Computational Thermochemistry - American Chemical Society

Chapter 9

Downloaded by NORTH CAROLINA STATE UNIV on September 30, 2012 | http://pubs.acs.org Publication Date: February 1, 1998 | doi: 10.1021/bk-1998-0677.ch009

Bond-Additivity Correction of Ab Initio Computations for Accurate Prediction of Thermochemistry 1,3

2

Michael R. Zachariah , and Carl F . Melius 1

National Institute of Standards and Technology, Gaithersburg, M D 20899 Sandia National Laboratories, Livermore, C A 94551 2

This paper reviews a method for the correction o f ab-initio derived molecular energy computations, for determination of thermochemical data of sufficient accuracy for application to chemical modeling. The basic concept is the use of a computationally inexpensive approach M P 4 / 6 - 3 1 G * * / / H F - 6 - 3 1 G * , which enables a large number of molecules to be computed, and combines this with a bond-additivity correction scheme. The basic concept behind the bond additivity approach is that errors in the energy computation are systematic with the type o f bond, and that calibration for each bond class from comparison with molecules o f known energy allow for a correction to the computed energy.

The rapid increase in computer power has enabled the development o f ever more sophisticated "Computational Reacting F l u i d D y n a m i c s " ( C R F D ) models. These models use detailed chemical kinetic mechanisms to solve chemistry-flow interactions in a wide variety o f complex problems; e.g. chemical vapor deposition, combustion, plasma processing, atmospheric processes. A s computer models become more sophisticated, the need for the fundamental data that feed such models has become a major limiting factor. Thermochemistry (enthalpy, entropy, heat capacity) and kinetics (diffusion coefficients, thermal transport coefficients, reaction rate constants) are the life blood o f such models, and while the models, which in a sense are nothing more than sophisticated bookkeeping schemes for mass and energy conservation can be adapted from one problem to another, the chemistry is unique. In seeking a solution to the problem of lack of data, it is unreasonable to assume that we can measure our way out o f the problem. Fortunately modern computational chemistry methods offer a means to circumvent the need to measure everything. The task at hand is to provide to users methods that afford both accuracy sufficient for most C R F D computations and computational cost suitable for the task of generating the large data bases necessary to undertake useful C R F D computations. In this paper we w i l l describe a procedure that aims to satisfy the basic requirements set forth in the paragraph above. 3

Email address: [email protected]

162

© 1998 American Chemical Society

In Computational Thermochemistry; Irikura, K., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1905.

9.

Z A C H A R I A H & MELIUS

Correction of Ab Initio Computations

163


Computational Approach While it is true that given enough computer time one can compute molecular properties to great precision, a simpler and cheaper approach that sacrifices some of the scientific rigor may ultimately yield the same accuracy in a much more tractable format. The B A C procedure involves the systematic correction o f ab-initio molecular orbital computations, which enables the use of a computationally cheaper level of theory with the same level of potential accuracy. The B A C procedure is based on the observation that errors in electronic structure computations are systematic and therefore amenable to correction. Furthermore, B A C procedures assume that these errors are localized and are therefore additive. The best analogy can be drawn from the well known bond and groupadditivity methods developed by Benson, which state that the energy of a molecule can be constructed as a sum of the energies of its constituent parts, bonds or groups (1) (see also the chapter by Benson in this volume). The B A C procedure assumes that the error in computing a molecular energy is equivalent to the sum of the errors in computing the constituent parts of the molecules, namely the bonds. A s such the B A C approach is basically an extension of the isodesmic reaction approach. Since the error in computing a given type of bond can usually be determined by comparison with known bond energies, such a procedure enables the correction of the molecular energy in a relatively straightforward manner, as w i l l be illustrated. BAC-MP4

