Advances in Physical ChemistryVolume 2012 (2012), Article ID 362608, 9 pagesdoi:10.1155/2012/362608

Research Article

The NHF Interactions in the X-Pyridazine Complexes: Substituent Effects and Energy Components

Ali Ebrahimi, Mostafa Habibi-Khorassani, Farideh Badichi Akher, and Abdolkarim Farrokhzadeh

Department of Chemistry, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, Iran

Received 31 October 2011; Revised 4 January 2012; Accepted 24 January 2012

Academic Editor: Laimutis Bytautas

Copyright © 2012 Ali Ebrahimi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

The effects of substituents on the N⋯HF interactions in the X-pyridazine (X = N(CH₃)₂, NHCH₃, NH₂, C₂H₅, CH₃, OCH₃, OH, CN, OF, NO₂, F, Br, Cl, and ) complexes have been studied at the B3LYP/6-311++G(d,p) level of theory. In all complexes, the binding energies increase for the electron-donating substituents and decrease for the electron-withdrawing substituents. A negative cooperativity is observed for two hydrogen bond interactions. There are meaningful relationships between the Hammett constants and the energy data and the results of population analysis in the binary and ternary complexes. Symmetryadapted perturbation theory (SAPT) analysis was also carried out to unveil the nature of hydrogen bond in the complexes 2 and 3. The electron-donating substituents increase the magnitude of the SAPT interaction energy components and the electron-withdrawing substituents decrease those components. The highest/lowest change is observed for the component. The effect of C₂H₅ (or CH₃) on different components is higher than OCH₃ in the complex 2 while the trend is reversed in the complex 3. It is demonstrated that the electrostatic interaction plays a main role in the interaction, although induction and dispersion interactions are also important.

1. Introduction

The diazine rings are building blocks of many important natural and synthetic compounds [1]. They have been the subject of extensive research, particularly in the pharmaceutical and agrochemical areas due to their broad activities, such as antihypertensive and anti-inflammatory activity [2–5].

The hydrogen bond plays a crucial role in biology, chemistry and related disciplines [6–13]. Cooperativity is an important characteristic of hydrogen bond interactions. The role of hydrogen bond may be modified by the cooperativity of hydrogen bonds in many chemical and biological systems [14–16]. It plays an important role in controlling and regulating the processes occurring in living organisms. Many physical and chemical properties of materials are determined by hydrogen-bonding cooperativity [17–20]. For example, the hydrogen bond cooperativity is relevant for sustaining the stable conformers of biological molecules [21, 22] and constructing the crystal structures [22, 23].

The effects of substituents on the binding energies of the X-pyridazine(HF)n () complexes (represented by 1–3 in Scheme 1) and the cooperativity of the H-bond interactions have been investigated in the present study. Substituent X is located at position 4 of pyridazine ring, which is meta relative to N₂ in 1 and 2 and para relative to N₁ in 1 and 3. The relationship between binding energies and the Hammett constants have been studied for binary and ternary complexes. Also, the cooperativity of two hydrogen bond interactions and the strength of interactions have been investigated by the results of atoms in molecules (AIMs) [24], the natural bond orbital (NBO) [25], and molecular electrostatic potential (MEP) analysis. Symmetry-adapted perturbation theory (SAPT) [26] has been employed to determine the physically significant components of the total interaction energies for the complexes 2 and 3.

Scheme 1: The X-pyridazine(HF)n complexes considered in the present work (X = N(CH₃)₂, NHCH₃, NH₂, C₂H₅, CH₃, OCH₃, OH, CN, OF, NO₂, F, Br, Cl, and ).

