J . Phys. Chem. 1989, 93, 1588-1592
1588
association ions. Their equation is of the form AHDO(B-*.*HA)=
in kcal/mol, where x(A) and x(B) are the electronegativities of the respective heteroatoms in each partner within the complex. Application of the expression to bonds of the type S---HO, where S- is incorporated in C6H5S-, CH3S-, and HS-, yields a single correlation line represented by AHDo(S-.*.HO) = 23.9 0.234AAHoacid(in kcal/mol). Although the data seem to show separate correlations for the C6HSS- and the CH3S-, HSgroupings, with C6HSS-bonds exhibiting a slightly higher slope and intercept (Figure 3), the empirical relationship does reproduce the experimental bond strengths for C6HSS-complexes quite well, especially at higher values of AAHoaed,where A H D O is depressed. The experimental A H D O values for the monohydrates of HS- and CH3S- are almost identical with those predicted within measurement error, indicating the potential utility of eq 3. The individual values of A H D O derived from this relationship for the various complexes are included in Table I for comparison with the present results. Recently we established2 a correlation line for RO-...HO bonds of the form AHDO = 27.5 - 0.29AAHoaCid.Comparison of these parameters with those describing RS---HO interactions (eq 1 and 2) indicates that complexes incorporating 0- are more stable by 2-7 kcal/mol at AAHoacidvalues below 40 kcal/mol than those incorporating S-. The decreased stabilities for complexes having second-row elements at the site of ligand attachment have been considered in detail by Gao et a1.,12who performed high-level ab
initio M O calculations for a variety of anionic hydrates. They concluded that several factors are operative in weakening the bond strengths, including increased ionic radii and diminished covalent character of the hydrogen bond. These factors combine to increase the bond lengths, which were found to be -2.5 A for RS-sHOH complexes compared to only 1.5-1.6 A for those incorporating RO-eHOH bonds. Their calculated A H D O values for HS-eHOH and CH3S-.HOH of 15.6 and 15.4 kcal/mol are in very good agreement with the respective experimental values of 14.2 and 15.0 kcal/mol found for these combinations. The A H D O values for the stepwise addition of H 2 0 to HS- and CH3S- are given in Table I. Consistent with the trends found for other core ions,13A H D O decreases rather rapidly upon successive hydration up to n = 3, at which point the values are within 1 kcal/mol of AHovap(H20), 10.5 kcal/mol. Therefore the weak ionic contributions to solvation are effectively dissipated within the first 2-3 water molecules. Additional stepwise addition should proceed with bond energies near 10.5 kcal/mol, which we found for CH3S--(H20)4,9.6 kcal/mol, equal to the neutral condensation limit within experimental error. Based on criteria suggested earlier,I3there is no evidence for shell-fillingeffects in these weakly bound systems.
Acknowledgment. This research was supported by the Office of Basic Energy Sciences, United States Department of Energy. Registry No. C6HSS-,13133-62-5;HS-, 15035-72-0;CH$, 1730263-5; EtC02H, 79-09-4; CF3CH20H,75-89-8; MeC02H, 64-19-7; iPrOH, 67-63-0; t-BuOH, 75-65-0; EtOH, 64-17-5; HOH, 7732-18-5; MeOH, 67-56-1. (12) Gao, J.; Garner, D. S.; Jorgensen, W. L. J . Am. Chem. SOC.1986,
108, 4784.
(13) Meot-Ner (Mautner), M.; Speller, C. V. J. Phys. Chem. 1986, 90,
6616.