Methodology

The computational methodology is based on an M P 4 / 6 - 3 l G * * / / H F / 6 - 3 1 G * computation (2). Ab-initio computations in general tend to underestimate bond strengths as a result of finite basis set effects and the finite number of configurations used to treat the electron correlation. A s previously stated, the errors can be considered in large part to be bond-wise additive and depend on bond type, bond distance and a small correction due to nearest neighbor bonds. For the bond between A , and Aj in the molecule A k - A j - A j - A i , the error in calculating the electronic energy can be estimated through a pair-wise additive empirical bond correction E B A C of the form. E B A C (Aj-Aj) = fjj gidj gjji

(1)

where fij= Ajj exp(-ccij rjj),

(2)

Ay and ay are calibration constants (shown in Table I) that depend on bond type, and rjj is the bond length at the Hartree-Fock level. The multiplicative factor gky, gkij = (1 - h

i k

h|j)

is the nearest-neighbor bond correction (to the bond being considered), where


(3)

COMPUTATIONAL THERMOCHEMISTRY


Table I. B A C Parameters

Bond Type

a

H-H B-H C-H C-C N-H B-N C-N N-N O-H B-O C-O N-0 O-O F-H C-F N-F O-F F-F Si-H Si-C Si-N Si-O Si-F Si-Si P-H PC P-N P-O P-F S-H C-S N-S S-0 S-F S-S H-Cl B-Cl C-Cl N-Cl O-Cl F-Cl Si-Cl Cl-Cl P-Si

2 2 2 3.8 2 2.84 2.8 2.6 2 2.65 2.14 2.1 2 2 2.1 2 2 2 2 2.5 2.5 2.42 2 2.7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2.91

U

Ay (kcal/mol)

Atom Type

Bk

18.98 31.1 38.6 1444.1 70.1 370 462.3 472.6 72.45 206.9 175.6 226 169.8 84.2 143.3 170 189.7 129.2 38.6 893.7 848 628.3 260.6 3330.2 137.5 260 290 305 320 119.5 281.9 350 455 400 100 116.4 172.5 304.3 340 355.1 380 721.9 980.2 7085

H B C N O CI F Si S

0 0.2 0.31 0.2 0.225 0.42 0.33 0.2 0.56


9.


165


h = B exp (-oc (r - 1.4 A)) ik

k

ik

(4)

ik

The functional form implies that as the bond gets shorter (e.g. multiple bonds), the energy correction, EBAC> increases exponentially and primarily depends on the factor fy. The parameter g y is an empirically determined correction due to the neighboring bond A - A j , which reduces the size o f the bond correction. This was found to be a necessary correction to prevent the effects o f double counting o f the B A C due to superposition of the basis sets. The reduction in bond error results from the fact that the basis functions for atom A help describe the A - A i bond. k


k

k

k

The parameters A y , a y , and B are empirically determined by fitting the heats of formation calculated at the B A C - M P 4 level o f theory for selected molecules to experimental or i n some cases, high-quality ab-initio computations o f the heat of formation. They are summarized for a wide variety of bond types in Table I. For open-shell molecules, an additional correction is needed due to contamination of the wavefunction from higher spin states in the unrestricted HartreeF o c k ( U H F ) framework. This error is estimated using an approach developed by Schlegel (3) in which the spin energy correction E i (UHF) is obtained from: k

s p

E

s p i n

n

(UHF) = E(UMP3) - E(PUMP3)

(5)

where U M P 3 refers to unrestricted wavefunction at the M P 3 level (third-order MollerPlesset perturbation theory) and the P refers to the projected U M P 3 energy. For many radicals, E i is relatively small (e.g., 0.21 kcal/mol for O H ) , but it can become large for highly unsaturated molecules (e.g., 12.2 kcal/mol for C2H). Because the M P 4 method is a single-reference calculation, molecules with multireference character, such as O3, are not w e l l treated. E a c h closed-shell molecule computed is checked for any U H F instability i n the H F wavefunction. I f found to be unstable, the U H F wavefunction is calculated along with its spin contamination, defined by S(S+1), corrected by: s p

n

E

s p i n

(S2)= K S(S+1)

