivatives Mole&e C6hGH3 C6H6 C6HsF
C$H,Br 1,4-C,H&12 C6HSCI
1,3,5-C6H3q l,3-C6H4C12 C6HSI
1,2,4-C6H,ClS CbH50CH3 1,2,3-C6H,C1, I ,2-C6H4C12 C,H,COOH 1,4-CbH40CH3Cl 1,3-C6H40CH&1 C,HSOH CsH5NH2 1,2-C6HSOCH3C1 C,H,CN 1,4-Q,H&NCl 1,3-C6H4CNCl 1,4-C6H4N02CI 1,2-C6H&NCl 1,3-C6H4N02CI 1,2-C,H4N02C1
fI (kcalmol-‘) 4.63 4.85 5.56 5.94 6.24 6.25 6.28 6.31 7.12 7.14 7.43 7.52 7.62 8.24 8.32 8.52 8.63 9.28 9.60 9.98 10.33 10.53 Il.57 11.69 11.85 13.44
0.52 0.52 0.57 0.73b 0.75 0.65 0.73 0.73 0.82 0.81 0.74 0.86 0.78 0.90b 0.86 0.86 0.89 0.96 0.92 1.11 1.18 1.14 1.17 1.24 1.13 1.25
aRef. 24, except for CsHSBr and C,H,COOH. bRef. 38.
atoms (for which V(rJ = ps) to approximately 20 kcal mol-‘; e.g. it is 19.5 kcalmol-* for 1,3,5trinitrobenzene and 21.6 kcal mol-’ for water 112,191.Most organic molecules, however, have II values between 2 and 15 kcal mol-’ (Table 1). The exceptions to this in Table 1 are m-dinitrobenzene, formamide, acetonitrile and nitromethane, all of which exceed the normal range. We have shown for a group of more than 20 solvents that II correlates well with the (7r*+ d6) polarizability/polarity term of Kamlet et al. [22], where d = -0.4 [12]. It is noteworthy that this term has been viewed as reflecting primarily polarity when d = -0.40 [23]. Tabie 2 lists II values for 26 mono-, di- and trisubstituted benzene derivatives along with Abraham’s solute $ pola~zability/polarity parameters
59
[24]. There is a good correlation between II and SJ# for these molecules (Fig. 1); the linear correlation ~oe~cient is 0.966. This may seem surprising since ny is considered to reflect pola~~bility as well as polarity [25]. The fact that the former does not appear to affect this correlation may be because the sizes of the molecules (and hence their polarizabilities [26]) are relatively similar. Another very practical application of our computed II values is in the area of energetic materials research. A key objective here is to understand the factors affecting the impact/shock sensitivities of energetic compounds [27-291. We have recently demonstrated for a group of 12 trinitroaromatics that impact sensitivity, as measured by the impact drop height kso, correlates with II and II’ through a dual-parameter relationship of the form given in Eq. (5), where Q, /? and y are coefficients of positive sign [19]. (The higher is the value of hso, the lower is the sensitivity.) hso=CXII-+I12+y
(5)
The linear correlation coefficient corresponding Eq. (5) is 0.986 1191.
Cr:,,, a measure ofelectrostatic
to
interuGtion tendency
2 gtot, as defined by Eq. (3), is the sum of the variances of the positive and negative regions of surface potential, g+ and a?. Thus it is a single quantity that reflects both positive and negative electrostatic interactive tendencies. Table 1 lists a: and ~5 as well as o& for each molecule. CT&, covers a much wider range of ma~itudes than II, from about 3-4 (k~almol-1)2 for aliphatic hydrocarbons to 3 19 (kcal mol-‘)2 for formamide. While c& often increases as II increases, this is not always the case, as can be seen in Table 1. (For the one hundred molecules in Table 1, the linear correlation coefficient between II and u& is only 0.677.) In the course of studying supercritical solubility, we have investigated possible relationships between the computed properties of a group of solid solutes - naphthalene (1) and eight indole derivatives (2-9) - and their solubilities in supercritical
J.S. Murray et al./J. Mol. Struct.
60
10
-
8
-
6
-
(Theochem)
307 (1994) 55-64
l-I
4
0.5
I
I
I
I
I
I
I
0.6
0.7
0.8
0.9
1
1.1
1.2
Fig. 1. Plot of I1 (kcal mol-I) vs. ~7 for 26 mono-, di-, and tri-substituted is 0.966.
C2H6, C2H4, CO2 and CHF3 at pressures of lo,12 and 14MPa [13]. We found excellent linear correlations between solubility and of,, of the solutes, with solubility increasing as a:,, decreases; the relationships were quantitatively similar in all four solvents. It was concluded that solubility in these systems is enhanced by a relatively slowly-varying solute surface potential and is impeded by sharp changes and strongly positive or negative extrema. These
1.3
benzene derivatives. The linear correlation coefficient
results are fully consistent with the known correlation between supercritical solubility and solute vapor pressure [30-321, since a small value of a:,, is indicative of weak solute-solute interactions and this favors high vapor pressure. While & was found to effectively reflect electronic factors influencing solubility for l-9 under the conditions being considered, in general the size of the solute molecule is also expected to be important [33-351. (l-9 are very similar in this respect .CH3
,CH3
J.S. Murray et a/./J. Mol. Struct. (Theochem)
cr
61
307 (1994) 55-64
OH
Cl
0
Cl,C-ccl,
Cl
14
16
15
and, not surprisingly, the inclusion of a term reflecting size (area or volume) did not significantly improve the solubility correlations mentioned above [ 131). When we extended our investigation to a larger and more heterogeneous group of 21 solutes, including 10-17, we found that size dependence did need to be introduced into our solubility expressions [14]. Our best double-variable relationship for solubility in supercritical CO2 at 14 MPa is of the form given in Eq. (6), In (solubility)
= cr(v01)-‘.~ - ,L?(&,)~- y
(6)
where a, p, and y are positive coefficients; the linear correlation coefficient is 0.948 [14]. It decreases slightly, by 0.01, when volume is replaced by solute surface area in Eq. (6). While our introduction of &,, occurred in conjunction with our investigations of supercritical solubility, we have since found more general applications for this quantity, which we view as a measure of electrostatic interaction tendency. These will be described in the next two sections, as part of our discussion of the “balance” parameter w and our generalized approach for understanding physical properties dependent upon noncovalent interactions. v, an electrostatic “balance” term, and the product uo-k,
In order to achieve greater insight into how c&,
17
