J Mol Model (2014) 20:2436 DOI 10.1007/s00894-014-2436-9
ORIGINAL PAPER
Substituent effects on cooperativity of pnicogen bonds Mehdi D. Esrafili & Mojhgan Ghanbari & Fariba Mohammadian-Sabet
Received: 15 June 2014 / Accepted: 25 August 2014 # Springer-Verlag Berlin Heidelberg 2014
Abstract Substituent effects on cooperativity of P···N pnicogen bonds are studied in XH2P···NCH2P···NCY (X=F, Cl; Y=H, F, CN, OH, NH2) complexes using high-level ab initio calculations. An increased attraction or a positive cooperativity is observed on introduction of a third molecule to the XH2P···NCH2P and NCH2P···NCY dyads. The shortening of the each pnicogen bond distance in the triads is dependent on the strength of the P···N bond and is increased in the order Y = NH2 > OH > H > F > CN. The energy decomposition analysis indicates that the polarization energy is the important element in the interaction energy of P···N bond and may be regarded as being responsible for the stabilization in these systems. Natural bond orbital theory is used to characterize the interactions and analyze their enhancement with varying orbital interactions. Keywords ab initio . Cooperativity . Electrostatic potential . NBO . Pnicogen bond
Introduction The importance of noncovalent interactions has been recognized in a wide range of chemical and biophysical phenomena. They are responsible for stabilization of many important molecules, for example, DNA, proteins and enzyme-substrate complexes [1]. The classical hydrogen bond, an example of a strong intermolecular interaction, has been extensively studied Electronic supplementary material The online version of this article (doi:10.1007/s00894-014-2436-9) contains supplementary material, which is available to authorized users. M. D. Esrafili (*) : M. Ghanbari : F. Mohammadian-Sabet Laboratory of Theoretical Chemistry, Department of Chemistry, University of Maragheh, P.O. Box: 5513864596, Maragheh, Iran e-mail: [email protected]
from both theoretical and experimental viewpoints [2–5]. Halogen bonding is another important noncovalent interaction [6–11]. Like hydrogen bonding, halogen bonding involves sharing an atom (a halogen rather than a hydrogen) between a donor molecule R–X and an acceptor B. The R−X···B angle is typically close to 180°, which suggests that the halogen bond is a highly directional interaction. Halogen bond interactions play critical roles in a wide variety of biochemical phenomena such as protein–ligand complexation [12, 13], and can be utilized effectively in drug design [14, 15]. Recently, other weaker interactions, for example, nonclassical hydrogen bonds [16], π–π stacking [17, 18], and pnicogen bond [19–21] have been examined with a view to utilization in ligand binding and molecular folding. Pnicogen bonding is a much more recently defined concept. It can be defined as a rather strong, directional, noncovalent interaction of an electropositive pnicogen atom (N, P, As, Sb or Bi) and an electron donor [22–25]. Politzer and Murray [26–30] associated its origin with the presence of an electropositive region of the electrostatic potential in the prolongation of the R–Pn bond (where R is an electronwithdrawing group and Pn is a pnicogen atom), called “σhole”, that interacts with an electron-rich moiety of a Lewis base (B) through an essentially electrostatic Pn···B interaction. The size of the σ-hole increases with pnicogen size in going from the lighter to the heavier atoms, as polarizability increases and electronegativity decreases. However, Scheiner [20–25] and Alkorta et al. [31, 32] have demonstrated that charge transfer from the lone pair of the base to the σ*Pn−X orbital of the acid plays an essential role in the stabilization of complexes with pnicogen bonds. Pnicogen bond interaction has been widely studied, both experimentally [33, 34] and theoretically [19–32]. The pnicogen bonds involving phosphorous, in particular, have been an area of increasing interest over the past years due to their potential roles in medicinal chemistry and biological systems [35–38].