(6)

where K = 10 kcal/mol, based on obtaining reasonable heats o f formation for O3 and !CH . 2

The resulting total B A C energy correction for a given molecule. E B A C (Total) = Zy E

B A C

(Ai-Aj) + E

s p i n

(UHF) + E

s p i n

(S2)

(7)

where ij is summed over a l l chemical bonds i n the molecule. This energy is then subtracted from the ab-initio computed heat of formation. A basic summary of the methodology is shown schematically in Figure. 1 and a sample script using the Gaussian series of programs is shown i n the Appendix. Note that the methodology is not limited to minima on potential energy surfaces but can be used for defining thermochemistry at transition states for chemical reactions (2j). B A C - M P 4 E r r o r Estimation L i k e any computational approach, B A C - M P 4 can give more accurate results for some species than for others. H a v i n g a method that allows for a rough estimate o f the




Bond Additivitv Corrected Quantum Chemical Calculation Method

Hartree-Fock (HF) or MP2 Calculation of Potential Energy Surface; 6-31G*

Geometries and Frequencies

Many-Body Perturbation Theory (MP4) calculation of Potential Energy at 6-31G**

Bond Additivity Correction (BAC) to Potential Energy

(^Corrected Energy^)

Statistical Mechanics Calculations

Enthalpies, Entropies and Free Energies

-Calibrate energy of each type of chemical bond against literature values, -Treat errors as bond-wise additive -Express BA correction as exponential of calculated bond length L e

-

E

A

A

A

ex

a

R

BAC< r j) = i j P ( " i j i j ) E

BAC

(Total)= I E

B A C

(A Aj) +E r

2

B A C

(Spin S )

where Rjj is the length of the chemical bond between atoms Aj and Aj and Ay and ay are fitting constants.

Figure 1. B A C - M P 4 computational procedure.


9.


167


accuracy of the computed enthalpy provides for a more intelligent approach to using the results of computations from a large number of species. The error estimation is based on calculation of the heat of formation at lower levels of perturbation theory, i.e. B A C M P 2 , B A C - M P 3 , B A C - M P 4 S D Q , each with its own set o f B A C correction parameters. The general trend in the correction terms fy are:


fij(MP2) < fij(MP4) < fij(MP3) - fij(MP4SDQ) However, all the correction terms are similar implying that the primary error in the M0ller-Plesset perturbation theory calculation is due to the finite basis set. B y comparing the resulting heat of formation at the various levels one can estimate the extent of the error. If the results between the various levels are consistent then the error should be small, while differences, or lack of convergence, would indicate a larger error. The B A C - M P 4 error estimate is defined as: Error(BAC-MP4) =

{1.0 kcal-moH + AH AC-MP4 - AH AC-MP3 } B

+ (AH AC-MP4 - AH AC-MP4SDQ) B

+ 0.25 ( E

2

B

2

B

B A C

( S p i n 52) or E

B A C

(Spin

U H F

-i))

2

}

1 / 2

(8)

Note that the error estimate includes terms arising from spin contamination and U H F instability and a 1.0 k c a l - m o H inherent error estimate it also requires knowledge of B A C parameters at lower levels of theory in order to estimate the error.

Results A large body of data have appeared in the literature using the B A C procedure (2). Most of these computations have been directed to carbon-based compounds, particularly as they are related to combustion chemistry; however, a non-trivial number of other firstand second-row elements have also been computed (2). In general, the bond energy correction for H bonded to atoms of the first row of the periodic table increases with atomic number with a near exponential behavior. A similar behavior is also seen for first row elements with each other, although there is more scatter. Such trends help in the assignment of bond correction parameters when data are either unavailable or are of questionable accuracy. This latter point is particularly relevant as one proceeds to the second row where experimental data are in many cases suspect. Heats of formation accurate enough for chemical computation and modeling applications generally require a target of uncertainty within 2.5 kcal/mol to be of practical value. Comparisons between the B A C method and literature values show that one can achieve such accuracies for first-row elements. In Table II we present results from the computations for various hydrocarbons. The results show that the B A C approach seems to work well for both stable and radical species and can treat the resonance energy of the aromatic ring. The B A C approach also has been shown to be able to treat molecules with nonconventional hypervalent or dative bonding ( e.g. N2O and nitro compounds). W e have recently completed an extensive study on 110 C\ and C 2 hydrofluorocarbons ( C / H / F / O ) in which 70 literature values were compared. The results showed an average deviation of about 2.1 kcal/mol (9 kJ/mol), shown in Figure. 2 (4). Such large comparisons on a single chemical system enable one to have confidence in the methodology.



