dorofeeva 2017 isodesmic method

Computational and Theoretical Chemistry 1106 (2017) 28–35
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Computational and Theoretical Chemistry
journal homepage: www.elsevier.com/locate/comptc
Performance of DFT, MP2, and composite ab initio methods for the
prediction of enthalpies of formations of CHON compounds using
isodesmic reactions
Olga V. Dorofeeva a,⇑, Evgeniya L. Osina b
a
b
Faculty of Chemistry, Lomonosov Moscow State University, 1-3 Leninskie Gory, Moscow 119991, Russia
Joint Institute for High Temperatures, Russian Academy of Sciences, 13-2 Izhorskaya Street, Moscow 125412, Russia
a r t i c l e
i n f o
Article history:
Received 2 October 2016
Received in revised form 6 January 2017
Accepted 3 March 2017
Available online 6 March 2017
Keywords:
Enthalpy of formation
Quantum chemistry
Composite methods
Isodesmic reactions
Hydrazine
a b s t r a c t
This paper assesses the performance of quantum chemical models with regard to the calculation of
enthalpy of formation of CHON molecules using isodesmic reactions. The high accuracy of prediction
of enthalpy of formation of CHON compounds can be achieved by the combination of isodesmic reaction
scheme with composite ab initio methods. The best composite methods, such as G4, G4MP2, CBS-QB3,
and CBS-APNO, can attain near chemical accuracy or better depending on reaction type. Other composite
methods yield the same accuracy only in conjunction with isodesmic or homodesmotic reactions. The
DFT and MP2 methods lead to good results if they are used with homodesmotic reactions. For CHO compounds, all composite methods demonstrate the high accuracy not only with isodesmic and homodesmotic reactions, but also with isogyric reactions. Moreover, the DFT and MP2 methods can also yield
a high accuracy estimate of the enthalpy of formation when they are used with isodesmic or homodesmotic reactions. Four composite methods (G4, G3, CBS-APNO, and CBS-QB3) employed in conjunction
with 45 isogyric reactions yield the enthalpy of formation of hydrazine (97.7 ± 2.0 kJ/mol) in agreement
with the best approximating to CCSD(T)/CBS energy, thus calling into question the usually quoted experimental value of 95.5 kJ/mol.
Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction
The standard approach of calculating the enthalpy of formation
uses the atomization reactions [1] and requires exceptionally high
levels of theory such as complete basis set extrapolations of CCSD
(T) method [2,3]. However, to date such calculations are extremely
computation demanding and hence, are only applicable to the
small molecules. A technique for evaluating the accurate enthalpies of formation (Df H298 ) for larger systems is to derive them by
using isogyric, isodesmic or other balanced reactions rather than
atomization reactions [4,5]. In an isodesmic scheme, owing to better error cancellations, thermochemical predictions of chemical
accuracy (4 kJ/mol) can be obtained using lower level of theory
[4–6]. The various types of balanced reactions are used in the computational thermochemistry. The isodesmic concept was extended
by introducing the concept of homodesmotic reactions [7].
Recently a new hierarchy of homodesmotic reactions [8,9] and a
generalized ‘‘connectivity-based hierarchy” [10] were proposed.
⇑ Corresponding author.
E-mail address: [email protected] (O.V. Dorofeeva).
http://dx.doi.org/10.1016/j.comptc.2017.03.006
2210-271X/Ó 2017 Elsevier B.V. All rights reserved.
The methodology of ring conserved isodesmic reactions [11] was
used to calculate the enthalpies of formation of aromatic
hydrocarbons.
A fairly large number of papers dealing with the use of different
reaction type with the various method/basis set combinations has
been published, but most of these studies have focused on hydrocarbons [12–18]. However, it should be noted that the enthalpies
of formation of hydrocarbons can be calculated with high accuracy
from atomization energies using the composite methods such as
G4, CBS-APNO, and ccCA [17,19]. There are much less works dealing with the use of isodesmic reactions for oxygen and nitrogen
compounds, whereas it was shown that the Df H298 values calculated for these compounds by composite methods from the
atomization energies can have fairly large systematic errors [20–
22]. Especially large errors were identified for nitro compounds
[23,24], which, however, could not always be found due to the
uncertainties in the experimental data used for comparison [25].
