A Unified Theory for the Blue- and Red-Shifting Phenomena in

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A Unified Theory for the Blue- and Red-Shifting Phenomena in Hydrogen and Halogen Bonds Changwei Wang, David Danovich, Sason Shaik, and Yirong Mo J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.6b01133 • Publication Date (Web): 02 Mar 2017 Downloaded from http://pubs.acs.org on March 5, 2017

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Journal of Chemical Theory and Computation

A Unified Theory for the Blue- and Red-Shifting Phenomena in Hydrogen and Halogen Bonds

Changwei Wang,*a David Danovich,b Sason Shaik,*b Yirong Mo*c

a

Department of Chemistry, School of Science, China University of Petroleum (East China),

Changjiangxi Road 66, 266580 Tsingtao, China. E-mail: [email protected] b

Institute of Chemistry and Lise Meitner Minerva Center for Computational Quantum Chemistry,

The Hebrew University, Jerusalem 91904 Israel. E-mail: [email protected] c

Department of Chemistry, Western Michigan University, Kalamazoo, MI 49008, USA. E-mail:

[email protected]

1

ACS Paragon Plus Environment


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Abstract Typical hydrogen and halogen bonds exhibit red shifts of their vibrational frequencies upon the formation of hydrogen and halogen bonding complexes (denoted as D···Y−A, Y = H and X). The finding of blue shifts in certain complexes is of significant interest, which has led to numerous studies of the origins of the phenomenon. Since charge-transfer mixing (i.e., hyperconjugation in bonding systems) has been regarded as one of key forces, it would be illuminating to compare the structures and vibrational frequencies in bonding complexes with the charge transfer effect “turned on and off”. Turning off the charge-transfer mixing can be achieved by employing the block-localized wavefunction (BLW) method, which is an ab initio valence bond (VB) method. Besides, with the BLW method, the overall stability gained in the formation of a complex can be analyzed in terms of a few physically meaningful terms. Thus, the BLW method provides a unique way to explore the nature of red- and blue-shifting phenomena in both hydrogen and halogen bonding complexes. In this study, a direct correlation between the total stability and the variation of the Y−A bond length is established based on our BLW computations and the consistent roles of all energy components are clarified. The n(D)→σ*(Y−A) electron transfer stretches the Y−A bond, while the polarization due to the approach of interacting moieties reduces the HOMO-LUMO gap and results in a stronger orbital mixing within the YA monomer. As a consequence, both the charge transfer and polarization stabilize bonding systems with the Y−A bond stretched and red-shift the vibrational frequency of the Y−A bond. Notably, the energy of the frozen wave function is the only energy component which prefers the shrinking of the Y−A bond and thus is responsible for the associated blue-shifting. The total variations of the Y−A bond length and the corresponding stretching vibrational frequency are thus determined by the competition between the frozen-energy term and the sum of polarization and charge transfer energy terms. Since the frozen energy is composed of electrostatic and Pauli exchange interactions, and frequency shifting is a long-range phenomenon, we conclude that long-range electrostatic interaction is the driving force behind the frozen energy term. 2


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Introduction As the most important non-covalent interaction, which favorably stabilizes related systems, hydrogen bond (H-bond) plays fundamental roles in chemistry, molecular biology and material science.1-11 Generally, H-bond can be represented as D···H−A, where D is an electron rich Lewis base that serves as the H-bond accepter, while H−A is the H-bond donor possessing electron-poor hydrogen. It is believed that electrostatic interaction is the driving force for H-bonds,12,13 but the contribution of charge transfer from the H-bond accepter to the H-bond donor is also significant.14-20 An elongation of the H−A bond upon the formation of a H-bonding complex can be predicted using both the electrostatic and charge transfer origins for the nature of H-bond. First, the electron-rich D tends to pull the positively charged hydrogen atom closer, resulting in the stretching and weakening of the H−A bond.21 Second, due to the orbital interaction between the lone pair on D and the anti-bonding orbital of H−A, there is substantial electron transfer, i.e., n(D)→σ*(H−A), leading to the weakening and elongation of the H−A bond, accompanied with a red shift of its stretching vibrational frequency and an enhancement of the intensity.22,23 Consequently, the red shift with increased intensity in IR spectra has been regarded as the “fingerprint” of H-bond for decades.24,25 However, this situation started to get complicated since the discovery of blue-shifting H-bonds in which the H−A bond contracts and its stretching mode shifts to higher frequency with a reduced intensity.26-30 The first experimental evidence for blue-shifting H-bond was provided by Trudeau et al. in the year 1980,31 followed by the second experiment in 1989 by Buděšínský et al..32 A milestone of integrated experimental and computational investigation, which proved the existence of blue-shifting H-bond even in gas phase, was achieved by Hobza and coworkers, when they investigated in 1999 the complex of fluorobenzene and chloroform using the double-resonance IR ion-depletion spectroscopy and computational chemistry.33 Since then, numerous blue-shifting complexes have been identified and investigated. Much like H-bond, halogen bond (X-bond), which refers to the interaction between an electron rich Lewis base D and the halogen atom in a X−A molecule, is also ubiquitous in 3



