# The N⋯HF Interactions in the X-Pyridazine⋯(HF)2 Complexes: Substituent Effects and Energy Components

Authors: Ali Ebrahimi; Mostafa Habibi-Khorassani; Farideh Badichi Akher; Abdolkarim Farrokhzadeh
Journal: Advances in Physical Chemistry
 (2012)

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## Abstract

The effects of substituents on the N⋯HF interactions in the X-pyridazine⋯(HF)n (X = N(CH3)2, NHCH3, NH2, C2H5, CH3, OCH3, OH, CN, OF, NO2, F, Br, Cl, and n=1, 2) 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 Eexch/Edisp 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.


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## Body

## 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 (n=1,2) 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 n=1,2).


## 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 (Vmin) 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 Table1. The maximum and minimum values of the N⋯H bond length correspond to NO2 and N(CH3)2 substituents, respectively, in all cases. Also, the N⋯H bond length in the complex 1is longer than that in the complexes 2 and 3. On the other hand, the N⋯H bond length in the complex 2is longer than that in the complex 3. These results show that the cooperativity of H-bond interactions leads to the elongation of the N⋯H bond lengths.Table 1
The N⋯H bond lengths optimized at the B3LYP/6-311++G(d,p) level in (Å) and the Hammett constants.
Bond lengthHammett constantsComplex1Complex2Complex3σmσpσtotalσIσRN(CH3)21.67 (1.69)1.641.63−0.15−0.83−0.980.15−0.98NHCH31.68 (1.70)1.651.63−0.52−0.74−1.260.03−0.73NH21.68 (1.71)1.651.64−0.16−0.66−0.820.08−0.74CH31.71 (1.71)1.661.66−0.07−0.17−0.240.01−0.18C2H51.71 (1.71)1.661.66−0.07−0.15−0.220.00−0.15OCH31.70 (1.72)1.671.650.12−0.27−0.150.29−0.56OH1.71  (1.73)1.671.660.12−0.37−0.250.30−0.70H1.72 (1.72)1.671.670.000.000.00OF1.73 (1.74)1.701.680.470.360.83CN1.75 (1.70)1.711.700.560.661.220.510.15NO21.76 (1.76)1.721.710.710.781.490.600.13F1.73 (1.74)1.691.680.340.060.400.45−0.39Br1.73 (1.74)1.691.690.390.230.620.40−0.22Cl1.73 (1.74)1.691.680.370.230.600.42−0.19The data in the parentheses correspond to the N2⋯H 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 3are 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.
Complex1Complex2Complex3B3LYPMP2PBE1KCISB3LYPMP2PBE1KCISB3LYPMP2PBE1KCISN(CH3)225.7521.90 (23.52)26.22 (25.86)13.9211.90 (12.81)14.19 (14.03)14.4811.72 (12.70)14.71 (14.49)NHCH325.3221.80 (23.23)25.81 (25.42)13.7312.00 (12.74)13.99 (13.82)14.3111.82 (12.60)14.54 (14.31)NH224.5120.30 (22.12)25.06 (24.66)13.2711.30 (12.14)13.55 (13.38)13.8811.14 (12.10)14.15 (13.91)CH322.9819.80 (21.10)23.44 (23.07)12.8010.90 (11.63)13.03 (12.85)12.8610.82 (11.50)13.08 (12.88)C2H523.3419.80 (21.44)23.88 (23.64)13.0110.90 (11.86)13.32 (13.24)13.0910.78 (11.80)13.40 (13.31)OCH323.1919.90 (21.24)23.65 (23.31)12.6110.90 (11.55)12.85 (12.68)13.2010.99 (11.70)13.43 (13.24)OH22.4219.30 (20.69)22.96 (22.67)12.2910.60 (11.34)12.57 (12.43)12.7210.61 (11.30)12.98 (12.81)H22.0119.00 (20.28)22.45 (22.07)12.3310.50 (11.17)12.55 (12.35)12.3310.50 (11.20)12.55 (12.35)OF20.1017.60 (18.89)20.70 (20.56)10.999.59 (10.29)11.29 (11.21)11.569.82 (10.50)11.86 (11.76)CN18.3316.00 (17.10)18.76 (18.42)10.218.66 (9.26)10.41 (10.22)10.439.03 (9.62)10.64 (10.46)NO217.5915.50 (16.74)18.14 (17.95)9.858.40 (9.04)10.10 (9.99)10.038.88 (9.50)10.30 (10.19)F20.3017.60 (18.86)20.84 (20.57)11.209.65 (10.28)11.46 (11.31)11.639.86 (10.50)11.89 (11.75)Br20.2817.70 (18.86)20.79 (20.42)11.169.63 (10.23)11.41 (11.23)11.519.89 (10.50)11.75 (11.58)Cl20.2917.70 (18.81)20.80 (20.44)11.189.65 (10.22)11.43 (11.24)11.559.91 (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 Table2. 