Thus the results of using isodesmic reactions for nitrogen containing compounds are of interest for comparison with the experimental data.
O.V. Dorofeeva, E.L. Osina / Computational and Theoretical Chemistry 1106 (2017) 28–35
Although density functional methods combined with isodesmic reaction energies can yield accurate thermochemistry for
large molecules [6], Raghavachari et al. [26] have demonstrated
that the combination of bond separation reactions with composite G2 method leads to a dramatic improvement in the accuracy
of theoretically evaluated enthalpies of formation. The isodesmic
reactions in conjunction with composite ab initio methods such
as those of the Gaussian-n (Gn) and complete basis set (CBS)
varieties have been used extensively by Bozzelli et al. [27–33]
to compute accurate enthalpies of formation of aldehydes,
ketones, hydroperoxides, nitro and nitrite compounds, nitrocarbonyls, nitroolefins, and others. It has been shown that the use
of isodesmic work reactions with composite ab initio methods
(CBS-QB3, CBS-APNO, G3, G3MP2B3, G4) can lead to error reductions from around ±4 kJ/mol to ±2 kJ/mol or less. The DFT methods (B3LYP/6-31G(d,p), B3LYP/6-311G(2d,2p), and M06-2X/6-311
+G(2d,d,p)) were also used by Bozzelli et al. in calculating
enthalpies of formation [30–33]. In some cases, the authors point
out that the results from DFT and ab initio calculations were in
excellent agreement [32], whereas more often these methods
demonstrate relatively high standard deviations, which were
two or more times higher than the composite method
calculations.
A variety of isodesmic or homodesmotic reactions, where the
bonding environments are similar in products and reagents, has
been used in the above mentioned works [27–33]. However,
such reactions are not always possible to design for larger molecules with complex structure. Moreover, it becomes often impossible to carry out high level composite ab initio calculations for
such molecules. For example, to estimate the enthalpy of formation of polycyclic nitramine CL-20, two not well balanced
reactions
ðCHÞ6 ðNNO2 Þ6 ðCL-20Þ þ 12 CH4 þ 6 NH3
! 3 CH3 CH3 þ 6 CH3 NHCH3 þ 6 H2 NNO2
ðCHÞ6 ðNNO2 Þ6 ðCL-20Þ þ 24 CH3 NH2
! 3 CH3 CH3 þ 6 CH3 NðNO2 ÞCH3 þ 12 NH2 CH2 NH2
were used in conjunction with the B3LYP/6-31G(d,p) model [34–
37]. In our later study [38], it was shown that this approach overestimates the enthalpy of formation of CL-20 by 160–200 kJ/mol.
Therefore, it is important to know the errors associated with the
type of reactions and quantum chemical methods used in calculation of enthalpies of formation of molecules of different size and
composition.
In the present work, we show that the isodesmic and other error
canceling reactions can offer significant benefit and increased
accuracy when composite ab initio methods are used to calculate
the reaction enthalpies. Our conclusion is based on a large number
of calculations for different CHON compounds by composite G4
method applied to both atomization and isodesmic reactions
[21–24,38–42]. In these works, it was shown that the G4 method
combined with atomization reaction is highly accurate for the prediction of enthalpies of formation CHO compounds [21,42], while
its accuracy is decreased for nitrogen containing compounds, especially for nitro compounds [23,24]. In the present work, it will be
shown that the atomic composition of the target molecule is also
important when the isodesmic reactions are used. To clearly show
this, we chose two molecules, CH3ONO2 and CH3OCH3, with reliable experimental Df H298 values and used them to examine the
performance of DFT, MP2, and composite ab initio models in the
calculation of enthalpies of formation using isodesmic and other
balanced reactions.
