J. Phys. Chem. 1993,97, 9369-9373
9369
Relationships of Critical Constants and Boiling Points to Computed Molecular Surface Properties Jane S. Murray, Pat Lane, Tore Brinck, Kim Paulsen, M. Edward Grice, and Peter Politzer’ Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70148 Received: April 23, 1993’
It is shown, for a large number of organic compounds of a variety of types, that their critical constants (TC, and P,) and normal boiling points can be related to computed properties of the respective molecular surfaces. One of these is the surface area; the other is a measure of the molecule’s tendency for electrostatic interactions. These properties are obtained by ab initio SCF computations at the STO-5G* level, using STO-3G* optimized geometries.
v,,
Introduction and Background The electrostatic potential V(r) created in the space around a molecule by its nuclei and electrons is given rigorously by eq 1.
V(r) =
E-
=A
A IRA-
4
-
JE lr’- rl
(1)
Z, is the charge on nucleus A, located at RA,and p(r) is the electronic density function. V(r) is a real physical property which gives the net electrical effect of a molecule’s nuclei and electrons at any point in space r. It can be determined experimentally by diffraction methods as well as computationally’ and is wellestablished as an effective guide to molecular reactivebehavior.l.2 We and others have demonstrated that V(r) is particularly wellsuited for studiesof intermolecularinteractions,2-14e.g., hydrogen bonding tendencies, solute/solvent (or solute/solute) and recognition interactions; these can be viewed as being determined largely by electrostatic factors. It has seemed reasonable, therefore, to investigate the possibility of using V(r) as a basis for rationalizing and predicting physical properties, such as the critical constants, that presumably reflect tendencies for intermolecular interactions. In the course of recent work in the area of solute/solvent interactions and supercritical solubility, we have introduced two quantities, the total variance uta$ and a “balance” parameter u, that are derived from the electrostatic potential computed on molecular surfaces. These surfaces are defined, following Bader et a1.,15 as the 0.001 au contour of the electronicdensity p(r). utot and u are given by eqs 2 and 3.11J4 V+(ri) and V-(rj) are the .
m
Y
= u+2sZ/[uto~]z
(3)
v8+ v,-
positive and negative values of V(r) on the surface, and and vc are their averages: = ( l / m ) E ~ , ~ ( rand J = (1/4y*lwj). The total variance, uta?, is a measure of the spread of the surface potential and is particularly sensitive to variations in its magnitude, emphasizing positive and negative extremes.” We interpret it as indicativeof a molecule’s tendency for electrostatic interactions. For example, it is effective (in conjuction with
vs+
To whom corrapondence should bc addressed. *Abstract published in Aduance ACS Abstracts, Septembcr 1, 1993.
molecular volume or surface area) in correlating solubilities in supercritical C02, apparently because it reflects solute-solute interactions.13 The balance parameter u helps to more accurately represent the manner in which um2affects interactive tendencies.14 u attains its maximum value, 0.250, when u + ~and are equal. The closer that u is to 0.250, the more likely is it that the molecule interacts to a similar extent (whether strongly or weakly) through both its positive and negative regions. For example, ethanol and n-butanol have u values of 0.159 and 0.144, while those of their structural isomers dimethyl and diethyl ether are significantly lower, 0.049 and 0.055, respectively (Table I). This is consistent with the fact that the alcohols are known to be relatively strong hydrogen-bond donors and also acceptors, while the ethers act only as hydrogen bond acceptors.16
Present Objectives A compound‘s critical constants are of both fundamental and practical interest.17-19 Above its critical temperature T,, a compound can exist only in a single fluid phase. On a pressure volume plot, the isotherm corresponding to Tc goes through a saddle point; the pressure and molar volume at this point are designated as the compound’s critical pressure and volume, Pc and The term “supercritical fluid” is used to describe the system at temperatures above T,, the magnitude of which is often interpreted as reflecting the strength of intermolecular interactiom20 Critical temperatures, pressures and volumes can be determined experimentallyz1or they can be predicted using theoretical procedures, often empirical or semiempirical in n a t ~ r e . ~Grigoras ~ - ~ ~ has recently introduced a computational technique for estimating critical properties that is based on molecular surface areas and surface interactions computed from atomic radii and atomic charges.25 Extending Grigoras’ approach, we have investigated the possibility of relating critical constants and also boiling points to molecular surface areas and/or properties related to the surface electrostatic potential, obtained using ab initio self-consistentfield molecular orbital (SCF-MO) calculations. We have focused on utotand v (eqs 2 and 3) and surface area as molecular descriptors to be used in correlations with critical temperature, pressure and volume, and boiling point. Thus our approach uses only quantities that are specific to the molecule being considered and can be determined computationally.
vc.