Force-Field Calculations Giving Accurate Conformation, AH,' ( T ) , S o( T ) , and C, O ( T ) for Unsaturated Acyclic and Cyclic Hydrocarbons Terry G. Lenz**+and John D. Vaughan*,* Department of Chemical Engineering and Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523 (Received: June 7 , 1988)
A modified version of the Boyd MOLBD3 force-field method has been employed to compute the structure, standard enthalpy of formation, and standard absolute entropy for a variety of dienes and unsaturated ring and methylene-bridged compounds. The modifications to M O L B D ~included incorporation of -ene and -diene parameters suggested by Anet and Yavari, as well as our adjustment of C(sp2)-C(sp2)-C(sp2) and C(sp2)-C(spz)-C(sp3) bond angle parameters for unsaturated five-member rings and methylene-bridged compounds. Our MOLBD3 results for 1,3-butadiene, 1,3-pentadiene, 1,3-~yclohexadiene,1,3cycloheptadiene, cyclopentene, norbornane, norbornene, norbornadiene, bicyclo[3.2.lloctane, bicyclo[3.3.llnonane, and 1,3-~yclopentadieneare generally in excellent agreement (typically f 1 kcal/mol for AH?,and f l cal/(mol.K) for S o )with observed values and with calculations we and others have made with the Allinger MMPZ and Ermer-Lifson CFF-3 programs. These molecular mechanics methods are thus capable of predicting thermochemical properties with sufficient accuracy for useful thermodynamic calculations.
Introduction At present there are powerful empirical and semiempirical methods available for calculating structural and thermodynamic properties of isolated molecules. Two particular methods that have received considerable attention during the past two decades are the force-field (molecular mechanic^)'^^^ and molecular orbital methods (such as MINDO, MNDO, and AM1).2 Such computational methods provide a basis for accurate calculation of molecular geometries, vibrational frequencies, and thermodynamic 'Department of Chemical Engineering. *Department of Chemistry.
0022-3654/89/2093- 1588$01.50/0
properties for a wide range of molecules having nontrivial structures. Molecular mechanics methods in particular have proven capable of computing standard enthalpies of formation, AH?,agreeing to within i=1 kcal/mol of experimental values and (1) (a) Burkert, U.; Allinger, N. L. Molecular Mechanics; ACS Monograph 177; American Chemical Society: Washington, D.C., 1982. (b) The M M P ~program employed in our studies was obtained from the Quantum Chemistry Program Exchange, Indiana University. (2) (a) Dewar, M. J. S.; Ford, G. P. J . Am. Chem. SOC.1977, 99, 7822. (b) Dewar, M. J. S.; Storch, D. M. J . Am. Chem. Soc. 1985, 107, 3898. (c) Dewar, M. J. S.; Zoebisch, E. G.;Healy, E. F.; Stewart, J. J. P. J . Am. Chem. SOC.1985, 107, 3902.
0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 4, 1989 1589
Structures of Unsaturated Hydrocarbons TABLE I:
M O L B D ~Parameters' bond stretchingb
kR
RO
4.55 4.45 5 .O
1.09 1.09 1.07
4.4 5.1 5.8 6.8
1.53 1.50 1.46 1.33
source
W0
C-H sp3-H (allylic) sp3-H (nonallylic) sp2-H
c-c
sp3-sp' sp2-spJ
sp2-sp2 (single) sp2-sp2 (double) bond-anele bendine' ka H-C-H 0.508 H-sp3-H 0.290 H-sp2-H H-C-C
B C
B
1,3-butadiene ( u = 2)b transoid
Ad
B B
cisoid
A A
c-c-c
SU3-SU2-SD3
} sp2-sp2-sp2 s,-,p2-,2
en
source
107.9 118.9
B A
0.608
109.5
B
0.35 0.605
119.5
120.5
B B
1 1 1.0
B
119.0
B
0.62
bond torsion' ~~
124.7 B C
k,
B source
= 1)b transoid cisoid transoid cisoid
c=c
/ H h
1 -1 1 -1
3 3 2 2
A A A A
transoid cisoid transoid cisoid
A
0.28
A
C '
c=cYH hC'
nonbonded interactions' C.-C C-H H*-H
a
P
Y
4.45 0.96 0.19
104.0 30.0 18.4
3.090 3.415 3.740
'Energies are in units of lo-" erg/molecule; Ro,R,r in angstroms; 8, Bo, #, {in degrees. bE, = llzkR(R- Ro)2.CBoydand co-workers, ref ' E , = l/2k+(B + 3. dAnet and Yavari, ref Sa. ' E B= 1/zke(8cos C#). BEl = 1/2k&{2).hOut-of-planeatom. iE,b(r) = a/# + 0 exp(-v). standard absolute entropies, So, generally agreeing within less than f 1 cal/(mol.K) of experimental results. In the present work two well-established force-field programs have been employed to calculate geometries and thermodynamic properties for a number of acyclic and cyclic dienes and methylene-bridged compounds not heretofore treated in comparable detail. The two force-field programs we have employed are the MOLBD3 program of Boyd and co-workers3 and the MMPZ program of Allinger and co-workers.lb MMPZ is the more highly developed of the two, capable of predicting detailed structures and standard enthalpies of formation for a very wide variety of both saturated and unsaturated hydrocarbons, and for many heteroatomic organic compounds. The ~ ~ ~ 2 - c a l c u l aAHfO t e d values of hydrocarbons are in general particularly a ~ c u r a t e . ~The original M O L B D 3 program of Boyd and co-workers had parameters for saturated and unsaturated hydrocarbons; benzene rings could be treated, but delocalized systems such as dienes and trienes and naphthalenic compounds could not. However, Anet and YavariSaintroduced (3) (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 . Phys. Chem. 1976, 75, 1264. (4) Reference 1, p 173 ff.