29
2. Computational details
Three DFT functionals (B3LYP, B3PW91, and M06-2X), MP2
method, and seven composite ab initio models (G4, G4MP2, G3,
G3MP2B3, G2, CBS-QB3, and CBS-APNO) were assessed for the
evaluation of enthalpies of formation of CH3ONO2 and CH3OCH3.
Two relatively large basis sets, 6-311+G(3df,2p) and cc-pVTZ, were
considered initially to derive the total energies for the different
DFT techniques and MP2 method. In terms of mean absolute deviation (MAD) from experiment, the DFT models with 6-311+G
(3df,2p) provide more accurate results than the use of cc-pVTZ
basis set. Conversely, the MP2 method gives significantly better
results with cc-pVTZ basis set. For this reason, only the results
obtained at DFT/6-311+G(3df,2p) and MP2/cc-pVTZ levels are
given finally in Tables 1 and 2 and discussed further in next section. All quantum chemical calculations were performed using
the Gaussian 03 package of programs [43].
Thirteen reactions of different type (isogyric, isodesmic, and
homodesmotic) were constructed for each molecule (Tables 1
and 2). These reactions contain radicals, inorganic, and organic reference species. The accurate values of enthalpies of formation recommended in Active Thermochemical Tables (ATcT) [44] were
accepted for most reference species, with the exception of ethers
(C2H5OC2H5, CH3OC3H7, (CH3)2CHOCH3, and C6H5OCH3), nitrates
(CH3CH2ONO2, C3H7ONO2, and (CH3)2CHONO2), and nitro compounds (CH3NO2, C2H5NO2, CH3NHNO2, and CH3N(NO2)CH3). For
anisole, the accurate enthalpy of formation determined recently
by Simões et al. [45] was used in this work. The Df H298 values for
aliphatic ethers and nitrates were taken from the thermochemical
archive by Pedley [46]; these values give consistent results for
reactions 11–13 (Tables 1 and 2), thus confirming their accuracy.
The enthalpies of formation of four nitro compounds are those recommended in Ref. [23].
The resulting enthalpy of formation was calculated combining
the calculated enthalpy of reaction with the experimental enthalpies of formation of reference molecules. The scale factors for
DFT and MP2 frequencies needed to calculate the zero-point energies and thermal corrections were taken from Ref. [47]. For comparison, the Df H298 values calculated using atomization reaction
were also included in Tables 1 and 2.
3. Results and discussion
The enthalpies of formation of CH3ONO2 and CH3OCH3 calculated from thirteen work reactions using different quantum chemical models are given in Tables 1 and 2. These tables also include
the error statistics for each method: the mean absolute deviation
(MAD), the root-mean-square deviation (RMSD), maximum negative and maximum positive deviation from the corresponding
experimental value. The value of Df H298 (CH3ONO2, g) =
122.2 ± 1.3 kJ/mol was determined by Ray and Ogg [48] from
calorimetric investigation of the gas phase enthalpy of the reaction
between N2O5 and CH3ONO to form an equilibrium mixture of NO2
and N2O4 plus CH3ONO2. This value is cited in the NIST Chemistry
WebBook [49] and recommended by Pedley [46]. However, this
value becomes somewhat more positive when the more recent
enthalpies of formation of reaction components are used. The value
of 119.4 kJ/mol was obtained in the present work using the
enthalpies of formation of nitrogen oxides represented in ATcT
[44] and experimental enthalpy of formation of CH3ONO recommended on the basis of quantum chemical calculations [29].
Another value of Df H298 (CH3ONO2, g) = 123.0 ± 3.3 kJ/mol was
found by combining the available value of the enthalpy of formation of liquid CH3ONO2 with the enthalpy of vaporization [48].