relates to electrostatic interactive tendencies, we have defined the “balance” parameter V, given by Eq. (4). w approaches the limit of 0.250 as 0: and 2 approach the same magnitude. For example, benzene has J+ and a? values of 7.1 and 9.3 (kcalmol-‘)2, respectively; its w is 0.246. Ethanol and n-butanol, with w = 0.159 and 0.144, are more “balanced” than their structural isomers dimethyl ether and diethyl ether, for which v = 0.049 and 0.055, respectively. This is consistent with the fact that the alcohols are known to be relatively strong as both hydrogen bond donors and acceptors, while the ethers act only as hydrogen bond acceptors [37]. (Table 1 shows that the ethers have extremely low 02+values relative to 02-.) We have found that the product u&, also included in Table 1, is of key importance for understanding properties related to how well a molecule interacts electrostatically with other molecules of its own kind [16]. v& values in Table 1 range from 1 (kcalmol-‘)2 for saturated hydrocarbons to 62.5 (kcalmol-1)2 for formamide. A large value of 7~&, such as the latter, is indicative of a molecule that has relatively strong electrostatic interaction tendencies through both its positive and negative regions. We have recently shown for the variety of molecules in Table 1 that their critical constants (7’,, c and P,) and normal boiling points (Tbp) can be related to the computed molecular surface properties v& and/or surface area [ 161.The general forms of these relationships are given in Eqs. (7)-(lo),
J.S. Murray et al.lJ. Mol. Struct. (Theochem)
62
where a, p and y are coefficients of positive sign. V, = a: (area)‘.5 + p
(7)
Tbp = a (area) + p (vc&) o’5- y
(8)
r, = CrJarea+ p\l(wf3fo,)o~5 -y P, = -a(area)
+/3(7&)/area
+ y
(10)
Eqs. (8)-(10) each involve area and V& but in different forms. Both Tbp and T, are seen to increase with size and electrostatic self-interaction tendency, while PC increases with VO& but decreases with size [16]. It is interesting to note that the independent variables in Eq. (9) are the square roots of those in Eq. (8). This may be viewed as an attenuation of the effects of size and electrostatic interaction in determining T,, and may reflect the much lower density of a fluid at its critical temperature compared to a liquid at its normal boiling point. Another application of VC&,has been in the area of solute-solvent interactions in supercritical solubility. The solubility of a solid in a supercritical fluid reflects primarily two factors: the vapor pressure of the solid and solute-solvent interactions. At low densities, the former has been found to be the more important [31-331. We view our In (solubility) relationships, discussed earlier, as consistent with this observation [ 12- 131;the fact that solubility decreases with increasing &, indicates that strong solute-solute interactions (which lead to low vapor pressures) are impeding solubility in low density supercritical solutions. In order to focus on the secondary factor in lowdensity supercritical solubility, solute-solvent interactions, Johnston et al. have defined an enhancement factor, E (Eq. (11)) E = y2PlPy’
(11)
where y2 and Py’ are the solubility and vapor pressure of the solute and P is the pressure of the system. Py’/P can be viewed as the ideal gas solubility; E therefore indicates how much greater is the actual solubility, y2, due to solute-solvent interactions. For a group of 12 organic solutes in supercritical C02, at 20 MPa, we have found the
307 (1994) 55-64
following relationship between E and the computed 2 ‘uand ~a:,, of the solute [15] (Eq. (12)). area, cttot, E = -a (area)-‘.5 +~&+Y-+CT:,t)
-rl
(12)
where Q, /I, y, E and 77are positive coefficients. Eq. (12) indicates that solute-solvent interactions increase with solute size, electrostatic interaction tendency (as measured by o$,,), and “balance”, as measured by V, while Eq. (6) shows that overall solubility decreases with increasing size and L&,. In other words, both the area and &, of a solute have simultaneously opposing effects upon its behavior. This may explain the need for the cross-term VU:,, in Eq. (12), which comes in with a negative sign (at least in supercritical C02). It may be a damping term which reflects the fact that high a:,,, and w values also promote solutesolute interactions, which in turn impede solubility. General interaction properties function (GIPF)
The different specific applications that have been discussed can be united through Eq. (13), which is a generalized function for describing properties determined primarily by non-covalent interactions. This equation involves computed surface areas and surface electrostatic potential quantities (II, c&, and V) in a functional form that depends upon the specific property of interest. Property =f(area,
II, a:,,, U)
(13)
In our initial statistical explorations we generally 2 include area, II, ai, a!, a:,,, w, ~a,,,, and various powers and products of these terms as independent variables. In most instances we find reasonable two- or three-parameter relationships for the experimentally-determined properties being investigated, e.g. Eqs. (5), (6), (8)-(10) [14-16,18,19]. A very recent example of the use of our general interaction properties function (GIPF) has been in seeking to correlate our computed properties with the octanol-water partition coefficient Pow [ 181. For a group of 67 molecules, we have found a number of satisfactory relationships, some of which are listed in Table 3 in order of increasing
J.S. Murray ef al./J. Mol. Struct. (Theochem) 307 (1994) 55-64 Table 3 Summary of some relationships
63
between log POWand computed propertie?
dot)
Correlation coefficient
Standard deviation
Two-parameter 2 log Pow = cY(area) - pq,r - y
0.938
0.552
Three-parameter log P,, = Ly(area) - P& - yII + 6 log Pow = cr(area) - &,, - y(area)II - 6 log P,, = cY(area) - @-y(area)II - ~5
0.949 0.957 0.962
0.505 0.466 0.436
Lo&,
=f(area, K
aTaken from Ref. 18.
correlation coefficient. A very simple two-parameter expression with area and C& as independent variables gives a linear correlation coefficient of 0.938. We find improvement by adding a third term, e.g. JT or even better (area)II. Our best relationship is given in Eq. (14), with R = 0.962. log P,, = a(area) - pa! - y (area) II - 6
(14)
Summary
We have shown that a variety of physical properties determined primarily by non-covalent interactions can be expressed quantitatively in terms of molecular surface area plus three statisticallybased quantities obtained from the surface electrostatic potential. The different specific relationships can be summarized by a general interaction properties function (Eq. (13)) the form of which depends upon the property of interest. Acknowledgment
We greatly appreciate the support provided by DARPA/ONR Contract No. NOOO14-91-J-1897, administered by ONR. References 1 P. Politzer and KC. Daiker, in B.M. Deb (Ed.), The Force Concept in Chemistry, Van Nostrand Reinhold, New York, 1981, Chapter 6.
