J . Phys. Chem. 1994,98, 2489-2493
2489
Predictive Force-Field Calculations for the Equilibrium Dimerization of Isoprene Mangalya Kar,+Terry G. Lenz,'q+ and John D. Vaughan'?* Department of Chemical Engineering and Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523 Received: October 26, 1993'
The Diels-Alder dimerization of isoprene is an important reaction; dipentene (or racemic limonene), one of the products formed in this reaction, has major applications in the manufacture of polymers and adhesives.' Dipentene also has various uses in the food and pharmaceutical industries.' In the present work, the Q C F F force field program2 was used to calculate gas-phase thermodynamic properties of the monomer (isoprene) and the dimers 1-methyl-5-( 1-methylethenyl)cyclohexene(diprene) and 1-methyl-4-( 1-methylethenyl)cyclohexene (dipentene) for the temperature range 298.15-1000 K. These QCFF-calculated thermodynamic values were compared, when possible, with corresponding values obtained experimentally or from other force field programs, and the agreement was found to be satisfactory. The Q C F F values were further used to derive gas-phase equilibrium properties-AHO, ASo, AGO, and &-for the isoprene dimerization reaction at various temperatures. These computational results suggest that, based upon thermodynamics, diprene and dipentene are about equally favored dimerization products of isoprene and that reported experimental data reflect kinetic control of dipentene formation at lower temperatures. The equilibrium thermodynamics data for the isoprene dimerization reaction presented in this paper are felt to be sufficiently reliable that they can be utilized in the absence of any additional experimental data; the present work thus illustrates the power of predictive thermodynamic computational techniques in extending the thermochemical database.
Introduction In the recent past, a large number of force-field methods have been developed to predict structures, vibrational frequencies,and energies for a wide range of isolated molecules. However, very few of these force-field methods have been demonstrated to accurately compute gas-phase So and Copvalues. Previously, MOLDB3 (Boyd and co-workers)' and more recently QCFF (Warshel and Karplus)2 and MM3 (Allinger and co-~orkers)~ have been employed to calculate So and COP values for certain compounds. The present work has involved dxtending and parametrizing the QCFF program originally written by Warshel and Karplusz for computation of accurate AHof, So, and COP values for a large number of saturated and unsaturated hydroc a r b o n ~ .This ~ work is continuing with current parametrization of the QCFF program for heteroatomic compounds. Because of its ability to compute accurate So and COP values for isolated molecules, QCFF thus provides a basis for predicting reaction equilibria for gas-phase reactions. Lenz and Vaughan accurately calculated the equilibrium thermodynamic properties for some Diels-Alder reactions using force field meth~ds.~adIn this paper, the QCFF program has been employed to compute the gas-phase equilibrium constant, the standard enthalpy of reaction, and the standard entropy of reaction at various temperatures for the Diels-Alder dimerization of 2-methyl-1,3 butadiene (isoprene). To date, there have been no reported reliable equilibrium thermodynamicdata on the DielsAlder dimerization reaction of isoprene. However, this dimerization reaction of isoprene is important; l-methyl-4-( l-methyletheny1)cyclohexene (dipentene), one of the products formed in the reaction, has major applications in the manufacture of polymers and adhesives.6 Dipentene also has various uses in the food and pharmaceutical industries.6 Results and Discussion The Diels-Alder dimerization of isoprene yields' both diprene, l-methyl-5-( 1-methyletheny1)cyclohexene (l),and dipentene (or Department of Chemical Engineering. t Department of Chemistry. * Abstract published in Aduance ACS Abstracts, February 1, 1994.
f
5
1
y
3
4
2
4
%0'
2
3
3
7 9
Dimer 1
Dimer 2
Figure 1. 2-Methyl-l,3-butadiene (isoprene), l-methyl-5-(l-methyletheny1)cyclohexene (l),and 1-methyl-4-( 1-methylethenyl)cyclohexene (2). Numericvaluescorrespond to thoseemployed in Table 3 for structural results.
