Classical Electrostatic Interaction Is the Origin for Blue-Shifting

Article Cite This: Inorg. Chem. 2019, 58, 8577−8586

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Classical Electrostatic Interaction Is the Origin for Blue-Shifting Halogen Bonds Changwei Wang*,† and Yirong Mo*,‡ †

Key Laboratory for Macromolecular Science of Shaanxi Province, School of Chemistry and Chemical Engineering, Shaanxi Normal University, Xi’an 710119, China ‡ Department of Chemistry, Western Michigan University, Kalamazoo, Michigan 49008, United States

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S Supporting Information *

ABSTRACT: Studies have shown that, on the one hand, charge transfer (CT) plays a key role in halogen bonds (D···X−A) (D = donor; X = halogen atom; A = acceptor), suggesting considerable covalent character of halogen bonding. But, on the other hand, it has been proposed that halogen bonding is dominated by the electrostatic attraction between the electropositive σ-hole at the halogen atom X and the electronegative donor D. It has also been wellrecognized that the CT from the donor D to the antibonding σ*(X−A) would weaken and lengthen the X−A bond. Yet, intriguingly, there is a blue-shifting phenomenon in halogen bonding, where the X−A bond contracts with an enhanced stretching vibrational frequency. Here we explored the nature of blueshifting halogen bonds with the iconic case of H3N···ClNO2, which exhibits the blue-shifting phenomenon along with a strong CT interaction and its analogous H3N···XNY2 (X = Cl, Br, and I; Y = O, S). By decomposing the binding energy to a number of energy components and exploring their energy profiles along with the halogen-bonding distances with the block-localized wave function (BLW) method, we showed that the classical electrostatic interaction is the governing factor for the blue-shifting of the X−N bonds. This is further supported by the similar magnitudes of blue-shifting obtained when NH3 is replaced with atomic point charges in the complexes. Alternatively, by applying external electric field (E-field) along the X−N bond direction, the blue-to-red shifting transition can be identified. This is because both polarization and CT interactions tend to stretch the X−N bond, and both are enhanced simultaneously under the external E-field. Finally, roles of individual energy components are reconfirmed using the force analysis based on the BLW energy decomposition approach.

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INTRODUCTION Noncovalent interactions in the general form of D···Z−A (D = donor; A = acceptor) are major driving forces in shaping new materials including self-assembling polymers, nanoparticles, and biomolecular assembles.1−6 As such, there is a current and intense interest in the elucidation of the nature of novel noncovalent interactions such as halogen bonding, chalcogen bonding, pnicogen bonding, tetrel bonding, etc.7−24 For many of these interactions, the classical electrostatic interaction, as highlighted with the σ-hole concept,25−28 has been proposed to account for most of the observable trends. A σ-hole can be understood as a region with positive electrostatic potential surrounded by a ring of negative electrostatic potential along the extension of a σ-bond. The positive potential region enables the site to attract a Lewis base with a partially negative charge as well as accept electrons from the base. The significance of the σ-hole concept lies in that electrostatic interaction could be directional just like the covalent (i.e., charge transfer or CT) interaction. For hydrogen bonds (Z = H), it has been well-recognized that there is secondary CT from the lone pair on D to the antibonding orbital of H−A, or n(D) → σ*(H−A), which results in the weakening, elongation, © 2019 American Chemical Society

and red-shifting in the stretching frequency of the H−A bond.29−32 However, blue-shifting hydrogen bonds in which the H−A bond contracts later were identified.33−39 Various theoretical analyses have been performed in an attempt to elucidate and unify the red- and blue-shifts due to hydrogen bonding.40−44 Recently, halogen bond (D···X−A, where X is a halogen atom) received a great deal of attention due to its ubiquitous existence in chemistry, pharmacy, and material science and its similarity to hydrogen bond.18−20,27,45−67 Enormous efforts have been put in finding and explaining blue-shifting halogen bonds,68−75 though in most cases halogen bonds elongate and exhibit red-shifts due to the significant CT interaction.18,76 We note that there is strong coupling of the X−A stretching vibration with other vibrational modes and, as a consequence, there are very few pure X−A normal stretching modes.69,77−80 Cremer and his co-workers81−83 demonstrated that local stretching modes can be derived from normal modes by solving the Wilson equation.84 This method was applied to the Received: March 26, 2019 Published: June 11, 2019 8577

