Structural Chemistry

, Volume 18, Issue 6, pp 797–805

Substitution effects in phenyl and N-pyrrole derivatives along the periodic table

Authors

  • Krzysztof Zborowski
    • Faculty of ChemistryJagiellonian University
    • Instituto de Química Médica (C.S.I.C.)
  • José Elguero
    • Instituto de Química Médica (C.S.I.C.)
Original Paper

DOI: 10.1007/s11224-007-9245-z

Cite this article as:
Zborowski, K., Alkorta, I. & Elguero, J. Struct Chem (2007) 18: 797. doi:10.1007/s11224-007-9245-z

Abstract

A theoretical study of the monosubstitution effects of all the atoms of the second and third row of the periodic table on the phenyl and pyrrole rings has been carried out by means of B3LYP/6-31 + G(d,p) DFT calculations. The geometric and electronic properties, calculated using the Atoms In Molecules methodology, have been analyzed. Some of the results have been rationalized based on the electronegativity of the substituents. In addition, the different parameters obtained have been compared with different aromaticity indexes (HOMA, NICS, and ASE), as well as with Taft’s σ0R parameter.

Keywords

BenzenePyrroleSubstituent effectsAromaticityAIM

Introduction

Phenyl and pyrrole derivatives can be considered as prototypes of aromatic and heteroaromatic systems. Due to their importance in all fields of modern chemistry a large number of studies have been devoted to them. In particular, a number of aromaticity scales have been developed to allow the classification of these systems in agreement with their physico-chemical and reactivity properties [110].

In previous articles, some of us have compared benzenes 1 and pyrazoles 3 [11, 12]. In these publications, the effects of a large series of substituents, including some of the present study (H, BH2, CH3, NH2, OH, AlH2, SiH3, PH2, F) were examined. The geometries were discussed using Paul–Curtin plots; the angle on N1 in pyrazoles was shown to be related linearly with the angle on C1 in benzenes. The stability of pyrazole rings (Pz) were analyzed by means of “methyl stabilization energies” [11]. The calculated GIAO absolute shieldings were statistically discussed using Principal Component Analysis (PCA), concluding that the transmission of substituent effects through the carbon in 1 and through nitrogen in 3 is quite different, the effect on N1 being especially unique [12] (Scheme 1).
https://static-content.springer.com/image/art%3A10.1007%2Fs11224-007-9245-z/MediaObjects/11224_2007_9245_Sch1_HTML.gif
Scheme 1

Systems considered in the present article

In the present article, the geometrical and electronic properties of phenyl and pyrrole derivatives of all the atoms of the second and third row of the periodic table have been evaluated and compared. In addition, atomic partition of the energy, charge and volume of the systems have been carried out with the AIM methodology. Finally, several aromaticity indexes have been evaluated and compared to the geometrical and electronic properties previously considered.

Methods

The geometry of the molecules has been fully optimized with the hybrid HF/DFT method, B3LYP [13, 14], and the 6-31 + G(d,p) basis set [15], using the ultrafine grid option and the Berny algorithm with the default parameters of the Gaussian-03 package [16]. Frequency calculations have been carried out at the same computational level to confirm that the structures obtained correspond to energetic minima.

The electron density of the systems has been analyzed with the Atoms In Molecules (AIM) methodology [17] and the AIMPAC program [18]. The atomic properties (volume, charge, and energy) have been evaluated by integration of the electron density within the atomic basins. The value of the integrated Laplacian has been used as an initial measure of the quality of integration. Ideally, a null value should be obtained in the integrated Laplacian within the atomic basins. Values smaller than 1 × 10−3 for all the atoms of a system have proven to provide small errors in the energy and charge of the molecules [19]. Thus, the conditions of the integration have been changed when the previous condition was not satisfied. In the molecules studied here, the largest absolute value of the error in the energy and charge has been 0.6 kJ mol−1 and 0.001 e.