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Like hydrogen [39, 40] and halogen bonds [41–43], pnicogen bonds have been shown to have a cooperative effect with each other [44]. Thus, the strength of pnicogen bonds in the clusters usually increases as further molecules are added; also, the frequencies of some vibrational modes are shifted by effect of the incorporation of new molecule(s) in some pnicogen-bonded clusters. For example, Li et al. [45] found a positive cooperative effect between the pnicogen- and halogen-bonding interactions in XCl···FH2P···NH3 (X=F, OH, CN, NC, and FCC) complex. The increased value of the pnicogen and halogen bonds energies varies in the order: CCF CN. This reveals that the N atom in the NCH2P···NCY dyad is a stronger electron donor than that of free NCH2P molecule, which would enhance the attraction between the dyad and the XH2P in the XH2P···NCH2P···NCY complex. These findings are consistent with the enhanced interaction energies of the P···N in ternary systems relative to binary ones. Figure 4 shows a plot of MP2 interaction energies for the XH2P (NCH2P NCY) dyads versus the magnitudes of the product of VS,max and VS,min associated with P and N, respectively. The correlation is excellent, with a correlation coefficient R2 of 0.99. This may be a strong indicator of the electrostatically driven natures of these interactions. NBO analysis Further insight into the cooperativity of P···N pnicogen bond can be obtained by examining the NBO wave function overlaps (Fock matrix elements) Fij, the second-order perturbation stabilization energies E(2), and the amount of charge transfer qCT associated with the N lone pair → σ*P−X charge-transfer transitions across the pnicogen bond in
Table 5. One can see that for the XH 2P···NCH2P and NCH2P···NCY binary complexes, both Fij and E(2) values follow the same order with the interaction energies. That is, the largest E(2) value of NCH2P···NCY is found for the complex NCH2P···NCNH2, which has the stronger P···N interaction. The P···N bond in these complexes has some partial covalent character as indicated by its larger Eexch-rep and Epol terms. Moreover, for the FH2P···NCH2P complex, the Fij and E(2) values are greater than those for the ClH2P···NCH2P complexes. These indicate that the orbital interaction is of importance in formation of P···N pnicogen bonds. The strong cooperativity between the P N interactions is also reflected in the magnitude of the charge transfer qCT, which is accompanied by a typical elongation of the P–X and P–CN bond distances of the triads with respect to the binary systems. These qCT are listed in Table 4, and a clear correlation with the other properties is evident. That is, the stronger the pnicogen bond interaction, the larger the magnitude of the qCT. The strength of pnicogen bond can also be estimated with the Wiberg bond index (WBI) at the P···N bonds. This is the sum of squares of off-diagonal density matrix elements between the two atoms, which gives a measure of the bond interaction. For our purposes, it shows the extent of bond overlap associated with each pnicogen bond and it also weighs covalent character of the bond. Hence, the variation in the WBI value in a triad with respect to the corresponding dyads can be used to analyze the mutual influence of the two interactions. One sees from Table 4 that the
Fig. 4 Relationship between interaction energy of XH2P···(NCH2P···NCY) and the magnitude product of most positive and negative electrostatic potentials (VS,max ×VS,min)
J Mol Model (2014) 20:2436 Table 5 NBO analysis of donoracceptor interactions in XH2P···NCH2P···NCY complexes showing Fock matrix interaction elements Fij (in au), stabilization E(2) values (in kJ mol−1), charge transfer qCT (in e) and Wiberg bond index (WBI)
Page 7 of 9, 2436
Complex
A···B
B···C
Fij
E(2)
qCT
WBI
Fij
E(2)
FH2P···NCH2P
0.084
31.76
0.011
0.052
–
–
ClH2P···NCH2P NCH2P···NCH NCH2P···NCF NCH2P···NCCN NCH2P···NCOH NCH2P···NCNH2 FH2P···NCH2P···NCH FH2P···NCH2P···NCF FH2P···NCH2P···NCCN FH2P···NCH2P···NCOH FH2P···NCH2P···NCNH2 ClH2P···NCH2P···NCH ClH2P···NCH2P···NCF ClH2P···NCH2P···NCCN ClH2P···NCH2P···NCOH ClH2P···NCH2P···NCNH2
0.074 – – – – – 0.088 0.088 0.086 0.089 0.090 0.079 0.079 0.077 0.080 0.081
28.49 – – – – – 35.65 35.31 33.97 36.48 37.28 32.64 32.22 30.63 33.76 34.81
0.011 – – – – – 0.012 0.012 0.011 0.012 0.013 0.012 0.012 0.012 0.013 0.013
0.039 – – – – – 0.058 0.057 0.055 0.059 0.061 0.044 0.043 0.042 0.045 0.047
– 0.056 0.057 0.052 0.062 0.065 0.060 0.060 0.054 0.067 0.070 0.060 0.060 0.054 0.067 0.070
WBI at the P···N bond of FH2P···NCH2P is larger than that at ClH2P···NCH2P. This supports the fact that the pnicogen bond is stronger in the former complex. Moreover, it is evident that the WBI value associated to P···N bond in the triads are slightly greater than that in the corresponding dyads. This finding confirms that the pnicogen bond interactions in the triads are reinforced with respect to the binary systems. In fact, good linear correlations are found between the magnitudes of cooperative energy Ecoop and WBI values in the ternary systems (Fig. 5).