MMPZh
MOLBD3h MMPZh
lit .cJ lit .dJ
1,3-cyclohexadiene ( u = 2)b
MOLBD3h MMPZh
lit! lit:
1,3-cycloheptadiene ( u =
MOLBD3' MMP28
lit!
source
0.08
1000
298.15 1000
26.56 68.09 25.09 27.65 68.77 26.87 26.33 66.62 26.3
103.67
19.04 40.51
104.33
18.92 40.53
102.89
19.01 40.52
18.92 77.69 123.53 20.03 78.59 124.53 17.15 19.02 18.60 76.40 23.18 18.2
23.92 53.17 23.84 53.19
20.21 78.25 23.53 23.34 20.48 24.46 18.70 77.50 23.18 19.4 25.38 74.07c 22.67'
23.70 53.19
24.70 52.60
( Z ) -1,3-pentadiene (a = 1)b
~
0.0158 -0.0133 -0.0295 -0.1135 kr
MOLBDJh
lit?'
1 -c-c-2
c-sp3-sp3-c c-sp"sp2-c C=~p~-spkC C-sp~sp2-C out-of-ulane bending8
CPO
S O
298.15 298.15
( E ) - 1,3-pentadiene (u
0.65
MOLBDJ MMPZh MOLBD3 MMPZh
lit?,'
~~
H-sp2-sp3 H-sp2-sp2
TABLE 11: Thermodynamic Properties of Selected Dienes:' 298.15 and 1000 K
22.60 52.20 23.16 57.85
25.35 25.41 72.49' 25.9 22.90 80.81
121.48.
22.50 58.47
139.62
27.54 70.55
22.73 22.5
139.91
28.12 71.27
80.00
AHf0 units, kcal/mol; So and CPounits, cal/(mol-K). u is the symmetry number. 'Reference 8. dReference 9. ' R In 2 included in So because of optical isomers. /Reference 10. 8Reported by T. Clark, ref ll. hThis work. Where literature values are cited for compounds having cisoid and transoid conformers, these values are presumably for an equilibrium mixture.
'
parameters for MOLBD3 specifically for cyclic dienes and trienes. The primary objective of the present research was to assess the potential of the MOLBD3 program of Boyd et ai.' for accurate calculation of thermodynamic properties, with the view toward use in predicting reaction thermodynamics for nontrivial systems.
Computational Details Standard absolute entropy and heat capacity calculations were based on the assumption of independent internal degrees of freedom
so= s o , + s o , + so,
c;
=
c;,
4- c ; , 4-
c;,
where t, r, and v refer to translation, rotation, and vibration, (5) (a) Anet, F. L.; Yavari, I. Tetrahedron 1978, 34, 2879. (b) Anet, F. L.; Yavari, I. J . Am. Chem. SOC.1978, 100, 7814. (6) Hill, T. Statistical Thermodynamics; Dover: New York, 1986. (7) Boyd, R. H.; Breitling, S.M.; Mansfield, M. A I C H E J. 1973, 19, 1016. (8) Stull, D.R.; Westrum, E. F. Jr.; Sinke, G. C. The Chemical Thermodynamics of Organic Compounds: Wiley: New York, 1969. (9) Pedley, J. B.;Naylor, R. D.; Kirby, S. P. Thermochemical Data of Organic Compounds, 2nd ed.; Chapman and Hall: New York, 1986. (10)Dorofeeva, 0.V.;Gurvich, L. V.; Jorish, V. S. J . Phys. Chem. Ref Data 1986, 15, 437. (1 1) Clark, T. A Handbook of Computational Chemistry; Wiley: New York, 1985. (12)Joshi, R. M. J . Polym. Sci. 1970, 8, 673. (13) Turnbull, A. G.; Hull, H. S. Ausr. J . Chem. 1968, 21, 1789. (14) Davis, M.I.; Muecke, T. W. J . Phys. Chem. 1970, 74, 1104. (15) Ermer, 0.; Lifson, S. J. J . Am. Chem. SOC.1973, 95, 4121. (16) Damiani, D.; Ferrelli, L.; Gallinella, E. Chem. Phys. Lerr. 1976, 37, 265.
