The Calculation of Standard Enthalpies of Formation of Alkanes

Information • Textbooks • Media • Resources

The Calculation of Standard Enthalpies of Formation of Alkanes: Illustrating Molecular Mechanics and Spreadsheet Programs Eric Leigh Hawk Department of Chemistry and Physics, State University of New York, College at Old Westbury, Old Westbury, NY 11568

Chemistry, like many other disciplines, has witnessed the profound effects of recent advances in computing. Calculations that were once considered impossible are becoming routine. For example, theoretical chemists working on the interface of chemistry, biology, physics, mathematics, and computer science are attempting to solve such complex problems as protein folding and drug binding. Computational chemistry is coming of age and chemical software is ubiquitous. In response to this, chemical educators have begun to incorporate more computational chemistry into their curricula. The computational chemistry experiment presented here requires the use of a spreadsheet and Molecular Mechanics (MM) software programs. The experiment was adapted from the literature and modified to suit the needs of chemistry undergraduates. It is ideally suited for a physical chemistry laboratory, but it may be used in an organic chemistry course as well. Defining Steric Energy At the heart of computational chemistry are structure and energy. The two are inseparable. If one wants to know, for example, how a protein folds, then a knowledge of its energy is a prerequisite. Unfortunately, the various forms a system’s energy can take are often confused with one another. In chemistry we have terms like the Gibbs free energy, enthalpy, internal energy, and other thermodynamic energy relations that depend on the state of the system. In this experiment we are interested in calculating the standard enthalpy of formation (∆H°f,298) of an alkane with a molecular mechanics program. Most students are introduced to ∆H °f, 298 in freshman chemistry. However, here the ∆H°f, 298 is to be calculated in part by use of the alkane’s steric energy, a term that most students are not familiar with. Therefore, the primary goal of this computational experiment is to explain the meaning of steric energy through its relation to the standard enthalpy of formation at 298 K. To calculate a molecule’s steric energy via an MM approach (1), the energy of a molecule is expressed as a function of two-, three-, and four-body terms. (An example of a twobody term is the function for the chemical bond between two nuclei; a three-body term is the function for the angle formed by three nuclei; etc.). These various energy terms are expressed as simple mathematical functions that are dependent on the internal coordinates of the molecule. These equations are called potential functions. Associated with these potential functions are constants. For instance, a bond stretch constant for a C–C bond is different from that for a C–H bond even though they both employ two-body terms. These constants are known as parameters. The collection of potential functions and their associated parameters are generally referred to as the force field. When a molecule is selected for a molecular mechanics analysis, the various bond, angle, torsion, and nonbonded interactions are assigned their respective potential functions. 278

During the calculation, the bond, angle, torsion, and nonbonding1 potential functions are summed. This sum is called the molecule’s steric energy. The steric energy is therefore a function of the relative positions of the nuclei in the same way that a Morse potential is a function of the internuclear distance of a diatomic molecule. The difference is one of degree. In the case of the diatomic molecule only one variable describes the Morse potential energy surface, whereas for a molecule of sufficient size there are many variables. The term multidimensional potential energy surface is used in the latter case of several variables. A molecule’s geometry (i.e., conformation) will correspond to a point on the potential energy surface having a unique steric energy. The potential energy surface may contain welldefined minima and maxima. A conformation that corresponds to a minimum is defined as a conformer. In general, the steric energy for a conformer is calculated. In this experiment we are interested in finding the lowest steric energy conformer known as the global minimum. To locate a minimum on the multidimensional potential energy surface, an optimization method is selected from within the MM program. The conjugate gradient method is a good example of an optimization method (2). The entire optimization process is called minimization, and through successive iterations the molecule is taken to new conformations having lower steric energies. The minimization process is often viewed on the computer screen. If the minimization procedure goes well, the final geometry should correspond to a local minimum. However, the local minimum may not be the global minimum. For large molecules, finding the global minimum is highly improbable, but in this experiment, intuition on the part of the student usually leads to the correct global minimum structure. If all force fields gave the same steric energy for all minimized structures, then we would know that the calculations are robust. Unfortunately they’re not. Consider the following cases: (i) two different force fields give the same geometry but different steric energies; and (ii) two different force fields give the same ∆H°f, 298 but different geometries. In the latter case, the force field was developed to predict standard enthalpies of formation, not geometries. And in the former case, the force fields were designed to obtain geometries and not steric energies. The point is, force fields are often developed to predict various properties with not all the results being necessarily self consistent. It is worth noting that there has been interest in a consistent force field (3)—that is, one that can simultaneously reproduce most physical properties accurately. In this experiment we are interested in using steric energies to predict standard enthalpies of formation. We must therefore choose a force field that was designed with this intent. Allinger’s MM3 force field makes a good choice because it was developed to predict standard enthalpies of formation.2 In fact, the MM3 force field gave a standard deviation of 0.41