Conclusions In summary, we investigated the substituent effects on cooperative behavior between pnicogen bonds interactions in the
– 13.89 13.60 11.34 16.65 18.95 16.11 15.52 12.47 19.83 21.80 16.15 15.52 12.51 19.75 21.92
qCT
WBI
–
–
– 0.004 0.004 0.004 0.005 0.006 0.005 0.005 0.004 0.006 0.007 0.005 0.005 0.004 0.006 0.007
– 0.016 0.015 0.013 0.018 0.021 0.018 0.016 0.014 0.021 0.024 0.018 0.016 0.014 0.021 0.024
XH2P···NCH2P···NCY (X=F, Cl; Y= H, F, CN, OH, NH2) complexes using MP2/aug-cc-pVTZ calculations. Our results indicated that P···N pnicogen bond interactions in the title complexes enhance each other, i.e., there is a positive cooperative effect between the monomers. This is confirmed by geometric and energetic parameters; the binding distance becomes shorter and the interaction energy becomes more negative in the triads. For a given X substitution, the shortening of P N distance is increased in the order Y = NH2 > OH > H > F > CN. This reveals that in a ternary complex, the strong interaction has a great influence on the weak one. The polarization energy term is the important element in the interaction energy of pnicogen-bonded complexes. The partially covalent nature for the pnicogen bonds is confirmed with the NBO analysis. The pnicogen-bonded complexes were analyzed by molecular electrostatic potentials. This study reveals that the nature of the substituent Y is important in cooperativity of pnicogen-bond interaction.
References
Fig. 5 Correlation between cooperative energy and WBI
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ORIGINAL PAPER
Substituent effects on cooperativity of pnicogen bonds Mehdi D. Esrafili & Mojhgan Ghanbari & Fariba Mohammadian-Sabet
Received: 15 June 2014 / Accepted: 25 August 2014 # Springer-Verlag Berlin Heidelberg 2014
Abstract Substituent effects on cooperativity of P···N pnicogen bonds are studied in XH2P···NCH2P···NCY (X=F, Cl; Y=H, F, CN, OH, NH2) complexes using high-level ab initio calculations. An increased attraction or a positive cooperativity is observed on introduction of a third molecule to the XH2P···NCH2P and NCH2P···NCY dyads. The shortening of the each pnicogen bond distance in the triads is dependent on the strength of the P···N bond and is increased in the order Y = NH2 > OH > H > F > CN. The energy decomposition analysis indicates that the polarization energy is the important element in the interaction energy of P···N bond and may be regarded as being responsible for the stabilization in these systems. Natural bond orbital theory is used to characterize the interactions and analyze their enhancement with varying orbital interactions. Keywords ab initio . Cooperativity . Electrostatic potential . NBO . Pnicogen bond
Introduction The importance of noncovalent interactions has been recognized in a wide range of chemical and biophysical phenomena. They are responsible for stabilization of many important molecules, for example, DNA, proteins and enzyme-substrate complexes [1]. The classical hydrogen bond, an example of a strong intermolecular interaction, has been extensively studied Electronic supplementary material The online version of this article (doi:10.1007/s00894-014-2436-9) contains supplementary material, which is available to authorized users. M. D. Esrafili (*) : M. Ghanbari : F. Mohammadian-Sabet Laboratory of Theoretical Chemistry, Department of Chemistry, University of Maragheh, P.O. Box: 5513864596, Maragheh, Iran e-mail: [email protected]
from both theoretical and experimental viewpoints [2–5]. Halogen bonding is another important noncovalent interaction [6–11]. Like hydrogen bonding, halogen bonding involves sharing an atom (a halogen rather than a hydrogen) between a donor molecule R–X and an acceptor B. The R−X···B angle is typically close to 180°, which suggests that the halogen bond is a highly directional interaction. Halogen bond interactions play critical roles in a wide variety of biochemical phenomena such as protein–ligand complexation [12, 13], and can be utilized effectively in drug design [14, 15]. Recently, other weaker interactions, for