2 P. Sjoberg, J.S. Murray, T. Brinck and P. Politzer, Can. J. Chem., 68 (1990) 1440. 3 P. Politzer and J.S. Murray, in K.B. Lipkowitz and D.B. Boyd (Eds.), Reviews in Computational Chemistry, VCH, New York, 1991, Chapter 7. 4 T. Brinck, J.S. Murray and P. Politzer, J. Org. Chem., 56 (1991) 5012. 5 E. Scrocco and J. Tomasi, in Topics in Current Chemistry, New Concepts II, No. 42, Springer, Berlin, 1973, p. 95. 6 P. Politzer and D.G. Truhlar (Eds.), Chemical Applications of Atomic and Molecular Electrostatic Potentials, Plenum, New York, 1981. 7 P. Politzer, P.R. Laurence and K. Jayasuriya, Environ. Health Perspect. 61 (1985) 191. 8 J.S. Murray, K. Paulsen and P. Politzer, Indian Acad. Sci., in press. 9 T. Brinck, J.S. Murray and P. Politzer, Int. J. Quantum Chem., Quantum Biol. Symp., 19 (1992) 57. 10 J.S. Murray and P. Politzer, J. Org. Chem., 56 (1991) 6715. 11 J.S. Murray and P. Politzer, J. Chem. Res. (S), 110 (1992). 12 T. Brinck, J.S. Murray and P. Politzer, Mol. Phys., 76 (1992) 609. 13 P. Politzer, P. Lane, J.S. Murray and T. Brinck, J. Phys. Chem., 96 (1992) 7938. 14 P. Politzer, J.S. Murray, P. Lane and T. Brinck, J. Phys. Chem., 97 (1993) 729. 15 J.S. Murray, P. Lane, T. Brinck and P. Politzer, J. Phys. Chem., 97 (1993) 5144. 16 J.S. Murray, P. Lane, T. Brinck, K. Paulsen, M.E. Grice and P. Politzer, J. Phys. Chem., 97 (1993) 9369. 17 P. Politzer, J.S. Murray, MC. Concha and T. Brinck, J. Mol. Struct. (Theochem), 281 (1993) 107. 18 T. Brinck, J.S. Murray and P. Politzer, J. Org. Chem., in press. 19 J.S. Murray, P. Lane, T. Brinck and P. Politzer, Chem. Phys. Lett., submitted for publication. H.B. Schlegel, K. 20 M.J. Frisch, M. Head-Gordon,
J.S. Murray et al/J. Mol. Struct. (Theochem)
64
21 22 23 24
25 26 27 28
Raghavachari, J.S. Binkley, C. Gonzalez, D.J. DeFrees, D.J. Fox, R.A. Whiteside, R. Seeger, C.F. Melius, J. Baker, R. Martin, L.R. Kahn, J.J.P. Stewart, E.M. Fleuder, S. Topiol and J.A. Pople, GAUSSIAN 88,Gaussian Inc., Pittsburgh, PA, 1988. SAS, SAS Institute Inc., Cary, NC 27511. M.J. Kamlet, J.-L.M. Abboud, M.H. Abraham and R.W. Taft, J. Org. Chem., 48 (1983) 2877. M.J. Kamlet, R.M. Doherty, M.H. Abraham, Y. Marcus and R.W. Taft, J. Phys. Chem., 92 (1988) 5244. M.H. Abraham, Proc. Meeting on Solute/Solvent Interactions, G.R. Famini (Ed.), Edgewood Research, Development and Engineering Center, Aberdeen Proving Ground, MD, April 1993. M.H. Abraham, G.S. Whiting, R.M. Doherty and W.J. Shuely, J. Chromatogr., 587 (1991) 213. T. Brinck, J.S. Murray and P. Politzer, J. Chem. Phys., 98 (1993) 4305. M.J. Kamlet and H.G. Adolph, Propellants Explos. Pyrotech., 4 (1979) 30. C.B. Storm, J.R. Stine and J.F. Kramer, in S.N. Bulusu (Ed.), Chemistry and Physics of Energetic Materials, Kluwer, Dordrecht, 1990, Chapter 27.
307 (1994) 55-64
29 J.S. Murray and P. Politzer, in S.N. Bulusu (Ed.), Chemistry and Physics of Energetic Materials, Kluwer, Dordrecht, 1990, Chapter 8. 30 J.M. Dobbs and K.P. Johnston, Ind. Eng. Chem. Res., 26 (1987) 1476. 31 CT. Lira, in B.A. Charpentier and M.R. Sevenants (Eds.), Supercritical Fluid Extraction and Chromatography, ACS Symp. Ser. 366, American Chemical Society, Washington, DC, 1988, Chapter 1. 32 K.P. Johnston, D.G. Peck and S. Kim, Ind. Eng. Chem. Res., 28 (1989) 1115. 33 G.G. Hall and C.M. Smith, J. Mol. Struct. (Theochem), 179 (1988) 293. 34 CM. Smith, J. Mol. Strnct. (Theochem), 184 (1989) 103, 343. 35 R.B. Hermann, J. Phys. Chem., 76 (1972) 2754. 36 P. Politzer and J.S. Murray, in S. Patai (Ed.), Supplement E2: Chemistry of Hydroxyl, Ether and Peroxide Groups, Vol. 2, Wiley, Chichester, 1993, Chapter 1. 37 D.R. Lide (Ed.), CRC Handbook of Chemistry and Physics, 71st Edn., CRC Press, Boca Raton, FL, 1990. 38 M.H. Abraham, personal communication, 1992.
55
Statistically-based interaction indices derived from molecular surface electrostatic potentials: a general interaction properties function (GIPF) Jane S. Murray, Tore Brinck, Pat Lane, Kim Paulsen, Peter Politzer* Department of Chemistry, University of New Orleans, New Orleans, LA 70148, USA (Received 19 July 1993; accepted 14 August 1993) Abstract A number of physical properties determined primarily by non-covalent interactions can be expressed quantitatively in terms of molecular surface area plus three statistically-based quantities obtained from the surface electrostatic potential: II, a measure of local polarity; a:,,, which indicates the variability of the potential on the surface; II, a measure of the balance between positive and negative regions. In the applications discussed, these quantities and the area are obtained through ab initio computations. The various specific relationships can be summarized through a general interaction properties function (GIPF), property =f(area, II, &, v), the functional form of which depends upon the property of interest.
Introduction
A continuing focus of our computational studies is the interpretation and prediction of molecular reactive behavior [l-4]. Pursuant to this objective, we have developed several statistically-based interaction indices which are obtained by plotting the computed electrostatic potential V(r) on molecular surfaces defined by the 0.001 a.u. contour of the electronic density p(r). V(r) is defined by Eq. (1).
Z, is the charge on nucleus A located at RA,and p(r’) is the total electronic density. During the past 20 years, the electrostatic potential has been used extensively in a qualitative manner to identify molecular regions most susceptible to electrophilic and/or nucleophilic attack, and also * Corresponding
author.