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chemistry, pharmacy and material science, and has attracted a great deal of attention recently.34-41 The existence of X-bond is surprising because both the Lewis base and the halogen atom are negatively charged, and thus supposed to be repulsive of each other. But instead, there is an attraction between D and X−A leading to a bond. This fascinating phenomenon can be well explained using the “σ-hole” concept proposed by Politzer et al.,42-46 which describes a positive electrostatic potential around the negatively charged halogen atom pointing along the extension of the X−A bond. Thus, an electrostatic nature of halogen bond is conferred by the σ-hole theory. Nevertheless, there is a much earlier theoretical explanation for X-bonding by Mulliken in 1950 who formulated the charge transfer theory and stated that the stability of X-bond origins mainly from the orbital interaction between the lone pair on D and the X−A anti-bonding orbital.47 This charge transfer explanation was confirmed by our most recent comprehensive study of 55 typical halogen bonding complexes,48 using both the ab initio valence bond (VB) theory49-52 and the block-localized wavefunction (BLW) method53-56. Obviously, it is safe to say that both the electrostatic interaction and the charge transfer mixing effect are important in both hydrogen and halogen bonds. Moreover, it is generally thought that X-bond has not only a similar strength and analogous properties34,57-59 but also a wide range of features shared with H-bonds, and interestingly, there are cases where H-bond and X-bond compete with each other.59-66 In the following, for the sake of convenience we use D···Y−A (Y = H or X) for both H-bond and X-bond. The similarity between H-bond and X-bond makes parallel comparative studies attractive and significant, and naturally leading to a question: does the blue-shifting X-bond exist and if does, then what is its origin? Different from H-bond, the experimental detection of X-bond is difficult due to the strong coupling of the X−A stretching vibration with other vibrations, in other words, there are very few pure X−A stretching modes.67-71 Consequently, theoretical studies turn to be more important and illuminating as they can provide complete information for non-covalent interactions, particularly with the use of bond length variation as an indicator of X−A stretching frequency shifts.72-74 Before exploring the existence and nature of blue-shifting X-bond, we briefly revisit the 4


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theoretical interpretations for the well-studied blue-shifting H-bond.27 A consistent explanation for both red- and blue-shifting H-bonds was proposed by Alabugin and co-workers based on the charge transfer effect,75 who claimed that the frequency variation is controlled by a balance between the n(D)→σ*(H−A) charge transfer, which tends to elongate the H−A bond and leads to a red shifting of the IR stretching frequency, and the “H−A bond contracting factors” including the polarization of H−A bond and the change of s character of the H−A bonding orbital due to the rehybridization. But prominent counter-example (water dimer) was noted by Joseph and Jemmis,76 who found that the s character at the O atom in the hydrogen donor increases as water molecules approach, yet the elongation of H−A begins at a long intermolecular distance even before the rehybridization plays any role. Instead, they proposed a unified explanation in the “A vs B” pattern centered on the classical electrostatic interaction. On one hand, the elongation is preferred by the electrostatic attraction between the electron-deficient hydrogen atom and the electron-rich D. On the other hand, the presence of D polarizes the electron density of H−A by increasing the electron density on A and decreasing the electron density on H, resulting in a shortening of the bond due to the stronger electrostatic attraction between H and A. An alternative electrostatic explanation was proposed by Li et al.77 They discovered that the blue shifting can be well reproduced by replacing the H-bond accepter D with a set of charges (2 negative and one positive charges fixed in space which can impose an approximately equivalent electric field as the H-bond accepter), indicating that the stability of the complex and the change of the H−A bond can be simply explained in terms of the competition between the attractive and Pauli repulsive forces.77 Further evidence for the electrostatic nature in blue-shifting H-bonds was provided by our recent study, in which the energetic, geometrical and spectral variations with the deactivation of electron transfer were obtained using the BLW method.78 We confirmed the long-range character of the blue-shifting H-bond, and concluded that blue shifting is predominantly caused by the electrostatic interaction, which is the only energy component of long-range character. The final variation of frequency changes is determined by the competition between the charge transfer effect and the electrostatic interaction, and there is no essential 5