Methods and Procedure This study encompasses99 organic molecules, which are listed in Table I in order of increasing boiling point; they comprise a large variety of aliphatic and aromatic hydrocarbons and their derivatives, including alcohols, ethers, ketones, aldehydes, amines, and halogenated systems. The optimized geometry of each
0022-3654/93/2091-9369$04.QQ/Q0 1993 American Chemical Society
9370
The Journal of Physical Chemistry, Vol. 97, No. 37, 1993
Murray et al.
TABLE I: Experimentally Determined Physical Propertiesaand Calculated Molecular Properties*
cc4
CH\CHzOH
CHpCH2S(CHz)zCI
109.2 144.2 169.5 184.6 189.2 191.2 194.8 195.0 221.6 225.8 225.9 231.1 235.5 246.7 248.3 248.5 250.0 261.6 268.8 272.7 280.1 282.7 285.5 286.4 289.8 307.7 309.3 310.5 324.1 325.7 329.4 330.2 338.2 340.2 342.0 345.6 347.2 349.7 351.7 353.3 353.7 353.9 355.5 355.6 358.3 365.3 374.0 383.8 384.2 388.7 390.4 390.4 391.1 398.9 405.2 426.2 428.2 429.2 429.2 438.2 446.2 447.2 448.1 453.2 453.7 454.9 457.2 459.2 462.2 463.9 466.7 469.2 469.2 470.6 470.7 47 1.7 477.2
191.1 227.5 283.1 305.4 308.7 299.1 317.8 292.9
99 140 129 148 113 133 124 225
46.4 37.4 51.2 48.8 62.4 47.5 58.8 29.4
365.1 346.5 369.8 375.4
181 22 1 203 169
46.0 37.6 42.5 50.2
400.0 386.6 401.0 408.2 425.2 425.0 437.7 433.8 460.4 469.0 456.4 466.7 469.7 503.1 507.0 506.0 508.7 506.9 513.2
178 181
53.3 45.0 53.5 36.5 43.3 38.0 53.1 32.0 52.7 71.9 56.4 36.4 33.7 55.2 39.5 51.7 47.0 46.9 79.5
263 221 255 187 303 199 140 182 280 304 295 209 228 118
507.0 491.3
370
30.1 32.6
556.3 513.9 562.1 516.7 553.6 506.2 508.3 560.1 557.0 588.0 591.8
276 167 259
173 316
45.6 63.8 49.2 33.0 40.5 39.7 47.6 45.5 38.6 63.1 42.1
620.0 563.0 593.0 592.7 568.8 632.4
254 275 206 171 492 308
56.3 44.2
645.6 670.0
330 324
42.5 45.2
684.0 685.0
359 372
38.5 39.5
697.3 694.2 699.0
360 229 274
41.0 61.3 53.1
699.4
310
42.2
645.0
186
77.0
275 220 269
57.9 25.1 45.2
55.5 65.5 68.9 77.5 59.8 63.0 58.2 95.2 60.7 90.2 86.1 98.5 80.7 89.4 87.3 83.5 83.3 116.7 102.6 118.8 92.8 132.4 94.2 75.3 92.2 131.4 139.7 98.5 130.4 90.0 99.4 109.3 64.7 112.2 159.6 95.6 96.2 120.3 87.1 115.3 132.0 136.8 123.5 107.0 117.7 140.9 81.2 136.0 68.9 110.4 127.9 106.8 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
5.4 66.9 7.2 3.4 36.3 58.2 12.3 70.9 24.4 5.5 15.4 3.1 9.8 46.0 9.0 17.2 13.9 3.1 7.6 2.9 17.0 3.1 14.3 11.6 27.5 8.0 2.8 7.2 13.2 18.0 15.9 9.7 49.6 6.2 2.7 141.8 85.0 28.8 45.1 7.1 39.1 2.5 31.1 35.5 12.0 4.2 34.4 6.8 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
3.5 2.9 8.3 0.6 20.5 11.6 51.8 2.2 22.0 9.5 18.1 0.8 71.2 12.8 164.8 29.4 27.0 1.o 7.5 0.8 224.2 1.1 28.4 130.0 264.3 129.8 0.9 25.4 42.5 143.7 159.8 129.2 181.5 184.0 0.9 38.7 50.2 2.5 182.4 9.2 6.1 0.7 182.7 184.2 32.9 22.3 81.7 11.1 233.6 212.3 165.9 234.6 112.1 1.o 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