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−1for 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−1larger 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 complex1 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 σp values are more negative than the σm 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 OCH3and OH substituents electron-withdrawing by the inductive effect; this is reflected in the positive value for σm.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 σI(R=0.91), ΔE and σI+σR(R=0.98), respectively, in the complexes 2 and 3. Comparing the σ values for the meta and para indicates that the electron-donating resonance effect (σR) dominates over the electron-withdrawing inductive effect (σI). Therefore, these substituents are more electron-donating in the complex 3 in comparison to the complex 2. The σm  and σp  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 σ values for the meta and para indicates that the σI dominates over the σR. 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.Theσm and σp constants can be used as appropriate parameters for the description of the intermolecular interaction in the X-pyridazine⋯(HF)2complex. The linear correlation coefficient between the ΔE values and the σm, σp, and σtotal(σm+σp) 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 σtotal 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 (ρ) calculated at the N2⋯H and N1⋯H bond critical points (BCPs) of complexes 1–3are gathered in Table 3.Table 3
Electron densitiesρ (in e/au3) at the N⋯H BCP in the X-pyridazine⋯(HF)n(n=1,2) complexes and individual H-bond energies E (in kcal mol−1) calculated for the complex 1.
Complex1Complex2Complex3ρBCP×102EρBCP×102ρBCP×102N(CH3)25.46, 5.23-14.41,-13.446.036.16NHCH35.40, 5.15-14.23,-13.185.955.95NH25.32, 5.05-13.85,-12.735.825.97CH34.99, 4.95-12.36,-12.215.695.69C2H55.02, 5.00-12.76,-12.675.735.74OCH35.08, 4.91-12.98,-12.295.605.79OH5.02, 4.79-12.66,-11.755.565.65H4.83, 4.83-12.04,-12.045.545.54OF4.70, 4.55-11.37,-10.815.195.35CN4.45, 4.43-10.22,-10.155.015.07NO24.42, 4.45-10.08,-10.194.904.90F4.71, 4.57-11.46,-10.925.235.36Br4.69, 4.61-11.33,-11.025.245.33Cl4.69, 4.60-11.36,-11.025.255.35The bold and italicized values correspond to the N1⋯H and N2⋯H hydrogen bonds, respectively.The maximum and minimum values correspond to the N(CH3)2 and NO2substituents, respectively, (with the exception of ρN2H in the complex 1 where the minimum value corresponds to the CN substituent). The topological properties of ρ 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 ρ values at the N⋯H BCP, while the electron-donating substituents increase the ρ values and enhance the hydrogen bond strength. The ρ values calculated at the N⋯H 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 ρ values of N⋯H hydrogen bond of complex 1 are lower than the values calculated at the N2⋯H and N1⋯H hydrogen bonds in the complexes 2 and 3. Thus, a negative cooperativity is predicted from the comparison between ρN⋯H values in the complex 1and the complexes 2 and 3. The N⋯H bond length decreases linearly by the increase in the ρ values calculated at the N⋯H BCP for all categories (R2≃0.99). Also, there is a linear relationship between ρ and ΔE for all cases. A linear relationship (R2=0.99) is observed between the ΔE values calculated at the B3LYP/6-311++G(d,p) level and the ρ values calculated at the N⋯H BCPs in the complex 1.Because of linear relationship between ΔEand ρNH values, the ΔE=cρNH 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 (R=0.99) between individual H-bond energies and the N⋯H bond lengths.Table 4
The results of NBO analysis for the X-pyridazine⋯(HF)n (n=1,2) complexes at the HF/6-311++G(d,p) level of theory.