Thus, the values of 119.4 kJ/mol and 123.0 kJ/mol can be
30
O.V. Dorofeeva, E.L. Osina / Computational and Theoretical Chemistry 1106 (2017) 28–35
Table 1
Gas-phase enthalpy of formation of methyl nitrate calculated from different reactions using different quantum chemical methods (in kJ/mol).
a
c
d
B3PW91a
Atomization reaction
CH3ONO2 ? C(cr) + 1.5 H2(g) + 0.5 N2(g) + 1.5 O2(g)
118.6 126.8 138.1
119.8
131.0
124.2 132.2
141.8 137.3 140.0 161.5
Isogyric reactions
1
CH3ONO2 + CH4 ? CH3OH + CH3NO2
2
CH3ONO2 + CH3CH3 ? CH3OH + CH3CH2NO2
3
CH3ONO2 + NH2OH ? H2O2 + CH3NHNO2
4
CH3ONO2 + CH3NH2 ? CH3N(NO2)CH3 + H2O
5
CH3ONO2 + H2O ? CH3OOH + HNO2(trans)
6
CH3ONO2 + CH3 ? CH3OCH3 + NO2
7
CH3ONO2 + CH3 ? CH3CH3 + NO3
118.0
119.0
122.4
121.9
121.6
118.7
125.1
122.2
122.7
122.8
121.5
126.5
121.3
121.5
119.5
120.2
125.3
122.5
122.7
123.4
132.3
123.9
124.7
122.6
122.9
128.5
117.9
131.0
122.1
122.9
124.3
121.6
128.8
126.6
142.2
128.4
133.2
124.7
137.7
125.4
123.8
115.8
Isodesmic
8
9
10
121.7 121.3 122.8
121.5 121.2 122.2
120.2 120.0 121.7
123.5
123.0
120.2
122.7
122.6
120.1
123.8 118.5
123.2 120.5
122.9 127.1
115.7 122.4 120.1 114.8
118.3 121.3 121.0 118.2
119.7 123.0 111.8 121.1
Homodesmotic reactions
11
CH3ONO2 + CH3CH2CH3 ? CH3CH2ONO2 + CH3CH3 120.4 119.9 119.1
12
CH3ONO2 + C3H7CH3 ? C3H7ONO2 + CH3CH3
120.2 119.7 118.5
13
CH3ONO2 + (CH3)3CH ? (CH3)2CHONO2 + CH3CH3 119.9 118.6 117.0
119.6
119.0
118.0
119.7
119.2
117.2
118.8 119.2
117.9 119.5
115.7 119.0
119.6 119.3 120.5 119.9
119.1 118.7 119.9 119.4
118.0 116.6 119.2 118.8
122.2
2.7
3.7
11.1
3.2
122.5
3.2
4.1
9.8
4.0
123.9
4.4
6.8
21.0
5.5
123.0
5.3
8.6
16.5
5.5
reactions
CH3ONO2 + H2O ? CH3OH + HONO2
CH3ONO2 + H2O2 ? CH3OOH + HONO2
2 CH3ONO2 ? CH3OCH3 + O2NONO2
Average of all reactions
MADc
RMSd
Maximum negative deviation
Maximum positive deviation
b
MP2b
G4MP2 G4
120.8
1.5
1.8
3.9
3.2
120.1
120.8
122.5
123.0
125.2
123.0
125.7
121.6
1.7
2.1
4.5
2.6
CBS-QB3 G3MP2B3 CBS-APNO G3
M06-2Xa B3LYPa G2
Reaction
121.5
1.7
2.3
5.3
4.2
121.0
122.7
123.4
121.7
127.6
125.4
158.5
124.9
5.2
6.8
37.3
2.7
120.4
141.1
125.7
123.6
126.4
124.2
144.5
125.2
5.5
8.9
23.3
4.6
127.2
127.0
123.7
120.2
147.5
135.0
110.2
123.3
6.2
9.5
26.3
11.0
128.3
135.3
124.1
134.3
139.8
128.7
112.5
124.3
6.7
10.8
18.6
8.7
6-311+G(3df,2p) basis set.
cc-pVTZ basis set.
Mean absolute deviation.
Root-mean-square deviation.