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difference between the red- and blue-shifting phenomena. Theoretical investigations of blue-shifting X-bonds and the difference between H- and X-bonds were carried out by Wang et al..67,79,80 By analyzing the eight criteria for H-bonds proposed by Popelier within the AIM formalism,81-83 and electron density variations upon the formation of X-bonds using the natural bond orbital (NBO) approach,84 they claimed that blue-shifting H-bond and X-bonds have strong differences in physical nature, yet their origins are the same, namely the negative permanent dipole moment derivative of donor molecules.67 Later, they proposed that the elongation of the X−A bond is dominated by the charge transfer from D to the X−A σ anti-bonding orbital, while the contraction originates from the decrease of the electron density on the atom bonding to X due to the presence of the Lewis base D.79 The latter is actually identical to the Joseph-Jemmis theory for blue-shifting H-bond.76 Another electrostatic explanation for the blue-shifting X-bond was proposed by Politzer et al.85 In consistency with earlier models developed by Hermansson86 and Qian-Krimm87, they found that the reverse direction of the derivative of the X-bond donor’s permanent dipole moment to the electric field imposed by D is the necessary but not sufficient condition for blue shifts of X-bond.85 The differences of properties between blue-shifting H- and X-bonds were also explored by Wang and coworkers, who commented that the blue shifting phenomenon happens more frequently and significantly in X-bonding complexes than in H-bonds.80 Interestingly, by analyzing the electron density variation using the NBO method, they found that the differences are caused by the electron density transfer from the lone pair orbitals of X to the remote part of the donor. This long movement of electrons density is absent in H-bonding systems.80 The correlation between the stretching vibrational frequency shift and the bond length variation can be anticipated and has been investigated by Wang et al. who confirmed a good linear relationship.88 Significantly, Jemmis and coworkers proposed a general theory for all D···Y−A weak bonds where Y can be hydrogen, halogen, chalcogen and pnicogen.73,74 They hypothesized that there is negative hyperconjugative donation from the A-group to the antibonding orbital σ*(Y−A), and the Pauli exchange repulsion between D and the electron density on σ*(Y−A) 6


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leads to the contraction, i.e., blue-shifting, of the Y−A bond. As a consequence, the balance between the negative hyperconjugation (plus the subsequent Pauli repulsion) and the n(D)→σ*(Y−A) charge transfer determines the direction and magnitude of the Y−A stretching frequency shifting. However, we note that the electron density movement on the partially occupied σ*(Y−A) is regarded as a part of polarization effect in literature. Thus, the general theory by Jemmis and coworkers is similar to the earlier explanation by Alabugin et al.,75 though a particular electron movement is singled out in the new theory. We also note that Pauli exchange repulsion is largely short-range and blue-shifting (or bond contraction) appears at long-range distances.78 In this work, we intend to probe H-bonds and X-bonds together with the BLW method which can uniquely generate optimal geometries and vibrational frequencies with the n(D)→σ*(Y−A) electron transfer quenched, as well as energy components for the bonding in D···Y−A. The electron density difference between regular DFT and BLW solutions can also show the movement of electrons in the process of electron transfer. Of particular, the correlation between the total stability of the complex and the variation of the Y−A bond length will be explored, in attempt to obtain a unified picture for the red- and blue-shifting H- and X-bonds.

Method Block-localized wavefunction (BLW) method As a classic and well-developed theory in quantum mechanics, ab initio valence bond (VB) theory describes a many-electron wavefunction with a series of chemically meaningful VB or Heitler-London-Slater-Pauling (HLSP) functions, and each VB function corresponds to an electron-localized Lewis (resonance) structure. Thus, the resonance energy (or charge transfer energy among molecules) can be obtained as the energy difference between the most stable VB function and the overall wavefunction, which is a superposition of all VB functions. In contrast to the popular molecular orbital (MO) methods where all orbitals are delocalized and orthogonal, orbitals in VB theory are strictly localized and nonorthogonal, as the concept that orbitals overlap 7



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to form bonds plays a central role in chemistry theory. While the localization and nonorthogonality of orbitals in VB theory lead to physically and chemically appealing insights into chemical bonding nature, computationally they are far unfavorable compared with MO-based methods. As the simplest variant of VB theory, the BLW method retains the nonorthgonality of orbitals but defines the electron-localized state with one Slater determinant, leading to a significant reduction of computational complexity and cost. In the BLW method, all electrons and basis functions are partitioned into several subgroups (blocks) and each orbital (BL-MO) is expanded in only one block. Orbitals in the same block are subject to the orthogonality constraint while orbitals belonging to different blocks are nonorthogonal. In the study of intermolecular non-covalent interactions between Lewis acid A and Lewis base B, the complex can be simply partitioned into two blocks and the intermediate state in which the charge transfer is “turned off” can be defined as Ψ୆୐୛଴ = ‫ܣ‬መ(Ψ୅଴ Ψ୆଴ )