racemic limonene), 1-methyLC( 1-methylethenyl)cyclohexene (2). The molecular structures of the monomer (isoprene) and the dimers 1and 2 aregiven in Figure 1. The dimerizationreaction occurs according to the following equations: 2C,H8 = C,,H,,
(dimer 1)
(A)
2C,H8 = C,,H,,
(dimer 2)
(B)
However, only reaction A is observed at the room temperature, but both reaction products have been reported at higher temperatures.' We used the QCFF program to calculate the optimum geometry,vibrational frequencies,and thermodynamic properties ( A H O F , So, COP and HOT- PO) for the reactant, isoprene, and the dimers 1 and 2. The QCFF parameters used for the present calculations are given in Tables 1 and 2. Some supplemental torsion potential functions were added to existing torsional functions for certain carbon-carbon bonds (Table 2). These supplemental torsion potential functions were used to improve AHof and the enthalpy differences between two different conformers for various saturated and unsaturated compounds. The QCFF-calculated structures and vibrational frequencies for isoprene and its dimers are summarized in Table 3 and Table 4, respectively. Isoprene is found to have two low-energy conformers, trans and gauche, and the trans conformer is more
0022-365419412098-2489%04.50/0 0 1994 American Chemical Society
2490 The Journal of Physical Chemistry, Vol. 98, No. 9, 1994 TABLE 1: Altered QCFF Bond Energy, Bond Angle, and Torsion Parameters"4"
Kar et al. TABLE 3: Structural Results for 2-MethyI-1,fbutadiene (Isoprene) and 1-Methyl-4-(1-methyletheny1)cyclobexene
Bond Stretch: ER = KBl(R - Ro)2- KB3
KB 1
Ro
200.0 (250.0) 250.0
1.49 (1.465) 1.47 (1.45) 1.45
bond
cc BC AC AB CH AH
KB3 87.067 (86.0) 88.000 (86.0)
xccx XBCX XAAX XACX, XABX
25.3 (18.3) 21.5 (24.0) 18.3 (25.3) 37.5 (39.5)
42.0 (42.9) 42.0 (51.7) 42.0 (42.9)
Torsion Energy:
+ KPl COS 4 + KPZ(61- eo)(e2 - eo) COS 4
KP1 1.5 (1.161) 1.2 (1.161) 1.8 (2.54) -0.8 (-0.9)
KP2 0.0 (-2.3) 0.0 (-9.5)
KP3 -20.0 (-9.5) -20.0 (0.0) 0.0 (-2.3)
TABLE 4
c1
c2
c3
-0.10378 0.04204 1.3605
0.32673 0.02481 -0,1165
-0,26835 -0.38049 1.4832
BAAAg
0.6140
-2.0358
-0).6414h -0.2172'
c4
c5
0.351 11 1.Y 1.of
0.27306
C represents saturated carbon (cSp3), B saturated methyl carbon, and A ethylenic carbon (Csp2). F(6) = Cl(1 + cos 4) + Cz(1 -cos 24) + C3( 1 cos 34); 4 is the dihedral angle. F(4)= Cl( 1 + cos 4) + C2( 1 + COS 24) + c3(1 + C O S 3 4 ) c4(1 + C O S 46) c5(1 +COS 56). d F ( ~ ) = C1(C2+ cos 6) - C3(l -cos 24)(1 + C4 cos 4). C4 = 1.5 for 0.0' < 4 < 80.0'. fC4 = 1.0 for 80.0' < 4 < 180.0'. g F ( 6 ) = Cl(C2 -cos 4)(1 + C3 sin 4). C3 = -0.6414 for 0.0' < 4 < 80.0'. C3 = -0.2772 for 80.0' < rb < 180.0°.
+
stable than the gauche conformer by -2.6 kcal m01-l.~ The potential energy curve of internal rotation for isoprene was computed using the QCFF program, and the calculated curve was found to be in excellent agreement with the one computed by Panchenko et al. using experimentally refined Hartree-Fock calculations (Figure 2).9 The dihedral angle C=C-C=C for the gauche conformer of isoprene obtained from QCFF calculations was found to be 40° (as evident from Figure 2). The root mean square (rms) error and the mean error between the observed vibrational frequencies and the QCFF-calculated vibrational frequencies were found to be 25.0 and -2.5 wavenumbers, respectively. The QCFF-calculated thermodynamic values for isoprene and its dimers are given in Table 5 and Table 6,respectively. The QCFF-calculated thermodynamic values for isoprene were found to be in excellent agreement with the corresponding literature
1.340 1.463 1.512 1.076 1.110 121.4 127.3 121.0 180.0
Vibrational Freauencies of Isoprene ~~
Supplemental Torsion Parameters.