1590 The Journal of Physical Chemistry, Vol. 93, No. 4, 1989 TABLE 111: Effect of eoa on Thermodynamic Propertiesb Cyclopentene and 1,3-Cyclopentadiene: 298.15 and 1000 K 80
AH,' 298.15
SO
298.15
1000
TABLE IV: Effect of Bo on Molecular Geometry:" Cyclopentene and 1,3-Cyclopentadiene
lit." litc MMPZh
19.97 8.36 7.96 7.60 7.29 7.02 6.81 7.82 8.3 8.24
68.60 70.25 70.03 69.85 69.70 69.58 69.49 69.61
111.99 113.61 113.40 113.22 113.08 112.95 112.87 112.97
Cyclopentene
CPO 298.15 1000
19.64 19.61 19.61 19.62 19.62 19.73 19.63 19.43
52.83 52.82 52.82 52.82 52.83 52.83 52.83 52.58
124.7 119.0 118.0 117.0 liLc M M P CFF-3"
kit! lit.8
litd MMPZh
123 110.4 112.1 111.9 111.8 111.0 ~ 112.1 111.8
234 109.1 104.5 104.6 104.7 103.0 101.8 103.0
345 101.0 105.7 105.5 105.3 104.0 106.1 105.8
12 1.329 1.328 1.329 1.329 1.342 1.338 1.340
8
40.40 33.36 32.28 3 I .30 29.63 29.33 32.1 32.0 31.82 31.3 32.72
on
65.85 65.99 66.02 66.05 66.11 66.13
103.53 103.70 103.74 103.78 103.87 103.89
7.68 7.75 7.76 7.78 7.81 7.82
44.94 44.95 44.94 44.94 44.96 44.96
65.32 65.6 65.50
103.47
7.47
45.41
104.43
8.01
45.78
34 1.539 1.538 1.537 1.536 1.546 1.543 1.548
pb
0.0 10.6 11.8 12.9 28.8 22.7 21.4
1.3-Cvclo~entadiene
1,3-Cyclopentadiene 124.7< 120.0 119.0 118.0 116.0 115.0 kc
R 23 1.500 1.499 1.500 1.500 1.519 1.504 1.521
8
eo
Cyclopentene 124.7' 120.0 119.0 118.0 117.0 116.9 115.0
Lenz and Vaughan
124.7 120.0 118.0 116.0 Ike M M P
123 108.3 109.1 109.3 109.4 109.3 ~ 107.8
234 110.7 110.1 109.7 109.3 109.2 113.0
154 100.8 101.5 102.0 102.6 102.9 99.3
12 1.329 1.330 1.330 1.330 1.344 1.350
R 23 1.456 1.457 1.458 1.459 1.458 1.456
45 1.505 1.504 1.503 1.502 1.506 1.509
"Angles are expressed in degrees and bond distances in angstroms. bPucker angle (Figure 2). 'Reference 14. "Consistent Force Field 'Reference 16. 'This (CFF-3) results reported by Ermer and Lif~on.'~ work.
Bo for C(sp2)-C(sp2)-C(spz)and C(sp2)-C(sp2)-C(sps)in degrees. b A H p units, kcal/mol; 9 'and :C units, cal/(mol.K). / 6 rings (C(sp2)-C(sp2)-C(sp2)and C(sp2)-C(sp2)-C(sps)). dReference IO. Reference 9. 'Reference 12. g Reference 13.