Several aromaticity indices have been used in this study. They are based on different criteria of aromaticity [20], such as energetic (Aromatic Stabilization Energy, ASE), geometric (Harmonic Oscillator Model of Aromaticity, HOMA), and magnetic (Nuclear Independent Chemical Shift, NICS). There are several reaction schemes used for ASE calculations [21]. This quantity strongly depends on the kind of reaction. Values presented in this work are based on the equations shown in Scheme 2.
https://static-content.springer.com/image/art%3A10.1007%2Fs11224-007-9245-z/MediaObjects/11224_2007_9245_Sch2_HTML.gif
Scheme 2

ASE reaction considered in the present article

The HOMA index [22] is geometry-based and can be obtained from bond lengths using the equation: \( {\text{HOMA}} = 1 - {\left[ {\frac{\alpha } {n}{\sum {{\left( {R_{{{\text{opt}}}} - R_{{\text{i}}} } \right)}} }^{2} } \right]}, \) where Ropt and Ri are optimal bond length and bond length in the real system, respectively. α is an empirical factor that provides a value of HOMA equal to 0 for the Kekulé structure of benzene and a value of 1 for benzene with optimal ‘aromatic’ bond length. Finally, n is the number of the bond considered.

The NICS index is defined as the negative absolute magnetic shielding computed in the center of the ring [23]. The NICS(1) index is calculated 1 Å above the ring center [24]. Another descriptor is the out of plane component of the NICS(1) magnetic tensor, NICS(1)ZZ [25]. Rings with highly negative NICS values are aromatic whereas those with positive values are anti-aromatic.

In addition, it was considered also of interest to analyze the stabilization effects of the substituents on the pyrrole system. For this purpose, we shall use the so called “methyl stabilization energies” (MSE) [26], defined as the energy of the reaction shown in Scheme 3.
https://static-content.springer.com/image/art%3A10.1007%2Fs11224-007-9245-z/MediaObjects/11224_2007_9245_Sch3_HTML.gif
Scheme 3

Equation used to evaluate the “methyl Stabilization energy” (MSE)

Results and discussion

The 15 systems considered have been represented in Scheme 1 both for 1 and 2 (X = H, Li, BeH, BH2, CH3, NH2, OH, F, Na, MgH, AlH2, SiH3, PH2, SH, Cl). They include all the simplest substituents of the second and third row of the periodic table, where the remaining valences have been filled with hydrogen. Thus, a wide range of electronic properties is considered in the present set of compounds.

Geometries

The bond distances obtained in the optimized structures and the experimental values of the compounds in gas phase (microwave and electron diffraction data) have been gathered in Table 1. The calculated data nicely reproduce the experimental ones. A graphical representation (Fig. 1) of the variation of the bond distances with respect to the unsubstituted derivative, X = H, show that for most of the cases, the effect of the substituents of the first row are similar to the corresponding ones of the second row. In addition, the largest variations are obtained in the BH2 substituted compounds. The reason for this fact could be the empty orbital in the boron atom and the short bond between boron and the C/N of the phenyl/pyrrole. Whereas Li and Be, as well as Na, Mg, and Al present empty orbitals, their bonds to the aromatic rings are much larger.
Table 1

Calculated bond distances (Å) and angles (°) at the B3LYP/6–31 + G** of the systems considered

System

C1–C2

C2–C3

C3–C4

C4–C5

C5–C6

C6–C1

C1–X

C6–C1–C2

C6H5–H

1.398 (1.399)a

1.398 (1.399)

1.398 (1.399)

1.398 (1.399)

1.398 (1.399)

1.398 (1.399)

1.086 (1.101)

120.0 (120.0)

C6H5–Li

1.417

1.402

1.398

1.398

1.402

1.417

1.970

114.4

C6H5–BeH

1.415

1.397

1.398

1.398

1.397

1.415

1.673

116.4

C6H5–BH2

1.415

1.395

1.400

1.400

1.395

1.415

1.538

117.5

C6H5–CH3

1.403 (1.395)b

1.398 (1.396)

1.398 (1.395)

1.398 (1.395)

1.398 (1.396)

1.403 (1.395)

1.512 (1.515)

118.2 (119.3)

C6H5–NH2

1.406 (1.397)c

1.395 (1.394)

1.398 (1.396)

1.398 (1.396)

1.395 (1.394)

1.406 (1.397)

1.399 (1.402)

118.6 (119.3)

C6H5–OH

1.400 (1.391)d

1.398 (1.394)

1.397 (1.395)

1.399 (1.395)

1.395 (1.394)

1.399 (1.391)

1.372 (1.374)