Complex1Complex2Complex3E2lpNσ
*
HF (× 102)E2lpNσ
*
HF (×102)E2lpNσ
*
HF (×102)N(CH3)234.16, 30.471.911, 1.9144.509, 5.03039.481.9045.76742.411.9026.166NHCH333.46, 29.711.912, 1.9154.395, 4.93438.661.9065.65141.791.9036.087NH232.52, 28.721.913, 1.9174.236, 4.79337.351.9085.43840.051.9055.838CH328.59, 27.951.919, 1.9204.148, 4.23936.071.9115.28936.441.9105.333C2H528.94, 28.421.919, 1.9194.213, 4.28836.621.9105.39436.911.9105.399OCH329.60, 27.511.917, 1.9205.604, 5.94635.081.9125.10137.701.9005.503OH29.01, 25.991.918, 1.9213.859, 4.28634.391.9125.03136.121.9105.273H26.79, 26.731.921, 1.9213.982, 3.98234.691.9125.09334.691.9125.093OF25.44, 23.611.922, 1.9244.931, 5.23830.951.9184.52032.491.9154.760CN22.58, 22.521.928, 1.9263.348, 3.35228.571.9194.20029.041.9214.259NO221.48, 21.681.929, 1.9284.566, 4.55627.261.9223.99327.641.9224.041F25.50, 23.921.922, 1.9253.533, 3.78530.951.9184.52032.631.9144.774Br25.29, 24.361.923, 1.9233.622, 3.75731.141.9154.57532.231.9164.723Cl25.36, 24.281.923, 1.9233.602, 3.76331.161.9164.57032.401.9154.745TheE2 values are in kcal mol−1. The bold and italicized values correspond to the N1⋯H and N2⋯H bonds, respectively.For a better understanding of the hydrogen bond interaction in the complexes1–3, 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 (E2) 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 lpN2→σ*HF   and lpN1→σ*HFinteractions in the complexes 2 and 3are higher than those in the complex 1. So, the negative cooperativity decreases the E2 values of lpN2→σ*HF  and lpN1→σ*HFdonor-acceptor interactions in the complex 1relative 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 E2 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 E2 values and both the σtotal values and N⋯H bond lengths.Table 5
The results of MEP analysis (Vmin×103) and charge transfer (Δq×103 in au) calculated from ChelpG charges.
