ХИМИЯ ГЕТЕРОЦИКЛИЧЕСКИХ СОЕДИНЕНИЙ. — 2014. — № 3. — С. 341—348
L. K. Sviatenko1,2, L. Gorb3, F. C. Hill4, D. Leszczynska5, J. Leszczynski1*
THEORETICAL STUDY OF ONE-ELECTRON REDUCTION
AND OXIDATION POTENTIALS OF N-HETEROCYCLIC COMPOUNDS
Computational protocols that successfully predict standard reduction potentials of
N-heterocyclic compounds in dimethyl formamide and their standard oxidation potentials
in acetonitrile were developed. Different solvation models were verified in conjunction
with the MPWB1K/6-31+G(d) level of Density Functional Theory. For reduction potentials
calculations, the PCM(UA0) and SMD(Bondi) models were used to compute solvation
energies of neutral forms and anion-radical forms, respectively. For oxidation potentials
calculations, the best results were obtained by a combination of SMD(UAHF) and
PCM(Bondi) models to compute solvation energies of neutral forms and cation-radical
forms, respectively. The mean absolute deviations (MAD) and root mean square errors
(RMSE) of the current theoretical models for reduction potentials were found to be 0.09 V
and 0.10, respectively, and for oxidation potentials MAD = 0.12 V and RMSE = 0.16.
Keywords: N-heterocyclic compounds, DFT calculations, electrochemistry, redox
potential, solvation.
Redox reactions of N-heterocyclic compounds are widely distributed in nature
and used in different areas of industry and organic syntheses [1–3]. To predict the
reactivity of these compounds, knowledge of fundamental characteristics such as
reduction and oxidation potentials is needed. However, experimental measurements
are often difficult due to the complexity of chemical equilibria or due to the
difficulty in synthesizing molecules with desired redox properties. Therefore,
accurate prediction of theoretical redox potentials is important in understanding the
nature of electron-transfer reactions and in the optimization of electrochemical
reaction conditions. Redox properties of N-heterocyclic compounds have been
predicted by our team in our previous publications [4, 5]. The focus of these studies
was on the schemes which provided accurate estimate for both gas phase electron
transfer as well as solvation of oxidizing and reducing forms. The outcome of these
studies were computational protocols which accurately predict both electron
affinities (EA) and reduction potentials for N-heterocyclic compounds in dimethyl
formamide (DMF), and ionization potentials (IP) and oxidation potentials in
acetonitrile (AN). These studies showed that increased accuracy of the solvation
estimation may be obtained by exploiting two different set of radii (or even
different models with different radii) for neutral and ion-radical species. This is not
surprising that the radii of anions and cations differ from the radii of neutral
molecules, as it has been showed earlier [6, 7].
The present study continues our work in prediction of one-electron oxidation
properties for nitrogen-containing heterocyclic compounds. The primary goal of
this study is to establish a computational protocol based on the application of
Density Functional Theory (DFT) approximation that accurately calculates
reduction and oxidation potentials for N-heterocyclic compounds and is able to
predict redox properties for compounds where experimentally measured potentials
are unavailable. For the present study, 42 mono- and polycyclic aza compounds
with available experimental reduction or oxidation potentials were chosen (Fig. 1).
341
N
N
N
N
Pyrazine
2
Pyridazine
1
N
N
Methylpyrazine
3
Me
N
Cl
N
Quinazoline
12
N
N
H
6-Chloro-3-(4-cyanophenyl)aminopyridazine
17
N
Cinnoline
9
Cl
N
N
N
N
H
Pyrazole
18
N
N
Pyrimidine
6
Me
N
Phtalazine
11
Cl
N
3-Amino6-chloropyridazine
15
N
NH2
N
N
N
NHEt
6-Chloro3-ethylaminopyridazine
16
N
N
N
H
Benzotriazole
21
N
Me
N
N
H
Purine
24
N
H
2-Methylbenzimidazole
25
Ph
N
H
2-Phenylbenzimidazole
26
Me
Ph
N
H
2-Phenylindole
28
N
N
Quinoxaline
10
Cl
N
N
N
N
N
N
N
N
H
H
1H-1,2,3-Triazole 1H-1,2,4-Triazole
19
20
N
N
H
Benzimidazole
23
N
H
2-Methylindole
27
N
OMe
6-Chloro3-methoxypyridazine
14
N
N
H
Indazole
22
N
Pyridine
5
N
Cl
3,6-Dichloropyridazine
13
CN
N
N
N
2,6-Dimethylpyrazine
4
N
Phenazine
8
N
N
Me
N
N
N
1,3,5-Triazine
7
Cl
Me
N
Ph
N
N
Me
1,2-Dimethylindole
29
Me
1-Methyl-2-phenylindole
30
N N
Me N
N Me
1,4-Dimethyl-1,4,5,6-tetrahydro-1,2,3,4-tetrazine
31
Bu -t
N
H
2-tert-Butylpyrrole
36
N
H
Pyrrole
32
H
N
N
H
2,2'-Bipyrrole
37
N
N
N
Quinoline
33
Acridine
34
H
N
Isoquinoline
35
H
N
Me
Me
Me
N
N
H
H
5-Methyl-2,2'-bipyrrole 5,5'-Dimethyl-2,2'-bipyrrole
39
38
Me
N
N N
Benzocinnoline
40
3-Methylisoquinoline
41
N
Phenantridine
42
Fig. 1. Numbering of azacyclic compounds with known reduction potentials, described in this study
342
These compounds contain varying numbers of nitrogen atoms in a heterocycle and
cover a wide range of substituents such as halogen, methyl, amino, methoxy, nitro,
and other groups.