DOI: 10.1021/acs.inorgchem.9b00875 Inorg. Chem. 2019, 58, 8577−8586

Article

Inorganic Chemistry study of halogen bonds by Oliveira et al.80 Alternatively, computational studies often focus on the bond length contraction/elongation as an indicator of bond strength and “pure” X−A stretching,72−74 though it has been known that fragmental interactions and relaxations may impact the correlation between bond lengths and bond strengths, and a local stretching force constant is the best indicator for intrinsic bond strength.80 Notably, Jemmis and co-workers found a continuum in the variation of the X−A bond length in weakly bonded complexes of D···X−A from blue- to red-shifting and proposed that the exchange repulsion between D and the electron density at σ*(X−A), which comes from the negative hyperconjugation from the A-group, leads to the blueshifting.72,73 Obviously, the electron density movement (reorganization) among particular orbitals within a molecule falls in the category of the polarization effect. As it has been well-recognized that the n(D) → σ*(Z−A) electron transfer results in the weakening and the subsequent red-shifting of the Z−A bond, Jemmis’s proposal essentially means that the competition between polarization and CT determines the direction of frequency shifts and bond distance changes. This echoes the previous proposal for hydrogen bonds by Alabugin et al., who suggested that one of the H−A bond contracting factors is the polarization of H−A bond.41 In contrast, our comparative study of a series of hydrogen-bonding and halogen-bonding systems showed that both CT and polarization stretch and red-shift the Z−A bond (hereafter, Z denotes either hydrogen or halogen atoms).74 To clarify the exact role of polarization in bond-stretching frequency shifts and the origin of frequency shifts in weakly bonded complexes, here we investigated the interesting and iconic case of H3N···ClNO2, which shows large-frequency blue-shifting even in the presence of strong charge transfer.72 In addition, analogous complexes of H3N···XNO2 (X = Br and I) and H3N···XNS2 (X = Cl, Br, and I), in which enhanced polarization effect is observed with less significant contraction of the X−N bonds compared with the H3N···ClNO2 complex, are also examined and compared. The present study is based on the block-localized wave function (BLW) method,85−88 alternatively called the strictly localized molecular orbital (SLMO) method by the Head-Gordon group,89 which is a variant of the ab initio valence band (VB) theory90−93 and is able to quantify the electrostatic, polarization, and electrontransfer interactions. The unique advantage of the BLW method is its capability of deriving optimal electron-localized states and geometries self-consistently, allowing the determination of the electron-transfer (covalent) interactions therein.94

stable diabatic states. Within the BLW method, the intermolecular binding energy ΔEb is decomposed to five energy terms as ΔE b = ΔEs + ΔECT = E(ΨAB) − [E(ΨA) + E(ΨB)] + BSSE =ΔEdef + ΔEF + ΔEpol + ΔECT + ΔEdisp

(1)

where the steric energy component (ΔEs) involves deformation (ΔEdef), frozen (ΔEF), polarization (ΔEpol), and dispersion energy (ΔEdisp) terms, and ΔECT is the chargetransfer stabilization energy. BSSE refers to the basis set superposition error. The sum of the last four terms in eq 1 can also be defined as the interaction energy (ΔEint) ΔEint = ΔE F + ΔEpol + ΔECT + ΔEdisp

(2)

In this way, the binding energy (ΔEb) is the sum of the deformation energy (ΔEdef) and the interaction energy. More detailed information can be found in literature.95,96 Computational Details. The BLW code with the geometry optimization capability94 has been ported to the GAMESS software97 in our laboratories. The optimal electronlocalized state essentially corresponds to a van der Waals complex, where the charge-transfer effect is strictly absent. Thus, the geometrical and energetic changes or even spectral changes due to the electron-transfer effect can be critically examined.98 All BLW energy decomposition computations were performed at the DFT(M06-2X)/cc-pVTZ level of theory, which is augmented by Grimme’s D3-dispersion correction.99−101 Binding energies were corrected for BSSE with the counterpoise method.102 To justify the above computational level, benchmark calculations were performed using the spin-component-scaled second-order Møller−Plesset (SCS-MP2) theory with the aug-cc-pVTZ basis set.103 For iodine, the basis set of cc-pVTZ-PP104,105 that includes a relativistic pseudopotential was used.

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RESULTS AND DISCUSSION We examined the halogen bonding in six complexes H3N··· XNY2 (X = Cl, Br, and I; Y = O and S) as shown in Figure 1 at

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Figure 1. Complexes 1−6 studied in this work.