Complex1Complex2Complex3VminΔqVminΔqVminΔqN(CH3)297205,194103295107309NHCH396199,187101282106293NH294193,18999283103294CH387189,1959629497291C2H588190,2009729298296OCH389181,2049828899295OH86192,1889229396295H84194,1959430094300OF79182,1828827889280CN73175,1858327782279NO272178,1828127880270F79186,1818828089279Br80213,1638932590328Cl80189,1768927590285The bold and italicized values correspond to the charge transfer from N1 and N2 atoms to HF unit, respectively.The occupation numbers oflpN2, lpN1, and σ*HF are given in Table 4. The maximum and minimum occupancies for lpN2  and lpN1  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 lpN2  and lpN1  is accompanied with the decrease in the occupation number of σ*HF for all complexes. The occupancies of lpN2  and lpN1  in the complex 1 are larger than those in the complexes2and 3, while the occupancy of σ*HF in the complexes 2and 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 N⋯HF interaction. This confirms the negative cooperativity in the complex 1. There is a little difference between the occupancies of lpN2 and lpN1 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 lpN2, lpN1, and σ*HFare in agreement with the binding energies in all categories. A linear relationship(R2=1.0) is observed between the ΔE values and the sum of E2 values of lpN1→σ*HF  and lpN1→σ*HF in the complex 1. The high linear correlation (R2=1.0) indicates the additivity of the E2 values of two H-bond interactions.There is also a linear relationship between theE2 values and the occupancies of lpN2, lpN1,  and   σHF*. In addition, there is a linear relationship between E2 and N⋯H hydrogen bond lengths in three categories. Linear relationships are observed for the E2 value of lpN2→σ*HFversus rN2⋯H(R2=0.98) and the E2 values of lpN1 → σ*HFversus rN1⋯H(R2=0.99) in the complex 1.On the base of charges calculated by the ChelpG method (see Table5), 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 (Vmin)  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 Vmin  values and the σtotal values (see Figure 2). Therefore, those values can be used to predict the Hammett constants. The trend in the Vmin  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 (Vmin) around the nitrogen atoms of the pyridazine and the Hammett electronic parameters for the complex 1.The MEP,V(r), is directly related to electron density ρ(r) through the Poisson’s equation [52]:(1)∇2V(r)=4πρ(r).
Is there a liner relationship between Vmin  and theρ values calculated at the HBCPs? The Vmin  values become more negative with increasing ρ values calculated at HBCPs in X-pyridazine⋯(HF)n complexes. The linear correlation coefficients between the Vmin  values and the ρvalues 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 Vmin  values and ∑ρ values for the complex 1 (R=1.00). Similarly, there is a linear relationship (R=0.99) between Vmin and E2 of lpN→σ*HF  interaction, Vmin,  and the N2⋯H and N1⋯H bond lengths. Also, there is a good linear correlation between Vmin  values and ∑E2  in the complex 1 (R=1.00).Figure 3
Interplay between theVmin  value around the nitrogen of pyridazine versus the sum of ρ values calculated at the N⋯H 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 complexes2 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 (Eels),  induction energy (Eind), and dispersion energy (Edisp) are negative, whereas the exchange energy (Eexch)  is positive for all complexes. Thus, the stabilization/destabilization of the complexes by substitution is represented simply by the sum from Eels, Eind,  and Edisp  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 Eels, Eind,  and Edisp  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 Edisp  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.
Complex2Complex3EelsEindEexchEdispEintSAPTEelsEindEexchEdispEintSAPTN(CH3)2−25.53−17.7434.24−5.16−14.18−26.21−18.4835.29−5.27−14.67NHCH3−25.15−17.4133.69−5.08−13.94−25.93−18.2935.00−5.22−14.45NH2−24.34−16.8132.71−4.95−13.39−25.16−17.6633.94−5.09−13.97CH3−23.5−16.3531.87−4.84−12.83−23.51−16.4031.90−4.84−12.84C2H5−23.73−16.5332.16−4.88−12.98−23.75−16.5932.23−4.88−13.00OCH3−22.95−15.8631.01−4.75−12.55−23.99−16.8332.64−4.94−13.11OH−22.62−15.7230.90−4.74−12.19−23.08−16.1631.54−4.80−12.51H−22.80−14.8929.63−4.06−12.12−22.70−15.7330.81−4.69−12.31OF−20.06−14.0727.96−4.41−10.59−21.04−14.7829.27−4.54−11.09CN−18.92−13.4826.85−4.28−9.84−19.37−13.6527.22−4.31−10.11NO2−18.05−12.9225.87−4.17−9.28−18.64−13.0626.27−4.20−9.62F−20.35−14.2728.35−4.43−10.71−21.13−14.8429.39−4.54−11.12Cl−20.52−14.4928.57−4.48−10.93−21.13−14.8429.29−4.55−11.23All energies are in kcal mol−1. EintSAPT=Eels+Eind+Edisp+Eexch.In the complex2, 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 (R=0.98)  is observed between the calculated SAPT interaction energy components and σpin the complex 3. In the complex 2, a linear relationship with correlation coefficient 0.96 is found between the Eels and σm.Linear relationship between the calculated SAPT interaction energy components (●Eels, ■ Eind, and ▲Edis in kcal mol−1) and σp for the complex 3 (a), and the electrostatic energy and σm for the complex 2 (b).