2. Methods

The geometries of the complexes were fully optimized with the B3LYP [27] method using the 6-311++G(d,p) basis set by the Gaussian 03 program package [28]. The single-point calculations were carried out using the MP2 [29] and PBE1KCIS [30] methods in conjunction with the 6-311++G(d,p) and aug-cc-pVDZ basis sets. The interaction energies were corrected with the basis set superposition error (BSSE) using the counterpoise method of Boys and Bernardi [31]. The frequency calculations were performed at the B3LYP/6-311++G(d,p) level of theory. The obtained wave functions at the B3LYP/6-311++G(d,p) computational level have been used to analyze the electron density within the AIM methodology by the AIM2000 program [32]. The NBO analysis has been performed using the HF method in conjunction with the 6-311++G(d,p) basis set using the NBO3.1 program in the Gaussian03 package. Also, the ChelpG [33] charges were calculated at the B3LYP/6-311++G(d,p) level of theory to investigate the charge transfer between two units. Cube files containing the MEP information have been generated for complexes at the B3LYP/6-311++G(d,p) level of theory. The freely available MOLEKEL program [34] has been used for the visualization of the MEP data. The most negative-valued MEP point () can be obtained from visual inspection of MEP data for the lone-pair region of the nitrogen atoms in pyridazine. The B3LYP-optimized geometries with the 6-311++G(d,p) basis set were then used to perform interaction energy decomposition using the SAPT scheme. Molecular integrals were first obtained with the GAMESS package [35], and the SAPT partitioning was performed using the SAPT2008 program [36].

3. Results and Discussion

The most important geometrical parameters of complexes optimized at the B3LYP/6-311++G(d,p) level of theory are gathered in Table 1. The maximum and minimum values of the NH bond length correspond to NO₂ and N(CH₃)₂ substituents, respectively, in all cases. Also, the NH bond length in the complex 1 is longer than that in the complexes 2 and 3. On the other hand, the NH bond length in the complex 2 is longer than that in the complex 3. These results show that the cooperativity of H-bond interactions leads to the elongation of the NH bond lengths.

Table 1: The NH bond lengths optimized at the B3LYP/6-311++G(d,p) level in () and the Hammett constants.

Bond length
Hammett constants

Complex 1
Complex 2
Complex 3
σ m
σ p
σ total
σ I
σ R

N(CH₃)₂
1.67 (1.69)
1.64
1.63
−0.15
−0.83
−0.98
0.15
−0.98

NHCH₃
1.68 (1.70)
1.65
1.63
−0.52
−0.74
−1.26
0.03
−0.73

NH₂
1.68 (1.71)
1.65
1.64
−0.16
−0.66
−0.82
0.08
−0.74

CH₃
1.71 (1.71)
1.66
1.66
−0.07
−0.17
−0.24
0.01
−0.18

C₂H₅
1.71 (1.71)
1.66
1.66
−0.07
−0.15
−0.22
0.00
−0.15

OCH₃
1.70 (1.72)
1.67
1.65
0.12
−0.27
−0.15
0.29
−0.56

OH
1.71 (1.73)
1.67
1.66
0.12
−0.37
−0.25
0.30
−0.70

H
1.72 (1.72)
1.67
1.67
0.00
0.00
0.00

OF
1.73 (1.74)
1.70
1.68
0.47
0.36
0.83

CN
1.75 (1.70)
1.71
1.70
0.56
0.66
1.22
0.51
0.15

NO₂
1.76 (1.76)
1.72
1.71
0.71
0.78
1.49
0.60
0.13

F
1.73 (1.74)
1.69
1.68
0.34
0.06
0.40
0.45
−0.39

Br
1.73 (1.74)
1.69
1.69
0.39
0.23
0.62
0.40
−0.22

Cl
1.73 (1.74)
1.69
1.68
0.37
0.23
0.60
0.42
−0.19

The data in the parentheses correspond to the N₂H bond length. The σ values are taken from [37].

The total binding energies of complexes (ΔE) calculated at the B3LYP/6-311++G(d,p) level of theory and corrected for BSSE are summarized in Table 2. The results show that the stabilization energies of the complex 3 are larger than those of complex 2. As can be seen, the maximum and minimum values of ΔE calculated at the B3LYP/6-311++G(d,p) level of theory correspond to the N(CH₃)₂ and NO₂ substituents, respectively.

Table 2: The binding energies (−ΔE in kcal mol⁻¹) corrected for BSSE calculated at different levels.