*This work. respectively. Translational, rotational, and vibrational contribu, C were calculated by means of the usual standard tions to So and ' formulas for ideal gases.6 The MOLBD37 standard enthalpy of formation can be calculated at any specified temperature, whereas the MMP24 value is that at 298.15 K. All calculations were done with the DEC MicroVax I1 supermicrocomputer.
Figure 1. Cyclopentene and 1,3-cyclopentadiene.
2 0
3
&-a-
----
4
Results and Discussion
Figure 2. Cyclopentene ring pucker.
A . Acyclic and Cyclic Dienes. The purpose of the calculations described in this section was to determine the accuracy of the MOLBD3 parameters of Anet and Yavari," primarily for thermodynamic properties, and secondarily for the structures of typical dienes; these authors discussed the conformational properties of a number of unsaturated hydrocarbons but did not report AH,' nor So for them5 Parallel MMPZ calculations were also carried out. The parameters used for the MOLBD3 calculations are listed in Table I. Pertinent calculated and observed thermodynamic properties are listed in Table I1 for representative acyclic and cyclic dienes. The AH? values calculated by MOLBD3 exhibited somewhat better agreement with experiment than did MMPZ for the acyclic dienes, and were roughly comparable to the MMPZ results for the cyclic dienes. Structural properties such as bond lengths, bond angles, and dihedral angles differed relatively little for the dienes from model to model. For example, both MOLBD3 and M M P ~predicted correctly that 1,3-cyclohexadiene has a twisted nonplanar (C,) structure and 1,3-~ycloheptadienea "semiplanar" (C,) structure in their ground states. B. Fioe-Member Rings. Heretofore the MOLBD3 program has been applied only to saturated five-member rings. Boyd and c o - w o r k e r ~observed ~~ that parameters that worked well for saturated n 2 6 rings failed for n = 5 rings; the calculated and observed AH,' values did not agree. These authors obtained satisfactory agreement between calculated and observed AH? for n = 5 rings by decreasing the C(sp3)-C(sp3)-C(sp3) bond angle parameter Bo from 11 1.0' to 109.5' and setting the H-C(sp3)-H parameter to 109.5' from 107.9'. No changes in bending ( k e ) and torsion (K,) force constant parameters were made. Similarly, our calculations on cyclopentene and 1,3-~yclopentadieneusing n 3 6 ring parameters gave calculated AHf' values considerably
higher than corresponding observed values. Comparison of these MOLBD3 calculations with MMPZ calculations indicated that the high MOLBD3 AH,' values resulted from excessive C(sp2)-C(sp2)-C(sp2) and/or C(sp2)-C(spz)-C(sp3) angle strain in the five-member rings. Following the Boyd initiative, we investigated the effect of the parameter 80 for these angles on the calculated properties of the n = 5 -ene and -diene. The results are shown in Tables 111 and IV together with MMPZ and literature values; Figure 1 shows the numbers assigned to the atoms in the two rings. Clearly, AH,' exhibited considerable sensitivity to changes in Bo while So and C', exhibited very little. Similarly, calculated bond angles and bond distances proved to be relatively insensitive to Bo. The largest discrepancy between the MOLBD3 calculated and observed structures was in the pucker angle /3 in cyclopentene that measures the deviation of the ring from planarity (Figure 2); the calculated angle /3 was significantly more sensitive to 0, than were ring bond angles. Values of Bo ranging from 118' to 119' produce AH,', So, C,', bond angles, and bond distances that agree satisfactorily with observed values, while 8, values outside of this range yield AH? either too large or too small. We have selected Bo = 118', because it minimizes the difference between calculated and observed ring puckering in cyclopentene; note that MMP2 and CFF-3 give better estimates of /3 than M O L B D ~ . C. Methylene-Bridged Compounds. These compounds were of interest in the present investigation because, first, a number of them have bond angles that are as small as, or smaller than, typical n = 5 rings, and therefore provide good tests for MOLBD3 n = 5 ring parameters. Second, some of the compounds are Diels-Alder adducts, and others have structures similar to adducts, which is a chemistry of importance in our evolving predictive methods.