Journal of Chemical Education • Vol. 76 No. 2 February 1999 • JChemEd.chem.wisc.edu


kcal/mol between calculated and observed heats of formation for a set of 50 alkanes (4). Other force fields were developed with the same goal (5), so the student is advised to try other force fields and compare results. Presented below in the theory section is the derivation of the following equation ∆H°f, 298 = GE + SE + 4RT

(1)

where ∆H°f, 298 is the standard enthalpy of formation, GE is the group increment term (to be explained later), SE is the calculated steric energy at the conformer’s global minimum, and R is the ideal gas constant. The group increment term is evaluated first and thereafter only the steric energy needs to be calculated in order to predict a gas-phase ∆H°f at 298 K. Equation 1 is extremely helpful in explaining what a steric energy is and how it can be used. From the basic equations of thermodynamics,3 the steric energy in eq 1 is now understood as an internal energy. More specifically, in the MM framework, the steric energy is related to the molecule’s internal energy due to the lowest electronic state, Uel. In principle, Uel is obtained from quantum chemical calculations and the methods of statistical thermodynamics. An ab initio quantum chemical calculation may be used to calculate the geometry and electronic potential energy, Ee , for the lowest electronic state at 0 K. But since ab initio quantum calculations are computationally intensive, the geometry may be calculated by other methods such as MM. The MM approach is empirical and requires very little computer time. The force field is supposed to mimic the quantum mechanical potential energy surface while providing an accurate predicted geometry; that is, bond lengths and bond angles accurate to 0.01 Å and 2°. Once students learn that steric energy is an internal energy, they are less likely to confuse it with other forms of energy such as the Gibbs free energy. They are also less likely to assume that the global minimum structure derived from an MM calculation is the most stable structure. 4 To predict the most stable structure, other factors need to be considered such as the state of the system, total internal energy, enthalpy, and entropy. In addition, the MM calculation is for an isolated molecule at 0 K, so the chemical environment is of prime importance as well. It is also instructive for students to understand how steric energy differences are interpreted in conformational analysis. For example, in the case of butane, the experimental value for the enthalpy difference between the gas-phase gauche and anti conformers is 17.15 (± 0.84) kcal/mol (6 ). We can express this enthalpy difference as a chemical equation Conformer 1 Conformer 2 ∆H°rxn = ∆H°f (Conformer 2) – ∆H°f (Conformer 1) C4H10 (g, anti)

(2)

C4H10 (g, gauche)

∆H°rxn = ∆H°f (C4H 10 (g, gauche)) – ∆H°f (C4H10 (g, anti)) = 17.15 (± 0.84) kcal/mol

(3)

where the change in enthalpy is the standard value change for the reaction at 298 K. Substituting eq 1 into eq 3 gives ∆H°rxn = (GE + SE + 4RT )C 4H10(g,gauche) – (GE + SE + 4RT )C4H10(g,anti)

(4)

The group increment terms and the constant 4RT in eq 4 cancel to give ∆H°rxn = SEC 4H10(g,gauche) – SEC 4H10(g, anti)

(5)

This is a very important result. That is, the standard enthalpy change for a conformational change (eq 2) is simply equal to the steric energy difference. In the case of different molecules, the above relations will not result in the same conclusion because the GE terms may not cancel. Theory As noted above, we wish to derive the following equation useful to an MM approach ∆H°f, 298 = GE + SE + 4RT

(6)

As T is a constant, the last term in eq 6 is also a constant. Thus a knowledge of GE and SE (the latter derived from an MM calculation) will allow us to obtain the ∆H°f,298 . As a full derivation of eq 6 is beyond the scope of this paper, those interested in the full derivation can consult the cited references (7). Starting from thermodynamics, ∆H°f, 298 of a gaseous compound is ∆H°f, 298 = ∆U° + (∆n/mol)RT