8.9 69.8 15.5 4.0 56.7 69.8 64.4 73.1 46.4 15.1 33.5 3.9 81.1 58.8 173.7 46.6 40.9 4.1 15.1 3.7 241.2 4.2 42.7 141.5 29 1.9 137.8 3.6 32.6 55.7 161.7 175.7 138.9 23 1.O 190.2 3.6 180.5 135.2 31.3 227.5 16.3 45.3 3.2 213.8 219.7 45.0 26.6 116.0 17.9 319.1 230.8 201.0 273.7 153.3 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
0.238 0.040 0.249 0.128 0.231 0.139 0.154 0.029 0.249 0.229 0.248 0.163 0.106 0.170 0.049 0.232 0.224 0.184 0.250 0.170 0.066 0.193 0.223 0.075 0.085 0.055 0.194 0.172 0.181 0.099 0.082 0.065 0.169 0.032 0.188 0.168 0.233 0.073 0.159 0.246 0.116 0.171 0.124 0.135 0.195 0.132 0.209 0.236 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 0.21 1 0.228 0.165 0.250
2.1 2.8 3.9 0.5 13.1 9.7 9.9 2.1 11.6 3.5 8.3 0.6 8.6 10.0 8.5 10.8 9.2 0.8 3.8 0.6 15.9 0.8 9.5 10.6 24.8 7.6 0.7 5.6 10.1 16.0 14.4 9.0 39.0 6.1 0.7 30.3 31.5 2.3 36.2 4.0 5.3 0.5 26.5 29.7 8.8 3.5 24.2 4.2 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
The Journal of Physical Chemistry, Vol. 97,No. 37, 1993 9371
Computed Molecular Surface Properties
TABLE I (Continued)
vc
molecule Tbp (K) Tc (K) (cm3/mol) Pc(bar) surface area u+~ c2 ut012 V vuto? 1,3,5-C6HsC13 48 1.2 164.6 11.9 5.4 17.3 0.215 3.7 2,4-Cl#&OH 483.2 153.9 29.2 46.5 75.1 0.237 17.9 1,2,4-C&C13 486.7 160.5 18.0 12.5 30.5 0.242 7.4 139.1 80.1 53.6 133.7 0.240 32.1 m-C6H&lOH 487.2 10.9 (ClCH2CH2)2S 490.2 172.4 21.1 22.4 43.5 0.250 naphthalene 491.2 748.4 413 41.1 159.9 8.1 7.8 15.9 0.250 4.0 1,2,3-C6H$13 491.7 160.9 22.5 18.5 40.9 0.249 10.2 0.096 16.9 p-C6H&lCN 496.2 152.1 18.9 157.7 176.5 21.8 154.8 176.5 0.108 19.1 &6H&lCN 505.2 150.3 m-C&i&lN02 508.7 154.1 23.0 119.0 142.0 0.136 19.3 0.119 17.4 p-C6H&IN02 515.2 154.2 20.1 126.0 146.1 5-OCH3-indole 519.2 745.0 435 35.5 179.3 58.4 59.2 117.6 0.250 29.4 &6H4ClN02 519.2 152.8 22.9 125.9 148.9 0.130 19.4 C6H&OOH 522.2 752.0 341 45.6 143.3 41.0 106.8 147.9 0.200 29.6 96.6 0.169 16.3 indole 526.2 791.0 361 43.0 149.1 76.0 20.7 3.8 15.9 19.7 0.156 3.1 C6(CH3)6 538.2 767.2 23.2 221.9 3-CH3-indole 538.2 789.0 415 37.2 169.1 63.9 22.5 86.4 0.193 16.7 103.2 0.225 23.2 m-C&(NO2)2 564.2 160.4 35.3 67.9 2-naphthol 568.2 169.8 56.5 57.4 113.9 0.250 28.5 613.2 207.1 8.8 6.8 15.6 0.246 3.8 anthracene phenanthrene 613.2 203.0 9.7 7.1 16.8 0.244 4.1 16.1 82.7 98.8 0.136 13.4 acridine 618.2 204.3 a Experimentally determined properties are taken from refs 25, 29, and 30. The units of calculated properties are surface area, A2;c 2 , u+~, and utot2(kcal/mol)2. molecule was computed a t the a b initio SCF/STO-3G* level26 and used to calculate the SCF/STO-SG* electronic density and electrostatic potential V(r). Someof the molecules were included in our earlier investigations of hydrogen-bonding tendencies10 and supercritical solubility.llJ3J4 In this work, we have computed V(r) on 0,001 au molecular surfaces. A 0.28-bohr square grid was used to obtain the surface areas2' Thevalues of V(r) on this grid have been used to compute ut,,? and Y, as given by eqs 2 and 3. We have used the SAS statistical analysis program28 to investigate relationships between our computed properties and T,, V,, P,, and the boiling point.