The Journal of Physical Chemistry, Vol. 93, No. 4, 1989
Structures of Unsaturated Hydrocarbons
1591
TABLE VI: Standard Enthalpy' of Formation and Bond Angles"
7
8
Figure 3. Numbering scheme for norbornane, norbornene, and norbornadiene.
e 185 101.2 100.1
AH,'
TABLE V Effect of Bo" and Robon Thermodynamic and Molecular Geometric Propertiesf Norbornane, Norbornene, and Norbornadiene Norbornane ~~
-23.19 -23.09
eo
R~
109.5 106.0 105.0 104.0 lit.
1.530 1.550 1.550 1.550
S O
298.15 K -10.86 -12.61 -13.08 -13.52 -12.42' -13.19 -12.84'
298.15 K 73.73 73.81 73.82 73.83 74.0' 74.3h
e
R
94.2 92.5 92.2 91.9 93.6 92.Y
-fd
1.526 1.548 1.549 1.550 56& 1.'
113.5 113.6
115.v
Bicvclol3.3.11 nonane
115.v
e
Norbornene
on
R"
109.5 106.0 105.0 104.0 lit.
1.530 1.550 1.550 1.550
MMP2
SO AH," 298.15 K 298.15 K 560.0 K 24.09 74.03 22.27 74.10 21.64 74.11 96.89 21.14 74.11 21.4k -76.3' -100.6' 21.13h -74.3' -98.7' 97.95'" 19.32'
e
R
92.5 90.8 90.5 90.2
1.525 1.547 1.548 1.549
MOLBD~~
MMP2b
lit.23 112.8
93.41 1.545' 111.11
Norbornadiene 8, 109.5 106.0 105.0 104.0 lit. MMP2
S O AHfo Rn 298.15 K 298.15 K 600.0 K
1.53 1.55 1.55 1.55
60.92 58.82 58.24 59.05 57.4& 58.0h 58.89 55.24'
718 102.4 102.4
9
~
AH;
MMPl
MOLBD3b MMPZb
218 108.5 109.5
71.60 71.66 71.67 71.65 71.75h 70.64h
e
91.0 89.4 95.92 89.1 89.0 97.29h 9 2 . 6 95.50h 96.69 93.8'
R
Y
1.525 1.547 1.548 113.1 1.550 1.57/ 1 1 5 . 6 1.55'
113.W
"Bo and 0 refer to the methylene bridge angle (angle 376 of Figure 3). bRoand R refer to the bond lengths in the methylene bridge bonds (37 and 67). ,AH$ units, kcal/mol; So units, cal/(mol.K); Bo and 8 units, degrees; Ro and R units, angstroms. dAngle between the 3216 and 3456 planes (Figure 3). 'Reference 3a. 'Reference 18. 9Reference 9. hReference 20. 'Reference 1, p 183. 'This work. Reference 21. 'Reference 22. '"Reference 2a.
1 . Norbornane, Norbornene, and Norbornadiene. Each of these compounds can be viewed as a pair of n = 5 rings that share a methylene bridge (Figure 3). The resulting small bond angles require that n = 5 ring parameters be used in the MOLBD3 program rather than n 2 6 parameter^.'^ However, MOLBD3 calculations for the bridged compounds using n = 5 parameters gave AHf' values ranging from 5 to 16% too high. Examination of individual bond angle strain energies showed that the calculated strain energy for t h e methylene bridge angle (angle 3 7 6 in Figure 3) was disproportionately large. To relieve the excessive strain, we decreased the Bo parameter for that angle from its normal n = 5 ring value ( 1 0 9 . 5 O ) . We observed further that the calculated bond lengths for the methylene bridge bonds (R37and Rs7)were slightly shorter than normal sp3-sp3 bonds, whereas they are in fact longer than normal.'* To lengthen these bonds artificially, we increased the (17) MOLBD3-CalCUhted AH,' for norbornane was 7 kcal/mol too high when n 3 6 parameters were used.