XSD10166-1280(93)03572-O
to infer general patterns of positive and negative regions that promote or inhibit molecular interactions, as between drugs and receptors [l-3,5-9]. It has also been found possible to establish some quantitative relationships involving V(r) extrema: the most negative potential V&n and/or the most positive surface potential Vs,,,. For example, we have shown that within families of similar molecules, Vti, and Vs,,, correlate with hydrogen bond basicity and acidity, respectively [lO,l 11. In the course of the past two years, we have sought to develop more quantitative means for using the electrostatic potential to analyze noncovalent molecular interactions in which there is no significant polarization or charge transfer. This has led us to introduce several statisticallybased indices that reflect the entire surface potentials of molecules: (a) ll, a measure of local polarity [12], (b) CJ-&which indicates the variability of the potential on the molecular surface [13-161 and (c) V, a measure of the “balance” between positive and
56
J.S. Murray et al./J. Mol. Struct. (Theochem)
Table 1 Experimentally-determined Molecule
Tbp (K)
normal boiling point?
307 (1994) 55-64
and calculated molecular properties
Surface
II
2 g+
2
area (A2)
(kcal mol-‘)
(kcal mol-1)2
2
V
$cal mol-‘)2
2 V~tot
(kcal mol-‘)2
109.2
55.5
3.15
5.4
3.5
8.9
0.238
2.1
144.2 169.5
65.5 68.9
8.32 4.06
66.9 1.2
2.9 8.3
69.8 15.5
0.040 0.249
2.8 3.9
184.6 189.2
11.5
2.42 9.01
3.4
C2H2
0.6 20.5
4.0 56.1
0.128 0.231
0.5 13.1
CHF3 CH3F
191.2 194.8
63.0 58.2
11.74
36.3 58.2 12.3
11.6 51.8
69.8
9.78
195.0 221.6 225.8
95.2 60.7
70.9 24.4
CH4 CF4 C2H4 CZH6
59.8
0.139 0.154
9.7 9.9
2.2 22.0
64.4 73.1 46.4
0.029 0.249
2.1 11.6
5.5 15.4
9.5 18.1
15.1 33.5
0.229 0.248
3.5 8.3
0.8 71.2
3.9 81.1
0.163 0.106
0.6 8.6
0.170 0.049
10.0 8.5
0.232 0.224 0.184
10.8 9.2 0.8
0.250 0.170 0.066
3.8 0.6 15.9
0.193
0.8 9.5
90.2 86.1
C3Ht7
225.9 231.1
8.30 12.55 3.83 10.84
98.5
2.38
3.1
W-W
235.5
80.7
246.1
89.4 87.3
7.80 11.48
9.8 46.0
9.12
9.0
10.46 8.08 2.52 4.50
17.2 13.9
2.37
2.9 17.0
C2F6
CH;F, C3H6
CH3CF3
CH2FCF3 (CH3)20
CH3CHF2 HCCCH3 (CHWH H2CCHCHCH2 CH3(CHhCH3 (CH,hNH
92.8 132.4
8.64 2.76
94.2
9.00
3.1 14.3
1.1 28.4
4.2 42.1
10.33 9.84
11.6 27.5
130.0 264.3
6.68 2.35 4.41
8.0 2.8
286.4 289.8 307.1 309.3
75.3 92.2 131.4 139.7
310.5 324.1
98.5 130.4
325.7 329.4
90.0
H,CCHCHO CH3COCH3 CH3COOCH3 CH30H (CH2)40 CH3(CH2)4CH,
CF3COOH CF3CH20H cc14
CH3CH20H C6H6 C6F6
cycle-CgH,2 CH3CN (CHWOH CH3CHOHCH3 CsHsF (CH,CHhS CH3N02 CsH,CH3
3.7 241.2
280.1
CH3CH2NH2
(CH3M
15.1
102.6 118.8
CH20CH2
(CH3)3CCl,
7.5 0.8 224.2
268.8 272.7
CH3CH2Cl
(CH&H2hO CH3(CHWH,
58.8 113.1 46.6 40.9 4.1
83.5 83.3 116.7
282.7 285.5
C(CH314
12.8 164.8 29.4 21.0 1.0
248.3 248.5 250.0 261.6
330.2 338.2 340.2 342.0
99.4 109.3 64.7 112.2 159.6
10.6 24.8
129.8 0.9
137.8 3.6
0.055 0.194
7.6 0.7
1.2 13.2
25.4 42.5
32.6 55.7
18.0 15.9
143.7
161.7 175.7
0.172 0.181 0.099 0.082
5.6 10.1 16.0 14.4
138.9 231.0
0.065 0.169
9.0 39.0
190.2 3.6 180.5
0.032 0.188 0.168
6.1 0.7 30.3
135.2 31.3 227.5
0.233 0.073 0.159 0.246
31.5 2.3
0.116
5.3
0.171 0.108 0.124 0.135 0.195 0.132 0.209 0.236
0.5 20.7 26.5 29.7 8.8 3.5 24.2 4.2
9.7 49.6
8.17 2.33
6.2 2.1 141.8
96.2 120.3
13.95 15.20 5.22
351.7 353.3
87.1 115.3
10.05 4.83
353.1 353.9 354.8 355.5 355.6 358.3
132.0 136.8
365.3
140.9 81.2 136.0
10.35 2.16 17.12 7.69 8.70 5.56 3.55 19.90 4.63
15.9 123.5 107.0 117.7
141.5 291.9
0.223 0.075 0.085
10.03 12.79
345.6 347.2 349.1
374.0 383.8
95.6
8.06 9.36 9.40
3.1 7.6
85.0 28.8 45.1 7.1 39.1 2.5 23.6 31.1 35.5 12.0 4.2 34.4 6.8
159.8 129.2 181.5 184.0 0.9 38.7 50.2 2.5 182.4 9.2 6.1
16.3 45.3
0.7 167.8 182.7 184.2 32.9 22.3 81.7 11.1
3.2 191.4 213.8 219.7 45.0 26.6 116.0 17.9
36.2 4.0
JS.
Murray et al./J. Mol. Strut.