(a)(b)


## 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 (ρ) calculated at the N2⋯H and N1⋯H bond critical points (BCPs) of complexes 1–3are gathered in Table 3.Table 3
Electron densitiesρ (in e/au3) at the N⋯H BCP in the X-pyridazine⋯(HF)n(n=1,2) complexes and individual H-bond energies E (in kcal mol−1) calculated for the complex 1.
Complex1Complex2Complex3ρBCP×102EρBCP×102ρBCP×102N(CH3)25.46, 5.23-14.41,-13.446.036.16NHCH35.40, 5.15-14.23,-13.185.955.95NH25.32, 5.05-13.85,-12.735.825.97CH34.99, 4.95-12.36,-12.215.695.69C2H55.02, 5.00-12.76,-12.675.735.74OCH35.08, 4.91-12.98,-12.295.605.79OH5.02, 4.79-12.66,-11.755.565.65H4.83, 4.83-12.04,-12.045.545.54OF4.70, 4.55-11.37,-10.815.195.35CN4.45, 4.43-10.22,-10.155.015.07NO24.42, 4.45-10.08,-10.194.904.90F4.71, 4.57-11.46,-10.925.235.36Br4.69, 4.61-11.33,-11.025.245.33Cl4.69, 4.60-11.36,-11.025.255.35The bold and italicized values correspond to the N1⋯H and N2⋯H hydrogen bonds, respectively.The maximum and minimum values correspond to the N(CH3)2 and NO2substituents, respectively, (with the exception of ρN2H in the complex 1 where the minimum value corresponds to the CN substituent). The topological properties of ρ 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 ρ values at the N⋯H BCP, while the electron-donating substituents increase the ρ values and enhance the hydrogen bond strength. The ρ values calculated at the N⋯H 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 ρ values of N⋯H hydrogen bond of complex 1 are lower than the values calculated at the N2⋯H and N1⋯H hydrogen bonds in the complexes 2 and 3. Thus, a negative cooperativity is predicted from the comparison between ρN⋯H values in the complex 1and the complexes 2 and 3. The N⋯H bond length decreases linearly by the increase in the ρ values calculated at the N⋯H BCP for all categories (R2≃0.99). Also, there is a linear relationship between ρ and ΔE for all cases. A linear relationship (R2=0.99) is observed between the ΔE values calculated at the B3LYP/6-311++G(d,p) level and the ρ values calculated at the N⋯H BCPs in the complex 1.Because of linear relationship between ΔEand ρNH values, the ΔE=cρNH 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 (R=0.99) between individual H-bond energies and the N⋯H bond lengths.Table 4
The results of NBO analysis for the X-pyridazine⋯(HF)n (n=1,2) complexes at the HF/6-311++G(d,p) level of theory.