Standard reduction and oxidation potentials were calculated according to
Faraday's Law.
E0red = –
E0ox =
G0red
nF
G0ox
nF
+ EH
+ EH,
where n is the number of transferred electrons, F is the Faraday's Constant
(charge on a mole of electrons). The absolute potential of the normal hydrogen
electrode (NHE) reference electrode EH was taken as –4.36 V for DMF solutions
and as –4.52 V for AN solution [8, 9].
Free energies of reduction and oxidation (ΔG0red and ΔG0ox) were calculated as
the difference between free energies of anion-radical of reduced form and neutral
oxidized form in solution and as the difference between free energies of cationradical of oxidized form and neutral reduced form in solution, respectively.
G0red = G0solv(R – · ) – G0solv(O)
G0ox = G0solv(O + · ) – G0solv(R)
All of the calculations were performed using the Gaussian 09 program package
[10]. The geometry of neutral and radical species were optimized at
MPWB1K/6-31+G(d) level [11]. The present functional and basis set were chosen
because they showed good results in previous redox properties calculations [4, 5,
12, 13]. Harmonic vibrations were calculated for all structures obtained to establish
that a minimum was observed. The solvent effects were assessed by single-point
calculations using a number of PCM [14, 15, 16] and SMD [17, 18] solvation
models and different atomic radii designated in Gaussian-09 as UFF, UA0, UAHF,
UAKS, Pauling, and Bondi radii. All possible combinations were explored. The
notation (A1/A2) for solvation models was chosen for this study, where A1 relates to
the solvent approach applied for neutral molecules, and A2 relates to the model
chosen to compute Gibbs solvation free energy of the radical forms. Gibbs free
energy was calculated at 298.15 K.
The MPWB1K/6-31+G(d) level of theory combined with various solvation
models was applied for the compounds under consideration. Calculated reduction
and oxidation potentials of aza compounds were compared with experimental data.
Tables S1, S2 (Supplementary Material) summarize the RMSE for all of the
considered species. Good results for reduction potentials were obtained using both
PCM and SMD models with UFF, UA0, Pauling, Bondi radii for neutral forms and
with Pauling, Bondi radii for anion-radical ones and also combinations of PCM and
SMD with UAHF, UAKS, Pauling, Bondi radii for neutral forms and PCM and
SMD with UAHF and UAKS radii for anion-radical forms. Based on analysis of
RMSE one may conclude that the most accurate solvation models for these
calculations were found to be PCM(UA0)/SMD(Pauling), PCM(UFF)/SMD(Bondi)
and PCM(UA0)/SMD(Bondi). The calculated reduction potentials using aforementioned combinations are listed in Table 1. The corresponding calculated RMSE
is 0.10 with MAD of 0.09 V.
343
Table 1
MPWB1K/6-31+G(d) calculated and experimental
reduction potentials E0red of azacyclic compounds 1–17 in DMF,
RMSE and MAD of calculated values vs. experimental data
Calculated E0red, V
Compound
PCM(UA0)/
SMD(Pauling)/
MPWB1K/
6-31+G(d)
PCM(UFF)/
SMD(Bondi)/
MPWB1K/
6-31+G(d)
PCM(UA0)/
SMD(Bondi)/
MPWB1K/
6-31+G(d)
Experimental
E0red, V
Exp.