(Theochem)
307 (1994) 55-64
51
Table 1 (continued) Molecule
H2NCH0 CSNHS CH,(CH,)@H CH2
W2)2
CH,COOH CH,(CH&CH, C6H,Cl (CH3)2NCH0 C6HSOCH3 C6H& CH3CH2S(CH2)2Cl (CH3)2NCOCH3 ,?‘&jHz,Cl2 @6H4C12 o-C6H4C10H
C1(CH2)&l &5H4Cl2 ChH,OH CsH,NH, C2Cl6 (CH3)2S0 CbH,CN m-C6H4C10CH3 m-C6H4BrCl p-C6H4BrCl HOCH2CH20H p-C6H.&lOCH3 o-C6H&lOCH3 a-CbH$rCl 1,3,5-C,5H,Cl, 2,4-C12C6H30H 1,2,4-C(jH3C13 m-C6H&10H (ClCH2CH2)2S Naphthalene 1,2,3C6H,C13 pC,H,ClCN o-C6H4ClCN m-C6H4ClN02 p-C6H4ClN&
5-OCH3-indole o-C,H,ClN& C6HsCOOH Indole C6(CH3)6 3-CH,-indole m-C6H4(N02)2 2-Naphthol Anthracene
W
Surface II area (A)2 (kcalmol-‘)
384.2 388.7 390.4 390.4 391.1 398.9 405.2 426.2 428.2 429.2 429.2 438.2 446.2 447.2 448.1 453.2 453.7 454.9 457.2 459.2 462.2 463.9 466.7 469.2 469.2 470.6 470.7 471.7 477.2 481.2 483.2 486.7 487.2 490.2 491.2 491.7 496.2 505.2 508.7 515.2 519.2 519.2 522.2 526.2 538.2 538.2 564.2 568.2 613.2
110.4 127.9 106.8 86.4 200.6 132.2 112.2 144.2 137.0 163.8 130.8 148.3 148.5 137.7 170.3 146.3 124.7 129.5 161.8 107.8 135.6 160.8 152.0 152.6 96.4 160.8 159.9 150.1 164.6 153.9 160.5 139.7 172.4 159.9 160.9 152.1 150.3 154.1 154.2 179.3 152.8 143.3 149.1 221.9 169.1 160.4 169.8 207.1
Tb
68.9
17.31 8.55 7.54 14.82 12.89 2.32 6.25 11.07 7.43 5.94 6.66 10.08 6.31 6.24 6.75 9.51 7.62 8.63 9.28 5.42 15.39 9.98 8.52 6.12 6.06 13.52 8.32 9.60 7.34 6.00 7.18 7.14 8.61 9.55 5.12 8.27 10.33 11.69 11.85 11.57 9.56 13.44 8.24 8.39 3.89 7.55 17.08 8.14 5.30
2 g+
(kcal mol-1)2 85.5 18.5 35.0 39.0 41.2 2.6 14.4 18.6 15.9 13.4 11.3 17.3 19.7 18.1 23.9 17.9 22.4 63.8 50.4 28.0 24.3 18.4 26.0 18.9 17.5 68.5 26.0 23.7 21.7 11.9 29.2 18.0 80.1 21.1 8.1 22.5 18.9 21.8 23.0 20.1 58.4 22.9 41.0 76.0 3.8 63.9 35.3 56.5 8.8
0! (kcalmol-‘)2 233.6 212.3 165.9 234.6 112.1 1.0 22.9 158.8 61.3 18.8 28.9 169.6 10.5 10.1 69.7 23.3 23.2 73.7 95.5 3.4 271.7 176.9 47.4 9.8 9.3 157.2 47.8 89.9 21.6 5.4 46.5 12.5 53.6 22.4 7.8 18.5 157.7 154.8 119.0 126.0 59.2 125.9 106.8 20.7 15.9 22.5 67.9 57.4 6.8
2 gtot
u
(kcal mol-‘)2 319.1 230.8 201.0 273.7 153.3 3.6 37.4 177.4 77.2 32.2 40.2 186.9 30.2 28.3 93.6 41.5 45.6 137.4 145.8 31.4 296.0 195.3 73.4 28.7 26.8 225.7 73.8 113.6 43.3 17.3 75.7 30.5 133.7 43.5 15.9 40.9 176.5 176.5 142.0 146.1 117.6 148.9 147.9 96.6 19.7 86.4 103.2 113.9 15.6
2 VUt0t
(kcal mol-‘)2 0.196 0.074 0.144 0.122 0.197 0.201 0.236 0.094 0.164 0.243 0.202 0.084 0.227 0.228 0.190 0.242 0.250 0.249 0.226 0.097 0.075 0.085 0.229 0.225 0.227 0.211 0.228 0.165 0.250 0.215 0.237 0.242 0.240 0.250 0.250 0.249 0.096 0.108 0.136 0.119 0.250 0.130 0.200 0.169 0.156 0.193 0.225 0.250 0.246
62.5 17.1 28.9 33.4 30.2 0.7 8.8 16.7 12.7 7.8 8.1 15.7 6.9 6.5 17.8 10.0 11.4 34.2 33.0 3.0 22.2 16.6 16.8 6.5 6.1 47.6 16.8 18.7 10.8 3.7 17.9 7.4 32.1 10.9 4.0 10.2 16.9 19.1 19.3 17.4 29.4 19.4 29.6 16.3 3.1 16.7 23.2 28.5 3.8
58
J.S. Murray et al./J. Mol. Struct. (Theochem)
307 (1994) 55-64
Table 1 (contined) Molecule
Phenanthrene Acridine
Surface area (A*) 613.2 618.2
aExperimentally-determined
203.0 204.3 properties
II (kcal mol-‘) 5.28 6.49
2 u+
UT
2 ~tot
(kcal mol-‘)’
(kcal mol-‘)’
(kcal mol-‘)’
9.7 16.1
7.1 82.7
16.8 98.8
2)
2 U~tot
(kcal mol-‘) 0.244 0.136
4.1 13.4
are taken from Ref. 37.
negative extrema [ 15,163.II, a:,, and ware defined in terms of the surface electrostatic potential by Eqs. (2)-(4).