THEORY Block-Localized Wave Function (BLW) Method. For a complex composed of monomers A and B, the BLW function corresponds to the electron-localized (diabatic) state by assuming that all orbitals are block-localized and expanded within only one monomer’s basis space. Orbitals in the same monomer are subject to the orthogonality constraint, but orbitals belonging to different monomers are free to overlap and thus nonorthogonal. Since the electron-delocalized (adiabatic) state can be conveniently derived with molecular orbital (MO) methods, where all orbitals are delocalized over the whole system, the charge-transfer energy (or electron delocalization energy within the same molecule) can be conveniently defined by comparing the adiabatic and the most

the DFT(M06-2X)/cc-pVTZ level of theory. Table 1 compiles the intermolecular distances (R1), binding energies (ΔEb) with contributing energy components as defined in eqs 1 and 2, variations of the X−N bond distances (ΔR2), and the corresponding stretching vibrational frequencies (Δv) upon the formation of complexes. For comparison, SCS-MP2/augcc-pVTZ computations result in reduced binding energies (see Table S1 in Supporting Information). But this may largely be due to the overestimation of the counterpoise method in the BSSE correction for correlated methods, notably MP2,106,107 and Antony and Grimme demonstrated that the SCS-MP2/ccpVTZ level without counterpoise correction could lead to good binding energies in the study of intermolecular 8578


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Table 1. Optimal Bond Distances (Å), X−N Stretching Vibrational Frequencies (cm−1), and Various Energy Components (in kJ/mol) of the Binding Energy (ΔEb) at the M06-2X-D3/cc-pVTZ Level method

mol

R1

ΔR2a

Δva

ΔEdef

ΔEF

ΔEpol

ΔECT

ΔEdisp

ΔEint

ΔEb

DFT

1 2 3 4 5 6 1 2 3 4 5 6

2.739 2.700 2.667 2.693 2.612 2.582 3.024 3.041 3.028 2.998 3.012 2.987

−0.017 −0.011 0.001 −0.016 −0.016 −0.001 −0.023 −0.023 −0.020 −0.029 −0.040 −0.037

6.6 −1.3 −5.7 2.0 5.4 2.5 26.3 23.4 12.5 13.4 25.8 21.1

0.9 1.6 2.6 0.4 0.9 1.2 0.5 0.6 0.8 0.4 0.7 0.7

−3.0 0.9 6.5 0.2 11.5 22.5 −10.2 −13.2 −19.2 −9.4 −12.3 −18.3

−5.5 −10.0 −22.0 −6.6 −14.1 −31.3 −2.9 −4.4 −8.7 −3.3 −5.1 −10.6

−13.1 −21.4 −32.3 −15.5 −29.4 −42.9

−0.3 −0.2 −0.2 −0.4 −0.4 −0.3 −0.2 −0.2 −0.2 −0.4 −0.3 −0.3

−21.9 −30.8 −48.1 −22.3 −32.4 −52.1 −13.3 −17.8 −28.0 −13.1 −17.8 −29.1

−21.0 −29.2 −45.5 −21.9 −31.5 −51.0 −12.8 −17.2 −27.3 −12.7 −17.1 −28.5

BLW

ΔR2 and Δv are the variations from the individual monomer XNY2 to its complex with NH3.