+
lit.0
Reference 8. Bond distances in A. Bond angles and dihedral angles are in degrees.
QCFF
CCCCb CCAAc AAAAd
+
QCFF (Trans) 1.347 1.483 1.494 1.084 1.108 119.4 126.1 120.3 180.0
123 234 125 torsionC 3145 l-Methyl-4-( 1-methylethenyl)cyclohexene bond lengthb 12 1.341 110 1.495 56 1.537 47 1.511 79 1.498 78 1.339 bond angleC 2 1 10 120.8 165 111.2 347 110.0 978 119.6 torsionc 2165 13.9 6541 185.1 5478 126.3
KQ2 -5.0 (-6.3)
0 Original (default) parameters are enclosed by parentheses.2 Blank spaces indicate no alteration, or, if enclosed by parentheses, that no value was assigned by the original authorsS2 C represents saturated carbon (Csp3), B saturated methyl carbon, and A ethylenic carbon (Csp2). Q and Qoare 1,3-nonbondeddistances. e Dihedral angle; X refers to either C or H. /Parameter units yield energies in kcal mol-'. The meaning of the parameters are explained in detail in refs 2 and 4.
TABLE 2
bond angleC
40.0 (52.8) 16.0 (22.0) 29.0 (52.8)
E , = KPl( 1 + COS &J) anglee
4-H 5-H
88.000 103.935 (104.0) 103.485 (103.1)
Angle Bending: E8 = KTl(0 - eo)2 + KQ2(Q - Qo)+ KQ1(Qangle KT1 KQld CCC, BCC AAC, AAB BAB, CAC, BAC AAA CCH, BCH CBH AAH, CAH, BAH ACH, ABH HCH
bond lengthb
2-Methyl-l,3-butadiene 12 23 25
trans v(=CH2) asym. str. u(=CH2) asym. str. v(C-H) str. v(=CH2) sym. str. v(=CH2) sym. str. u(CH3) asym. str. v(CH3) sym. str. v ( C 4 ) sym. str. v(C=C) asym. str. S(CH3) asym. def. 8(=CH2) sym. scissor S(CH3) sym. def. S(=CH2) asym. scissor v(C-C) str. S(C-H) bend p(CH3) rock p(=CHz) rock p(=CH2) rock v(C-CH3) str. S(C=C-C) sym. bend S(C=C-CH3) bend S(C=C-C) asym. bend
3082 3063 306 1 2989 2988 2945 2871 1660 1616 1465 1435 1412 1396 1359 1269 1030 1021 952 814 537 393 296
v(CH3) asym. str. S(CH3) asym. def. p(CH3) rock x(C-H) wag x(=CHz) wag x(=CH2) twist T(=CH~)twist T ( = C H ~twist ) x(C-CH3) wag T(CHI))torsion T(C-C) torsion
2944 1448 993 959 94 1 933 735 642 442 185 131
a
gauche A 3084 3063 3062 2989 2988 2945 2871 1664 1634 1463 1428 1424 1395 1314 1254 1060 1029 955 813 537 390 292 A" 2943 1445 995 957 945 934 74 1 642 440 162 143
~~~
observed0 trans
gauche 3097 3092 3020 2988 2978 2928 2910 1638 1603
1466 1425 1414
1465 1460 1430 1388 1303
1291
1255 1069 1012 953 780
523 40 1 288 2956 1442 1034 990 903
1460 1010 920 891
755 622 412 199.3
750 655 550 152.7
Reference 8.