168

Table II. B A C - M P 4 heats of formation at 298 K and 1 atm standard state for various hydrocarbons along with the B A C error estimate. Energies are in kcal-mol- . 1

CxHy

2CH CH 2C H C2H2 2C H C H 2C H C2H6 C3H2


3

4

2

3

4

2

3

C H 3

298

Methyl Methane C H 2£+ Acetvlene Vinyl Ethylene Ethyl Ethane H CCC lAi H C C C H 1A' H C C C H 3B H C C C 3B! H CCCH Cycloprop-2-enyl CH CC Cycloprop-l-enyl CH3CCH CH CCH Cyclopropene CH2CHCH2 CH3CCH2 CH3CHCH, H C C H cis CH3CHCH H C C H trans Cyclopropyl CH3CHCH2 Cyclopropane CH3CHCH3 CH3CH2CH2 CH3CH2CH3 HCCCCH H2CCCCH H C C H C C H , H C C H cis H C C H C C H , H C C H trans CH CHCC CH CHCCH CH CCCH Methylene-cyclopropene 1,3-Cyclobutadiene Methyl-cyclo-propenylidene 1,2-Cyclobutadiene (Bicyclo) Tetrahedrane 2

2

2

Afti0

Molecule

5

2

2

2

2C3H3

2

3

C3H4

2

2

C H 3

5

C3H6

2C3H7 C3H C4H2 2C4H3 8

2

2

C4H4

2

2

2

34.9 -17.9 132.2 54.2 71.0 12.3 28.8 -20.8 133.4 141.4 129.4 160.7 83.0 117.0 123.8 126.0 45.8 47.7 68.0 38.7 61.0 64.7 65.0 69.3 5.3 11.8 21.4 24.8 -25.7 111.5 111.3 129.9 130.2 144.5 69.1 75.5 95.9 98.7 109.7 123.4 132.3

Error Estimate

1.2 1.0 6.4 1.0 3.5 1.0 1.3 1.0 2.5 4.7 8.4 7.8 5.8 3.6 6.3 3.0 2.6 3.4 2.7 4.2 3.5 3.5 3.5 2.1 1.2 1.5 1.5 1.3 1.0 5.6 15.9 8.6 8.3 14.1 3.3 6.1 5.6 4.8 4.4 1.3 5.4


Theor. -Exp.

0.1 0.0 4.5 0.0 2.6 -0.2 0.5 -0.7

1.2

1.4 2.0 1.8 -0.7

2.4 0.5 - 1.0 1.2 -0.8 -1.5

-3.7

9.



169

Table II. (continued) CxHy

Molecule

2C H 4

5

AjH0

298

CH CHCCH CH CCCH CH3CHCCH t r a n s - C H C H C H C H , H C C H cis t r a n s - C H C H C H C H , H C C H trans c i s - C H C H C H C H , H C C H cis c i s - C H C H C H C H , H C C H trans CH CHCHCH CH3CCCH3 CH3CH2CCH Cyclobutene CH2CCHCH3 Methylene-cyclopropane 1 -Methyl-cyclopropene 3-Methyl-cyclopropene trans-CH CHCHCH CH3CH2CHCH2 CH3-Cyclopropane Cyclobutane t-C4H9 i-C4Hio n-C4Hio H CCCCCH HCCHCCH Cyclopenta- 1 -yn-3-enyl CH CCHCCH HCCCH CCH 1,2,4-Cyclopentatriene Cyclopentadienyl Cyclopentadiene Cyclopentenyl trans,trans-CH CHCHCHCH cis,trans-CH CHCHCHCH Cyclopentene CH2CHCHCHCH3 2