(4) l’(ri) is the value of V(r) at point i on the surface, and Vs is the average value of the potential on the surface. In a similar fashion, V+(rJ and V-(ri) are the positive and negative values of V(r) on the surface, and Vs.+and Vs- are their averages:
II, as given by Eq. (2), is the average deviation of the electrostatic potential on the molecular surface. We have shown that II is an effective measure of local polarity (or charge separation), which may be quite significant even in a molecule having zero dipole moment, e.g. CO2 and @Z6H4(N02)z [12]. The total variance, a2tot, given by Eq. (3), is a measure of the spread of the surface potential, and is particularly sensitive to variations in its magnitude, emphasizing positive and negative extrema [13,14]. We interpret it as indicative of a molecule’s tendency for electrostatic interactions The “balance” parameter u (Eq. (4)) helps to more accurately represent the manner in which & affects electrostatic interactive tendencies [15,16]. The closer that w is to its maximum value of
0.250, the more likely it is that the molecule interacts to a similar extent (whether strongly OI weakly) through both its positive and negative regions. We have demonstrated the usefulness of II, o&,: v and ~a:,, in a number of applications [12-191. Our purpose in this article is to discuss these in the context of a generalized approach for understanding and predicting properties that are based on non-covalent molecular interactions. We also include a tabulation of calculated surface areas, II, d,,,, w and UC& values for one hundred molecules, arranged in order of increasing normal boiling point. Methods and procedure The optimized geometries of the molecules in Table 1 were computed at the ab initio SCF/STO3G* level using GAUSSIAN 88 [20]; these were used to calculate the SCF/STO-5G* electron density and electrostatic potential V(r). We computed V(r) on 0.28 bohr grids on 0.001 a.u. molecular surfaces, and used these values to obtain II, & and V, as given by Eqs. (2)-(4). The number of points on the molecular surface grids have been converted to surface areas (W2). & v and the surface area have been reported for nearly all of these molecules in earlier work [13-161, as has II for about 30 of them [12,13]. Relationships between our computed quantities and experimentally-determined physical properties [14-16,18,19] have been investigated using the SAS statistical analysis program [21]. l7, a measure of local polarity
II ranges from 0.0 for neutral
ground
state
J.S. Murray et a/./J. Mol. Struct. (Theochem) 307 (1994) 55-64 Tabie 2 Calculated II values and Abraham’s ~2” values’ for some mono-, di- and TV-substituted benzene derivatives Mole&e C6hGH3 C6H6 C6HsF
C$H,Br 1,4-C,H&12 C6HSCI
1,3,5-C6H3q l,3-C6H4C12 C6HSI
1,2,4-C6H,ClS CbH50CH3 1,2,3-C6H,C1, I ,2-C6H4C12 C,H,COOH 1,4-CbH40CH3Cl 1,3-C6H40CH&1 C,HSOH CsH5NH2 1,2-C6HSOCH3C1 C,H,CN 1,4-Q,H&NCl 1,3-C6H4CNCl 1,4-C6H4N02CI 1,2-C6H&NCl 1,3-C6H4N02CI 1,2-C,H4N02C1
fI (kcalmol-‘) 4.63 4.85 5.56 5.94 6.24 6.25 6.28 6.31 7.12 7.14 7.43 7.52 7.62 8.24 8.32 8.52 8.63 9.28 9.60 9.98 10.33 10.53 Il.57 11.69 11.85 13.44
0.52 0.52 0.57 0.73b 0.75 0.65 0.73 0.73 0.82 0.81 0.74 0.86 0.78 0.90b 0.86 0.86 0.89 0.96 0.92 1.11 1.18 1.14 1.17 1.24 1.13 1.25
aRef. 24, except for CsHSBr and C,H,COOH. bRef. 38.
atoms (for which V(rJ = ps) to approximately 20 kcal mol-‘; e.g. it is 19.5 kcalmol-* for 1,3,5trinitrobenzene and 21.6 kcal mol-’ for water 112,191.Most organic molecules, however, have II values between 2 and 15 kcal mol-’ (Table 1). The exceptions to this in Table 1 are m-dinitrobenzene, formamide, acetonitrile and nitromethane, all of which exceed the normal range. We have shown for a group of more than 20 solvents that II correlates well with the (7r*+ d6) polarizability/polarity term of Kamlet et al. [22], where d = -0.4 [12]. It is noteworthy that this term has been viewed as reflecting primarily polarity when d = -0.40 [23]. Tabie 2 lists II values for 26 mono-, di- and trisubstituted benzene derivatives along with Abraham’s solute $ pola~zability/polarity parameters
59
[24]. There is a good correlation between II and SJ# for these molecules (Fig. 1); the linear correlation ~oe~cient is 0.966. This may seem surprising since ny is considered to reflect pola~~bility as well as polarity [25]. The fact that the former does not appear to affect this correlation may be because the sizes of the molecules (and hence their polarizabilities [26]) are relatively similar. Another very practical application of our computed II values is in the area of energetic materials research. A key objective here is to understand the factors affecting the impact/shock sensitivities of energetic compounds [27-291. We have recently demonstrated for a group of 12 trinitroaromatics that impact sensitivity, as measured by the impact drop height kso, correlates with II and II’ through a dual-parameter relationship of the form given in Eq. (5), where Q, /? and y are coefficients of positive sign [19]. (The higher is the value of hso, the lower is the sensitivity.) hso=CXII-+I12+y
(5)
The linear correlation coefficient corresponding Eq. (5) is 0.986 1191.
Cr:,,, a measure ofelectrostatic
to
interuGtion tendency
2 gtot, as defined by Eq. (3), is the sum of the variances of the positive and negative regions of surface potential, g+ and a?. Thus it is a single quantity that reflects both positive and negative electrostatic interactive tendencies. Table 1 lists a: and ~5 as well as o& for each molecule. CT&, covers a much wider range of ma~itudes than II, from about 3-4 (k~almol-1)2 for aliphatic hydrocarbons to 3 19 (kcal mol-‘)2 for formamide. While c& often increases as II increases, this is not always the case, as can be seen in Table 1. (For the one hundred molecules in Table 1, the linear correlation coefficient between II and u& is only 0.677.) In the course of studying supercritical solubility, we have investigated possible relationships between the computed properties of a group of solid solutes - naphthalene (1) and eight indole derivatives (2-9) - and their solubilities in supercritical
J.S. Murray et al./J. Mol. Struct.
60
10
-
8
-
6
-
(Theochem)
307 (1994) 55-64
l-I
4
0.5
I
I
I
I
I
I
I
0.6
0.7
0.8
0.9
1
1.1
1.2
Fig. 1. Plot of I1 (kcal mol-I) vs. ~7 for 26 mono-, di-, and tri-substituted is 0.966.