(7)

where ∆U ° is the change in internal energy and (∆n/mol)RT was derived from the P∆V term (8). The ∆n term applies only to the change in the number of gaseous species. As an example, consider the following reaction: nC(graphite, s) + mH2(g) → CnH 2m(g) at 1 bar and 298 K (8) where ∆n is equal to 1 – m. Substituting this into eq 7 gives ∆H°f, 298 = ∆U° + RT – mRT

(9)

The change in total internal energy, ∆U °, can be written as a sum of the changes in internal energy due to translation, rotation, vibration, electronic and bond energies, such that ∆U° = ∆U°tr + ∆U °rot + ∆U °vib + ∆U °el + ∆U °bond energies (10) Since the terms in eq 10 are often difficult to evaluate, several approximations are made in the calculation of ∆U °. The validity of these approximations can be judged by how well the predicted standard enthalpies of formation compare with experimental data when available. The individual terms in eq 10 are now discussed. ⌬U ⴗtr: Again, using the reaction in eq 8 as an example, the change in internal energy due to translation may be written as ∆U °tr = (U°T,tr – U °0,tr)C nH2m(g) – m(U°T,tr – U°0,tr) H2(g) – n(U °T,tr – U°0,tr) C(graphite, s)

(11)

where U°0,tr is the internal energy reference point at 0 K. For a gas, (U°T,tr – U°0,tr) is equal to 3/2RT. For a solid, U°T,tr – U °0,tr is equal to zero. Thus, in the case of a gaseous alkane, eq 11 is rewritten as ∆U °tr = 3/2RT – 3/2mRT – 0

(12)

⌬U ⴗrot : An approach similar to that described for translation is taken for rotation. The rotational energy of a nonlinear gaseous molecule is 3/2RT ; that of the m linear H2 molecules is mRT. This yields the following equation:

JChemEd.chem.wisc.edu • Vol. 76 No. 2 February 1999 • Journal of Chemical Education

279


∆U °rot = 3/2RT – mRT – 0

(13)

where 3/2RT will be substituted by RT if the alkane is linear. ⌬U ⴗvib , ⌬U ⴗel, and ⌬U ⴗbond energies : Evaluation of these terms is more difficult. An alternative means to evaluate these terms is known as the group increment method (1, 4, 7, 9). This method deconstructs a molecule into fragment types that can include bond types, group types, or both. Each increment type contributes a fixed amount of energy, and the increments are assumed to be additive. The total group increment energy, GE, is written as GE = Σk j ⴢ u j

(14)

where j is the group type, k j is the number of j-groups in the molecule and u j is a group increment coefficient. In this experiment, an alkane molecule is deconstructed into four fundamental carbon groups (primary, secondary, tertiary, and quaternary). For example, the alkane 2,2,3,4,4-pentamethylhexane consists of seven primary (kp = 7), one secondary (ks = 1), one tertiary (k t = 1), and two quaternary (k q = 2) carbons that have a total group energy expression as

can be rewritten as Y n = (∆H°f, 298,exp – SE – 4RT ) n = (kp ⴢ up + ks ⴢ us + k t ⴢ ut + kq ⴢ uq)n

(22)

where n denotes the nth alkane of an input data set that is used to derive the group increment coefficients. For an input data set of n alkanes that contains experimentally determined gas-phase standard enthalpies of formation and calculated steric energies, we find that Y 1 = (kp ⴢ up + ks ⴢ us + k t ⴢ ut + kq ⴢ uq) 1

(23a)

Y 2 = (kp ⴢ up + ks ⴢ us + k t ⴢ ut + kq ⴢ uq) 2

(23b)

Y 3 = (kp ⴢ up + ks ⴢ us + k t ⴢ ut + kq ⴢ uq) 3 ⯗ Ynth = (kp ⴢ up + ks ⴢ us + k t ⴢ ut + kq ⴢ uq) n

(23c) (23d)

We now have n equations for the n alkanes and four unknown coefficients (up, us , ut, uq). The group increment coefficients are evaluated by performing a linear regression analysis on eqs 23. After the group increment coefficients are generated, the enthalpy of formation for an alkane can be easily calculated using eq 20. For example, the GE term in eq 20 is expanded to give

GE = kp ⴢ up + k s ⴢ us + k t ⴢ ut + kq ⴢ uq

(15)