Table 2
Gas-phase enthalpy of formation of dimethyl ether calculated from different reactions using different quantum chemical methods (in kJ/mol).
Atomization reaction
CH3OCH3 ? 2 C(cr) + 3 H2(g) + 0.5 O2(g)
184.8 183.3
182.4 189.4
185.5 191.7
192.2 142.1 196.0
189.8
184.5
Isogyric reactions
1
CH3OCH3 + CH4 ? CH3OH + CH3CH3
2
CH3OCH3 ? CH3CH2OH
3
CH3OCH3 + C6H6 ? C6H5CH3 + CH3OH
4
CH3OCH3 + H2O ? CH3OOH + CH4
5
CH3OCH3 + H2O2 ? HOCH2CH2OH + H2O
6
CH3OCH3 + OH ? CH3OH + CH3 O
7
CH3OCH3 + OH ? CH3OOH + CH3
185.2
186.4
184.1
183.7
184.4
181.7
185.1
183.7
185.3
183.3
185.9
182.6
181.8
187.3
185.2
185.5
184.6
184.8
181.7
186.2
185.7
187.4
188.3
186.0
184.7
183.3
184.2
186.9
189.3
192.1
192.8
190.1
185.1
179.1
192.9
184.7
188.6
190.0
177.7
195.2
165.7
180.9
188.6
192.2
195.2
173.8
202.0
166.2
179.6
Isodesmic
8
9
10
182.5 183.8
182.3 183.3
185.1 183.6
183.1 184.0
182.9 183.3
186.0 184.4
183.2 188.4
182.7 183.5
181.4 181.8
181.6 184.1 180.8
180.5 185.1 182.8
183.5 181.9 180.7
177.3
180.7
181.0
177.4
180.1
182.8
Homodesmotic reactions
11
CH3OCH3 + C2H5C2H5 ? C2H5OC2H5 + CH3CH3
184.0 183.6
12
CH3OCH3 + C2H5C2H5 ? CH3OC3H7 + CH3CH3
182.8 182.4
13
CH3OCH3 + (CH3)3CH ? (CH3)2CHOCH3 + CH3CH3 183.2 182.8
184.8 183.0
183.3 181.9
184.0 182.2
182.5 183.1
181.7 182.4
181.2 182.1
184.4 183.4 185.4
182.8 181.4 181.7
182.7 183.0 184.2
183.5
183.4
183.6
182.7
183.0
183.0
184.1
1.3
1.5
3.3
2.2
183.6
1.7
1.8
2.2
2.8
184.3
1.8
2.2
4.3
3.5
182.5
5.0
7.0
11.2
18.3
183.6
6.9
8.9
18.0
17.8
Average of all reactions
MADc
RMSDd
Maximum negative deviation
Maximum positive deviation
a
b
c
d
183.9
1.1
1.3
2.4
2.3
183.9
184.9
184.5
186.4
180.8
185.1
187.3
184.0
1.2
1.6
3.3
3.2
187.1
188.2
187.2
183.4
186.6
182.7
184.3
184.5
1.6
2.1
4.2
2.1
CBS-APNO G2
M06-2Xb B3PW91b B3LYPb
G4
reactions
CH3OCH3 + H2O ? 2 CH3OH
CH3OCH3 + H2O2 ? CH3OOH + CH3OH
CH3OCH3 + C6H5CH3 ? C6H5OCH3 + CH3CH3
G3MP2B3 G4MP2 CBS-QB3 G3
MP2a
Reaction
185.0
186.1
185.2
184.4
179.9
183.7
186.3
184.0
1.8
2.2
4.4
4.1
183.3
183.3
181.6
189.2
176.7
193.6
181.4
183.7
2.8
3.9
9.6
7.3
185.9
4.2
5.1
8.9
4.9
cc-pVTZ basis set.
6-311+G(3df,2p) basis set.
Mean absolute deviation.