vs. NHE
1
–2.08
–2.08
–2.11
–2.22*
–2.02
2
–2.04
–2.04
–2.06
–2.17*
–1.97
3
–2.08
–2.10
–2.11
–2.23*
–2.03
4
–2.14
–2.17
–2.16
–2.28*
–2.08
5
–2.70
–2.70
–2.73
–2.76*
–2.56
6
–2.21
–2.22
–2.24
–2.35*
–2.15
7
–1.79
–1.81
–1.82
–2.05*
–1.85
8
–0.99
–0.94
–0.99
–1.24**
–1.00
9
–1.52
–1.49
–1.52
–1.71**
–1.47
10
–1.53
–1.50
–1.54
–1.89**
–1.65
11
–1.93
–1.90
–1.93
–2.06**
–1.82
12
–1.66
–1.63
–1.66
–1.85**
–1.61
13
–1.50
–1.50
–1.52
–1.99***
–1.59
14
–1.65
–1.72
–1.70
–2.28***
–1.88
15
–1.88
–1.85
–1.91
–2.47***
–2.07
16
–1.95
–1.92
–1.97
–2.46***
–2.06
17
–1.72
–1.71
–1.76
–2.15***
–1.75
RMSE
0.10
0.10
0.10
–
–
MAD
0.09
0.09
0.09
–
–
* Experimental data are taken from [19]. To convert redox potential values measured relative
to Ag/AgCl electrode, we added 0.20 V to obtain the corresponding value for NHE.
** Experimental data are taken from [20]. To convert redox potential values measured relative
to standard calomel electrode (SCE), we added 0.24 V to obtain the corresponding value for NHE.
*** Experimental data are taken from [21]. To convert redox potential values quoted vs. the
ferrocene-ferrocenium couple, we added 0.40 V to obtain the corresponding value for NHE.
Good results for oxidation potentials were obtained using both PCM and SMD
models with UAHF, UAKS radii for neutral forms and with Bondi radii for cationradical species and also combinations of PCM and SMD with UFF, UA0, Pauling,
Bondi radii for neutral forms and PCM and SMD with UA0 radii for cation-radical
forms. Based on analysis of RMSE one may conclude that the most accurate
solvation
models
for
these
calculations
were
found
to
be
SMD(UAHF)/PCM(Bondi), SMD(UA0)/PCM(UA0) and SMD(UFF)/SMD(UA0).
The calculated oxidation potentials using aforementioned combinations are listed in
Table 2. The corresponding calculated RMSE varies from 0.16 up to 0.19, with
MAD in the range of 0.12–0.15 V.
Since the redox potentials are not reported for some compounds we have
predicted reduction potentials in DMF for compounds 18–52 and oxidation
344
potentials in AN for compounds 1–4, 6, 7, 9, 11–17, 43–52 (Fig. 1, 2) using
PCM(UA0)/SMD(Bondi)/MPWB1K/6-31+G(d) and SMD(UAHF)/PCM(Bondi)/
MPWB1K/6-31+G(d) levels of theory, respectively. The calculated results are
presented in Tables 3 and 4.
Table 2
MPWB1K/6-31+G(d) calculated using different solvation models
and experimental oxidation potentials E0ox of compounds 5, 8, 10, 18–42
in AN, RMSE and MAD of calculated values vs. experimental data
Calculated E0ox, V
SMD(UAHF)/
PCM(Bondi)/
MPWB1K/
6-31+G(d)
SMD(UA0)/
PCM(UA0)/
MPWB1K/
6-31+G(d)
SMD(UFF)/
SMD(UA0)/
MPWB1K/
6-31+G(d)
5
2.37
2.45
Compound
Experimental
E0ox, V
Exp.
vs. NHE
2.50
1.82* [22]
2.36
8
2.01
1.99
2.02
1.91** [23]
2.06
10
2.32
2.41
2.48
2.19** [23]
2.34
18
2.34
2.30
2.42
1.70* [24]
2.24
19
2.74
2.74
2.94
1.80* [24]
2.34
20
3.05
3.09
3.10
2.36* [25]
2.90
21
2.26
2.19
2.33
1.70* [24]
2.24
22
1.82
1.71
1.79
1.15* [24]
1.69
23
1.95
1.88
1.89
1.10* [24]
1.64
24
2.65
2.66
2.66
2.10* [24]
2.64
25
1.71
1.68
1.74
1.00* [24]
1.54
26
1.75
1.52
1.51
1.00* [24]
1.54
27
1.10
1.08
1.08
0.60* [24]
1.14
28
1.20
1.06
1.03
0.73* [26]
1.27
29
0.96
1.06
1.13
0.50* [24]
1.04
30
1.13
1.12
1.15
0.64* [26]
1.18
31
0.74
0.66
0.91
0.98** [27]
1.13
32
1.25
1.27
1.34
0.71* [28]
1.25
33
2.03
2.09
2.12
1.97** [23]
2.12
34
1.61
1.60
1.60
1.58** [23]
1.73
35
1.88
1.95
1.99
1.84** [23]
1.99
36
1.06
1.12
1.20
1.12** [29]
1.27
37
0.66
0.38
0.47
0.60** [29]
0.75
38
0.53
0.26
0.35
0.46** [29]
0.61
39
0.20
0.22
0.29
0.30** [29]
0.45
40
1.92
1.88
1.95
1.72** [23]
1.87
41
1.71
1.79
1.89
1.67** [23]
1.82
42
2.03
2.02
2.03
1.80** [23]
1.95
RMSE
0.16
0.19
0.19
–
–
MAD
0.12
0.14
0.15
–
–
* To convert oxidation potential values measured relative to Ag/Ag+ electrode, we added 0.54 V
to obtain the corresponding value for NHE.