a

frequencies once the CT is “turned off”.44,74 Decomposition analysis of the DFT binding energy based on the BLW method85,86 reveals that indeed the halogen bond in H3N··· XNY2 is dominated by the intermolecular CT interaction (ΔECT in Table 1) and further enhanced by the polarization interaction (ΔEpol) and the frozen energy (ΔEF) terms. With the CT interaction turned off, the halogen bond (R1, see Figure 1) is significantly elongated, leading to a nearly 50% reduction of the polarization energy. Remarkably, the frozen energy now overwhelmingly dominates the binding energy. Since the frozen energy is a sum of electron correlation, electrostatic interaction, and Pauli repulsion and the last one is a destabilizing short-range interaction, the stabilizing frozen energy must largely come from the electrostatic attraction between H3N and XNY2. Thus, our data in Table 1 strongly suggest the correlation between the blue-shifting phenomenon and electrostatic component of the bonding energy. To clarify the individual roles of each energy component in the blue-shifting phenomenon, we examined the energy profiles as well as the variation of the X−N bond length along the bonding distance (R1), as shown in Figure 2. For the example of complex 1, Figure 2 (1a) clearly shows that the contraction of the Cl−N bond occurs at a long distance, that is, at beyond 7 Å, when the two monomers start to approach one another. Since at this long distance, Pauli exchange, polarization, electron correlation, and CT interactions are essentially absent, as they are known to be short-range interactions as shown in Figure 2 (1b), the only remaining long-range interaction is undoubtedly the electrostatic interaction. Thus, it is safe to state that the electrostatic interaction is the only factor responsible for the blue-shifting of the Cl−N bond stretching vibrational frequency at a long range. We note that this finding holds true for both DFT and BLW optimal geometries, as the same magnitudes of the Cl−N bond shrinking can be observed with both the DFT and BLW optimal geometries, when the halogen-bonding distance (R1) is greater than 3.6 Å (Figure 2 (1a)). Once the bonding distance is less than 3.6 Å, the CT interaction starts to contribute to the lengthening of the Cl−N bond. This observation confirms the negative role of the CT interaction to the blue-shifting phenomenon. Figure 2 (1c) shows good linear correlations between individual energy components (except the insignificant correlation energy from the D3 correction as shown in Table 1, which is thus not examined) and the variation of the Cl−N

interactions.108 Notably, however, DFT(M06-2X-D3)/ccpVTZ optimizations result in reduced distance shortening (ΔR2) of the X−N bond in the binding and subsequently lower blue-shifting than the SCS-MP2/aug-cc-pVTZ optimizations (Table S1 in Supporting Information). As our focus is on the origin rather than the magnitude of the shifting, in the following our analyses and discussion will be based on the DFT(M06-2X-D3)/cc-pVTZ level, though in the end we will confirm our finding with the charge model at the SCS-MP2/ aug-cc-pVTZ level. Table 1 shows that, for the overall binding energy, there is a sequence of 6 > 3 > 5 > 2 > 4 > 1, and a heavier halogen atom or sulfur substitution always leads to the enhancement of the binding energy but the reduction of the contraction of the X− N bond. We note that the M06-2X-D3/cc-pVTZ geometry optimization results in a negligible stretching of X−N bond in complex 3, while shrinking was found in the benchmark calculation at the SCS-MP2/cc-pVTZ level (Table S1). Notably, however, the M06-2X-D3 method reproduces both the sequences of binding energies and the X−N bond variations compared with the benchmark results (Table S1). Thus, we continued the BLW geometrical optimizations at the same density functional theory (DFT) level by quenching the charge transfer between H3N and XNY2, and results were compiled in Table 1 as well. On the basis of the regular DFT calculations, we found that the magnitude of X−N bond shrinking decreases, while both the polarization and CT interactions get stronger from complex 1 to 3. Meanwhile, the frozen energy turns to be destabilizing, obviously due to the shortening of the intermolecular distance (R1), which enhances the Pauli repulsion. These two tendencies are also observed for complexes 4−6. Furthermore, polarization interaction is strengthened, when oxygen atoms are replaced with sulfurs, leading to shorter intermolecular distances and stronger CT interactions (1 vs 4; 2 vs 5, and 3 vs 6). Importantly, complex 1 exhibits the most significant contraction of the X−N bond, yet it has the lowest polarization and CT energies. With the deactivation of the charge transfer between H3N and XNY2, the BLW computations show even shorter X−N bond lengths and much more significant blue-shifting, as listed in Table 1. This is in accord with the current view that the n(D) → σ*(X−A) CT weakens and stretches the X−A bond. Previously, we also found that a majority of hydrogen- and halogen-bonding systems exhibit blue-shifted stretching 8579


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interaction to the blue-shifting phenomenon. Finally, the shortening and blue-shifting of the Cl−N bond is confirmed by the correlation of ΔEb versus ΔR2, which shows a more significant overall stability of complex, when the Cl−N bond contracts. We note that all these results and findings from the analyses of the complex H3N···ClNO2 can be applied to the remaining five systems. Thus, we propose that the classical electrostatic attraction, which is the stabilizing force in the frozen energy term, governs the blue-shifting in all H3N··· XNY2 complexes. To appreciate the CT and polarization interactions intuitively, we plot the electron density difference (EDD) maps corresponding to the electron density changes due to the CT and polarization interactions, as shown in Figure 3. For all systems, it can be seen that the CT interaction leads to an overall reduction of electron density on the electron-donating species H3N, especially in the nitrogen p orbital toward XNO2, which is originally occupied by a lone electron pair. This lost electron density mainly flows to the X−N bond direction and results in an effective accumulation of electron density in the