AHIo
195
219
234
218
-32.80 -30.50 -30.50
109.1 108.1 107.3
109.6 109.6
113.0 112.9 113.0
114.3 115.0
" A H f ounits, kcal/mol; 0 in degrees. bThis work.
bridge bond Ro parameter ~1ightly.l~The results of these parameter changes are shown in Table V. The angle y in Table V is that between the 3216 and 3456 planes of norbornane, norbornene, and norbornadiene. We chose Bo = 105' and Ro = 1.55 A for the methylene bridge angle and bonds, respectively, for bridged cyclic compounds with ring bond angles comparable to n = 5 rings. These parameters give very good agreement between calculated and observed AHfo,So,and y,but somewhat poorer agreement between calculated and observed methylene bridge bond angles (376). 2. Bicyclo[3.3.1]nonaneand Bicyclo[3.2.l]octane.The parameters used for the nonane calculations were those of any saturated alkane (Table I). Here, the bond angles, including the methylene bridge angle, are sufficiently large that no excessive angle strain is developed. The MOLBD3 program somewhat overestimates the stability of the compound, but both MOLBD3 and MMPZ agree well with literature values for the bond angles. For the bicyclooctane, n = 5 ring parameters (Bo = 109.5O) were used for the methylene bridge and the ethylene bridge, and n 2 6 ring parameters (Bo = 111.Oo) were used for the propylene bridge. That is, the methylene bridge was treated as if it were part of the five-member ring. Further, Bo = 11 1O was used for the angles at the juncture of the larger rings (217 and 456). Our treatment of bicyclooctane illustrates a procedure using n = 5 and n 2 6 ring parameters in MOLBD3 for larger methylene-bridged rings. That is, n = 5 ring parameters are used only in instances where the ring bond angles are comparable to those in five-member rings, as in the methylene and ethylene bridges in bicyclooctane. For smaller than five-member alkane rings, Boyd3ahas provided applicable parameters. (18) Morino, Y.; Kuchitsu, K.; Yokozeki, A. Bull. Chem. SOC.Jpn. 1967, 40, 1552.
(19) MMPZ compensates for the tendency of bond lengths to increase when the bond angle between them decreases by including a stretch-bend interaction. (20) Walsh, R.; Wells, J. M. J. Chem. Thermodyn. 1975, 7, 149. (21) Rogers, D. W.; Choi, L. S.; Girellini, R. S.; Holmes, T. J.; Allinger, N. L. J . Phys. Chem. 1980,84, 1810. (22) Walsh, R.; Wells, J. M. J. Chem. Thermodyn. 1976, 8, 55. (23) Mastryukov, V. S.; Popik, M. V.;Dorofeeva, 0. V.; Golubinskii, A. V.; Vilkov, L. V.; Belikova, N. A,; Allinger, N. L. J. Am. Chem. SOC.1981, 103, 1333.
J . Phys. Chem. 1989, 93, 1592-1596
1592
The calculated bond angles and AHfovalues for bicyclooctane and bicyclononane are given in Table VI. Agreement of MOLBD3 with MMPZ is seen to be quite good; no literature thermodynamic or structural data were found for the bicyclooctane.
Conclusions We have extended the MOLBD3 force-field method of Boyd and co-workers3 to include several dienes and unsaturated n 2 6 ring compounds. In our work we have employed the -ene and -diene parameters suggested by Anet and Y a ~ a r i .In~ addition, we have successfully treated unsaturated five-member rings by adjustment of the C(spz)-C(spz)-C(spz) and C(spz)-C(spz)-C(spJ) bond angle parameters. Our results for the n = 5 rings were further tested through study of methylene-bridged compounds having bond angles as small as or smaller than typical n = 5 rings, which again showed good agreement between calculated and observed structure, AH?, and So. Finally, we have found good agreement between
our MOLBD3 results and those of other force fields such as MMPZ and CFF-3. Our results indicate these molecular mechanics calculations to have the capability to predict AH: to typically within f l kcal/mol and So and Cpoto typically within f l cal/(mol.K) of measured values, which is sufficient to permit further useful thermodynamic computations. 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-FG02-86ER13582. We thank Professor Richard H. Boyd for providing the M O L B D ~program employed in our studies. Registry No. 1,3-Butadiene, 106-99-0; 1,3-pentadiene, 504-60-9; 1,3-cyclohexadiene, 592-57-4; 1,3-cycloheptadiene,4054-38-0; cyclopentene, 142-29-0;norbornane, 279-23-2; norbornene, 498-66-8; norbornadiene, 121-46-0;bicyclo[3.2.l]octane,6221-55-2;bicyclo[3.3.1]nonane, 280-65-9; 1,3-cyclopentadiene,542-92-7.