2


3

2

2

2

2

2

C4H6

2

C Hg 4

2

3

2C4H9 C4H10 2C5H3

C5H4

3

2

2

2

2

C H 5

5

2C H 5

7

2

2

C H 5

8

C H C6H4 5

I 0

2C H 6

C H 6

6

6

3

5

6

2C H C H

C(CH ) Ortho-benzyne Phenyl HCCCHCHCHCH Benzene Methylene-cyclopentadiene CH3CHCCHCCH Benzyl Cyclohexane

7

1 2

4

2

2

74.1 74.3 75.9 86.1 86.5 86.6 89.1 24.7 37.6 41.2 40.6 41.5 46.8 58.1 60.9 -1.7 1.0 5.0 7.0 13.2 -32.0 -30.6 128.2 135.0 168.9 106.1 111.1 131.8 63.8 31.6 40.6 45.3 47.6 9.9 17.4 -39.3 101.6 79.4 140.6 17.0 52.2 99.7 47.9 -29.4

Error Estimate 7.3 6.6 5.8 9.1 9.1 9.6 9.6 2.3 4.3 2.2 1.1 3.6 3.0 3.5 2.5 1.5 1.1 1.4 1.6 1.5 1.3 1.3 18.5 10.4 16.1 5.9 4.3 5.6 4.8 2.2 3.9 8.3 8.4 1.1 2.4 1.7 8.1 11.0 15.3 2.5 2.3 6.0 8.3 2.0


Theor. -Exp.

5.1

- 1.4 2.9 1.7 3.2 2.8

1.3 1.2 0.2 1.3 0.4 -0.3

-0.4

1.6 1.0 0.8 -2.8

0.1


Figure 2. Comparison of B A C - M P 4 and literature values for the heats of formation of fluorocarbons.


Η se

g

Ο η s

Η S Η Ρβ

> r

δ

Η > Η

ο

η

-α ο

9.



111

Example B A C - M P 4 correction calculations In this section, we use two examples to illustrate the B A C corrections. In the first example, we consider the isodesmic reaction,


CH3NO + N H

3

= H N O + CH3NH2

(9)

Table III shows the B A C corrections for each of the molecules. The table is an extraction of the output presented on the internet at http://herzberg.ca.sandia.gov/~melius in file ~melius/bac/bac.tar.gz. The energies are given in kcal-mol-i For each molecule, i f there is a spin correction (equation. 6, since these examples are closed-shell species), it is presented as Espin. Next, for each of the bonds in the molecule, the atom numbers, the bond type, the multiplicative factor (the product of the gy's defined by equation (3)), and the bond's B A C (equation. 1) are given. If there is a "hr" followed by a number i at the end of the line, it indicates that the bond is a hindered rotor represented by vibrational frequency number i . Next are listed the heats of formation of the molecule at 0 K corresponding to the raw M P 4 electronic energies and the resulting B A C - M P 4 . The B A C - M P 4 number corresponds to the M P 4 raw energy which includes the zero-point energy plus the B A C corrections (equation 7). The next line for each molecule provides the heats of formation at OK and 298K as well as the free energies at 300K, 600K, 1000K,1500K, and 2000K. Finally, the last line gives the B A C - M P 4 heat of formation at 300K followed by the error estimate, the difference with experiment (if available) and then the differences between the B A C M P 4 and B A C - M P 4 ( S D Q ) , B A C - M P 3 , and B A C - M P 2 respectively. One can see that for each of these molecules, all the methods ( B A C - M P 4 , B A C - M P 4 ( S D Q ) , B A C - M P 3 , and B A C - M P 2 ) are giving similar results, indicating that one should have confidence in the calculated heats of formation. For the isodesmic reaction 9, we see that there is a corresponding B A C correction for each bond type. For instance, the B A C correction for the C N bond is 6.95 kcal-mol- for C H N O and 7.90 kcal-mol- for C H N H . Likewise, the N O correction is 17.32 k c a l - m o H for C H 3 N O and 19.16 k c a l - m o H for H N O . The N H and C H corrections also balance. Even the U H F instability for C H N O and H N O (2.29 kcal-mol- and 3.66 kcal-moH) tend to balance. The net B A C corrections for each side of reaction 9, 68.15 kcal-mol- and 71.73 k c a l - m o l - , are quite large but nearly balancing, the difference being 3.58 kcal-mol- . The B A C method thus supports the isodesmic reaction approach, in general. However, in C H 3 N O , the nearest neighbor correction is worth 2.49 k c a l - m o l - (due to gky multiplicative factor of 0.907). Furthermore, the spin correction is 1.37 k c a l - m o l larger on the right side. Without these additional corrections, the simple corrections based on equation (2) would have been 68.36 kcal-mol- on the left vs. 68.08 k c a l - m o l on the right. Thus, the B A C method has improved on the isodesmic approach by including corrections for neighboring bonds and for spin corrections. 1