in Table 11,along with a statistical evaluation of each correlation. The two best general ones (for molecules) are for n = 1.5, which is consistent with dimensional considerations, and n = 1.2365 (R = 0.986 for both). V, calculated with n = 1.5 is ploted against the experimental data in Figure 1. It is interesting to note that when n = 1.2365, then @ = 0, so that the plot of Vc(calc) vs area passes through the origin. Our best dual-parameter relationship for boiling point, Tbp, is given in eq 5. As anticipated, it shows Tbp to increase with
ReSJlkS
molecular size and interaction tendency. The linear correlation coefficient R is 0.949 for the entire data set of 99 molecules. Tbp (calc) is plotted against Tbp (exp) in Figure 2. Our best dual-parameter relationship for critical temperature, T,, shown in eq 6, is very similar to eq 5. Our two independent
In Table I are listed the experimentally-determined boiling points, critical temperatures, volumes, and pressures (T,, V,, and P,), when available,25.29930as well as the computed surface areas and the u+2, u-2, uJ, and v values for 99 organic molecules. The cross-term vum2is also included in Table I. Our statistical analyses have shown this quantity to be of key importance for our present purposes, more so than either u,? or v alone. A large value of vuIo? is indicative of a molecule that has strong electrostatic interaction tendencies through both its positive and negative regions. Such a molecule is likely to interact well with its own kind (a feature that is particularly relevant in the present context). For example, the largest value of vutot2in Table I is 62.5 (kcal/ mo1)2, for formamide (HzNCHO), which also has an extremely high dielectric constant. Looking first at only the experimentally-determined properties, it can be seen that Tc generally increases in the same order as does the normal boiling point, Tbp. Indeed it has been pointed out that for most substances, Tc is approximately 1.6 Tbp.17 For the 66 molecules in Table I for which both Tcand Tbp are available, the relationship between the two is Tc = 1.40Tbp 44.1; the linear correlation coefficient is 0.992. Grigoras obtained a very similar result for a group of 137 organic ~olecules.*5However there are no strong correlations between V, or P, and T, or Tbp or each other. Proceeding now to our relationships between computed and measured properties, the simplest one is for the critical volume, which can be expressed in terms of just surface area, as given by eq 4. The constants a! and j3 for several values of n are listed
+
r,,
t, = a!(area)" + p
(4)
(5)
T, = CYG +
+y
(6)
variables in eq 6 are the square roots of those in eq 5. This may be viewed as an attenuation of the effects of size and electrostatic interaction and may reflect the much lower density of a fluid a t Tccompared to a liquid at its normal boiling point. Our data set includes 65 experimentally determined values of T,, for which the linear correlation coefficient is 0.914. T,(calc) is plotted against T,(exp) in Figure 3. Equation 7 gives our best dual-parameter relationship for the critical pressure, P,, which encompasses 57 of the 64 molecules in Table I for which Pcdata are available. (This set of 57 excludes
P, = cu(area) + @(vato,Z)/area+ y
(7)
the seven molecules having more than one fluorine; these have considerably lower Pc values than would be predicted from our computed surface areas and uutot2values.) The linear correlation coefficient is 0.910. The signs of a! and j3, given in Table I1 indicate that Pc increases with the tendency for electrostatic interaction and decreases with molecular size. (The same conclusion is reached from the formula that relates Pc and the van der Waals constants, P, = a/27b2.17) In Figure 4, P,(calc) is plotted against Pc(exp) for the 57 molecules. Equations 4-7 summarize our best single- or dual-parameter relationships for critical volume, normal boiling point, critical
9372 The Journal of Physical Chemistry, Vol. 97, No. 37, 1993
Murray et al.