Complex1Complex2Complex3E2lpNσ
*
HF (× 102)E2lpNσ
*
HF (×102)E2lpNσ
*
HF (×102)N(CH3)234.16, 30.471.911, 1.9144.509, 5.03039.481.9045.76742.411.9026.166NHCH333.46, 29.711.912, 1.9154.395, 4.93438.661.9065.65141.791.9036.087NH232.52, 28.721.913, 1.9174.236, 4.79337.351.9085.43840.051.9055.838CH328.59, 27.951.919, 1.9204.148, 4.23936.071.9115.28936.441.9105.333C2H528.94, 28.421.919, 1.9194.213, 4.28836.621.9105.39436.911.9105.399OCH329.60, 27.511.917, 1.9205.604, 5.94635.081.9125.10137.701.9005.503OH29.01, 25.991.918, 1.9213.859, 4.28634.391.9125.03136.121.9105.273H26.79, 26.731.921, 1.9213.982, 3.98234.691.9125.09334.691.9125.093OF25.44, 23.611.922, 1.9244.931, 5.23830.951.9184.52032.491.9154.760CN22.58, 22.521.928, 1.9263.348, 3.35228.571.9194.20029.041.9214.259NO221.48, 21.681.929, 1.9284.566, 4.55627.261.9223.99327.641.9224.041F25.50, 23.921.922, 1.9253.533, 3.78530.951.9184.52032.631.9144.774Br25.29, 24.361.923, 1.9233.622, 3.75731.141.9154.57532.231.9164.723Cl25.36, 24.281.923, 1.9233.602, 3.76331.161.9164.57032.401.9154.745TheE2 values are in kcal mol−1. The bold and italicized values correspond to the N1⋯H and N2⋯H bonds, respectively.For a better understanding of the hydrogen bond interaction in the complexes1–3, 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 (E2) 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 lpN2→σ*HF   and lpN1→σ*HFinteractions in the complexes 2 and 3are higher than those in the complex 1. So, the negative cooperativity decreases the E2 values of lpN2→σ*HF  and lpN1→σ*HFdonor-acceptor interactions in the complex 1relative 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 E2 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 E2 values and both the σtotal values and N⋯H bond lengths.Table 5
The results of MEP analysis (Vmin×103) and charge transfer (Δq×103 in au) calculated from ChelpG charges.
Complex1Complex2Complex3VminΔqVminΔqVminΔqN(CH3)297205,194103295107309NHCH396199,187101282106293NH294193,18999283103294CH387189,1959629497291C2H588190,2009729298296OCH389181,2049828899295OH86192,1889229396295H84194,1959430094300OF79182,1828827889280CN73175,1858327782279NO272178,1828127880270F79186,1818828089279Br80213,1638932590328Cl80189,1768927590285The bold and italicized values correspond to the charge transfer from N1 and N2 atoms to HF unit, respectively.The occupation numbers oflpN2, lpN1, and σ*HF are given in Table 4. The maximum and minimum occupancies for lpN2  and lpN1  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 lpN2  and lpN1  is accompanied with the decrease in the occupation number of σ*HF for all complexes. The occupancies of lpN2  and lpN1  in the complex 1 are larger than those in the complexes2and 3, while the occupancy of σ*HF in the complexes 2and 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 N⋯HF interaction. This confirms the negative cooperativity in the complex 1. There is a little difference between the occupancies of lpN2 and lpN1 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 lpN2, lpN1, and σ*HFare in agreement with the binding energies in all categories. A linear relationship(R2=1.0) is observed between the ΔE values and the sum of E2 values of lpN1→σ*HF  and lpN1→σ*HF in the complex 1. The high linear correlation (R2=1.0) indicates the additivity of the E2 values of two H-bond interactions.There is also a linear relationship between theE2 values and the occupancies of lpN2, lpN1,  and   σHF*. In addition, there is a linear relationship between E2 and N⋯H hydrogen bond lengths in three categories. Linear relationships are observed for the E2 value of lpN2→σ*HFversus rN2⋯H(R2=0.98) and the E2 values of lpN1 → σ*HFversus rN1⋯H(R2=0.99) in the complex 1.On the base of charges calculated by the ChelpG method (see Table5), 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 (Vmin)  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 Vmin  values and the σtotal values (see Figure 2). Therefore, those values can be used to predict the Hammett constants. The trend in the Vmin  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 (Vmin) around the nitrogen atoms of the pyridazine and the Hammett electronic parameters for the complex 1.The MEP,V(r), is directly related to electron density ρ(r) through the Poisson’s equation [52]:(1)∇2V(r)=4πρ(r).