1

3

3

2

3

1

1

1

1

1

1

1

1

M o r e importantly, since the B A C method includes the corrections, one no longer needs to restrict oneself in the type of reaction considered. One can break bonds and, indeed, calculate heats of atomization. Using the experimentally determined heats of formation of the atoms, one can therefore derive heats of formation for each molecule. A s a second example, we consider the isomers C H 3 N O , C H 2 N H O , and C H 2 N O H . The B A C corrections are also given in Table III. The resulting net B A C corrections are 39.84 k c a l - m o l for C H N O , 48.06 k c a l - m o l for C H N H O , and 1

1

3

2




Table III. B A C Corrections for Example Problems CH3NO ONCH CIS NITROSO M E T H A N E S**2 = 0.229 Espin = 2.29 2 1 R( C N ) = 1.4640 With Fmult = 0.907 Bac = 6.95 hr 3 2 R( NO ) = 1.1766 With Fmult = 0.907 Bac = 17.32 4 1 R( C H )= 1.0819 With Fmult = 1.000 Bac = 4.44 5 1 R( C H ) = 1.0839 With Fmult = 1.000 Bac = 4.42 6 1 R( C H ) = 1.0839 With Fmult = 1.000 Bac = 4.42 MP4= 61.17 Bac-MP4= 21.33 21.33 18.87 28.8 39.3 53.9 72.3 90.3 18.88 1.38 u2.29 -0.72 -0.43 1.06 NH3 2 1 R( N H ) = 1.0025 With Fmult = 1.000 Bac = 3 1 R( N H ) = 1.0025 With Fmult = 1.000 Bac = 4 1 R( N H ) = 1.0025 With Fmult = 1.000 Bac = MP4= 19.08 Bac-MP4= -9.23 -9.23 -10.99 -3.9 3.7 14.8 28.9 -10.98 1.00 0.00 0.01 -0.01 0.00

9.44 9.44 9.44 43.0

HNO S**2 = 0.366 Espin = 3.66 2 1 R( NO ) = 1.1752 With Fmult = 1.000 Bac = 19.16 3 1 R( N H )= 1.0317 With Fmult = 1.000 Bac = 8.90 MP4= 55.66 Bac-MP4= 23.94 23.94 23.20 26.3 29.6 34.4 40.5 46.7 23.20 1.32 -0.60 u 3.66 0.06 -0.44 0.19 H3CNH2 R( C N ) = 1.4533 With Fmult = 1.000 Bac = R( C H ) = 1.0910 With Fmult = 1.000 Bac = R( C H ) = 1.0839 With Fmult = 1.000 Bac = R( C H ) = 1.0839 With Fmult = 1.000 Bac = R( N H ) = 1.0014 With Fmult = 1.000 Bac = R( N H ) = 1.0014 With Fmult = 1.000 Bac = = 38.17 Bac-MP4= -1.84 -1.84 -5.55 7.7 22.1 42.8 68.6 -5.53 1.03 -0.03 -0.10 -0.22 -0.12