GE = 7 ⴢ up + 1 ⴢ us + 1 ⴢ ut + 2 ⴢ uq

(16)

∆H°f, 298,cal = kp ⴢ up + ks ⴢ us + kt ⴢ ut + kq ⴢ uq + SE + 4RT (24)

where up, us, ut, and uq are the group increment coefficients for primary, secondary, tertiary, and quaternary carbons, respectively. The steric energy (SE) that is derived from an MM calculation is added to the group increment term to correct for the steric effects. Overall, the internal energy due to ∆U °vib, ∆U °el, and ∆U °bond energies is approximated as a sum of group increments and the alkane’s steric energy, such that

where the constants kj, uj, and 4RT are simply inserted; however, the SE term is inserted after the alkane’s global steric energy is calculated.

∆U°vib + ∆U°el + ∆U°bond energies = GE + SE

(17)

Substituting eqs 12, 13 and 17 into eq 10 gives ∆U ° = GE + SE + 3RT – 3/2 mRT – mRT

(18)

Now if we substitute eq 18 into eq 9, we get the total standard enthalpy of formation: ∆H°f, 298 = GE + SE + 4RT – 7/2mRT

(19)

The 7/2mRT may be accounted for in two ways. First, the number of moles of hydrogen, m, for each reaction could be inserted in eq 19. The second way assumes that 7/2mRT is included within the GE term via the group increment coefficients. If we adopt this second approach we get ∆H°f, 298 = GE + SE + 4RT

(20)

where the group increment coefficients would be different from those used eq 19. Equation 20 is the desired result. Group Increment Coefficients To solve for the group increment coefficients for the reaction in eq 8, eq 20 is rearranged to give ∆H°f, 298,exp – SE – 4RT = GE = kp ⴢ up + ks ⴢ us + k t ⴢ ut + kq ⴢ uq

(21)

where ∆H°f,298,exp is taken from tabulated standard enthalpy of formation values (10). The right side of eq 21 is taken from eq 15. Using shorthand notation, the left side of eq 21 280

Calculations The steric energies of the alkanes were calculated by the molecular mechanics option in SYBYL version 6.1.5 This molecular modeling software runs on a Silicon Graphics, Inc., Indy computer.6 The following was selected from within SYBYL: (i) Force Field—Allinger’s MM3; (ii) Geometry Optimization—conjugate gradient method with a gradient convergence of 0.05 kcal/mol. The spreadsheet software program used was Microsoft Excel 97.7 For the linear regression analysis the regression analysis tool was selected from Excel 97. Experimental Procedure The following procedure should be followed sequentially.

Input and Output Data Sets Develop the input and output data sets by selecting 10 or more alkanes for each set. The data sets must contain all four group increment types: primary, secondary, tertiary and quaternary carbons. The selected alkanes in Tables 1 and 2 can be duplicated; however, it may be instructive to have each student create his or her own input and output data set. Molecular Mechanics Calculations/Steric Energies Using any of the existing MM packages,2 calculate the global minimum steric energy (expressed in kcal/mol) for each alkane. (The global minimum steric energy must be found in order to predict accurate calculated enthalpies of formation.) This entails three basic steps: building the alkane, selecting the force field, and minimizing the structure. In regard to the global minimum, most of the alkanes selected will prefer an anti conformation around each carbon–carbon bond. Record the steric energies for each alkane.



Begin the Input Data Set Worksheet Using one of the standard spreadsheet software programs, construct an input data set worksheet similar in design to that given in Table 1. The input data set worksheet should include the following for each alkane: (i) nth run or trial number; (ii) name of alkane; (iii) experimental standard enthalpy of formation (∆H°f, 298,exp, kcal/mol); (iv) calculated standard enthalpy of formation (∆H°f,298,cal , kcal/mol). Leave the formula entry (see eq 24) for ∆H°f,298,cal blank for the moment. It will be completed during a subsequent step; (v) absolute error (∆∆H °f, kcal/mol), which is equal to ∆H °f, 298,cal – ∆H°f, 298,exp; (vi) steric energy, kcal/mol; (vii) 4RT (T = 298 K) equivalent to 2.4 kcal/mol; (viii) Yn, kcal/mol (Yn is a formula entry as given in eq 22); and (ix) type and number of carbon group (kp, ks, kt , and kq).