Root-mean-square deviation.
considered as the upper and lower limits for the enthalpy of formation of CH3ONO2. The average of these two values 121.2 ± 2.0 kJ/mol is accepted in this work for the enthalpy of formation of
CH3ONO2. For CH3OCH3, the gas-phase enthalpy formation
(184.0 ± 0.4 kJ/mol) recommended in ATcT [44] is used in this
work. The average values determined by each method are com-
pared with experimental ones in Figs. 1 and 2. These figures also
show the scatter of the calculated Df H298 values about their
average.
A comparison of Tables 1 and 2 and Figs. 1 and 2 (for clarity, the
figures are shown at the same scale) reveals that, in general, the
accuracy of calculated values for CH3ONO2, is substantially lower
31
O.V. Dorofeeva, E.L. Osina / Computational and Theoretical Chemistry 1106 (2017) 28–35
-110
-115
CBS-QB3
G4MP2
G2
CBS-APNO
M06-2X
-120
-125
G4
-130
G3MP2B3
-135
-140
B3LYP
B3PW91
G3
-145
-150
MP2
-155
CH3ONO2
-160
Fig. 1. Comparison of the performance of different methods used in isodesmic reaction calculations of enthalpy of formation of CH3ONO2. The dashed lines represent the
upper and lower limits for the available experimental values. The red and black circles are the average values obtained by each method. The vertical lines with caps show the
range between the maximum and minimum values obtained for reactions 1–13 (Table 1). The methods are arranged in ascending order of the MAD; the methods with MAD
and RMSD values less than 3 kJ/mol are marked in red color. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this
article.)
°
,
-155
-160
B3LYP
-165
-170
MP2
-175
-180
G2
G3
G4MP2
G4
M06-2X
-185
-190
G3MP2B3
CBS-QB3
CBS-APNO
-195
B3PW91
-200
CH3OCH3
-205
Fig. 2. Comparison of the performance of different methods used in isodesmic reaction calculations of enthalpy of formation of CH3OCH3. The dashed lines represent the
uncertainty of experimental value. The red and black circles are the average values obtained by each method. The vertical lines with caps show the range between the
maximum and minimum values obtained for reactions 1–13 (Table 2). The methods are arranged in ascending order of the MAD; the methods with MAD and RMSD values
less than 3 kJ/mol are marked in red color. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
than that for CH3OCH3. For CH3ONO2, only three composite methods, G4MP2, G4, and CBS-QB3, are found to have MAD and RMSD
less than 3 kJ/mol, while all seven composite methods lead to
almost the same result for CH3OCH3: the MAD and RMSD do not
exceed 1.8 and 2.2 kJ/mol, respectively (Table 2). Concerning the
MP2 and DFT methods, they all have large error for both molecules.
At the same time, we can see that the average values calculated by
each method reproduce relatively well the experimental enthalpy
of formation: the deviations do not exceed 4 kJ/mol for CH3ONO2
and 1.5 kJ/mol for CH3OCH3. Thus, even the methods with a large
spread of values around the average (these methods are marked
in black in Figs. 1 and 2) can give reasonable estimations if a
32
O.V. Dorofeeva, E.L. Osina / Computational and Theoretical Chemistry 1106 (2017) 28–35
40
35
CH3ONO2
30
25
20
isogyric
isodesmic
homodesmoc
15
10
5
0
Fig. 3. The differences between the maximum and minimum enthalpies of formation of CH3ONO2 calculated using different types of work reactions (isogyric, isodesmic, and
homodesmotic) and different quantum chemical methods.