Complex 1
Complex 2
Complex 3

B3LYP
MP2
PBE1KCIS
B3LYP
MP2
PBE1KCIS
B3LYP
MP2
PBE1KCIS

N(CH₃)₂
25.75
21.90 (23.52)
26.22 (25.86)
13.92
11.90 (12.81)
14.19 (14.03)
14.48
11.72 (12.70)
14.71 (14.49)

NHCH₃
25.32
21.80 (23.23)
25.81 (25.42)
13.73
12.00 (12.74)
13.99 (13.82)
14.31
11.82 (12.60)
14.54 (14.31)

NH₂
24.51
20.30 (22.12)
25.06 (24.66)
13.27
11.30 (12.14)
13.55 (13.38)
13.88
11.14 (12.10)
14.15 (13.91)

CH₃
22.98
19.80 (21.10)
23.44 (23.07)
12.80
10.90 (11.63)
13.03 (12.85)
12.86
10.82 (11.50)
13.08 (12.88)

C₂H₅
23.34
19.80 (21.44)
23.88 (23.64)
13.01
10.90 (11.86)
13.32 (13.24)
13.09
10.78 (11.80)
13.40 (13.31)

OCH₃
23.19
19.90 (21.24)
23.65 (23.31)
12.61
10.90 (11.55)
12.85 (12.68)
13.20
10.99 (11.70)
13.43 (13.24)

OH
22.42
19.30 (20.69)
22.96 (22.67)
12.29
10.60 (11.34)
12.57 (12.43)
12.72
10.61 (11.30)
12.98 (12.81)

H
22.01
19.00 (20.28)
22.45 (22.07)
12.33
10.50 (11.17)
12.55 (12.35)
12.33
10.50 (11.20)
12.55 (12.35)

OF
20.10
17.60 (18.89)
20.70 (20.56)
10.99
9.59 (10.29)
11.29 (11.21)
11.56
9.82 (10.50)
11.86 (11.76)

CN
18.33
16.00 (17.10)
18.76 (18.42)
10.21
8.66 (9.26)
10.41 (10.22)
10.43
9.03 (9.62)
10.64 (10.46)

NO₂
17.59
15.50 (16.74)
18.14 (17.95)
9.85
8.40 (9.04)
10.10 (9.99)
10.03
8.88 (9.50)
10.30 (10.19)

F
20.30
17.60 (18.86)
20.84 (20.57)
11.20
9.65 (10.28)
11.46 (11.31)
11.63
9.86 (10.50)
11.89 (11.75)

Br
20.28
17.70 (18.86)
20.79 (20.42)
11.16
9.63 (10.23)
11.41 (11.23)
11.51
9.89 (10.50)
11.75 (11.58)

Cl
20.29
17.70 (18.81)
20.80 (20.44)
11.18
9.65 (10.22)
11.43 (11.24)
11.55
9.91 (10.50)
11.80 (11.61)

The data in the parenthesis correspond to the aug-cc-pVDZ basis set.

The results of single-point energy calculation at the MP2/6-311++G (d,p), MP2/aug-cc-pVDZ, PBE1KCIS/6-311++G(d,p), and PBE1KCIS/aug-cc-pVDZ levels of theory on the geometries optimized at the B3LYP/6-311++G(d,p) level of theory are also given in Table 2. The maximum and minimum ΔE values correspond to N(CH₃)₂ and NO₂ substituents, respectively, at all levels of theory.

The ΔE values calculated by the MP2 method increase by 13.8 to 7.6 percent going from 6-311++G(d,p) to aug-cc-pVDZ basis sets. The corresponding changes are in the range of −0.51 to −0.19 kcal mol−1  for the values calculated by the PBE1KCIS method.

The absolute values of ΔE calculated at the MP2/6-311++G(d,p) level are 2.07 to 4.22 kcal mol⁻¹ smaller than those calculated at the B3LYP/6-311++G(d,p) level. The absolute values of ΔE calculated by the PBE1KCIS method are approximately 3.54 to 0.51 kcal mol−1  larger than the values calculated by the MP2 and B3LYP methods. The ΔE values calculated at the PBE1KCIS/aug-cc-pVDZ level are approximately identical with the values calculated at the B3LYP/6-311++G(d,p) level of theory.