Regression Output Worksheet and Group Increment Coefficients Within the spreadsheet software program perform a linear regression analysis on the equations contained in the input data set worksheet (see the highlighted portion of Table 1 and eqs 23). The summary output worksheet created from the linear regression analysis contains the group increment coefficients (up, us , ut, and uq) in kcal/mol. The summary output worksheet also contains additional terms that need not be reported. Therefore, one is advised to create a new linear regression output worksheet (see Table 3). The new linear regression worksheet should contain the group increment coefficients as well as selected regression statistics, such as R square, adjusted R Square, and the standard error.

Table 1. Input Data Set for Selected Alkanes Run

∆H°f,exp,298/ ∆H°f,cal,298/ ∆∆H°f/ (kcal/mol)a (kcal/mol)b (kcal/mol)

Alkane IUPAC

SE/ (kcal/mol)

Yn/ 4RT/ (kcal/mol) (kcal/mol)c

No. of Group Increment

Rel Errord (%)

kp

ks

kt

kq

1

2,2,3-Trimethylbutane

᎑48.87

᎑48.86

0.01

8.27

2.4

᎑59.54

5

0

1

1

0.02

2

3,3-Dimethylpentane

᎑48.08

᎑47.45

0.63

8.26

2.4

᎑58.74

4

2

0

1

1.31

3

Neopentane

᎑40.14

᎑40.78

᎑0.64

2.27

2.4

᎑44.81

4

0

0

1

1.60

4

3-Methylpentane

᎑41.33

᎑41.34

᎑0.01

5.53

2.4

᎑49.26

3

2

1

0

0.03

5

n-Pentane

᎑35.56

᎑36.30

᎑-0.74

2.82

2.4

᎑40.78

2

3

0

0

2.07

6

n-Butane

᎑30.60

᎑30.62

᎑0.02

2.17

2.4

᎑35.17

2

2

0

0

0.08

7

Propane

᎑24.83

᎑24.97

᎑0.14

1.50

2.4

᎑28.73

2

1

0

0

0.57

8

Ethane

᎑20.24

᎑19.33

0.91

0.82

2.4

᎑23.46

2

0

0

0

4.51

9

Cyclohexane

᎑29.50

᎑29.00

0.50

6.55

2.4

᎑38.45

0

6

0

0

1.70

10

Cyclobutane

6.78

6.32

᎑0.46

29.22

2.4

᎑24.84

0

4

0

0

Average

0.41

6.78

1.87

experimental standard enthalpies of formation at 25 °C (gas phase) were taken from ref 10. calculated standard enthalpies of formation at 25 °C (gas phase) were derived from a linear regression analysis on the above shaded data representing eqs 23. cDerived using left side of eq 22. d|(∆H° f,exp – ∆H°f,cal)/∆ H° f,exp)| × 100. aThe bThe

Table 2. Output Data Set for Selected Alkanes Run

∆H°f,exp,298/ (kcal/mol)a

Alkane IUPAC or common name

∆H°f,cal,298/ (kcal/mol)b

∆∆H°f/ (kcal/mol)

No. of Group Increment SE/ 4RT/ (kcal/mol) (kcal/mol) k ks kt kq p

Rel Errorc (%)

1

2,2,3,3-Tetramethylbutane

᎑53.83

᎑53.96

᎑0.13

12.00

2.4

6

0

0

2

0.25

2

Methylcyclopentane

᎑25.50

᎑25.41

0.09

11.56

2.4

1

4

1

0

0.35

3

endo-Tricyclo[5.2.1.0]decane

᎑14.38

᎑14.32

0.07

33.53

2.4

0

7

2

1

0.45

4

1,1-Dimethylcyclohexane

᎑43.23

᎑42.87

0.36

9.27

2.4

2

5

0

1

0.84

5

Cubane

148.70

151.50

2.80

171.52

2.4

0

0

8

0

1.88

6

Cyclooctane

᎑29.73

᎑28.79

0.94

19.41

2.4

0

8

0

0

3.16

7

Bicyclo[4.3.0]nonane (trans-Hydrindane)

᎑31.42

᎑30.35

1.07

17.13

2.4

0

7

2

0

3.41

8

Bicyclo[4.3.0]nonane (cis-Hydrindane)