(1a)

Ψ୆୐୛ = ‫ܣ‬መ(Ψ୅ Ψ୆ )

(1b)

where Ψ୆୐୛଴ is the initial electron-localized wavefunction composed of optimal orbitals ( Ψ0A and Ψ0B ) of separated A and B at the geometries in complex; Ψ୆୐୛ refers to the stable electron-localized wavefunction which is optimized self-consistently. Note that the BLW method has been extended to the density functional theory level54 with Grimme’s dispersion correction89,90 also included. An energy decomposition approach based on the BLW method (called BLW-ED)55,56 was proposed in order to further probe the non-covalent interactions between A and B. Alternatively, the strictly localized molecular orbital EDA (SLMO-EDA)91 is identical to the BLW-ED approach. The binding energy ∆Eb in the BLW-ED method is defined as the balance between the intermolecular interaction energy ∆Eint and the deformation energy ∆Edef, which is the energetic cost for deforming monomers A and B from their free and optimal structures to the geometries in complex. Thus, Δ‫ܧ‬ୠ = Δ‫ܧ‬ୢୣ୤ + Δ‫ܧ‬୧୬୲

(2) 8


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where the interaction energy is the energy difference between the complex and the energetic sum of distorted monomers with the basis set superposition error (BSSE) corrected. The interaction energy can be further decomposed to a number of components as Δ‫ܧ‬୧୬୲ = ‫(ܧ‬Ψ୅୆ ) − ሾ‫(ܧ‬Ψ୅଴ ) + ‫(ܧ‬Ψ୆଴ )ሿ + BSSE = Δ‫ܧ‬୊ + Δ‫ܧ‬୮୭୪ + Δ‫ܧ‬େ୘ + Δ‫ܧ‬ୢ୧ୱ୮

(3)

In Eq. 3 the frozen energy ∆EF is the energy variation caused by the formation of complex from the free and distorted monomers, without disturbing the electron density of each individual monomer. It is composed of the contributions from the electrostatic and Pauli exchange interactions. The polarization energy ∆Epol results from the energy-lowering effect caused by the reorganization of electron densities within individual monomers due to the electric field and Pauli exchange imposed by others. The complex can be further stabilized by extending the redistribution of electrons from individual monomers to the entire complex. After correcting for the BSSE, this energy variation is denoted as the charge transfer energy ∆ECT. At last, the contribution of electron correlation (largely dispersion ∆Edisp) to the binding energy is computed ୈ୊୘ as the difference of Grimme’s dispersion correction energies between the complex (‫ܧ‬ୢ୧ୱ୮ ) and ௜ the total of distorted individual monomers (‫ܧ‬ୢ୧ୱ୮ , i=A and B). The expressions for these energy

components are Δ‫ܧ‬୊ = ‫(ܧ‬Ψ୆୐୛଴ ) − ሾ‫(ܧ‬Ψ୅଴ ) + ‫(ܧ‬Ψ୆଴ )ሿ

(4a)

Δ‫ܧ‬୮୭୪ = ‫(ܧ‬Ψ୆୐୛ ) − ‫(ܧ‬Ψ୆୐୛଴ )

(4b)

Δ‫ܧ‬େ୘ = ‫(ܧ‬Ψୈ୊୘ ) − ‫(ܧ‬Ψ୆୐୛ ) + BSSE

(4c)

ୈ୊୘ ୅ ୆ Δ‫ܧ‬ୢ୧ୱ୮ = ‫ܧ‬ୢ୧ୱ୮ − ‫ܧ‬ୢ୧ୱ୮ − ‫ܧ‬ୢ୧ୱ୮

(4d)

Geometry optimization and vibrational frequency calculation of electron localized states are both available using the in-house version of GAMESS software.92 Thus, the effect of charge transfer on stability, geometry, and spectra can be quantified by comparing the regular DFT and the BLW results.