values.lI As is evident from Table 5, the differences between present thermodynamic values and the corresponding literature values for isoprene become slightly larger a t higher temperatures. Such variation can be attributed to the contributions due to hindered internal rotation, which was not included during present
The Journal of Physical Chemistry, Vol. 98, No. 9, 1994 2491
Predictive Force-Field Calculations TABLE 5
Thermodynamic Properties of 2-Methyl-1,3-butadiene (Isoprene)
WP QCFF
P
17.96 20.48 18.03
t,
298.15
g
400.00
mix t 8 mix
500.00
t
QCFF 74.95 76.43 75.25 82.78 84.27 83.46 90.13 91.61 91.15 97.08 98.57 98.39 103.65 105.13 105.16 109.84 1 1 1.32 1 1 1.50 115.67 117.16 117.45 121.18 122.67 123.05
18.10
8 mix 600.00
t
700.00
g mix t g
mix
800.00
t
900.00
8 mix t B mix t
1000.0
co,cd
HOr-Ij029a.15~
SO'
lit.c
liter 75.44 83.78 91.47 98.62 105.28 111.49 117.30
QCFF
1it.c
0.00 0.00 0.00 2.73 2.73 2.87 6.03 6.03 6.32 9.86 9.86 10.30 14.12 14.12 14.70 18.76 18.76 19.45 23.72 23.72 24.50 28.95 28.95 29.81
0.00 2.91 6.37 10.30 14.62 19.27 24.21
QCFF 23.48 23.48 24.50 30.09 30.08 31.58 35.78 35.78 37.34 40.57 40.57 42.01 44.61 44.61 45.85 48.06 48.06 49.10 51.01 51.01 51.89 53.56 53.56 54.31
lit.* 25.00 31.80 37.10 41.40 45.00 48.00 50.60
g 122.75 29.38 52.90 mix Units, cal mol-l K-I. Pp(Tjis a cubic fit of Cop values: COp(T)= A + BT + CF + DF,for 100 K intervals a Units, K. Units, kcal mol - I . from 298.15 to 1000 K; cal mol-* K-I. For tram-isoprene: A = -2.694,B = 0.1063,C = -6.765 X 10-5, D = 1.756 X 10-8. For gauche-isoprene: A = -2.658,B = 0.1061,C = -6.731 X 1P5, D = 1.739 X lo-*. For equilibrium mixture of truns- and guuche-isoprene: A = -5.289,B = 0.1263, C = -9.774 X D = 3.105X 10-8. The literature values correspond to 298 K;ref 11. f t refers to trans conformers, g refers to gauche conformers, and mix refers to an equilibrium mixture of trans and gauche conformers;the gauche conformer of isoprene has two enantiomers,and the QCFF values correspond to the equimolar mixture of the enantiomers.
-Ab-initio 0
-50
C
Hartree- Fock Calculations (Panchenko et al.) QCFF
50 100 Angle, deg
0
150
200
Figure 2. Potential function of internal rotation for isoprene.
calculations of the thermodynamic functions. The w 0 f , 2 9 8 . 1 5 value for dimer 2 obtained from present calculations agreed well with the corresponding experimental value.I0 However, there were no Soand Copvalues for 2 in the literature for comparison. Muja et al. calculated the standard enthalpy of formation and the standard entropy of 1 at 298.15 K, using a group contribution technique." Their calculated value of A H O f for 1 was found to be a positive quantity. However, the W f v a l u e sfor 1, obtained from both QCFF and MMP2 calculations, and the experimental AHOfvalue for 2 were all found to be negative quantities (Table 6). Since group contribution methods do not explicitly include vibrational contributions to thermodynamic functions, the Muja et al. calculation of these quantities is not likely to be as accurate as force-field calculations. The thermodynamic properties for the equilibrium mixture of conformers were calculated by the following equations:
cxiMo C
f,298.15
=
f,298.15 ( i )
C
where c is the total number of conformers and $i represents the mole fraction of canformer i at temperature T. Hi = [AH0f,298.15( 9 - ~ o f , z 9 8 . ~ s ( -l )(H0298.is l -'Wo)i + (H0298.is - H0o)i + ( W T -HOO)~ - (PTHo0)l, where i = 1 is the confomer with the lowest AH0f,298.15 value and (HOT - HOO)~ is the enthalpy function for the ith conformer a t temperature T. The quantity ( H O T - Hoo)/T is computed directly from QCFF calculations. The following equation is used to calculate Xi:
where
AG'Ai) = AHo&i) - TSoT(i)
(6)
The QCFF-calculated Mor, So, and COP values for the reactants and products were used to derive the equilibrium thermodynamic properties at various temperatures for the gasphase reactions A and B. Theseequilibriumproperties for reaction A and B-AHo, ASo, AGO, and Kp-are summarized in Table I. The near constancy of AHo and &To indicates that In Kp is
Kar et al.