Figure 2. Correlations of (a) the X−N bond length (ΔR2 in Å) and (b) energy components (in kJ/mol) using the DFT optimal geometries along the halogen-bond distance (R1). (c) Correlation between energy components (kJ/mol) and the variation of the X−N bond length (Å).

bond length at a relatively short range around the ground state. Here the viable range adopted for the halogen bond distance R1 runs from 2.0 Å, which is the shortest in our calculation, to the sum of van der Waals radii of N and Cl atoms, which is 3.3 Å. Obviously, on one hand, the elongation of the Cl−N bond is always associated with the enhancement of both polarization and CT interactions, implying their negative roles in the contraction of the Cl−N bond. On the other hand, a shorter Cl−N bond corresponds to a stronger stabilizing frozen interaction, suggesting a positive contribution from the frozen

Figure 3. EDD maps showing the electron density changes due to (a) intermolecular CT and (b) polarization interactions. The red color means a gain of electron density, while the blue represents a loss of electron density. The isodensity values are equal to 0.0005 e Å−3. 8580


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X−N bond (Figure S1a). However, the blue-shifting upon the formation of complex is compromised and switched to redshifting continuously due to the positive E-field (Figure 4b), accompanied by the enhancement of both polarization and charge transfer interactions (Figure 5). Clearly, the positive E-

common area between two monomers. The picture is consistent with the n(D) → σ*(X−A) CT within the MO theory. The CT-induced electron density accumulation forms a double-faced adhesive tape, which glues two monomers together. The polarization interaction shifts the electron density from the hydrogen atoms to the nitrogen lone-pair orbital area within H3N, whereas in XNY2 the electron density shifts from the halogen atom to the NY2 side. The pattern of electron density movement due to polarization can be regarded as a preparation step for the subsequent CT interaction. Interestingly, analyses of the EDD maps reveal two common features of electron density variations caused by polarization and CT interactions. First, the electron densities are generally shifted in the same direction, which are from the left (donor) to the right (acceptor) sides of each system, as denoted by the arrows in Figure 3 (1a and 1b). Second, electron density flows through a nodal plane due to polarizations or CT interactions, where the variation of electron density reaches a local minimum and switches its characteristics (loss or gain). This pattern of electron density variation looks like the shape of σ*(X−N), but they have completely different meanings. Clearly, this observation is consistent with the further shrinking of the X−N bond, when CT interaction is quenched, and also suggests that polarization interactions tend to stretch the X−N bond as well. The elongation effect of the polarization and CT interactions can also be verified by their coherent response to the external electric field (E-field)109,110 imposed along the X−N direction (positive direction, as shown in Figure 4a).

Figure 5. Correlations between various energy components and the strength of the external E-field.

field shifts the electron density in the same direction as polarization and CT interactions do and, consequently, strengthens them. This is in accord with the main direction of the electron density flow suggested by EDD maps (Figure 3). Both polarization and CT interactions decrease monotonously along ΔR2 in the external E-field for all cases (Figure 4c,d), indicating that the elongation of the X−N bond is energetically preferred by both polarization and CT interactions. This is in line with the likely gain of electrons in the σ*(X−N) orbital due to the polarization and CT interactions, as suggested by EDD maps. The “ΔECT versus ΔR2” curve is always steeper than the “ΔEpol versus ΔR2” curve as shown in the Supporting Information (Table S2), suggesting that the CT interaction is the major force for the elongation of the X−N bond and that the polarization effect plays the secondary role. In addition, the coherent response of the polarization and CT interactions to the external E-field is also confirmed by the correlations between their energy components (i.e., ΔECT vs ΔEpol), which exhibit excellent linear relationships (Figure S1b). Significantly, on the one hand, the frozen-energy term is the only component destabilized in the positive external E-field (Figure 5), accompanied by the reduction of the blue-shifting magnitude (Figure 4b). On the other hand, a negative E-field (along the X−N direction) always suppresses the polarization and CT interactions and generally makes the frozen energy less repulsive, leading to a more significant shrinking of the X−N bond upon the

Figure 4. (a) Definition of the positive direction of the external Efield; (b) correlations between the variations of X−R bond lengths upon the formation of complexes in external E-field and the strength of the E-field imposed; and correlations between the CT energy (c) or polarization energy (d) and ΔR2, calculated in external E-field with various strengths for all systems.