᎑30.38

᎑29.17

1.21

18.31

2.4

0

7

2

0

3.98

9

trans-syn-trans-Perhydroanthracene

᎑58.10

᎑55.89

2.21

16.17

2.4

0

10

4

0

3.80

10

trans-anti-trans-Perhydroanthracene

᎑52.02

᎑49.80

2.22

22.26

2.4

0

10

4

0

4.28

11

cis-Bicyclo[3.3.0]octane

᎑22.77

᎑21.56

1.21

19.59

2.4

0

6

2

0

5.31

12

Norborane

᎑12.42

᎑11.74

0.69

23.09

2.4

0

5

2

0

5.52 5.91

13

Adamantane

᎑31.55

᎑29.68

1.87

17.07

2.4

0

6

4

0

14

trans-Bicyclo[3.3.0]octane

᎑15.73

᎑14.53

1.20

26.63

2.4

0

6

2

0

7.65

15

Bicyclo[2.2.2]octane

᎑23.75

᎑21.57

2.18

19.59

2.4

0

6

2

0

9.19

Average aThe bThe

1.22

3.73

experimental standard enthalpies of formation at 25 °C (gas phase) were taken from ref 10. calculated standard enthalpies of formation at 25 °C (gas phase) were generated from eq 24 using the group increment coefficients listed in Table 3. f,exp – ∆H°f,cal )/∆H°f,exp)| ⴢ 100.

c|(∆H°


281


Complete the Input Data Set Worksheet Once the group increment coefficients are known, the calculated enthalpies of formation (∆H°f, 298,cal) can be easily generated using eq 24. Format eq 24 into the input data set worksheet for column entry ∆H°f, 298, cal. Alternatively, the ∆H°f, 298,cal values can be taken directly from the summary output worksheet created from the linear regression analysis. The ∆∆H°f values should now appear in the input data set worksheet. Report the average ∆∆H°f value [(∆∆H°f)av ]. For the case of the input data set worksheet, the ∆∆H°f values are equal to the residuals reported in the summary output worksheet created from the linear regression analysis. Complete the Output Data Set Worksheet Repeat the steps in “Begin the Input Data Set Worksheet” for the output data set. However, for step iv, format eq 24 into the worksheet. The group increment coefficients used in eq 24 are taken from the linear regression worksheet. Report (∆∆H°f)av. NOTE: Step viii and the steps in the next two sections are only for the input data set. Discussion Students are expected to calculate and comment on the average absolute error of the standard enthalpy of formation [(∆∆H°f) av ] for the output data set. In Table 2, (∆∆H°f,298) av is 1.22 kcal/mol. The average absolute error for ∆H°f,exp should lie somewhere between 0.4 and 0.6 kcal/mol (11). The value of (∆∆H°f,298) av may decrease as the number and type of alkanes in the input data set increases. Other factors that affect the reported (∆∆H°f,298) av value are (i) an incorrect entry for ∆H°f,298,exp; (ii) an incorrect entry for the steric energy; (iii) a poor linear regression fit; (iv) a poor input data set that fails to represent the alkanes as a whole; and (v) neglect of additional correction terms in eq 24 (6 ). Students should pay particular attention to the steric energy. For instance, it is common for students to select an initial conformation that does not lead to the global minimum. Since the global minimum is the lowest possible steric energy, reported steric energies for conformers other then the global minimum will be greater then expected. A high steric energy will result in a high ∆H°f,298,cal as well. In fact, a ∆H °f,298,cal value that is greater than the ∆H °f,298,exp value is an excellent indicator of failure to locate the global minimum. If students suspect a high steric energy, they should attempt to find a conformer with a lower steric energy. A poor input data set may include a list of alkanes with too few tertiary and quaternary carbons. The input data set in Table 1 may be lacking in this respect and can be one reason why (∆∆H°f )av is on the order of 1.22 kcal/mol. The input data set can be improved by including additional alkanes such as endo-tricyclo[5.2.1.0]decane or 2,2,3,3-tetramethylbutane. To prevent some of the errors above from happening, we have found that it is best to devote two laboratory sessions to this experiment. Students are expected to bring a list of alkanes with their corresponding experimental standard enthalpies of formation to the first session. They are also expected to know how the atoms are connected in the structure. During the first session, the students work with the MM software. They are expected to master building and inputting a structure, selecting a force field, and minimizing the structure. After they have generated a sufficient input data 282