9



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Potential energy surface analysis based on the BLW-ED approach An effective way to elucidate the nature of red- and blue-shifting H-bonds has been the correlation between the H−A bond length or the stability of the complex and the distance between D and H−A.76,78 This strategy can also be adopted in the investigation of halogen bonding complexes,73,74 because short-range interactions (i.e., charge transfer, polarization and Pauli exchange) can be turned off when the interacting moieties are far away from each other. Moreover, the role of the charge transfer interaction can be quantified directly using the BLW method, and the contribution of electrostatic and polarization interaction can also be deduced (see Eq. 4). Here we adopted a novel potential energy surface analysis based on the BLW-ED approach, in order to clarify the role of each energy component in the variation of the Y−A bond length and the associated stretching vibrational frequency. Since the binding energy is a sum of five components (Eqs. 2 and 3) in the BLW-ED method, we can express the change in the total binding force, ∆Fb, which is the first-order derivative of binding energy with respect to the Y−A bond length R2, in terms of ∆‫ܨ‬ୠ =

ௗ∆ாౘ ௗோమ

=

ௗ∆ாౚ౛౜ ௗோమ

+

ௗ∆ாూ ௗோమ

+

ௗ∆ா౦౥ౢ ௗோమ

+

ௗ∆ாి౐ ௗோమ

+

ௗ∆ாౚ౟౩౦ ௗோమ

= ∆‫ܨ‬ୢୣ୤ + ∆‫ܨ‬୊ + ∆‫ܨ‬୮୭୪ + ∆‫ܨ‬େ୘ + ∆‫ܨ‬ୢ୧ୱ୮

(5)

By computing each term in the right side of Eq. 5, we can clarify the factors governing the variations in vibrational frequency and bond length of Y−A (R2). The elongation of R2 due to the formation of complex can be characterized by a negative derivative value at the origin, while the shrinking can be characterized by a positive derivative value as represented in Fig. 1.

10


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(a) Elongation

∆Eb

(b) Shrinking

∆Eb

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-0.1

0.0 ∆R2

-0.1

0.1

0.0 ∆R2

0.1

Figure 1. Correlation between the binding energy of the non-covalent interaction in complex D···Y−A and the variation of its Y−A bond length (∆R2=0 corresponds to the parental monomer YA).

Computational details Eight representative systems, as shown in Fig. 2, have been chosen and analyzed in this work. Among them, five (1, 3, 4, 7 and 8) are red-shifting H-bonding and X-bonding complexes, while the rest three (2, 5 and 6) are blue-shifting H-bonding and X-bonding complexes. In addition, these complexes can also be classified into four groups (1 vs 2, 3 vs 4, 5 vs 6 and 7 vs 8), each of which is consisted with two complexes formed by the same Lewis acid but different Lewis bases. Thus, the effect of Lewis bases can be evaluated by comparing the complexes in the same group. The energy profiles of all complexes were obtained by varying the Y−A bond length from its value in the free and optimal structure of monomer with all the rest structural parameters optimized. The spin-component-scaled second-order Møller–Plesset (SCSMP2) theory, in which the same spin is scaled down and the opposite spin is enlarged in order to improve the description of molecular ground stated energies, has been proven to be a reliable theory for the study of non-covalent interactions.93-96 Thus we performed here benchmark computations at the SCSMP2/aug-cc-pVTZ level of theory with optimal geometries derived, and the variations of bond length, vibrational frequency and the IR intensity of Y−A bond up on formation of complex, 11



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as well as the binding energy, were also calculated. Contraction and blue-shift of stretching vibrational frequency were observed in complexes 2, 5 and 6 for their Y−A bonds, while elongation and red-shift of the Y−A bond complexes 1, 3, 4, 7 and 8 were identified, as tabulated in Table S1 (see Supplementary Information). Regarding the binding energy, the sequence in the benchmark work is 3 > 7 > 4 > 8 > 1 > 2 > 5 > 6. In comparison, various DFT functionals including M062X, B3LYP, BHHLYP and PEPB augmented by Grimme’s D3-dispersion correction were also tested with the cc-pVTZ basis set. The same tendency of bond-length variation, stretching vibrational frequency shift of the Y−A bond upon the formation of complex, and also the relative stability of all systems were well reproduced by preforming these DFT-D3 calculations (see Table S2 and S3). Among the tested functionals, M062X-D3 produces the results closest to the SCSMP2 benchmarks. For example, the discrepancy in the Y−A bond-length variation between SCSMP2 and M062X-D3 calculations is less than 0.001 Å for all complexes with only one exception (0.011 Å in complex 7). Consequently, M062X-D3 is the best choice for our BLW-ED analyses considering its much lower computational expense and the appropriate computational accuracy with reference to the SCSMP2 theory. As such, in this study all computations and analyses were carried out at the M062X-D3/cc-pVTZ level of theory using the in-house version of GAMESS software.92

H3N···HCF3 (1)

H2O···HCF3 (2)

H3N···HF (3)

H2O···HF (4)

12


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H3N···ClCF3 (5)

H2O···ClCF3 (6)

H3N···ClF (7)

H2O···ClF (8)

Figure 2. Model hydrogen- and halogen-bonding complexes analyzed in this work.