2 1 3 1 4 1 5 1 6 2 7 2 MP4

7.90 4.36 4.42 4.42 9.46 9.46 94.1

H2C=NOH FORMALDOXIME CNOH TRANS S**2 = 0.060 Espin = 0.60 2 1 R( C N ) = 1.2493 With Fmult = 0.886 Bac = 12.40 hr 3 3 2 R( N O ) =1.3687 With Fmult = 0.886 Bac =11.31 hr 1 4 3 R( OH ) = 0.9468 With Fmult = 1.000 Bac =10.91 5 1 R( C H ) = 1.0775 With Fmult = 1.000 Bac = 4.48 6 1 R( C H ) = 1.0735 With Fmult = 1.000 Bac = 4.51 M P 4 = 51.92 Bac-MP4= 7.72 7.72 5.11 15.5 26.4 41.7 60.9 79.9 5.13 2.50 u0.60 -1.63 -1.61 2.26 H2CNHO * * 2 = o.425 Espin = 4.25 2 1 R( C N ) = 1.2692 With Fmult = 0.863 Bac = 11.42 hr 2 3 2 R( NO ) = 1.2542 With Fmult = 0.863 Bac = 14.01 4 1 R( C H ) = 1.0704 With Fmult = 1.000 Bac = 4.54 5 1 R( C H ) = 1.0703 With Fmult = 1.000 Bac = 4.54 6 2 R( N H ) = 1.0099 With Fmult = 1.000 Bac = 9.30 M P 4 = 64.96 Bac-MP4= 16.90 16.90 14.09 24.8 36.3 52.4 72.6 92.7 14.11 1.92 u4.25 -0.43 1.33 1.94 s


9.



173

44.20 k c a l - m o l for C H 2 N O H . The primary difference in these corrections results from the much smaller B A C correction for the C H bond compared to the N H and O H bonds and due to the large spin correction for C H 2 N H O . Note that the N O bond in C H 2 N H O is best described as a dative bond (i.e., the nitrogen is not trivalent). Thus, the types of bonds have changed quite significantly between C H 3 N O , C H 2 N H O , and C H N O H . B u t this does not matter i n the B A C - M P 4 method, since the B A C corrections only depend on the bond distance for a given pair of atomic elements. The B A C method does not require that one identify the bond type (e.g., a single, double, triple, dative, resonance, or some mixture). F o r instance, the C C bond distance in N C C N (1.398 A) is similar in length to that in benzene (1.386 A), indicative o f significant delocalization (diradical resonance character). 1


2

It should be noted that for any given reaction, it is not necessary to know the experimental heats of formation of the atoms or of the element's standard state in order to determine the heat of reaction. This w i l l become important as the B A C method is extended to heavier elements of the periodic table, for which the experimental heats of formation of the atoms are not well known. Indeed, the heats of reaction determined computationally w i l l not be affected by changes in the heat of formation of the reference state, as has occurred for phosphorous. The important thing to remember is that the heats of formation on both sides of the reaction must be treated consistently. When one mixes theoretical and experimental heats of formation, potential inconsistencies can arise. Conclusions The bond additivity correction ( B A C ) procedure is a powerful method for extending the practical application o f ab-initio methods for the prediction o f thermochemical properties of molecular species. Comparison of the B A C - M P 4 computations with experiment indicate the method works for both stable and radical species, and provides heats o f formation with accuracies comparable to experiment. A n error estimate provides an indicator of the reliability of a given computation and can be used as a screening procedure when a large body of data are being computed. The ultimate utility of the method lies in the promise of a computational economical method for computing large bodies of thermochemical information on systems where experimental data are unavailable. Such data are finding increased use as the feedstock to ever more sophisticated Computational Reacting Fluid Dynamics programs and are the ultimate motivation for much of the work.