TABLE II: Summary of Correlations between Computed Properties and V, Tb Tn and P, correlation V, = a(area)" + B
57
1.o
160
1.2365 1.5 2.0 1.5
99 220
2.736 2.759
65 2w
75.72 74.17
576 2w
-0,1764 -0.1512
ci
Tbp = a(area)
+ B(vuat2)0.S+ y
a
G + B(vut1,2)0.'
T,= a
+y
a
Pc = cr(area) + B(vumz)/area a
+y
linear correlation coefficient. R
standard deviation
-55.9 0.0 42.3 93.2 39.8
0.985 0.986 0.986 0.980 0.993
15.8 cm3/mol 15.0 cm3/mol 15.1 cm3/mol 18.1 cm3/mol 13.8cm3/mol
-72.05 -97.38
0.949 0.959
36.5 K 41.0 K
0.914 0.941
59.7K 53.3 K
0.910 0.934
4.8 bar 3.7bar
values of constants
no. of molecules
2.71 0.717 0.168 1.14X 1C2 0.168
B 33.31 44.80
B
Y
150.2 163.8
-538.6 -536.1
B
Y
48.69 64.42
61.73 57.07
Molecules containing atoms other than carbon and hydrogen are omitted from data set. Molecules with more than one fluorine are omitted from
the data set.
700
-
600
-
500 -
Tc(calc.)
0' 0
I 100
200
300
400
500
200
300
400
vc (CXP.)
500
1
600
800
700
900
I
I
Figure 3. Tc(calc) plotted against T,(exp) for 65 molecules, using the relationship given in Table 11. The line drawn corresponds to T,(calc) = Tc(exp). 80
600
70
500
so
400
50 Pc (calc.)
T (calc.) bp
40
300
i 100 100
4.
Tc(exp.)
Figure 1. V,(calc) plotted against V,(exp) for 57 molecules, using the relationship giv_enin Table I1 with n = 1.5. The line drawn corresponds to Vc(caIc) = V,(exp). 700
x*
4
100
800
*J"
.
400 -
300 200 100
..1.' e
' . *
30
20
200
300
400
500
600
700
Tbp (exp.)
20
1
/ 30
40
50
60
70
80
PE(exp.)
Figure 2. Tb(calc) plotted against Tb(exp) for 99 molecules, using the relationship given in Table 11. The line drawn corresponds to Tbp(cak) = TdexP).
Figure 4. Pc(calc) plotted against Pc(exp) for 57 molecules, using the relationship given in Table 11. The seven molecules in Table I that have more than one fluorine are not included in the data set. The line drawn corresponds to Pc(calc) = Pc(exp).
temperature and critical pressure, respectively, for the data given in Table I. In each case, many possible variables were tried in our statistical analyses, including powers of area and vu,,?, as well as vuJ(area), vum2/area, a+*, c 2 , q0?,and v, taken separately. For the inclusion of a second variable, vuto?, in addition to resulted in an improvement of only 0.002 in R and was not viewed as significant. For the physical properties Tbp,T,, and Pc,again only marginal improvementswere obtained by the addition of a third and/or fourth variable.
Discussion and Summary We have sought to include in our data base a wide variety of molecular types. Accordingly it is gratifying that we are able to satisfactorily represent all our properties ( Tbp, T,,and Pc) in terms of two easily justifiable quantities which reflect molecular size and tendency for electrostatic interaction. It should be noted that these quantities are computed for isolated molecules, but evidently can be used to predict fluid-phase properties.
vc,
v,,
Computed Molecular Surface Properties As a point of interest, Table I1 also presents the results of considering only the subset of hydrocarbons. As anticipated, the correlations are improved by being limited to relatively similar molecules, but it is pleasing that the a,8, and y values are overall not drastically different from what they are for the larger data sets. This supports the validity of fitting all of the compounds to the same relationships. The critical temperature may be viewed as the point beyond which the molecular velocities are so great that no amount of pressure suffices to cause coalescence. The stronger are the intermolecularattractive forces, the higher are the velocities that must be achieved in order that coalescence be unattainable, and hence the greater is To Strong intermolecular attractions also increasePc,since higher velocities mean that the greatest pressure that can still produce coalescence must likewise be higher. On the other hand, Pc increases with diminishing molecular size, since at a given temperature, smaller molecules have greater velocities. The fact that eq 7 exaggerates Pc for the polyfluoro derivatives may be because uutot2overestimatestheir interactive tendencies. These molecules can be expected to have anomalously low polarizabilities31J2and therefore to be less interactivethan would be predicted from vuto? alone.