Table 3. Selected Linear Regression Output Group Increment Coefficients/(kcal/mol)

up

us ᎑11.27

ut ᎑6.33

uq ᎑2.8

᎑0.37

Regression Statistics R Square 0.99

Adjusted R Square 0.83

Standard Error (Yn) 0.67

N OTE: Derived from a linear regression analysis on shaded data contained in Table 1. The linear regression analysis option was selected from within Microsoft Excel 97.7

set, they can complete the third, fourth, and fifth sections in the experimental procedure. During the second session, students can refine their input data set and correct for any errors in their reported steric energies. The output data set worksheet can be completed at this time as well. In addition, students must report the computer(s), MM program, force field, minimization routine, minimization convergence criteria, and spreadsheet program used in the experiment. For more sophisticated MM packages, students working together can compare the results from two different force fields. As part of their discussions, students should report which of the two force fields was better in predicting the standard enthalpies of formation. Most of the MM software packages available generate calculated standard enthalpies of formation. Students may ask if the standard enthalpies of formation can be derived directly from the MM program itself. The answer is, of course, yes. However, students should be reminded that a black-box approach to computing is not the solution and, more importantly, often leads to erroneous results. Notes 1. Nonbonded refers to dipole–dipole, charge–charge, and dispersion forces. 2. The following vendors offer molecular mechanics programs that run on conventional PC’s. (a) Allinger’s MM3 program is available to academic users from the Quantum Chemistry Program Exchange (QCPE), Creative Arts Building, 181 Indiana University Bloomington, IN 47405. (b) PC SPARTAN 1.0 or MacSPARTAN is available from Wavefunction, Inc., 18401 Von Karman Avenue, Suite 370, Irvine, CA 92612. (c) HyperChem Release 5 is available from Hypercube, Inc., 1115 North West 4th Street, Gainesville, FL 32601. (d) Pcmodel is available from Serena Software, Box 3076, Bloomington, IN 474023076. (e) In addition, modeling software is available from Oxford Molecular Group, Inc., 2105 South Bascom Avenue, Suite 200, Campbell, CA 95008. 3. H = U + PV. 4. At constant temperature and pressure the most stable structure here refers to the Gibbs free energy global minimum. 5. SYBYL is available from Tripos, Inc., 1699 South Hanley Road, Saint Louis, MO 63144. 6. INDY, 100/50 MHz R4600PC, 32 MB computer from Silicon Graphics, Inc., 2011 North Shoreline Boulevard, P.O. Box 7311, Mountain View, CA 94043. 7. Excel 97 is available from Microsoft Corporation, One Microsoft Way, Redmond, WA 98052-6399.



Literature Cited 1. For an excellent and highly recommended text on molecular mechanics see Burkert, U.; Allinger, N. L. Molecular Mechanics; American Chemical Society: Washington, DC, 1982. 2. Press, W. H.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes in C: The Art of Scientific Computing, 2nd ed.; Cambridge University Press: New York, 1993. Press, W. H.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed.; Cambridge University Press: New York, 1992. 3. Lifson, S.; Warshel, A. J. Chem. Phys. 1968, 49, 5116. 4. Lii, J-H; Allinger, N. L. J. Am. Chem. Soc. 1989, 111, 8566. 5. Engler, E. M.; Andose, J. D.; Schleyer, P. v. R. J. Am. Chem. Soc. 1973, 95, 8005.

6. Burkert, U.; Allinger, N. L. Molecular Mechanics; American Chemical Society: Washington, DC, 1982; p 47. 7. Allinger, N. L.; Schmitz, L. R.; Motoc, I.; Bender, C.; Labanowski, J. K. J. Am. Chem. Soc. 1992, 114, 2880. 8. Levine, I. N. Physical Chemistry, 4th ed.; McGraw-Hill: New York, 1995; p 141. 9. Benson, S. V. Thermochemical Kinetics, 2nd ed.; Wiley: New York, 1976. Gasteiger, J. Comput. Chem. 1978, 2, 85. Gasteiger, J. Tetrahedron 1979, 35, 1419. Gasteiger, J.; Jacob, P.; Strauss, U. Tetrahedron 1979, 35, 139. 10. Cox, J. D.; Pilcher, G. Thermochemistry of Organic and Organometallic Compounds; Academic: New York, 1970. 11. Burkert, U.; Allinger, N. L. Molecular Mechanics; American Chemical Society: Washington, DC, 1982; pp 175–176.


283

The Calculation of Standard Enthalpies of Formation of Alkanes

Recommend Documents