C2H6, C2H4, CO2 and CHF3 at pressures of lo,12 and 14MPa [13]. We found excellent linear correlations between solubility and of,, of the solutes, with solubility increasing as a:,, decreases; the relationships were quantitatively similar in all four solvents. It was concluded that solubility in these systems is enhanced by a relatively slowly-varying solute surface potential and is impeded by sharp changes and strongly positive or negative extrema. These
1.3
benzene derivatives. The linear correlation coefficient
results are fully consistent with the known correlation between supercritical solubility and solute vapor pressure [30-321, since a small value of a:,, is indicative of weak solute-solute interactions and this favors high vapor pressure. While & was found to effectively reflect electronic factors influencing solubility for l-9 under the conditions being considered, in general the size of the solute molecule is also expected to be important [33-351. (l-9 are very similar in this respect .CH3
,CH3
J.S. Murray et a/./J. Mol. Struct. (Theochem)
cr
61
307 (1994) 55-64
OH
Cl
0
Cl,C-ccl,
Cl
14
16
15
and, not surprisingly, the inclusion of a term reflecting size (area or volume) did not significantly improve the solubility correlations mentioned above [ 131). When we extended our investigation to a larger and more heterogeneous group of 21 solutes, including 10-17, we found that size dependence did need to be introduced into our solubility expressions [14]. Our best double-variable relationship for solubility in supercritical CO2 at 14 MPa is of the form given in Eq. (6), In (solubility)
= cr(v01)-‘.~ - ,L?(&,)~- y
(6)
where a, p, and y are positive coefficients; the linear correlation coefficient is 0.948 [14]. It decreases slightly, by 0.01, when volume is replaced by solute surface area in Eq. (6). While our introduction of &,, occurred in conjunction with our investigations of supercritical solubility, we have since found more general applications for this quantity, which we view as a measure of electrostatic interaction tendency. These will be described in the next two sections, as part of our discussion of the “balance” parameter w and our generalized approach for understanding physical properties dependent upon noncovalent interactions. v, an electrostatic “balance” term, and the product uo-k,
In order to achieve greater insight into how c&,
17
relates to electrostatic interactive tendencies, we have defined the “balance” parameter V, given by Eq. (4). w approaches the limit of 0.250 as 0: and 2 approach the same magnitude. For example, benzene has J+ and a? values of 7.1 and 9.3 (kcalmol-‘)2, respectively; its w is 0.246. Ethanol and n-butanol, with w = 0.159 and 0.144, are more “balanced” than their structural isomers dimethyl ether and diethyl ether, for which v = 0.049 and 0.055, respectively. This is consistent with the fact that the alcohols are known to be relatively strong as both hydrogen bond donors and acceptors, while the ethers act only as hydrogen bond acceptors [37]. (Table 1 shows that the ethers have extremely low 02+values relative to 02-.) We have found that the product u&, also included in Table 1, is of key importance for understanding properties related to how well a molecule interacts electrostatically with other molecules of its own kind [16]. v& values in Table 1 range from 1 (kcalmol-‘)2 for saturated hydrocarbons to 62.5 (kcalmol-1)2 for formamide. A large value of 7~&, such as the latter, is indicative of a molecule that has relatively strong electrostatic interaction tendencies through both its positive and negative regions. We have recently shown for the variety of molecules in Table 1 that their critical constants (7’,, c and P,) and normal boiling points (Tbp) can be related to the computed molecular surface properties v& and/or surface area [ 161.The general forms of these relationships are given in Eqs. (7)-(lo),
J.S. Murray et al.lJ. Mol. Struct. (Theochem)
62
where a, p and y are coefficients of positive sign. V, = a: (area)‘.5 + p
(7)
Tbp = a (area) + p (vc&) o’5- y
(8)
r, = CrJarea+ p\l(wf3fo,)o~5 -y P, = -a(area)
+/3(7&)/area
+ y
(10)
Eqs. (8)-(10) each involve area and V& but in different forms. Both Tbp and T, are seen to increase with size and electrostatic self-interaction tendency, while PC increases with VO& but decreases with size [16]. It is interesting to note that the independent variables in Eq. (9) are the square roots of those in Eq. (8). This may be viewed as an attenuation of the effects of size and electrostatic interaction in determining T,, and may reflect the much lower density of a fluid at its critical temperature compared to a liquid at its normal boiling point. Another application of VC&,has been in the area of solute-solvent interactions in supercritical solubility. The solubility of a solid in a supercritical fluid reflects primarily two factors: the vapor pressure of the solid and solute-solvent interactions. At low densities, the former has been found to be the more important [31-331. We view our In (solubility) relationships, discussed earlier, as consistent with this observation [ 12- 131;the fact that solubility decreases with increasing &, indicates that strong solute-solute interactions (which lead to low vapor pressures) are impeding solubility in low density supercritical solutions. In order to focus on the secondary factor in lowdensity supercritical solubility, solute-solvent interactions, Johnston et al. have defined an enhancement factor, E (Eq. (11)) E = y2PlPy’
(11)
where y2 and Py’ are the solubility and vapor pressure of the solute and P is the pressure of the system. Py’/P can be viewed as the ideal gas solubility; E therefore indicates how much greater is the actual solubility, y2, due to solute-solvent interactions. For a group of 12 organic solutes in supercritical C02, at 20 MPa, we have found the
307 (1994) 55-64
following relationship between E and the computed 2 ‘uand ~a:,, of the solute [15] (Eq. (12)). area, cttot, E = -a (area)-‘.5 +~&+Y-+CT:,t)
-rl
(12)
where Q, /I, y, E and 77are positive coefficients. Eq. (12) indicates that solute-solvent interactions increase with solute size, electrostatic interaction tendency (as measured by o$,,), and “balance”, as measured by V, while Eq. (6) shows that overall solubility decreases with increasing size and L&,. In other words, both the area and &, of a solute have simultaneously opposing effects upon its behavior. This may explain the need for the cross-term VU:,, in Eq. (12), which comes in with a negative sign (at least in supercritical C02). It may be a damping term which reflects the fact that high a:,,, and w values also promote solutesolute interactions, which in turn impede solubility. General interaction properties function (GIPF)
The different specific applications that have been discussed can be united through Eq. (13), which is a generalized function for describing properties determined primarily by non-covalent interactions. This equation involves computed surface areas and surface electrostatic potential quantities (II, c&, and V) in a functional form that depends upon the specific property of interest. Property =f(area,
II, a:,,, U)
(13)
In our initial statistical explorations we generally 2 include area, II, ai, a!, a:,,, w, ~a,,,, and various powers and products of these terms as independent variables. In most instances we find reasonable two- or three-parameter relationships for the experimentally-determined properties being investigated, e.g. Eqs. (5), (6), (8)-(10) [14-16,18,19]. A very recent example of the use of our general interaction properties function (GIPF) has been in seeking to correlate our computed properties with the octanol-water partition coefficient Pow [ 181. For a group of 67 molecules, we have found a number of satisfactory relationships, some of which are listed in Table 3 in order of increasing
J.S. Murray ef al./J. Mol. Struct. (Theochem) 307 (1994) 55-64 Table 3 Summary of some relationships
63
between log POWand computed propertie?
dot)
Correlation coefficient
Standard deviation
Two-parameter 2 log Pow = cY(area) - pq,r - y
0.938
0.552
Three-parameter log P,, = Ly(area) - P& - yII + 6 log Pow = cr(area) - &,, - y(area)II - 6 log P,, = cY(area) - @-y(area)II - ~5
0.949 0.957 0.962
0.505 0.466 0.436
Lo&,
=f(area, K
aTaken from Ref. 18.