** To convert oxidation potential values measured relative to SCE electrode, we added 0.15 V to
obtain the corresponding value for NHE.
345
Table 3
PCM(UA0)/SMD(Bondi)/MPWB1K/6-31+G(d) calculated reduction potentials E0red
of azacyclic compounds 18–52 in DMF
Compound
E0red, V
Compound
E0red, V
Compound
E0red, V
18
–4.18
30
–2.52
42
–2.01
19
–3.66
31
–3.26
43
–1.99
20
–3.72
32
–4.08
44
–1.38
21
–2.34
33
–2.08
45
–0.48
22
–2.74
34
–1.46
46
–0.61
23
–2.91
35
–2.15
47
–0.33
24
–2.03
36
–4.08
48
–0.37
25
–3.03
37
–3.72
49
0.04
26
–2.17
38
–3.71
50
–0.78
27
–3.23
39
–3.70
51
–1.59
28
–2.48
40
–1.37
52
–3.80
29
–3.12
41
–2.33
N
N
N
N
1,2,3-Triazine
43
N
1,2,4-Triazine
44
N
NO2
O
ANTA
48
N
H
NTO
49
NO2
N
N
N
N
1,2,4,5-Tetrazine
45
H
N N
H
N N
H2N
N
N
N
NO2
N
O2N
N
O2N
N
RDX
46
NO2
N
N
N
N
N
N
N
3,6-Dihydro1,2,3,5-Tetrazine 1,2,4,5-tetrazine
50
51
NO2
N
N
NO2
N
O2N HMX
47
N
N
H
N
N
N
N
N
NH
N N
H H
HBT
52
Fig. 2. Numbering of azacyclic compounds in this study with unavailable redox potentials
Table 4
SMD(UAHF)/PCM(Bondi)/MPWB1K/6-31+G(d) calculated oxidation potentials E0ox
of azacompounds 1–4, 6, 7, 9, 11–17, 43–52 in AN
Compound
E0ox, V
Compound
E0ox, V
Compound
E0ox, V
1
1.92
12
2.61
45
2.22
2
2.44
13
3.07
46
6.20
3
2.32
14
2.37
47
7.15
4
2.26
15
1.93
48
2.59
6
2.62
16
1.78
49
2.96
7
3.18
17
1.65
50
2.56
9
1.87
43
2.31
51
3.18
11
1.94
44
2.16
52
3.00
346
Thus, we have determined computational protocols that provide accurate predictions of redox potentials for N-heterocyclic compounds. The approach for
reduction potential calculations of azacyclic compounds in DMF consists of Gibbs
free energies evaluation at the MPWB1K/6-31+G(d) level of theory and solvation
energies obtained using PCM(UA0) model to compute solvation energies of neutral
forms and SMD(Bondi) to compute solvation energies of anion-radical forms. The
approach for oxidation potentials calculation of azacyclic compounds in AN is
supported by calculations at the MPWB1K/6-31+G(d) level of theory which uses
SMD(UAHF) approximation for estimation of solvation energy of neutral
molecules and PCM(Bondi) model for cation-radical forms. The MAD and RMSE
of the current theoretical models for reduction potentials equal to 0.09 V and 0.10,
respectively, and for oxidation potentials they amount to 0.12 V and 0.16. Our
study provides reliable values of reduction and oxidation potentials for the
azacyclic compounds not evaluated experimentally.
We thank ERDC for financial support (grant number is W912HZ-13-P-0037).
The computation time was provided by the Extreme Science and Engineering
Discovery Environment (XSEDE) by National Science Foundation Grant Number
OCI-1053575 and XSEDE award allocation Number DMR110088 and by the
Mississippi Center for Supercomputer Research.
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1
Interdisciplinary Nanotoxicity Center,
Department of Chemistry and Biochemistry,
Jackson State University,
1400 John R. Lynch St., Jackson, Mississippi 39217, U.S.A.
e-mail: [email protected]
2
Kirovohrad Volodymyr Vynnychenko State Pedagogical University,
1 Shevchenko St., Kirovohrad 25006, Ukraine
3
Badger Technical Services, Inc.,
4815 Bradford Dr, NW Huntsville, AL 35805, U.S.A.
e-mail: [email protected]
4
US Army ERDC,
3909 Halls Ferry Road, Vicksburg, MS, 39180
e-mail: [email protected]
5
Interdisciplinary Nanotoxicity Center,
Department of Civil and Environmental Engineering,
Jackson State University,
1400 John R. Lynch St., Jackson, Mississippi 39217, U.S.A.
е-mail: [email protected]
348
Received 29.01.2014