120.3 (120.8)

C6H5–F

1.390 (1.385)e

1.398 (1.396)

1.398 (1.398)

1.398 (1.398)

1.398 (1.396)

1.390 (1.385)

1.361 (1.354)

122.8 (123.2)

C6H5–Na

1.413

1.403

1.398

1.398

1.403

1.413

2.297

115.1

C6H5–MgH

1.413

1.400

1.397

1.397

1.400

1.413

2.097

116.0

C6H5–AlH2

1.413

1.398

1.398

1.398

1.398

1.413

1.954

117.1

C6H5–SiH3

1.407 (1.392)f

1.398 (1.392)

1.397 (1.392)

1.397 (1.392)

1.398 (1.392)

1.407 (1.392)

1.883 (1.843)

117.9 (117.4)

C6H5–PH2

1.404 (1.405)g

1.399 (1.399)

1.396 (1.392)

1.399 (1.398)

1.396 (1.391)

1.405 (1.405)

1.857 (1.833)

118.5 (119.0)

C6H5–SH

1.402

1.397

1.397

1.398

1.396

1.403

1.788

119.4

C6H5–Cl

1.395 (1.391)h

1.398 (1.394)

1.398 (1.400)

1.398 (1.400)

1.398 (1.394)

1.395 (1.391)

1.760 (1.739)

121.5 (121.65)

System

N1–C2

C2–C3

C3–C4

C4–C5

C5–N1

N1–X

C5–N1–C2

 

C4H4N–H

1.377 (1.370)i

1.381 (1.382)

1.427 (1.417)

1.381 (1.382)

1.377 (1.370)

1.008 (0.996)

109.8 (109.8)

 

C4H4N–Li

1.381

1.389

1.423

1.389

1.381

1.803

105.7

 

C4H4N–BeH

1.396

1.374

1.430

1.374

1.396

1.536

106.6

 

C4H4N–BH2

1.404

1.365

1.443

1.365

1.404

1.420

107.1

 

C4H4N–CH3

1.377 (1.361)j

1.382 (1.393)

1.424 (1.422)

1.382 (1.393)

1.377 (1.361)

1.453 (1.452)

108.9 (110.5)

 

C4H4N–NH2

1.375

1.381

1.427

1.381

1.380

1.403

109.9

 

C4H4N–OH

1.371

1.384

1.425

1.384

1.371

1.387

111.6

 

C4H4N–F

1.364

1.387

1.424

1.387

1.364

1.375

113.9

 

C4H4N–Na

1.378

1.392

1.421

1.392

1.378

2.144

105.7

 

C4H4N–MgH

1.387

1.382

1.424

1.382

1.387

1.960

106.3

 

C4H4N–AlH2

1.396

1.374

1.432

1.374

1.396

1.829

106.7

 

C4H4N–SiH3

1.391 (1.382)k

1.376 (1.384)

1.428 (1.425)

1.376 (1.384)

1.391 (1.382)

1.770 (1.736)

107.5 (109.6)

 

C4H4N–PH2

1.390

1.376

1.429

1.376

1.387

1.752

108.2

 

C4H4N–SH

1.387

1.376

1.429

1.376

1.387

1.718

109.3

 

C4H4N–Cl

1.378

1.380

1.426

1.380

1.378

1.711

111.2

 

The experimental gas phase values are given in parenthesis

Taken from references a [27], [28], [29], [30], e  [31], [32], [33], [34], [35], j  [36], [37]

https://static-content.springer.com/image/art%3A10.1007%2Fs11224-007-9245-z/MediaObjects/11224_2007_9245_Fig1_HTML.gif
Fig. 1

Variation of the bond distances (Å) and angles (°) with respect to those of the unsubstituted derivatives. Black square and open circles correspond to the second row and third row substituents, respectively

In the phenyl derivatives, the effect of the substituents is larger in the C1–C2 bond than in the C2–C3, and the smallest variations are observed in the C3–C4 ones. An important elongation of the C1–C2 bond is observed with the more electropositive atoms, then gradually decreases up to the fluorine and chlorine derivatives, where it is shorter than in benzene itself. In the C2–C3 bond, only the most electropositive atoms present larger bond distances than benzene, while in the rest of the cases, they are shorter. Finally, in the C3–C4 bond, the differences with the C6H6 are small, the BH2 derivative being only larger than benzene.