2492 The Journal of Physical Chemistry, Vol. 98, No. 9, 1994 Thermodynamic Properties of l-Methyl-5-( 1-methylethenyl)cyclohexene (1) and l-Methyl-4-(1-methylethenyl)cyclohexene (2)
TABLE 6
M P P 298.15
SOC lit.
QCFF
lit.
le
-1.42
101.78
109.78
2
-1.25
-1.71f 1.2w -1.71f -0.62f 0.72h
1 2 1 2 1 2 1 2 1 2 1 2 1 2
400.00 500.00 600.00 700.00 800.00 900.00 1000.0
Pfid
H O T - H0298sSb
QCFF
QCFF
lit.
QCFF
0.00
44.00
101.69
0.00
43.98
116.73 116.64 131.14 131.04 145.03 144.93 158.29 158.19 170.87 170.77 182.79 182.68 194.07 193.97
5.22 5.22 11.70 11.69 19.33 19.33 27.95 27.94 37.38 37.37 47.50 47.49 58.21 58.20
58.34 58.32 70.91 70.89 8 1.53 81.51 90.43 90.42 97.95 97.95 104.35 104.34 109.82 109.81
lit.
+
a Units, K. Units, kcal mol-I. Units, cal mol-' K-l. COP( r ) is a cubic fit of PPvalues: Pp(T)= A E T + CF + DT),for 100 K intervals from 298.15 to 1000 K cal mol-' K-l. For 1: A = -12.42,B = 0.2269,C = -1.365 X 10-4, D = 3.188 X 10-8.For 2 A = -12.43,B = 0.2268,C -1.364 X 10-4, D = 3.182 X 10-8. e There are two enantiomers for both 1 and 2. The QCFF values correspond to the equimolar mixture of the enantiomers. f Reference 12c.g Reference 13. Reference 10.
TABLE 7: Equilibrium Thermodynamics for the Dimerization of Isoprene in the Gas Phase T,K QCFF
Lit!
298.15 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 300.0 400.0 500.0 600.0 700.0 800.0 T.K
QCFF
298.15 400.0 500.0 600.0 700.0 800.0 900.0 1000.0
M a ASob Reaction A -37.48 -48.72 -37.99 -50.16 -38.40 -51.12 -38.73 -51.70 -38.93 -52.02 -39.00 -52.12 -38.97 -52.09 -38.87 -51.99 -35 -41.18
M a ASob Reaction B -37.31 -48.81 -37.82 -50.26 -38.23 -5 1.22 -38.57 -51.80 -38.76 -52.12 -38.83 -52.22 -38.80 -52.20 -38.71 -52.09
AGO a
Kpf
O'
-8- EQ.9.QCFF for Reactions A -6-
or B
EQ.12. QCFFfor Reactions A+B
+EQ.11. Muja et d.for Ramon A
1
-22.95 -17.93 -12.84 -7.71 -2.52 2.70 7.91 13.12 -22.6 -18.5 -14.4 -10.2 -6.2 -2.1
6.72X 1OI6 6.24x 109 4.10X los 643.57 6.10 0.18 0.01 0.00 3.70X 10l6 1.28 X 1Olo 19.7 X lo5 5196 86.3 3.75
AGO
K.2'
-22.76 -17.72 -12.62 -7.49 -2.28 2.95 8.18 13.38
4.82X 10l6 4.79 x 109 3.29 X lo5 535.12 5.14 0.16 0.01 0.00
virtually a linear function of 1/T. A linear least-squares fit of the Kp values for reactions A and B (Table 7) resulted in the following expressions: reaction A:
In Kpl = 19283(1/T) - 25.711
reaction B:
In Kp2 = 19199(1/T) -25.822 (10)
(9)
Muja et al. obtained the followinginversetemperature relationship between In Kp and T for reaction A using a group contribution method:')
- 20.666
I
40
t 1
/
t -20
~
0.5
d" ~
1.5
2
A
/
,,
I 1
/
, 2.5
3
3.5
103m(K")
Figure3. Temperature dependenceof Kpfor the dimerization of isoprene.
a kcal mol-'. b cal mol-' K-I. C Kp = p ~ / pwhere ~ ~ D, refers to the dimer and M to the monomer; p is the pressure in atm. Reference 13.