Is there a liner relationship between Vmin  and theρ values calculated at the HBCPs? The Vmin  values become more negative with increasing ρ values calculated at HBCPs in X-pyridazine⋯(HF)n complexes. The linear correlation coefficients between the Vmin  values and the ρvalues 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 Vmin  values and ∑ρ values for the complex 1 (R=1.00). Similarly, there is a linear relationship (R=0.99) between Vmin and E2 of lpN→σ*HF  interaction, Vmin,  and the N2⋯H and N1⋯H bond lengths. Also, there is a good linear correlation between Vmin  values and ∑E2  in the complex 1 (R=1.00).Figure 3
Interplay between theVmin  value around the nitrogen of pyridazine versus the sum of ρ values calculated at the N⋯H 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 complexes2 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 (Eels),  induction energy (Eind), and dispersion energy (Edisp) are negative, whereas the exchange energy (Eexch)  is positive for all complexes. Thus, the stabilization/destabilization of the complexes by substitution is represented simply by the sum from Eels, Eind,  and Edisp  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 Eels, Eind,  and Edisp  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 Edisp  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.
Complex2Complex3EelsEindEexchEdispEintSAPTEelsEindEexchEdispEintSAPTN(CH3)2−25.53−17.7434.24−5.16−14.18−26.21−18.4835.29−5.27−14.67NHCH3−25.15−17.4133.69−5.08−13.94−25.93−18.2935.00−5.22−14.45NH2−24.34−16.8132.71−4.95−13.39−25.16−17.6633.94−5.09−13.97CH3−23.5−16.3531.87−4.84−12.83−23.51−16.4031.90−4.84−12.84C2H5−23.73−16.5332.16−4.88−12.98−23.75−16.5932.23−4.88−13.00OCH3−22.95−15.8631.01−4.75−12.55−23.99−16.8332.64−4.94−13.11OH−22.62−15.7230.90−4.74−12.19−23.08−16.1631.54−4.80−12.51H−22.80−14.8929.63−4.06−12.12−22.70−15.7330.81−4.69−12.31OF−20.06−14.0727.96−4.41−10.59−21.04−14.7829.27−4.54−11.09CN−18.92−13.4826.85−4.28−9.84−19.37−13.6527.22−4.31−10.11NO2−18.05−12.9225.87−4.17−9.28−18.64−13.0626.27−4.20−9.62F−20.35−14.2728.35−4.43−10.71−21.13−14.8429.39−4.54−11.12Cl−20.52−14.4928.57−4.48−10.93−21.13−14.8429.29−4.55−11.23All energies are in kcal mol−1. EintSAPT=Eels+Eind+Edisp+Eexch.In the complex2, 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 (R=0.98)  is observed between the calculated SAPT interaction energy components and σpin the complex 3. In the complex 2, a linear relationship with correlation coefficient 0.96 is found between the Eels and σm.Linear relationship between the calculated SAPT interaction energy components (●Eels, ■ Eind, and ▲Edis in kcal mol−1) and σp for the complex 3 (a), and the electrostatic energy and σm for the complex 2 (b).
(a)(b)


## 4. Conclusions

The results of quantum mechanical calculations indicate that the binding energy in the complex3 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 parametersσtotal 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 N⋯H BCPs in the X-pyridazine⋯(HF)2 complex.On the basis of the results of SAPT analysis, the portion of electrostatic force in the complex3 is smaller than 2, while the induction and dispersion portions are larger in the complex 3. The E2 values of lpN2→σ*HF and lpN1→σ*HF interactions in the complex 1 are smaller than those in the complexes 2 and 3. Thus, the cooperativity effect decreases the E2 values of lpN2→σ*HF and lpN1→σ*HF interactions in the complex 1. The occupation numbers of lpN2 and lpN1 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 theVmin  and ρBCP values, the Vmin  and the E2 values of lpN→σ*HF  interaction, and between the Vmin  and the σtotal  values.The SAPT calculations show that the electrostatic is the dominating interaction component in the complexes2 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 σp  and the calculated SAPT interaction energy components in the complex 3, while the linear relationship is only found between the Eels  and σm in the complex 2.



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*Source: 362608-2012-04-09.xml*