The BSSE-corrected binding energies of the complex 1 are lower than the sum of binding energies of the complexes 2 and 3 (see Table 2). In addition, the stabilization energies of complexes become more negative by the electron-donating substituents (with the exception of the OH substituent in the complex 2) relative to the pyridazine, while the behavior is reversed by the electron-withdrawing substituents.

The total substituent effect comprises inductive/field effects, which have electrostatic character, and resonance effects, which are not electrostatic in nature. Resonance effects are strongest at para position, while the electrostatic interactions inversely depend on distance [38, 39]. The Hammett substituent constants are presented in Table 1 [37]. For the N(CH₃)₂, NHCH₃, NH₂, CH₃, and C₂H₅ substituents, the values are more negative than the values, so, the electron donation of the aforementioned substituents in the complex 3 is higher than that in the complex 2. The high electronegativity of oxygen makes the OCH3   and OH substituents electron-withdrawing by the inductive effect; this is reflected in the positive value for .

Recall that the meta substituents only affect the reaction center by the inductive effects, whereas the para substituents affect it by both the inductive and resonance effects. Thus, there is a satisfactory linear relationship between ΔE and , ΔE and , respectively, in the complexes 2 and 3. Comparing the σ values for the meta and para indicates that the electron-donating resonance effect () dominates over the electron-withdrawing inductive effect (). Therefore, these substituents are more electron-donating in the complex 3 in comparison to the complex 2. The   and   values are positive for the OF, CN, NO₂, F, Br, and Cl substituents. Thus, these substituents are electron-withdrawing in both the meta and para positions. Comparison between the values for the meta and para indicates that the dominates over the . Since the inductive effect is inversely related to distance, the electron-withdrawing inductive effects are stronger in the complex 2 in comparison with the complex 3.

The and constants can be used as appropriate parameters for the description of the intermolecular interaction in the X-pyridazine(HF)2  complex. The linear correlation coefficient between the ΔE values and the , , and constants is equal to 0.95, 0.97, and 0.98, respectively. This indicates that the total electrostatic effect of the substituents as well as induction and resonance vitally impacts the two intermolecular interactions (see Figure 1).

Figure 1: Correlation between the binding energies (−ΔE in kcal mol⁻¹) and Hammett constant σ total for the complex 1.

3.1. AIM and NBO Analysis

A way to characterize the hydrogen bond is AIM analysis that interprets these interactions in terms of critical points [40, 41]. The values of electron density () calculated at the N₂H and N₁H bond critical points (BCPs) of complexes 1–3 are gathered in Table 3.

Table 3: Electron densities (in e/au³) at the NH BCP in the X-pyridazine(HF)n() complexes and individual H-bond energies (in kcal mol⁻¹) calculated for the complex 1.

Complex 1
Complex 2
Complex 3

N(CH₃)₂
5.46, 5.23
13.44
6.03
6.16

NHCH₃
5.40, 5.15
13.18
5.95
5.95

NH₂
5.32, 5.05
12.73
5.82
5.97

CH₃
4.99, 4.95
12.21
5.69
5.69

C₂H₅
5.02, 5.00
12.67
5.73
5.74

OCH₃
5.08, 4.91
12.29
5.60
5.79

OH
5.02, 4.79
11.75
5.56
5.65

H
4.83, 4.83
12.04
5.54
5.54

OF
4.70, 4.55
10.81
5.19
5.35

CN
4.45, 4.43
10.15
5.01
5.07

NO₂
4.42, 4.45
10.19
4.90
4.90

F
4.71, 4.57
10.92
5.23
5.36

Br
4.69, 4.61
11.02
5.24
5.33

Cl
4.69, 4.60
11.02
5.25
5.35

The bold and italicized values correspond to the N₁H and N₂H hydrogen bonds, respectively.