Appendix BAC-MP4

Run Procedure (Unix) For Gaussian94

set name=sch2 cat>"$name"_opt«EOF %chk=sch2.chk #p H F / 6 - 3 1 G * F O P T = Z - M A T R I X GEOM=(DIHEDRAL) CH2(1A1) hf/6-31g* optimization calculation 0,1 C H 1 R21 H 1 R21 2 A 3 1 2



174

R21 A312

1.0970591 103.02145745

EOF g92 / $name"_opt.out cp "$name".chk /"$name".chk cat>"$name"_frq«EOF %chk=sch2.chk M


#p H F / 6 - 3 1 G * F R E Q G E O M = C H E C K G U E S S = R E A D C H 2 ( 1 A 1 ) HF/6-31g* frequencies 0,1 EOF g92 /"$name"_frq.out cat>"$name"_mp4«EOF %chk=sch2.chk #p MP4(SDTQ)/6-31g** G E O M = C H E C K G U E S S = R E A D C H 2 ( 1 A 1 ) M P 4 / 6 - 3 1 G * * // HF/6-31g* structure 0,1 EOF g92 /"$name"_mp4.out cat>"$name _mp2«EOF %chk=sch2.chk #p R H F / 6 - 3 1 G * * S T A B L E = ( O P T , R U H F ) geom=check guess=read SCFCON=5 M

C H 2 ( 1 A 1 ) ump2/6-31G** // rhf/6-31g* structure 0,1 -linkl%chk=sch2.chk #P UMP2/6-31g** geom=check guess=read CH2(1A1) ump2/6-31G** //rhf/6-31g* structure 0,1 EOF g92 /"$name"_mp2.out cp $name .chk /"$name"_mp2.chk M

M

Literature Cited 1. Benson, S. Thermochemical Kinetics John Wiley and Sons; New York 1976. 2. (a) Ho, P.; Coltrin, M . E . ; Binkley, J.S.; Melius, C.F. J. Phys. Chem. 1985, 89, 4647.



9.



(b) Ho, P.; Coltrin, M.E.; Binkley, J.S.; Melius, C.F. J. Phys. Chem. 1986, 90, 3399. (c) Melius, C.F.; Binkley, J.S.Symp. (Inter.) Combust. 1986, 21, 1953. (d) Ho, P., and Melius, C.F. J. Phys. Chem. 1990, 94, 5120. (e) Melius, C.F.; Ho, P. J. Phys. Chem. 1991, 95, 1410. (f) Ho, P.; Melius, C.F. J. Phys. Chem. 1995, 99, 2166. (g) Melius, C.F.; Binkley, J.S.Symp. (Inter.) Combust. 1986, 21, 1953. (h) Allendorf, M.D.; Melius, C.F. J. Phys. Chem. 1992, 96, 428. (i) Allendorf, M.D.; Melius, C.F. J. Phys. Chem. 1993, 97, 720. (j) Zachariah, M.R.; Tsang, W.J. Phys. Chem.. 1995, 99, 5308. (k) Zachariah, M.R.; Westmoreland, P.R., Burgess Jr., D.R, Tsang, W. Melius, C.F. J. Phys. Chem . 1996, 100, 8737. (l) Zachariah, M.R.; Melius, C.F. J. Phys. Chem. 1997, 101, 913. (m) Allendorf, M.D.; Melius, C.F., Ho, P., and Zachariah, M.R., J. Phys. Chem. 1995, 99, 15285. 3.Schlegel, H.B. J. Chem. Phys. 1986, 84, 4530. 4. Zachariah, M.R.; Westmoreland, P.R.; Burgess Jr., D.R.; Tsang, W.; Melius, C.F. J. Phys. Chem . 1996, 100, 8737.


Computational Thermochemistry - American Chemical Society

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