example, nonclassical hydrogen bonds [16], π–π stacking [17, 18], and pnicogen bond [19–21] have been examined with a view to utilization in ligand binding and molecular folding. Pnicogen bonding is a much more recently defined concept. It can be defined as a rather strong, directional, noncovalent interaction of an electropositive pnicogen atom (N, P, As, Sb or Bi) and an electron donor [22–25]. Politzer and Murray [26–30] associated its origin with the presence of an electropositive region of the electrostatic potential in the prolongation of the R–Pn bond (where R is an electronwithdrawing group and Pn is a pnicogen atom), called “σhole”, that interacts with an electron-rich moiety of a Lewis base (B) through an essentially electrostatic Pn···B interaction. The size of the σ-hole increases with pnicogen size in going from the lighter to the heavier atoms, as polarizability increases and electronegativity decreases. However, Scheiner [20–25] and Alkorta et al. [31, 32] have demonstrated that charge transfer from the lone pair of the base to the σ*Pn−X orbital of the acid plays an essential role in the stabilization of complexes with pnicogen bonds. Pnicogen bond interaction has been widely studied, both experimentally [33, 34] and theoretically [19–32]. The pnicogen bonds involving phosphorous, in particular, have been an area of increasing interest over the past years due to their potential roles in medicinal chemistry and biological systems [35–38].
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Like hydrogen [39, 40] and halogen bonds [41–43], pnicogen bonds have been shown to have a cooperative effect with each other [44]. Thus, the strength of pnicogen bonds in the clusters usually increases as further molecules are added; also, the frequencies of some vibrational modes are shifted by effect of the incorporation of new molecule(s) in some pnicogen-bonded clusters. For example, Li et al. [45] found a positive cooperative effect between the pnicogen- and halogen-bonding interactions in XCl···FH2P···NH3 (X=F, OH, CN, NC, and FCC) complex. The increased value of the pnicogen and halogen bonds energies varies in the order: CCF CN. This reveals that the N atom in the NCH2P···NCY dyad is a stronger electron donor than that of free NCH2P molecule, which would enhance the attraction between the dyad and the XH2P in the XH2P···NCH2P···NCY complex. These findings are consistent with the enhanced interaction energies of the P···N in ternary systems relative to binary ones. Figure 4 shows a plot of MP2 interaction energies for the XH2P (NCH2P NCY) dyads versus the magnitudes of the product of VS,max and VS,min associated with P and N, respectively. The correlation is excellent, with a correlation coefficient R2 of 0.99. This may be a strong indicator of the electrostatically driven natures of these interactions. NBO analysis Further insight into the cooperativity of P···N pnicogen bond can be obtained by examining the NBO wave function overlaps (Fock matrix elements) Fij, the second-order perturbation stabilization energies E(2), and the amount of charge transfer qCT associated with the N lone pair → σ*P−X charge-transfer transitions across the pnicogen bond in
Table 5. One can see that for the XH 2P···NCH2P and NCH2P···NCY binary complexes, both Fij and E(2) values follow the same order with the interaction energies. That is, the largest E(2) value of NCH2P···NCY is found for the complex NCH2P···NCNH2, which has the stronger P···N interaction. The P···N bond in these complexes has some partial covalent character as indicated by its larger Eexch-rep and Epol terms. Moreover, for the FH2P···NCH2P complex, the Fij and E(2) values are greater than those for the ClH2P···NCH2P complexes. These indicate that the orbital interaction is of importance in formation of P···N pnicogen bonds. The strong cooperativity between the P N interactions is also reflected in the magnitude of the charge transfer qCT, which is accompanied by a typical elongation of the P–X and P–CN bond distances of the triads with respect to the binary systems. These