In K p = 17573(1/T)
T
(1 1)
Figure 3 illustrates the relationship between In Kp and 1 / T
obtained by QCFF calculations and the same calculated by Muja et al. In spite of the differences in m 0 f , 2 9 8 . 1 5 and S'298.IS values for 1, the In Kp line predicted by Muja et al. appears to be in close agreement with the one obtained from QCFF calculations. Such agreement is, however, fortuitous due to the compensating errors involved in the A H o f , 2 9 8 . 1 5 and S'298.15 values of Muja et al. Only the most stable conformers of 1 and 2 were considered during the calculation of Kpland Kp2,respectively,because inclusion of other conformers of the dimers had minimal effect on the In Kp vs 1/ T lines for both reactions A and B. For example, considering an equilibrium mixture of two conformers for dimer 2 with dihedral angles 5 4 7 8 (Figure 1)-126.3' (Table 3) and 330°, respectively-resulted in In Kpl values of 38.49 (298.15 K), 13.04 (500 K), and -5.57 (1000 K). The corresponding values obtained with only one conformer of dimer 2 (dihedral 126.3') included were 38.75 (298.15), 12.92 (500 K), and -6.60 (1000 K). A dihedral angle of 330' was chosen because in an earlier work:* the butadiene dimer (4-vinylcyclohex-1-ene) was found to have two stable conformers with the corresponding dihedral angles -120' and 330'. As mentioned earlier, at higher temperatures both 1 and 2 are formed in significant quantities? Theoverall equilibriumconstant is then the product of the individual equilibrium constants for reactions A and B, respectively: In Kp = In KPl + In Kp2. The expression for the overall Kp, thus calculated from eqs 9 and 10, is given by
The Journal of Physical Chemistry, Vol. 98, No. 9, I994 2493
Predictive Force-Field Calculations In K p = 38481(1/T) - 51.592
(12)
Here, Kp = ( ~ D I / P M ~ ) ( P D ~where / P M ~pD1 ) , and P D 2 are the equilibrium partial pressures of 1 and 2, respectively, and p~ is the equilibrium partial pressure of the monomer, isoprene. The ratio of the partial equilibrium pressures of dipentene (2) and diprene (1) can be readily obtained from the ratio of KP2fKpl. Assuming the ideal gas law, Kp2/Kpl is directly proportional to the ratio PD2fpD1. Figure 4 shows the relationship between the ratio KP2fKp1and temperature. As is evident from Figure 4, Kp2fKplincreases very slowly with temperature and reaches an asymptotic value of about equimolar ratio at an infinitely large temperature. It can thus be concluded that the formation of dipentene in the gas phase is about as favorable as deprene thermodynamically at ambient and higher temperatures but that dipentene formation is controlled by kinetics at lower temperatures. Hence, use of a suitable catalyst would likely lead to observablelevels of dipentene (reaction B) at lower temperatures. Also, the equilibrium data for the dimerization of butadiene, computed in an earlier work,)* were compared with the same for the dimerization of isoprene. For example, at 600 K, the Kp value for the dimerization of butadiene is 1.29 X 103, and the corresponding values for the dimerization of isoprene are 644 and 535, for reactions A and B, respectively; at 700 K, Kpfor the butadiene dimerization is 19, and the corresponding values for the dimerization of isoprene are 6 and 5 , for reactions A and B, respectively. This result suggests that introduction of a methyl group in the 2-position of isoprene destabilizes the dimer to a greater extent than the monomer. Conclusions Force-field methods have been shown in earlier work to be useful for reliable estimations of equilibrium properties for chemically reactive ~ystems.~JThese methods, applied to the study of isoprene dimerization in the present paper, indicate that the formation of dipentene is likely to be kinetics-limited at low and moderate temperatures. The excellent agreement between our calculated thermodynamic values of the reactantsf products and the corresponding MMPZ values (or experimental values, where applicable), and considering past evidence regarding the ability of force field methods to compute accurate reaction equilibria, provides additional confidence that the present calculations can be used as a reliable source to obtain equilibrium thermodynamicvalues for the gas-phase Diels-Alder dimerization of isoprenein the absence of experimental data. Thus, the present study further emphasizes the power of such predictive thermodynamic computational techniques in extending the thermochemical database. Also, the equilibrium thermodynamic properties for the isoprenedimerization reaction in dilute solution can be derived from the corresponding gas-phase properties using vapor pressure data of the reactants and products and the density values for the reaction s o l ~ e n t . ~
O.gOr
c
o.801 0.85
0.75
0.70‘ 200
I
400
I
I
I
600
800
1000
I
1200
T, K F i p e 4. Temperature dependence of the ratio of the equilibrium partial pressures of dipentene and diprene.