Employing Force-Field Calculations To Predict Equilibrium Constants and Other Thermodynamic Properties for the Dimerization of 1,&Cyclopentadiene Terry G. Lenz*?+and John D. Vaughan*,f Department of Chemical Engineering and Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523 (Received: June 13, 1988)
Although there have been many experimental investigations of the Diels-Alder dimerization of 1,3-~yclopentadiene,there remains considerable uncertainty in such thermodynamic properties as AHo, ASo,AGO, and K p for the reaction at various temperatures. Despite this uncertainty, the reaction is a good subject for computational models, because it is one of the few Diels-Alder reactions which has been studied extensively in the laboratory both in the gas and liquid phase over a wide range of temperatures. This paper describes application of a force-field model to calculate thermodynamic properties of the monomer and both endo and exo isomers of the dimer for temperatures ranging from 273 to 500 K. The Boyd MOLBDJ force-field program modified to include (1) -ene and -diene parameters introduced by Anet and Yavari and (2) five-member and methylene bridge parameters suggested by the present authors was used for the calculations. Calculated equilibrium constants for both the gas and liquid phase, and other thermodynamic properties, agreed satisfactorily with what appear to be somewhat inconsistent existing experimental data. This work thus indicates that force-field methods hold promise as a useful alternative to experimental methods for the study of equilibrium properties of chemically reactive systems involving nontrivial molecules.
Introduction During the past two decades, powerful force-field computational methods have evolved which provide a basis for accurate prediction of molecular geometries, energies, and vibrational frequencies. In particular, the MOLBD3 program of Boyd et al.'.' has the capability of calculating accurate AHf', So, and Cpo values. Therefore, when applied to reactant and product molecules, force-field methods provide a basis for calculating the equilibrium thermodynamic properties for gas-phase reactions. These gasphase results may also be coupled with other physical property data to compute thermodynamic properties for liquid-phase reactions. This paper describes an investigation of the suitability of force-field methods for calculating gas-phase equilibrium constants, standard enthalpies of reaction, and standard entropies of reaction. Despite the demonstrated accuracy of force-field cal~ulations,~ these methods have not been extensively exploited for chemical equilibria computations. The specific reaction studied in our work was the Diels-Alder dimerization of 1,3-~yclopentadiene,which was of special interest because it has been the subject of experimental investigations in both gas and liquid phases. Additionally, the vapor pressures of pure 1,3-cyclopentadiene and pure di-
'Department of Chemical Engineering. *Department of Chemistry.
0022-3654/89/2093- 1592$01.50/0
cyclopentadiene have been determined as functions of temperature," which enabled extending our force-field-based results to the liquid phase, for further comparison with available literature data. In our work we have utilized both the MOLBD3 program of Boyd Both MOLBD3 et al.' and the MMPZ program of Allinger et and MMPZ predict structures and AHf' values. Unlike MMP2, MOLBD3 carries out vibrational analyses on molecules, so that the thermodynamic functions ( G O - HoO),(HO - Hoe), Cpo,and absolute entropy, So,are calculated a t any of a number of temp e r a t u r e ~ . Hence, ~ MOLBD3 can be used directly for calculating AGO and Kp for gas-phase chemical reactions involving hydrocarbons. Because of its accuracy and generality, MMP;I AH? values and molecular geometries provided useful comparisons with MOLBD3, particularly in cases where experimental data were limited or lacking. (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 . Phys. Chem. 1976, IS, 1264. (2) Boyd, R. H.; Breitling, S. M.; Mansfield, M. AICHE J . 1973,19, 1016. ( 3 ) Burkert, U.; Allinger, N. L. Molecular Mechanic& ACS Monograph 177; American Chemical Society: Washington, D.C., 1982. (4) Turnbull, A. G.; Hull, H. S. Aust. J . Chem. 1968, 21, 1789. ( 5 ) (a) The Ermer and Lifson program (CFF-3),Sb like MOLBD3, calculates vibrational frequencies. (b) Ermer, 0.;Lifson, S . J. J . Am. Chem. Soc. 1973, 95, 4121.
0 1989 American Chemical Society