The angle variation around the substituted atom shows similar pattern for the two rows of the periodic table and the two aromatic systems considered. For the first atoms of the row, the bond angle is smaller than that of the unsubstituted derivatives and it increases as we move to the right in the periodic table. The values obtained for this parameter for the phenyl and pyrrole derivatives present a square correlation coefficient of 0.92 when all of them are considered and larger values when the data are separate in the second and third rows. Similar results have already been described between phenyl and pyrazole derivatives [11].

In the case of pyrrole derivatives, the more electropositive atoms, defined as the ones located in the first three columns of the periodic table, present a tendency while the rest have the opposite one for each bond. Thus, the N1–C2 bond tends to increase from the first to the third column of the periodic table, and then it decreases along the periodic table. The opposite happens with the C2–C3 bond and in the C3–C4 bond a small increment is observed in the first three atoms of each row and almost a constant value in the rest.

Electron density (AIM)

The analysis of the electron density within the AIM methodology allows to characterize the systems based on their critical points. In the molecules studied here, the analysis present bond critical points (bcp) and a ring critical point (rcp), approximately in the middle of the aromatic ring. The values of the electron density at the bcps have been shown to be highly correlated with the interatomic distances [3840] and thus it does not provide any additional information to that previously discussed for the bond distances. Regarding the rcps, a previous study has shown that it can be used as a useful parameter to account for the aromaticity of polycyclic systems [41].

The variation of the electron density and its Laplacian at the rcp with respect to the parent compounds has been represented in Fig. 2. The values of the electron density at the rcp present its maximum values in the more electropositive atoms decreasing for larger atoms and suffering a small recovery for the last two atoms of the second row and the last one of the third row, with the exception of N-methylpyrrole.
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Fig. 2

Variation of the ρ and Lap (a.u.) at the rcp of the systems studied. Black square and open circles correspond to the second row and third row substituents, respectively

Regarding the Laplacian of the rcp, it is positive for all the molecules and significantly in the two series, the larger value corresponds to the unsubstituted derivatives. The evolution of the values for the substituents of the second row in the C6H5X and N–X pyrrole series presents alternating tendencies in the first four atoms and an increasing tendency from the nitrogen to the fluorine. In the third row, the phenyl derivatives of the first four atoms increase their value, while in the pyrrole series the opposite happens.

The atomic integration of several properties (energy, charge, and volume) within the atomic basins has been carried out to obtain information of the evolution of these properties in the different moieties of the molecules. In the first step, the effect of the X group on the rest of the molecule has been studied. The energy, charge, and volume of the C6H5 and C4H4N fragments have been evaluated and represented versus the electronegativity of the substituents, as defined by Pauling [42], in Fig. 3. A simple look at the figures shows similar behavior of the phenyl and pyrrole derivatives for each property. In fact, very good correlation coefficients are obtained when the results of these two series are compared as function of the X group (R2 = 0.978, 0.964, and 0.986 for the energy, charge, and volume of the 15 X groups considered, respectively).
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Fig. 3

Integrated values (Total energy in hartrees, charge in e, and volume in a.u.) of the C6H5 and C4H4N fragments versus the electronegativity of the substituents. Triangle, black square and open circles correspond to the hydrogen, second row and third row substituents, respectively

The energy in the second row decreases from the lithium to the beryllium atom and in this point starts increasing up to the fluorine derivative that presents the maximum value for this row in both aromatic systems. In the second row, the energy increases as the electronegativity increases except for the SiH3 derivative, which is slightly less stable than the AlH2.

In the case of the charge and volume of the C6H5 and C4H4N fragments, the electronegativity of the substituent is a good descriptor and thus, the results obtained for the derivatives of the 2nd and 3rd row of the periodic table depends only on this parameter and can be considered together. In the case of the charge of the fragment considered goes from very negative in the case of electropositive atoms to positive in the more electronegative atoms. With respect to the volume, the larger volume is obtained with the atoms with the smaller electronegativity and decreases as its electronegativity increases.