qCT are listed in Table 4, and a clear correlation with the other properties is evident. That is, the stronger the pnicogen bond interaction, the larger the magnitude of the qCT. The strength of pnicogen bond can also be estimated with the Wiberg bond index (WBI) at the P···N bonds. This is the sum of squares of off-diagonal density matrix elements between the two atoms, which gives a measure of the bond interaction. For our purposes, it shows the extent of bond overlap associated with each pnicogen bond and it also weighs covalent character of the bond. Hence, the variation in the WBI value in a triad with respect to the corresponding dyads can be used to analyze the mutual influence of the two interactions. One sees from Table 4 that the
Fig. 4 Relationship between interaction energy of XH2P···(NCH2P···NCY) and the magnitude product of most positive and negative electrostatic potentials (VS,max ×VS,min)
J Mol Model (2014) 20:2436 Table 5 NBO analysis of donoracceptor interactions in XH2P···NCH2P···NCY complexes showing Fock matrix interaction elements Fij (in au), stabilization E(2) values (in kJ mol−1), charge transfer qCT (in e) and Wiberg bond index (WBI)
Page 7 of 9, 2436
Complex
A···B
B···C
Fij
E(2)
qCT
WBI
Fij
E(2)
FH2P···NCH2P
0.084
31.76
0.011
0.052
–
–
ClH2P···NCH2P NCH2P···NCH NCH2P···NCF NCH2P···NCCN NCH2P···NCOH NCH2P···NCNH2 FH2P···NCH2P···NCH FH2P···NCH2P···NCF FH2P···NCH2P···NCCN FH2P···NCH2P···NCOH FH2P···NCH2P···NCNH2 ClH2P···NCH2P···NCH ClH2P···NCH2P···NCF ClH2P···NCH2P···NCCN ClH2P···NCH2P···NCOH ClH2P···NCH2P···NCNH2
0.074 – – – – – 0.088 0.088 0.086 0.089 0.090 0.079 0.079 0.077 0.080 0.081
28.49 – – – – – 35.65 35.31 33.97 36.48 37.28 32.64 32.22 30.63 33.76 34.81
0.011 – – – – – 0.012 0.012 0.011 0.012 0.013 0.012 0.012 0.012 0.013 0.013
0.039 – – – – – 0.058 0.057 0.055 0.059 0.061 0.044 0.043 0.042 0.045 0.047
– 0.056 0.057 0.052 0.062 0.065 0.060 0.060 0.054 0.067 0.070 0.060 0.060 0.054 0.067 0.070
WBI at the P···N bond of FH2P···NCH2P is larger than that at ClH2P···NCH2P. This supports the fact that the pnicogen bond is stronger in the former complex. Moreover, it is evident that the WBI value associated to P···N bond in the triads are slightly greater than that in the corresponding dyads. This finding confirms that the pnicogen bond interactions in the triads are reinforced with respect to the binary systems. In fact, good linear correlations are found between the magnitudes of cooperative energy Ecoop and WBI values in the ternary systems (Fig. 5).
Conclusions In summary, we investigated the substituent effects on cooperative behavior between pnicogen bonds interactions in the
– 13.89 13.60 11.34 16.65 18.95 16.11 15.52 12.47 19.83 21.80 16.15 15.52 12.51 19.75 21.92
qCT
WBI
–
–
– 0.004 0.004 0.004 0.005 0.006 0.005 0.005 0.004 0.006 0.007 0.005 0.005 0.004 0.006 0.007
– 0.016 0.015 0.013 0.018 0.021 0.018 0.016 0.014 0.021 0.024 0.018 0.016 0.014 0.021 0.024
XH2P···NCH2P···NCY (X=F, Cl; Y= H, F, CN, OH, NH2) complexes using MP2/aug-cc-pVTZ calculations. Our results indicated that P···N pnicogen bond interactions in the title complexes enhance each other, i.e., there is a positive cooperative effect between the monomers. This is confirmed by geometric and energetic parameters; the binding distance becomes shorter and the interaction energy becomes more negative in the triads. For a given X substitution, the shortening of P N distance is increased in the order Y = NH2 > OH > H > F > CN. This reveals that in a ternary complex, the strong interaction has a great influence on the weak one. The polarization energy term is the important element in the interaction energy of pnicogen-bonded complexes. The partially covalent nature for the pnicogen bonds is confirmed with the NBO analysis. The pnicogen-bonded complexes were analyzed by molecular electrostatic potentials. This study reveals that the nature of the substituent Y is important in cooperativity of pnicogen-bond interaction.
References
Fig. 5 Correlation between cooperative energy and WBI
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