The maximum and minimum values correspond to the N(CH₃)₂ and NO2  substituents, respectively, (with the exception of in the complex 1 where the minimum value corresponds to the CN substituent). The topological properties of calculated at the BCP of the intermolecular hydrogen bonds may be treated as a measure of the hydrogen bond strength [42–44]. The electron-withdrawing substituents pull the lone pair of nitrogen atoms of pyridazine inside the ring and decrease the values at the NH BCP, while the electron-donating substituents increase the values and enhance the hydrogen bond strength. The values calculated at the NH BCP in the complex 3 are higher than those in the complex 2, and the complex 3 is more stable than the complex 2. On the other hand, the values of NH hydrogen bond of complex 1 are lower than the values calculated at the N₂H and N₁H hydrogen bonds in the complexes 2 and 3. Thus, a negative cooperativity is predicted from the comparison between ρ N⋯H values in the complex 1 and the complexes 2 and 3. The NH bond length decreases linearly by the increase in the values calculated at the NH BCP for all categories . Also, there is a linear relationship between and ΔE for all cases. A linear relationship is observed between the ΔE values calculated at the B3LYP/6-311++G(d,p) level and the values calculated at the NH BCPs in the complex 1.

Because of linear relationship between ΔE and values, the can be used for the calculation of individual H-bond energies in the complex 1 (see Table 4). All individual H-bond energies calculated for the complex 1 are lower than the values calculated for the complexes 2 and 3. Also, there is a linear relationship with high correlation coefficient () between individual H-bond energies and the NH bond lengths.

Table 4: The results of NBO analysis for the X-pyridazine(HF)n () complexes at the HF/6-311++G(d,p) level of theory.

Complex 1
Complex 2
Complex 3

lpN
σ * HF (× 10²)

lpN
σ * HF (×10²)

lpN
σ * HF (×10²)

N(CH₃)₂
34.16, 30.47
1.911, 1.914
4.509, 5.030
39.48
1.904
5.767
42.41
1.902
6.166

NHCH₃
33.46, 29.71
1.912, 1.915
4.395, 4.934
38.66
1.906
5.651
41.79
1.903
6.087

NH₂
32.52, 28.72
1.913, 1.917
4.236, 4.793
37.35
1.908
5.438
40.05
1.905
5.838

CH₃
28.59, 27.95
1.919, 1.920
4.148, 4.239
36.07
1.911
5.289
36.44
1.910
5.333

C₂H₅
28.94, 28.42
1.919, 1.919
4.213, 4.288
36.62
1.910
5.394
36.91
1.910
5.399

OCH₃
29.60, 27.51
1.917, 1.920
5.604, 5.946
35.08
1.912
5.101
37.70
1.900
5.503

OH
29.01, 25.99
1.918, 1.921
3.859, 4.286
34.39
1.912
5.031
36.12
1.910
5.273

H
26.79, 26.73
1.921, 1.921
3.982, 3.982
34.69
1.912
5.093
34.69
1.912
5.093

OF
25.44, 23.61
1.922, 1.924
4.931, 5.238
30.95
1.918
4.520
32.49
1.915
4.760

CN
22.58, 22.52
1.928, 1.926
3.348, 3.352
28.57
1.919
4.200
29.04
1.921
4.259

NO₂
21.48, 21.68
1.929, 1.928
4.566, 4.556
27.26
1.922
3.993
27.64
1.922
4.041

F
25.50, 23.92
1.922, 1.925
3.533, 3.785
30.95
1.918
4.520
32.63
1.914
4.774

Br
25.29, 24.36
1.923, 1.923
3.622, 3.757
31.14
1.915
4.575
32.23
1.916
4.723

Cl
25.36, 24.28
1.923, 1.923
3.602, 3.763
31.16
1.916
4.570
32.40
1.915
4.745

The values are in kcal mol⁻¹. The bold and italicized values correspond to the N₁H and N₂H bonds, respectively.