40
CH3OCH3
35
30
25
20
isogyric
isodesmic
homodesmoc
15
10
5
0
Fig. 4. The differences between the maximum and minimum enthalpies of formation of CH3OCH3 calculated using different types of work reactions (isogyric, isodesmic, and
homodesmotic) and different quantum chemical methods.
sufficient large number of reactions is used. However, in practice
much less reactions are actually used; for complex molecules, the
prediction of enthalpy of formation is often based on a single reaction. Therefore, it is important to know how the accuracy of calculation varies when different work reactions are used. To have a
better understanding of this issue, we analyzed the spread of the
calculated Df H298 values depending on the type of work reactions
and method used (Figs. 3 and 4). The isogyric reactions, as
expected, have the largest differences between the maximum
and minimum values for all methods. However, it should be noted
that these differences are not so important for methods with low
values of MAD and RMSD (methods marked by red in Figs. 1 and
2). In other words, even isogyric reactions give reasonable agreement with the experimental values, when the composite G4MP2,
G4, and CBS-QB3 methods are used for CH3ONO2 and when any
of the composite methods are used for CH3OCH3.
Compared to isogyric reactions, isodesmic and homodesmotic
reactions result in a much smaller spread of the calculated values.
The isodesmic and homodesmotic reactions show almost the same
good results for CH3ONO2, when they are used in combination with
any of the composite models (Fig. 3). As concerns DFT and MP2
methods, they give much more reliable results with homodesmotic
reactions, while the isodesmic reactions result in less accurate predictions. On the other hand, as follows from Fig. 4, in general, the
O.V. Dorofeeva, E.L. Osina / Computational and Theoretical Chemistry 1106 (2017) 28–35
33
115
B3LYP
M06-2X
MP2
110
G2
G4MP2
105
G3
CBS-QB3
G4
100
95
W3X-L
exp
90
CBS-APNO
G3MP2B3
85
80
B3PW91
H2NNH2
75
Fig. 5. Comparison of the performance of different methods used in isogyric reaction calculations of enthalpy of formation of H2NNH2. The dashed lines correspond to the
experimental value of 95.55 kJ/mol [44] (blue line) and to the W3X-L value of 97.5 kJ/mol [3] (green line). The red and black circles are the average values obtained by each
method. The vertical lines with caps show the range between the maximum and minimum values obtained for 45 reactions (Table S1). The methods are arranged in ascending
order of the MAD; the methods with MAD and RMSD values less than 2 kJ/mol are marked in red color. (For interpretation of the references to colour in this figure legend, the
reader is referred to the web version of this article.)
close Df H298 values are estimated for CH3OCH3 using all methods
(composite, DFT, or MP2) in conjunction with isodesmic or homodesmotic reactions. Moreover, some composite methods (G4,
G4MP2, G3, and G3MP2B3) reproduce well the experimental
enthalpy of formation even when the atomization reaction is used
(Table 2). Therefore, we can conclude that the accuracy of calculated values depends on the atomic composition of the molecule
and it is lower for CHON compounds than for CHO.
A large difference between the results for CHON and CHO compounds is observed not for all nitrogen containing compounds. A
smaller effect is observed, for example, for amines. However, this
effect increases with the increasing number of amino groups, while
it decreases with the presence, for example, of AC@O group
[22,41]. The purpose of this work is to draw attention to the need
for more careful selection of work reactions and the method of calculation for nitrogen containing compounds.
The Df H298 values of some nitroalkanes and alkyl nitrites were
calculated by Snitsiriwat et al. [30] at B3LYP/6-31G(d,p),
B3LYP/6-31 + G(2d,2p), and the composite CBS-QB3 levels using
three work reactions for each species. Although the authors note
that the values computed by CBS-QB3 method are close to the
experimental data, the B3LYP calculations also reproduce the
experimental values reasonably well. This result is due to homodesmotic and isodesmic reactions used in Ref. [30], and it is in excellent agreement with the results obtained in the present work for
CBS-QB3 and B3LYP models (Fig. 3). Unfortunately, the isodesmic
and especially homodesmotic reactions cannot always be used
because of a lack of reference species with accurately known
enthalpies of formation. Besides, it is often impossible to construct
the isodesmic reactions for some species. One such molecule,
hydrazine, we would like to discuss in more detail.