Here the variation of the X−N bond upon the formation of complexes was investigated by optimizing both the monomers and complex in the E-field of various strengths. For XNY2 monomers, a positive E-field pushes the negatively charged halogen atom toward the nitrogen atom and pulls the positively charged nitrogen atom toward the halogen, subsequently resulting in a shrinking and blue-shifting of the 8581


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LUMO energy gap to 0.323 au (8.79 eV). At last, the electron flow from HOMO to LUMO stabilizes the former but destabilizes the latter. Accordingly, energy decomposition analysis in Table 1 shows that the stabilization due to this CT is 13.2 kJ/mol. Similar tendencies of orbital energy evolutions were also found in each of the other systems investigated (Table S3). To critically examine the role of Pauli repulsion between the two interacting monomers in H3N···XNY2 complexes and verify the above finding that the classical electrostatic attraction is the origin of the blue-shifting in these halogen-bonding complexes, we replaced H3N with point charges based on the simple Mulliken population analysis of NH3. There are two possible ways to determine the charges; one is from the free NH3 (i.e., not polarized), and the other is from the BLW result of the complex (polarized). By freezing the distances of the atomic point charges to the halogen atom at the optimal complex geometries, we derived the optimal geometry of XNY2 and the X−N stretching vibrational frequency. Table 2 listed the major results. With both sets of charges, we observe similar bond contraction and blue-shifted frequencies of the X−N bond with trends comparable to the BLW computations (Table 1). The similarity between Table 1 and Table 2 indicates that the electrostatic interaction between H3N and XNY2 is indeed the driving force for the blue-shifting of the X− N bond stretching frequency. Computations at the SCS-MP2/ aug-cc-pVTZ level reach the similar conclusion (Table S4). Finally, we performed the force analysis74 based on the BLW-electron density (ED) approach for H 3 N···XNY 2 complexes. As the binding energy is a sum of several energy components and the total binding force is the first-order derivative of the binding energy with respect to the halogenbond length R2, we can examine the corresponding forces of individual energy terms. Figure 7 shows the variations of energy terms as a function of the variation of R2. Both ΔEpol and ΔECT decrease with the increasing ΔR2, indicating that these interactions lead to the elongation and frequency redshifting of the X−N bond. In contrast, the frozen energy term, which is the sum of electron correlation, electrostatic interaction, and Pauli exchange repulsion, decreases notably with the contraction and frequency blue-shifting of the X−N bond. As a long-range phenomenon (Figure 2a), frequency blue-shifting must originate from the electrostatic interaction, which is the only long-range energy component.

formation of complex. At the present DFT(X06−2X-D3) level, the dispersion correction is insensitive to the external E-field compared with the other energy components and thus is not shown in Figure 5. In the terms of MO theory, the CT interaction can be elucidated with the orbital interaction diagrams. Instead of using non-interacting orbitals from separated monomers as we are much familiar with, the BLW method can obtain the localized (non-interacting) orbitals when monomers are at the positions of their complex. For the example of the H3N··· ClNO2 complex, the CT interaction can be described with the evolution of the orbital energies and the “in situ” orbital correlation diagram between highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) (red dashed frame) as shown in Figure 6. The

Figure 6. Orbital correlation diagram upon the formation of the H3N···ClNO2 complex, where d- and bl- denote the distorted and block-localized monomers at the DFT optimal complex geometry (energy levels in hartree).

HOMO of H3N (donor) corresponds to the nitrogen lone pair, while the LUMO of ClNO2 is the virtual antibonding orbital of the Cl−N bond. Computations of optimal monomers show the compatibility of the HOMO of NH3 and the LUMO of ClNO2 with an energy gap 0.276 au (7.51 eV). The structural deformation to the monomer geometries in the optimal complex changes the energy levels slightly (d-H3N and d-ClNO2 in Figure 6). However, when the two molecules approach to their optimal positions in the halogen-bonding complex, there is considerable shifting of orbital energy levels (bl-H3N and bl-ClNO2 in Figure 6), due to the mutual electrostatic interactions and the associated rearrangement (polarization) of the electron densities within monomers. The nitrogen lone-pair orbital energy decreases, but the σ*(Cl−N) energy increases, leading to the expansion of the HOMO−