Acknowledgment. We greatly appreciate the support provided by DARPA/ONR Contract No. N00014-91-J-1897, administered by ONR.
The Journal of Physical Chemistry, Vol. 97, No. 37, 1993 9373 (7) Weinstein, H.; Osman, R.; Green, J. P.; Topiol, S. In Chemical Applications of Atomic and Molecular Electrostatic Potentials; Politzer, P., Truhlar, D. G., Us.; Plenum Press: New York, 1981; p 309. (8) Sjoberg, P.; Murray, J. S.;Brinck, T.; Evans, P.; Politzer, P. J. Mol. Graphics 1990, 8, 81. (9) Murray, J.S.;Grice,M. E.;Politzer,P.;Etter,M.C.Mol. Eng. 1991, 1, 75. (10) Murray, J. S.; Politzer, P. J . Chem. Res. 1992 ( S ) , 110. (1 1) P o k e r , P.; Lane, P.; Murray, J. S.; Brinck, T. J. Phys. Chem. 1992, 96. 7938. (12) Brinck, T.; Murray, J. S.; Politzer,P. Int. J . Quantum Chem., Quantum Biol. Symp. 19, 1992, 57. (13) Politzer, P.; Murray, J. S.;Lane, P.; Brinck, T. J. Phys. Chem. 1993, 97, 729. (14) Murray, J. S.; Lane,P.;Brinck, T.;Politzer, P. J . Phys. Chem. 1993, 97. 5144. (15) Bader, R. F. W.;Carroll, M. T.;Cheeseman, J. R.; Chang, C. J. Am. Chem. Soc. 1987, 109,7968. (16) Politzer, P.; Murray, J. S.InSupplement E Z Chemistry of Hydroxyl Ether and Peroxide Groups;John Wiley & Sons: Chichester, England, 1993; Chapter 1. (17) Levine, I. N. Physical Chemistry; McGraw-Hill Book Co.: New York, 1988. (18) Palmieri, M. D. J. Chem. Educ. 1988,10, A254. (19) Johnston, K. P., Penninger, J. M. L., Eds.,Supercritical Fluid Science
Technology;American Chemical Society: Washington, DC; ACS Symp.Series
406, 1989. (20) Sadus, R. J. Fluid Phase Equilib. 1992, 77, 269. (21) Hicks, C. P.; Young, C. L. Chem. Rev. 1975, 75, 121. (22) Ambrose, D.; Townsend, R. Trans. Faraday Soc. 1968, 64, 2622. (23) Somayajulu, G. R. Chem. Eng. Data 1989, 34, 106. (24) Teja, A. S.;Lee, R. J.; Rosenthal, D.; Anselme, M. Fluid Phase Equilib. 1990, 56, 153. (25) Grigoras, S.J . Comput. Chem. 1990, 11,493. (26) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.;
References and Notes
Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.;Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley,
(1) Politzer, P., Truhlar, D. G. Eds. Chemical Applications ofAtomic and Molecular Electrostatic Potentials, Plenum Press: New York, 1981. (2) Politzer, P.; Murray, J. S.In Reuiews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; VCH Publishers: New York, 1991; Chapter 7. (3) Petrongolo, C.; Tomasi, J. Int. J . Quantum Chem., Quantum Biol. Symp. 2 1975, 181. (4) Loew, G. H.; Berkowitz, D. S . J. Med. Chem. 1975, 18, 656. (5) Hayes, D. M.; Kollman, P. A. J . Am. Chem. SOC.1976,98, 7811. (6) Weinstein. H.: Osman.. R.:.ToDiol. . S.:Green, J. P. Ann. N.Y. Acad. Sci. 1981, 367, 434.
PA, 1992. (27) Theprogramsused tocompute propertieson surfaces havebcenwritten by Dr. Per Sjoberg and Dr. Tore Brinck. (28) SAS, SAS Institute Inc., Cary, NC 2751 1. (29) Lide, D. R., ed., CRCHandbook of Chemistry and Physics, 71st ed.; CRC Press: h a Ration, FL, 1990. (30) Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids, 3rd ed.; McGraw-Hill: New York, 1977. (31) Politzer, P. J. Chem. Phys. 1987, 86, 1072. (32) Brink, T.; Murray, J. S.; Politzer, P. J . Chem. Phys. 1993,98,4305.
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