In addition, the integrated properties of the N1, C2 and C3 of pyrrole have been compared with their analogs in the phenyl derivatives (Table 2). In the case of C2 and C3, the C2–H and C3–H fragments have been taken into account. The results show good square correlation coefficient in the energy of the C2 and C3 atoms and their corresponding fragments with the hydrogen attached. Regarding the charge, the N1/C1, C3, and C3–H3 present good correlations between the two aromatic rings. Finally, the volume of the N1/C1 atoms are highly correlated, while in the rest of the cases considered, the square correlation coefficients is smaller than 0.9.
Table 2

Square correlation coefficients of the integrated properties in the atoms and fragments of the pyrrole and phenyl derivatives

 

Energy

Charge

Volume

N1/C1

0.65

0.93

0.97

C2

0.96

0.04

0.52

C2–H2

0.95

0.67

0.80

C3

1.00

0.91

0.56

C3–H3

1.00

0.97

0.87

An interesting feature of Table 2 is the fact that the correlation coefficient of the CH fragment is better than the corresponding carbon atom alone. This could be an indication of the redistribution of the different properties along the molecule, and in this case, in the molecular fragments.

Aromaticity

The calculated aromaticity indexes and “methyl stabilization energy” (MSE) have been gathered in Table 3. The comparison of the results obtained for the phenyl and pyrrole derivatives indicate very poor correlations between the two sets for each aromaticity index. The best correlation obtained corresponds to the NICS(0) with a square correlation coefficient of 0.6.
Table 3

Values of the aromaticity indexes for all the systems considered in the present publication

 

HOMA

NICS(0)

NICS(1)

NICS(1)zz

ASE3

Methyl SE

C6H6

0.97

−8.12

−10.19

−28.83

137.92

0.0

C6H5Li

0.90

−6.72

−9.63

−27.93

132.24

17.1

C6H5BeH

0.92

−7.57

−10.08

−28.24

129.15

7.4

C6H5BH2

0.92

−7.09

−9.80

−27.29

126.24

34.0

C6H5CH3

0.97

−8.11

−9.96

−27.96

132.66

14.0

C6H5NH2

0.96

−7.94

−8.92

−24.41

131.15

44.2

C6H5OH

0.97

−9.11

−9.80

−26.45

132.46

44.3

C6H5F

0.98

−9.99

−10.37

−27.93

139.31

30.8

C6H5Na

0.92

−6.95

−9.59

−27.85

129.31

13.7

C6H5MgH

0.93

−7.26

−9.90

−27.14

130.10

3.5

C6H6AlH2

0.93

−7.39

−10.08

−28.15

111.65

13.6

C6H5SiH3

0.95

−7.54

−10.02

−28.14

130.85

0.2

C6H5PH2

0.96

−7.98

−10.07

−27.84

133.06

5.1

C6H5SH

0.97

−7.98

−9.48

−25.83

131.54

12.8

C6H5Cl

0.98

−9.02

−10.05

−27.14

136.46

13.7

 

HOMA

NICS(0)

NICS(1)

NICS(1)zz

ASE3

Methyl

Pyrrole

0.85

−13.86

−10.09

−30.81

74.87

0.0

Pyrrole_Li

0.85

−12.99

−10.41

−32.86

82.58

148.2

Pyrrole_BeH

0.74

−12.94

−9.90

−29.64

63.57

104.9

Pyrrole_BH2

0.61

−9.22

−8.21

−24.00

37.20

123.8

Pyrrole_CH3

0.86

−13.10

−9.59

−28.99

61.38

−9.4

Pyrrole_NH2

0.85

−13.83

−9.40

−27.92

54.65

−64.0

Pyrrole_OH

0.87

−15.06

−9.60

−28.35

50.89

−125.3

Pyrrole_F

0.90

−16.53

−9.92

−28.51

35.32

−192.5

Pyrrole_Na

0.87

−13.00

−10.28

−33.19

85.28

132.5

Pyrrole_MgH

0.82

−13.20

−10.22

−31.94

78.79

96.6

Pyrrole_AlH2

0.74

−11.66

−9.49

−29.12

60.53

97.2

Pyrrole_SiH3

0.78

−12.48

−9.58

−28.49

69.03

42.0

Pyrrole_PH2

0.79

−12.51

−9.31

−27.68

76.01

6.9

Pyrrole_SH

0.79

−13.28

−9.55

−27.51

66.49

−45.7

Pyrrole_Cl

0.85

−14.46

−9.51

−28.13

52.47

−118.7

R2

0.20

0.60

0.01

0.11

0.00

0.17

The square correlation coefficients of the indexes for the two families of compounds are included