For a better understanding of the hydrogen bond interaction in the complexes 1–3, the NBO analysis has been carried out at the HF/6-311++G(d,p) level of theory. The lpN→σ*HF interaction, which can be considered as a measure of charge transfer, has been evaluated in the complexes 1–3 (see Table 5). The donor-acceptor interaction energy value of this interaction can be used to predict the strength of the N···H hydrogen bond. In all cases, the maximum and minimum values correspond to the N(CH₃)₂ and NO₂ substituents, respectively. As can be seen in Table 4, the E² values of the →σ*HF   and →σ*HF  interactions in the complexes 2 and 3 are higher than those in the complex 1. So, the negative cooperativity decreases the E² values of →σ*HF  and →σ*HF  donor-acceptor interactions in the complex 1 relative to the complexes 2 and 3. The electron-donating substituents increase the electron density on the nitrogen atoms of pyridazine ring (with the exception of OH substituent in the complex 2) and increase their inclination on polarization of HF, which increase the value of the lpN→σ*HF interaction. Though OH is an electron-donating substituent, but it destabilizes the complex 2 relative to the pyridazine. This behavior is not observed for the OCH₃ functional group. The NBO atomic charge on the O (−0.71) of OH substituent is more negative than O (−0.61) of the OCH₃ substituent. Thus, electron-withdrawing induction effect is predominant over the electron-donating resonance effect by the high electronegativity of O atom in the OH substituent. Moreover, there are good linear relationships between the values and both the values and NH bond lengths.

Table 5: The results of MEP analysis () and charge transfer ( in au) calculated from ChelpG charges.

Complex 1
Complex 2
Complex 3

N(CH₃)₂
97
205, 194
103
295
107
309

NHCH₃
96
199, 187
101
282
106
293

NH₂
94
193, 189
99
283
103
294

CH₃
87
189, 195
96
294
97
291

C₂H₅
88
190, 200
97
292
98
296

OCH₃
89
181, 204
98
288
99
295

OH
86
192, 188
92
293
96
295

H
84
194, 195
94
300
94
300

OF
79
182, 182
88
278
89
280

CN
73
175, 185
83
277
82
279

NO₂
72
178, 182
81
278
80
270

F
79
186, 181
88
280
89
279

Br
80
213, 163
89
325
90
328

Cl
80
189, 176
89
275
90
285

The bold and italicized values correspond to the charge transfer from N₁ and N₂ atoms to HF unit, respectively.

The occupation numbers of , , and σ*HF are given in Table 4. The maximum and minimum occupancies for   and   correspond to NO₂ and N(CH₃)₂, respectively, the maximum and minimum occupancies of σ*HF  correspond to N(CH₃)₂ and NO₂, respectively. As can be seen in Table 4, increasing the occupation numbers of   and   is accompanied with the decrease in the occupation number of σ*HF for all complexes. The occupancies of   and   in the complex 1 are larger than those in the complexes 2 and 3, while the occupancy of σ*HF in the complexes 2 and 3 is larger than that in the complex 1. Thus, the occupancy of the first lpN/σ*HF increases/decreases in the presence of second NHF interaction. This confirms the negative cooperativity in the complex 1. There is a little difference between the occupancies of and in the complexes 2 and 3. Also, the occupancy of σ*HF in the complex 3 is larger than that in the complex 2. Therefore, the changes of occupation numbers of , , and σ*HF  are in agreement with the binding energies in all categories. A linear relationship is observed between the ΔE values and the sum of values of →σ*HF  and →σ*HF in the complex 1. The high linear correlation indicates the additivity of the values of two H-bond interactions.

There is also a linear relationship between the values and the occupancies of , ,  and   . In addition, there is a linear relationship between and NH hydrogen bond lengths in three categories. Linear relationships are observed for the value of →σ*HF    versus and the values of → σ*HF    versus in the complex 1.

On the base of charges calculated by the ChelpG method (see Table 5), the charge transfer occurred from X-pyridazine to HF unit, The electron-donating substituents promote the charge transfer from X-pyridazine to HF unit, and enhance the basicity of the nitrogen atoms in the X-pyridazine. In the complex 3, the charge transfer is larger and the basicity of N atom is higher than those in the complex 2; this can be a reason for the stability of complex 3. On the other hand, the charge transfer in the complex 1 is lower than that in complexes 2 and 3; this is in agreement with the negative cooperativity of two hydrogen bond interactions.