Results and Discussion The D···Y distances, variations of the Y−A bond length, stretching vibrational frequencies and the corresponding IR intensities due to the formation of H- or X-bonds were computed using both the regular DFT and BLW methods, and the results are summarized in Table 1. Two notable findings can be derived from the results of regular DFT optimizations. First, for all cases, red shift is accomplished with an enhanced IR intensity while blue shift is associated with a reduction in IR intensity, with two exceptions (complexes 1 and 6) which are verified by the SCSMP2 calculations (Table S1). Second, the lengthening of the Y−A bond is found in all red-shifting cases, and the shrinking of Y−A bond is always associated with a blue-shifting either H- or X-bonds. Moreover, the linear correlation between the shift of stretching vibrational frequency and the bond length change in X-bonds once discovered by Wang et al.,68 was confirmed in our study as shown in Fig. 3a. This “∆ʋ vs ∆R2” linear correlation was also found in H-bonding complexes by Li et al.77 and reproduced in our study. The slope of the linear fitting equation between ∆ʋ and ∆R2 for the H-bonds is much greater than for the X-bonds, indicating that the variation of vibrational frequency is more sensitive to the bond-length change in H-bonds than in X-bonds. According to our previous studies,78,97 the charge-transfer interaction is dominantly responsible for the elongation of the Y−A bond in both H- and X-Bonding systems. Moreover, 13



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the charge transfer interaction plays a key role for the stability, selectivity48, and directionality97 of most X-bonding systems. Thus it is of great importance to clarify the contribution of charge transfer to the shifts of Y−A stretching vibrational frequencies. With the charge transfer interaction between the Lewis base (D) and Lewis acid (Y−A) deactivated, BLW optimizations essentially result in van der Waals complexes. Thus the comparison between the regular DFT and BLW results using the same functional and basis set can provide insight to the contribution from the charge transfer interaction to red- or blue-shift directly. Two significant conclusions can be obtained by comparing the differences in key structural parameters and Y−A stretching vibrational frequencies between the regular DFT and BLW calculations. First, charge transfer interactions tend to elongate the Y−A bond, as shrinking (i.e., decrement of ∆R2 value from regular DFT to BLW-DFT in Table 1) can be observed after charge transfer interactions are turned off. This observation can be easily explained using the orbital interaction between the lone pair orbital of D and the anti-bond orbital σ*(Y−A). This is certainly in accord with all previous works except that we provide quantitative data here. Second, an associated increment of Y−A stretching vibrational frequencies was found for most complexes with the “turning off” of charge transfer interactions. For all red-shifting H- and X-bonds (complexes 1, 3, 4, 7 and 8), the magnitude of red shifts is reduced due to the turning off of charge transfer interactions. An illuminating example is complex 1, in which the red shift predicted by the regular DFT calculation turns to be a blue shift after the charge transfer interaction herein is quenched. The blue-shifting observed in complex 2, however, is further enhanced due to the deactivation of charge transfer interactions. Exceptions were found in complexes 5 and 6, in which the blue shifts change a little with the turning off of charge transfer interactions. This could be caused by the coupling between the Y−A stretching vibrational frequency with other vibrations as Wang et al. discussed previously.68 Moreover, the decrements of ∆ʋ in 5 and 6 are less than 1 cm-1, which is extremely small, and the magnitudes of the shrinking of the Y−A bond are similarly insignificant. Our present computations thus strongly indicate that the contribution from the charge transfer interaction to the variations of bond length 14


Page 15 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


and stretching vibrational frequency is consistent for both H- and X-bonds.

Table 1. Variations of Y−A bond length (∆R2 in Å), stretching vibrational frequencies (∆ʋ in cm-1) and the corresponding IR intensity (∆I in Debye2/muÅ-2) upon the formation of a complex calculated at M062X-D3/cc-pVTZ level of theory. Complex1)

Regular DFT

BLW-DFT

R1

∆R22)

∆ʋ2)

∆I2)

R1

∆R2

∆ʋ

∆I

1

2.302

0.001

-6.2

-0.486

2.389

-0.002

39.4

-0.749

2

2.195

-0.002

34.2

-0.697

2.274

-0.002

46.2

-0.748

3

1.686

0.033

-754.2

32.285

1.948

0.009

-136.5

9.462

4

1.693

0.017

-409.9

20.026

1.871

0.006

-73.4

7.262

5

2.972

-0.007

14.1

-0.288

3.122

-0.009

13.2

-0.667

6

2.910

-0.006

11.9

0.142

3.002

-0.008

10.9

0.367

7

2.342

0.049

-163.5

4.463

2.840

0.008

-41.4

0.555

8

2.535

0.015

-67.5

1.506

2.744

0.006

-37.1

0.418

1) The serial numbers of complexes can be found in Fig. 2. 2) ∆R2, ∆ʋ, ∆I refers to the changes from monomer Y−A to complex D···Y−A.