The range of the aromaticity indexes is larger in the pyrrole derivatives than those of phenyl. Thus, while the HOMA index goes from 0.90 for the C6H5Li to 0.98 in the C6H5F, in the pyrrole series, the extremes are the fluorine derivative, 0.90, and the BH2 derivative, 0.61. This effect is even more important in the MSE reaction, since in the phenyl series their values oscillate between 0 and 44 kJ/mol, and in the pyrrole, between 148 and −192 kJ/mol. All these results indicate that the phenyl ring is more stable to the substitution than that of pyrrole.

In order to gain insight in the possible relationship between the aromaticity indexes reported in Table 3 and the parameters derived from the AIM analysis (energies, charge, and volume of all the isolated atoms, CH and ring moieties, and the electron density and Laplacian of the rcp) have been correlated. In the case of the phenyl derivatives, the best correlations are found between the charge of the C6H5 fragment or the C1 atom with the HOMA index (square correlation coefficient of 0.85 and 0.84 respectively). In the pyrrole derivatives, a square correlation coefficient of 0.91 is obtained between the charge of the C4H4N fragment and the MSE reaction. This relationship can be improved by dividing the data in the second row derivatives (0.97) and third row (0.92).

Finally, the MSE values obtained here have been compared with those reported previously for the corresponding analog derivatives of pyrazole [11]. An excellent linear relationship has been obtained for the two sets of values as shown in Fig. 4.
https://static-content.springer.com/image/art%3A10.1007%2Fs11224-007-9245-z/MediaObjects/11224_2007_9245_Fig4_HTML.gif
Fig. 4

Comparison of the “Methyl Stabilization Energy” (kJ/mol) obtained for the pyrrole derivatives 2 and those reported for the corresponding pyrazoles 3 [11]. The fitted line present the following equation: MSE(pyrazoles) = 20.16 + 0.93* MSE(Pyrroles), n = 7, R2 = 0.992

Linear energy relationships

Krygowski and Stepien have discussed the relationships between substituent effects, and σ- and π-electron delocalization in aromatic carbocyclic systems [2]. From the wealth of data of the previous sections, we have found that the C6H5 and C4H4N fragment charges are related to Taft’s σ0R values [43], if H is excluded (probably it is too small and the partition is not accurate enough). From the available 12 values of σ0R [44], we have calculated the following two equations:
$$ \sigma ^{0}_{R} {\text{ }}({\text{C}}_{6} {\text{H}}_{5} {\text{X}}) = - 0.41 \times {\text{charge}}-0.21,{\text{ }}R^{2} = 0.96 $$
(1)
$$ \sigma ^{0}_{R} {\text{ }}({\text{C}}_{4} {\text{H}}_{4} {\text{NX}}) = - 0.51 \times {\text{ charge}} - 0.36,{\text{ }}R^{2} = 0.94 $$
(2)

We have used Eq. 1 (benzenes) to predict new σ0R values: BeH 0.13, BH2 0.06, Na 0.10, MgH 0.11, and AlH2 0.09.

Conclusions

A theoretical study of the substitution effect of derivatives of all the atoms of the second and third row of the periodic table on benzene and pyrrole has been carried out by means of DFT calculations. The atomic contributions to the total energy, charge and volume have been calculated using the AIM methodology. The geometrical results have been analyzed taking into account their variations along the periodic table. The results obtained with the AIM methodology show good relationships with the electronegativity of the substituents.

In addition, several aromaticity indexes have been calculated and correlated with the AIM parameters obtained.

The “Methyl Stabilization Energy” obtained for pyrroles has been shown to be highly correlated with that previously reported for pyrazoles.

Acknowledgments

This work was carried out with financial support from the Ministerio de Ciencia y Tecnología (Project No. CTQ2006-14487-C02-01/BQU) and Comunidad Autónoma de Madrid (Project MADRISOLAR, ref. S-0505/PPQ/0225). Thanks are given to the CTI (CSIC) for allocation of computer time.

Copyright information

© Springer Science+Business Media, LLC 2007