3.2. MEP Analysis

The MEP is an important tool in exploring the nature of intermolecular interactions [45–51]. The capability of the N₂ and N₁ atoms to accept hydrogen bond was estimated through the minimum of the MEP   around the nitrogen atoms. As can be seen in Table 5, the MEP values become more negative with the electron-donating substituents. Thus, the electrostatic term depends on the electron donation or electron withdrawal character of the substituents. Also, a good linear relationship is observed between the   values and the values (see Figure 2). Therefore, those values can be used to predict the Hammett constants. The trend in the   values is 3 > 2 > 1; so, those values become less negative around the nitrogen atoms when both interactions coexist.

Figure 2: Linear correlation between molecular electrostatic potential minimum () around the nitrogen atoms of the pyridazine and the Hammett electronic parameters for the complex 1.

The MEP, , is directly related to electron density through the Poisson’s equation [52]: Is there a liner relationship between   and the values calculated at the HBCPs? The   values become more negative with increasing values calculated at HBCPs in X-pyridazine(HF)n complexes. The linear correlation coefficients between the   values and the values are equal to 0.98 and 0.99, respectively, in the complexes 2 and 3. As can be seen in Figure 3, there is a good correlation between   values and values for the complex 1 (). Similarly, there is a linear relationship () between and of lpN→σ*HF  interaction, ,  and the N₂H and N₁H bond lengths. Also, there is a good linear correlation between   values and in the complex 1 ().

Figure 3: Interplay between the   value around the nitrogen of pyridazine versus the sum of values calculated at the NH BCPs for complex 1.

3.3. SAPT Energy Decomposition

The SAPT analysis is a method for investigation the nature of the intermolecular interactions [53–55]. The SAPT method provides detailed information on the intermolecular interaction, as this method directly calculates magnitude of each term (electrostatic, dispersion, etc.) of the intermolecular interactions [56]. A detailed description of SAPT and some of its applications can be found in some recent references [57–59].

To determine the nature of the hydrogen bond in the complexes 2 and 3, the interaction energies were decomposed into physically meaningful components, including electrostatic, induction, dispersion, and exchange energies, using SAPT technique at the B3LYP/6-31G(d) level. It can be seen from Table 6 that the values of electrostatic energy ,  induction energy , and dispersion energy are negative, whereas the exchange energy   is positive for all complexes. Thus, the stabilization/destabilization of the complexes by substitution is represented simply by the sum from , ,  and   contributions. In both complexes, the absolute values for these three negative terms are largest for the N(CH₃)₂ substituent and are smallest for the NO₂ substituent. In the complex 3, the absolute values of , ,  and   are larger than those values in the complex 2. Thus, the complex 3 is more stable than the complex 2. The electron-donating substituents have positive effect and increase the magnitude of the calculated SAPT interaction energy components (with the exception of OH substituent in the complex 2 that decreases the magnitude of electrostatic energy relative to pyridazine). The electron-withdrawing substituents have negative effect and decrease the magnitude of interaction energy components, with the exception of   in the complex 2 that slightly increases in the presence of mentioned substituents. The dependence of the dispersion term to the substituent is smaller than other complexes. When position of HF changes from para to meta relative to the substituent, the electrostatic term changes by 2.8%, the induction term changes by 2.2%, and the dispersion term changes by 12.5%. Thus, the dispersion energy component of the SAPT analysis was found to be very sensitive to the position of HF relative to the substituent.

Table 6: SAPT interaction energy decomposition (in kcal mol⁻¹) for the complexes 2 and 3.