To further clarify the role of charge transfer in the elongation of Y−A bonds and the accompanied red-shifts, we conducted the BLW-ED analyses whose results are compiled in Table 2. The eight complexes can be divided into four groups as mentioned in the computational details subsection, and the significance of charge transfer interactions for the stretching of Y−A bonds can be confirmed by comparing the BLW-ED results of two complexes in the same group. For instance, complexes in the first group (1 and 2) are composed of the same Lewis acid (F3CH) with different Lewis bases (H3N and H2O, which are common hydrogen or halogen accepters for all groups). Compared with complex 2, complex 1 possesses higher charge transfer energy, which is associated with a more pronounced elongation of the Y−A bond and a reduction of its 15



stretching vibrational frequency. The same observation is also found in the second and fourth groups, and can be well explained using the n(D)→σ*(Y−A) orbital interaction in line with the literature. Compared with H2O, H3N is more basic and thus expected to have a stronger charge transfer interaction to the anti-bonding orbital of Y−A, which weakens the Y−A bond more significantly. However, exception is found in the third group. The Y−A bond length in complex 6 (F3CCl···OH2) is longer than in complex 5, although the charge transfer energy in 6 is lower. One reasonable explanation for this exception could be that the charge transfer is not the only elongating factor, and this assumption will be proved later in this paper. It should be reminded that the difference in Y−A bond lengths between complexes 5 and 6 is tiny (only 0.001Å), so is the difference in their charge transfer energies. Therefore, it is still sound to deduce that generally the charge transfer interaction elongates the Y−A bond and redshifts its stretching vibrational frequency for all H- and X-bonds. This statement is also supported with the good linear correlation between the charge transfer energy and the variation of Y−A bond length upon the formation of H-bond or X-bonding complexes (Fig. 3b).

-800

-42

(a)

∆ʋ = -23314∆R2 + 1 R² = 0.99 (H-bond)

-500

H-bond

-350

X-bond

-200 -50 100 -0.01

0.03

-28

∆ECT = -670∆R2- 7 R² = 0.98 (X-bond)

-21

X-bond

0 -0.01

0.05

H-bond

-14 -7

∆ʋ = -3170∆R2 - 11 R² = 0.99 (X-bond)

0.01

(b)

-35

∆ECT (kJ/mol)

-650

∆ʋ (cm-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 41

∆ECT = -464∆R2- 2 R² = 0.99 (H-bond)

0.01

0.03

0.05

∆R2 (Å)

∆R2 (Å)

Figure 3. Correlation between ∆ʋ (in cm-1) and ∆R2 (in Å) (a) and correlation between ∆ECT (in kJ/mol) and ∆R2 (in Å) (b).

16


Page 17 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2. Energy components of the optimal geometries at M062X-D3/cc-pVTZ level by means of BLWED approach (kJ/mol). Complex

∆Edef

∆EF

∆Edisp

∆Epol

∆ECT

∆Eint

∆Eb

1

0.4

-12.6

-0.4

-3.2

-1.8

-18.1

-17.7

2

0.3

-10.7

-0.3

-2.3

-1.5

-14.8

-14.5

3

0

-19.8

-0.1

-13.5

-16.9

-50.2

-50.2

4

0

-17.6

0

-9.4

-10.4

-37.5

-37.4

5

0.3

-5.9

-0.3

-2.5

-3.8

-12.5

-12.3

6

0.1

-4.9

-0.2

-1.5

-2.4

-9

-8.8

7

0.4

11.1

-0.1

-10.9

-40.9

-40.8

-40.4

8

0

-6.3

-0.1

-4.7

-13.7

-24.8

-24.8

The causality between the nature of non-covalent bonds and the variation of bond lengths and stretching vibrational frequencies has also been explored using the BLW-ED approach. We started the analysis with the red-shifting cases. Complex 1 (weak H-bond) is dominated by the frozen energy, representing an overwhelming electrostatic nature. Charge transfer interactions play the key role in 7 and 8 (strong X-bonds). In complexes 3 and 4 (medium-strong H-bonds), the binding energy is mainly contributed by the frozen interaction, but secondarily enhanced by the charge transfer energy interaction with a comparable strength. Obviously, the nature of non-covalent interaction in different groups is different, albeit the red shift is found in these cases. Remarkably, for blue-shifting cases (2, 5 and 6), there are much lower binding energies and charge transfer energies, compared with most of the red-shifting cases. Yet there is no obvious causality between the nature of non-covalent bonds and the tendency of bond length variations. An illuminating example is the comparison between complexes 1 and 2, which have close BLW-ED data as seen in Table 2 but very different variations of bond lengths and stretching vibrational frequencies (Table 1). The quantitative investigation of the charge transfer interaction in the above provides us 17