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CONCLUSION Compared with hydrogen bond, halogen bond generally involves stronger CT interaction from the donor D orbital to the antibonding orbital of the X−A bond. This kind of CT

Table 2. Variations of Optimal X−N Bond Distances (Å) and Stretching Vibrational Frequencies (cm−1) with Point Charges (QN and QH) for NH3 at the M06-2X-D3/cc-pVTZ Level free NH3

NH3 in complex

mol

QN

QH

ΔR2

Δv

QN

QH

ΔR2a

Δva

1 2 3 4 5 6

−0.555 −0.555 −0.557 −0.552 −0.558 −0.559

0.185 0.185 0.186 0.184 0.186 0.186

−0.015 −0.015 −0.012 −0.020 −0.028 −0.025

7.8 16.3 7.1 1.3 15.1 5.7

−0.684 −0.700 −0.772 −0.659 −0.718 −0.795

0.228 0.233 0.257 0.220 0.239 0.265

−0.018 −0.018 −0.016 −0.022 −0.033 −0.032

9.4 16.5 8.8 1.5 16.3 8.0

ΔR2 and Δv are the variations from the optimal monomer ClNO2.

a

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and differentiate the roles of electrostatic, polarization, and CT in these complexes analogous to H3N···ClNO2, which is known for its large blue-shifting of the Cl−N stretching frequency despite the strong CT from the lone pair of NH3 to the σ* orbital of Cl−N. Our results show that the blue-shifting in these halogen-bonding systems is a long-range phenomenon. As the electrostatic interaction is the only long-range term in energy decomposition analyses, we conclude that the classical electrostatic attraction is the origin for the blue-shifting of halogen bonds. The roles of each energy component to the blue-shifting phenomenon were analyzed by correlating them with the variation of the X−N bond length (ΔR2). Our studies show that the shrinking of the X−N bond is only preferred by the frozen energy term, in which electrostatic interaction is included, while both polarization and CT interactions increase when the X−N bond is stretched. Pictorial understanding of electron density movements due to polarization and CT interactions were provided using EDD maps, and a general pattern of electron density flows was observed. EDD maps show that both polarization and CT interactions shift the electron densities essentially in the same direction, and through the same pathway with a “nodal plane” around the X−N bond center, suggesting a kind of n → σ*(X−N) orbital interaction, which elongates the X−N bond. The roles of polarization and CT interactions in the elongation of X−N bonds were further confirmed by their coherent enhancements in external E-fields imposed along the N−X direction and by the continuous transition from the blue-shifting to red-shifting of the vibrational frequency. At last, the key role of the electrostatic interaction to the blue-shifting is reinforced by the charge model computations, where the donor NH3 is replaced by point charges on atomic centers. The charge model computations result in similar magnitudes of frequency blue-shifting and bond-length contraction. By performing the force analysis based on BLWED approach, the contributions of each energy component to the blue-shifting phenomenon were further clarified.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.9b00875. Optimal geometries; correlations of bond distances and energy components at external electric fields; SCSMP2/ aug-cc-pVTZ benchmark results (PDF)

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Figure 7. Energy profiles along the variation of the X−N bond length (Å). Right curve shows the variation of the destabilizing deformation energy term, while left curves are the profiles of frozen energy, polarization energy, CT energy, and the total binding energy.

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. (Y.M.) *E-mail: [email protected]. (C.W.) ORCID

interaction would weaken and elongate the X−A bond. Intriguingly, however, often a halogen-bonding system exhibits a contracted and vibrational frequency blue-shifted X−A bond. In this work, we performed geometric and energetic analyses of complexes H3N···XNY2 (X = Cl, Br, and I; Y = O and S) based on the BLW method, which can derive optimal wave functions for strictly electron-localized states. This enables us to identify

Yirong Mo: 0000-0002-2994-7754 Funding

National Natural Science Foundation of China and Western Michigan University. Notes

The authors declare no competing financial interest. 8583


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Inorganic Chemistry

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ACKNOWLEDGMENTS C.W. acknowledges support from the Natural Science Foundation of China (No. 21603274), the fundamental research funds for the central Universities (Nos. GK201903043 and GK201901007), and the talent introduction fund of Shaanxi Normal University. Y.M. thanks the Faculty Research and Creative Activities Award, Western Michigan University, for support.

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