Complex 2
Complex 3

N(CH₃)₂
−25.53
−17.74
34.24
−5.16
−14.18
−26.21
−18.48
35.29
−5.27
−14.67

NHCH₃
−25.15
−17.41
33.69
−5.08
−13.94
−25.93
−18.29
35.00
−5.22
−14.45

NH₂
−24.34
−16.81
32.71
−4.95
−13.39
−25.16
−17.66
33.94
−5.09
−13.97

CH₃
−23.5
−16.35
31.87
−4.84
−12.83
−23.51
−16.40
31.90
−4.84
−12.84

C₂H₅
−23.73
−16.53
32.16
−4.88
−12.98
−23.75
−16.59
32.23
−4.88
−13.00

OCH₃
−22.95
−15.86
31.01
−4.75
−12.55
−23.99
−16.83
32.64
−4.94
−13.11

OH
−22.62
−15.72
30.90
−4.74
−12.19
−23.08
−16.16
31.54
−4.80
−12.51

H
−22.80
−14.89
29.63
−4.06
−12.12
−22.70
−15.73
30.81
−4.69
−12.31

OF
−20.06
−14.07
27.96
−4.41
−10.59
−21.04
−14.78
29.27
−4.54
−11.09

CN
−18.92
−13.48
26.85
−4.28
−9.84
−19.37
−13.65
27.22
−4.31
−10.11

NO₂
−18.05
−12.92
25.87
−4.17
−9.28
−18.64
−13.06
26.27
−4.20
−9.62

F
−20.35
−14.27
28.35
−4.43
−10.71
−21.13
−14.84
29.39
−4.54
−11.12

Cl
−20.52
−14.49
28.57
−4.48
−10.93
−21.13
−14.84
29.29
−4.55
−11.23

All energies are in kcal mol⁻¹. .

In the complex 2, the electrostatic forces contribute about 52.0–54.6% to the total attractive interaction energy, the induction forces are about 35.6–43.6% of the total attractive energy, and the dispersion contribution is 9.7–11.9%. On the other hand, the electrostatic, induction, and dispersion contributions are 51.9–52.6%, 36.4–37.0%, and 10.5–11.7%, respectively, in the complex 3. Thus, we believe that the electrostatic interactions are mainly responsible for the binding energies and formation of hydrogen bonds, although the induction and dispersion interactions are also important. Since the electrostatic plays an important role, the polarization correlates with the electrostatic energy. The electron-withdrawing substituents hinder the electron transfer-driven polarization to the HF unit (which results in destabilization), whereas the electron-donating substituents allow strong polarization to the HF unit (which results in strong stabilization). It is also interesting to note that the polarization for the electron-donating and electron-withdrawing substituents in the complex 2 is slightly weaker than that in the complex 3. In the complex 3, the electron density at the para position is an important stabilizing factor, and thus the stabilization/destabilization by substituent of a pyridazine is governed mostly by the electrostatic energy. In Figure 4, a linear relationship with high correlation coefficient   is observed between the calculated SAPT interaction energy components and σ p  in the complex 3. In the complex 2, a linear relationship with correlation coefficient 0.96 is found between the Eels and σ m.

(a)

(b)

Figure 4: Linear relationship between the calculated SAPT interaction energy components (● , ■ , and ▲ in kcal mol⁻¹) and for the complex 3 (a), and the electrostatic energy and for the complex 2 (b).

4. Conclusions

The results of quantum mechanical calculations indicate that the binding energy in the complex 3 is larger than that in the complex 2. The sum of binding energies of the complexes 2 and 3 is larger than the binding energy of the complex 1. So, there is a negative cooperativity for two hydrogen bond interactions.

Very good linear correlations are observed between the binding energies and Hammett electronic parameters σ total of the substituents. The electron-donating substituents stabilize and the electron-withdrawing substituents destabilize the complexes relative to pyridazine. According to the results of AIM analysis, the cooperativity effect decreases the electron density at the NH BCPs in the X-pyridazine(HF)₂ complex.

On the basis of the results of SAPT analysis, the portion of electrostatic force in the complex 3 is smaller than 2, while the induction and dispersion portions are larger in the complex 3. The values of →σ*HF and →σ*HF interactions in the complex 1 are smaller than those in the complexes 2 and 3. Thus, the cooperativity effect decreases the values of →σ*HF and →σ*HF interactions in the complex 1. The occupation numbers of and in the complex 1 are larger than those in the complexes 2 and 3, respectively. The charge transfer, on the basis of ChelpG charges, is in agreement with the results of NBO and AIM analysis.

There are linear relationships between the   and values, the   and the values of lpN→σ*HF  interaction, and between the   and the   values.

The SAPT calculations show that the electrostatic is the dominating interaction component in the complexes 2 and 3, although the induction and dispersion interactions are also important. The dispersion energy component of the SAPT analysis was found to be very sensitive to the position of HF relative to the substituent. There is a good correlation between   and the calculated SAPT interaction energy components in the complex 3, while the linear relationship is only found between the   and in the complex 2.

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