Acknowledgment. This work was supported by the Chemical Sciences Division, Office of Basic Energy Sciences, Office of Energy Research, of the US. Department of Energy under Grant DE-FG03-93ER14341. References and Notes (1) (a) Chang, S.;McNally, D.; Shary-Tehrany,S.; Hickey, M. J.; Boyd, R. H. J . Am. Chem. Soc. 1970,92,3109. (b) Boyd, R. H.; Sanwal, S.N.; Shary-Tehrany,S.;McNally, D. J. J . Phys. Chem. 1976,75,1264. (c) Boyd, R. H.; Breitling, S.M.; Mansfield, M. AICHE J. 1973, 19, 1016. (2) (a) Lifson, S.;Warshel, A. J . Chem. Phys. 1968, 49, 5116. (b) Warshel, A.; Karplus, M. J. Am. Chem. Soc. 1972.94, 5612. (c) Warshel, A.; Levitt, M. QCPE 247. (d) Ramachandran, S.;Lenz, T. G.;Vaughan, J. D.; Rappt, A. K. QCPE 593. (3) Lii, J.-H.; Allinger, N. L. J . Am. Chem. SOC.1989, 111, 8566. (4) (a) Lenz, T. G.;Vaughan, J. D. J . Comp. Chem. 1990,ll (3), 351. (b) Kar, M.; Lenz, T. G.;Vaughan, J. D., manuscript submittedtoJ. Comput. Chem. (5) (a) Lenz, T. G.;Vaughan, J. D. J . Phys. Chem. 1989,93,1592 (b) Lenz, T. G.;Vaughan, J. D. J . Phys. Chem. 1989,93,1588. (c) Lcnz, T. G.; Vaughan, J. D. Chem. Eng. Sci. 1990,45 (7), 1755. (6) Thomas, A. F. Nat. Prod. Rep. 1989, 6 (3), 291. (7) Norton, J. A. Chem. Rev. 1942, 31, 319. (8) Traetteberg, M.;Paulcn, G.;Cyvin, S. J.; Panchenko, Yu. N.; Mochalov, V. I. J. Mol. Struct. 1984, 116, 141. (9) Panchenko, Yu. N.; Pupyshev, V. I.; Abramenkw, A. V.;Traetteberg, M.; Cyvin, S.J. J . Mol. Struct. 1985, 130, 355. (10) Pedley, J. E.; Naylor, R. D.; Kirby, S. P. Thermochemical Data of Organic Compounds, 2nd ed.; Chapman and Hall: New York, 1986. (11) Stull, D. R.; Westrum, Jr., E. F.; Sinke, G . C. The Chemical Thermodynamicsof Organic Compounds. John Wiley and Sons, Inc.: New York, 1969. (12) (a) Burkert, U.; Allinger, N. L. Molecular Mechanics. ACS Monograph 177. American Chemical Society: Washington, D.C., 1982, and numerous references cited therein. (b) Allinger, N. L.; Flanagan, H. L. J . Comp. Chem. 1983, 4, 399. (c) The MMPZ program was obtained from QCPE, Indiana University. (13) Muja, I.; Andreescu, G.;Corciovei, M.;Obogeanu, F. Rev. Chim. 1975, 26 (7), 545.