The value of Df H298 (H2NNH2, g) = 95.55 kJ/mol is recommended
in ATcT [44] based on the available experimental data; the close
value (95.35 kJ/mol) is presented at NIST Chemistry Webbook
[49]. However, this value disagrees with the values calculated by
composite methods (100.8 ± 2.0 kJ/mol, average of CBS-QB3, CBS-
APNO, G3, and G4 methods [20]; 98.3–101.7 kJ/mol, ccCA-P with
different basis sets [50]) and by accurate approximation to the
CCSD(T)/CBS energy (96.7 kJ/mol [51] and 97.5 kJ/mol, W3X-L
[3]). We have tried to estimate the enthalpy of formation of hydrazine using the combination of isogyric reactions with the different
methods, as it was done earlier for CH3ONO2 and CH3OCH3 (the
isodesmic reactions with hydrazine derivatives were not considered because of uncertainty in their experimental values). Among
the 45 reactions used there are 15 reactions with radicals, 15 reactions with small reference species and reliable experimental
enthalpies of formation from ATcT, and 15 reactions with larger
species not represented in ATcT (Table S1 of Supplementary material). The average values determined by each method are compared
with the experimental value and the most accurate calculated
W3X-L value in Fig. 5; this figure also shows the scatter of the calculated Df H298 values about their averages. It can be seen that the
results for H2NNH2 are similar to the picture observed for CH3
ONO2 (Fig. 1). Four composite methods, G3, G4, CBS-APNO, and
CBS-QBS, result in the lowest scatter of calculated values and in
very close average Df H298 values. Note that the average values for
three groups of isogyric reactions (Table S1 of Supplementary
material) are also in close agreement. The average value of four
composite methods, 97.7 kJ/mol, is in excellent agreement with
the W3X-L value of 97.5 kJ/mol [3]. Thus, the issue of difference
between the experimental and calculated values of enthalpy of formation of hydrazine remains open for further studies.
4. Conclusions
The method of isodesmic reactions utilizes a similarity in the
bonding environments for reactants and products in a work reaction and leads to a cancellation of systematic errors in the ab initio
or DFT calculations. The enthalpies of formation of CHO compounds can be estimated with chemical accuracy (errors < 4 kJ/
mol) using the isodesmic or homodesmotic reactions in
34
O.V. Dorofeeva, E.L. Osina / Computational and Theoretical Chemistry 1106 (2017) 28–35
conjunction with DFT, MP2, and composite ab initio methods. The
composite methods can often provide the chemical accuracy even
with isogyric reactions. A near subchemical accuracy (1 kJ/mol and
better) for CHO compounds can be achieved using the best composite methods (G4, G4MP2, CBS-QB3, and CBS-APNO) with
homodesmotic reactions. An additional example in support of this
statement is the calculation of enthalpy of formation of phenol by
G4 method using 36 work reactions of different types [42]. The following values of MAD, RMSD, and difference between the maximum and minimum values were obtained for 36 reactions,
respectively: 1.0, 1.2, and 3.9 kJ/mol.
For CHON compounds and especially for nitro compounds, DFT
(B3LYP, B3PW91, and M06-2X) and MP2 methods lead to a large
error when they are used in combination with isogyric or isodesmic reactions. Thus, it is desirable to avoid the use of DFT and
MP2 methods in isodesmic reaction calculations if it is impossible
to construct the homodesmotic reactions. The composite methods
demonstrate the higher accuracy comparing with the DFT and
MP2. The best composite methods, such as G4, CBS-QB3, and
CBS-APNO, yield chemical accuracy or better depending on reaction type. Because of this, the isodesmic reactions will continue
to be a useful tool for calculating the gas-phase enthalpies of formation, although the application of accurate correlated computational methods becomes feasible now for modestly sized
molecules.
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
Acknowledgments
[24]
This research was supported by the Russian Foundation for
Basic Research under Grant No. 14-03-00612.
[25]
Appendix A. Supplementary material
Supplementary data associated with this article can be found, in
the online version, at http://dx.doi.org/10.1016/j.comptc.2017.03.
006. These data include the enthalpy of formation of hydrazine calculated from different work reactions using different quantum
chemical methods.
[26]
[27]
[28]
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