correlation coefficient. A very simple two-parameter expression with area and C& as independent variables gives a linear correlation coefficient of 0.938. We find improvement by adding a third term, e.g. JT or even better (area)II. Our best relationship is given in Eq. (14), with R = 0.962. log P,, = a(area) - pa! - y (area) II - 6
(14)
Summary
We have shown that a variety of physical properties determined primarily by non-covalent interactions can be expressed quantitatively in terms of molecular surface area plus three statisticallybased quantities obtained from the surface electrostatic potential. The different specific relationships can be summarized by a general interaction properties function (Eq. (13)) the form of which depends upon the property of interest. Acknowledgment
We greatly appreciate the support provided by DARPA/ONR Contract No. NOOO14-91-J-1897, administered by ONR. References 1 P. Politzer and KC. Daiker, in B.M. Deb (Ed.), The Force Concept in Chemistry, Van Nostrand Reinhold, New York, 1981, Chapter 6.
2 P. Sjoberg, J.S. Murray, T. Brinck and P. Politzer, Can. J. Chem., 68 (1990) 1440. 3 P. Politzer and J.S. Murray, in K.B. Lipkowitz and D.B. Boyd (Eds.), Reviews in Computational Chemistry, VCH, New York, 1991, Chapter 7. 4 T. Brinck, J.S. Murray and P. Politzer, J. Org. Chem., 56 (1991) 5012. 5 E. Scrocco and J. Tomasi, in Topics in Current Chemistry, New Concepts II, No. 42, Springer, Berlin, 1973, p. 95. 6 P. Politzer and D.G. Truhlar (Eds.), Chemical Applications of Atomic and Molecular Electrostatic Potentials, Plenum, New York, 1981. 7 P. Politzer, P.R. Laurence and K. Jayasuriya, Environ. Health Perspect. 61 (1985) 191. 8 J.S. Murray, K. Paulsen and P. Politzer, Indian Acad. Sci., in press. 9 T. Brinck, J.S. Murray and P. Politzer, Int. J. Quantum Chem., Quantum Biol. Symp., 19 (1992) 57. 10 J.S. Murray and P. Politzer, J. Org. Chem., 56 (1991) 6715. 11 J.S. Murray and P. Politzer, J. Chem. Res. (S), 110 (1992). 12 T. Brinck, J.S. Murray and P. Politzer, Mol. Phys., 76 (1992) 609. 13 P. Politzer, P. Lane, J.S. Murray and T. Brinck, J. Phys. Chem., 96 (1992) 7938. 14 P. Politzer, J.S. Murray, P. Lane and T. Brinck, J. Phys. Chem., 97 (1993) 729. 15 J.S. Murray, P. Lane, T. Brinck and P. Politzer, J. Phys. Chem., 97 (1993) 5144. 16 J.S. Murray, P. Lane, T. Brinck, K. Paulsen, M.E. Grice and P. Politzer, J. Phys. Chem., 97 (1993) 9369. 17 P. Politzer, J.S. Murray, MC. Concha and T. Brinck, J. Mol. Struct. (Theochem), 281 (1993) 107. 18 T. Brinck, J.S. Murray and P. Politzer, J. Org. Chem., in press. 19 J.S. Murray, P. Lane, T. Brinck and P. Politzer, Chem. Phys. Lett., submitted for publication. H.B. Schlegel, K. 20 M.J. Frisch, M. Head-Gordon,
J.S. Murray et al/J. Mol. Struct. (Theochem)
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21 22 23 24
25 26 27 28
Raghavachari, J.S. Binkley, C. Gonzalez, D.J. DeFrees, D.J. Fox, R.A. Whiteside, R. Seeger, C.F. Melius, J. Baker, R. Martin, L.R. Kahn, J.J.P. Stewart, E.M. Fleuder, S. Topiol and J.A. Pople, GAUSSIAN 88,Gaussian Inc., Pittsburgh, PA, 1988. SAS, SAS Institute Inc., Cary, NC 27511. M.J. Kamlet, J.-L.M. Abboud, M.H. Abraham and R.W. Taft, J. Org. Chem., 48 (1983) 2877. M.J. Kamlet, R.M. Doherty, M.H. Abraham, Y. Marcus and R.W. Taft, J. Phys. Chem., 92 (1988) 5244. M.H. Abraham, Proc. Meeting on Solute/Solvent Interactions, G.R. Famini (Ed.), Edgewood Research, Development and Engineering Center, Aberdeen Proving Ground, MD, April 1993. M.H. Abraham, G.S. Whiting, R.M. Doherty and W.J. Shuely, J. Chromatogr., 587 (1991) 213. T. Brinck, J.S. Murray and P. Politzer, J. Chem. Phys., 98 (1993) 4305. M.J. Kamlet and H.G. Adolph, Propellants Explos. Pyrotech., 4 (1979) 30. C.B. Storm, J.R. Stine and J.F. Kramer, in S.N. Bulusu (Ed.), Chemistry and Physics of Energetic Materials, Kluwer, Dordrecht, 1990, Chapter 27.
307 (1994) 55-64
29 J.S. Murray and P. Politzer, in S.N. Bulusu (Ed.), Chemistry and Physics of Energetic Materials, Kluwer, Dordrecht, 1990, Chapter 8. 30 J.M. Dobbs and K.P. Johnston, Ind. Eng. Chem. Res., 26 (1987) 1476. 31 CT. Lira, in B.A. Charpentier and M.R. Sevenants (Eds.), Supercritical Fluid Extraction and Chromatography, ACS Symp. Ser. 366, American Chemical Society, Washington, DC, 1988, Chapter 1. 32 K.P. Johnston, D.G. Peck and S. Kim, Ind. Eng. Chem. Res., 28 (1989) 1115. 33 G.G. Hall and C.M. Smith, J. Mol. Struct. (Theochem), 179 (1988) 293. 34 CM. Smith, J. Mol. Strnct. (Theochem), 184 (1989) 103, 343. 35 R.B. Hermann, J. Phys. Chem., 76 (1972) 2754. 36 P. Politzer and J.S. Murray, in S. Patai (Ed.), Supplement E2: Chemistry of Hydroxyl, Ether and Peroxide Groups, Vol. 2, Wiley, Chichester, 1993, Chapter 1. 37 D.R. Lide (Ed.), CRC Handbook of Chemistry and Physics, 71st Edn., CRC Press, Boca Raton, FL, 1990. 38 M.H. Abraham, personal communication, 1992.