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Page 18 of 41

with a consistent conclusion, and also makes the intuitional visualization of the electron flows between and within Lewis base and acid desirable. Electron density difference (EDD) maps represent the electron density variations caused by the polarization effect and the charge transfer interaction, and can be plotted based on the differences between Ψ୆୐୛ and Ψ୆୐୛଴ , Ψୈ୊୘ and Ψ୆୐୛ , respectively. The density difference between Ψ୆୐୛ and Ψ୆୐୛଴ reflects the electron movement within each monomer due to the existence of others, while the difference between Ψୈ୊୘ and Ψ୆୐୛ highlights the electron flow between Lewis base and acid. EDD maps for complexes 2, 4, 6 and 8 are presented in Fig. 4, where the red color denotes a gain of electron density while the blue represents a loss of electron density. A much lower isodensity value was used in 2b and 6b (0.0002 a.u), which are both blue-shifting systems, because the electron density variation caused by charge transfer interactions in these cases are much less significant than the red-shifting cases (4b and 8b). This finding is in line with the conclusion based on BLW-ED analyses. For example, the inconspicuous EDD caused by charge transfer interactions in F3CH···OH2 complex (Fig. 4 (2b)) corresponds to the lowest charge transfer energy among all cases, which is only 1.5 kJ/mol. EDD maps showing the total density change from Ψ୆୐୛଴ to Ψୈ୊୘ are available in the Supporting Information (Fig. S1).

(2a)

(2b)

(4a)

(4b)

18


Page 19 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(6a)

(6b)

(8a)

(8b)

Figure 4. Electron density difference (EDD) maps showing the electron density changes due to the polarization (a) and intermolecular charge transfer interactions (b) of (2) H2O···HCF3 (4) H2O···HF (6) H2O···ClCF3 and (8) H2O···ClF. The isodensity values equal to 0.001 e Å-3 except for 2b and 6b whose isodensity value is 0.0002 a.u. The red color means a gain of electron density while the blue represents a loss of electron density.

Interestingly, analyses of the above EDD maps corresponding to the charge transfer interaction reveal a general pattern of electron density flow between the Lewis base and acid for both the red- and blue-shifting systems. The electron density in the region of the lone-pair orbital of the Lewis base is reduced, and there’s a loss of electron density around the atom Y of the Lewis acid as well. Most of the electron density accumulates in the common area between the Lewis base and acid, and form a “double faced adhesive tape, gluing” the two monomers together. This phenomenon was first discovered in our previous investigation of the self-association of graphane and graphene,98 and later observed in the EDD maps of the chalcogen and pnicogen bonds as well.97 Therefore, this “gluing” pattern in EDD maps caused by the electron density flow among monomers may generally exist in all sorts of non-covalent interactions, and suggests an enhancement in electrostatic interactions. It was also observed that in the Y−A bond area of each system there is a nodal plane, where the electron density variation reaches a local minima and changes the direction (gain or loss) on each side. This pattern of 19



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Page 20 of 41

electron density variation has the shape which is very similar to the σ*(Y−A) orbital, and may suggest a gain of electron density in it. This discovery is supported by the NBO calculations.84 The electron transfer from the lone pair on D to the σ*(Y−A) orbital is the most significant orbital interaction between monomers, and contributes more than 51.5% of the total charge transfer energy for all cases (Table S4). It should be emphasized that, in spite of qualitatively consistent results obtained using the NBO analysis, its charge transfer energy is much greater than the BLW value, largely due to the use of non-optimal localized orbitals.99 For example, the total charge transfer energy between F3CH and NH3 (complex 1) is 29.2 kJ/mol using the NBO method, which is even higher than the total binding energy between monomers. In contrast, the BLW value is merely 1.8 kJ/mol (see Table 2). The electron density variation caused by polarization interactions is also investigated and represented in Fig. 2 (2a, 4a, 6a and 8a). Different from the charge transfer, polarization interactions tend to increase the electron density in the region of the lone-pair orbital of the Lewis base, and reduce the electron density around the atom Y of the Lewis acid in all cases. This pattern of electron density variation suggests that any electron density polarization can be taken as a preparation for the subsequent electron transfer interaction.100 In addition, a nodal plane on the Y−A bond has also been found, suggesting that polarization interactions may also increase the electron population in the σ*(Y−A) orbital and elongate the Y−A bond. This elongating effect of polarization interactions is in contrast to previous theories73,74,76,79 and will be further proved in the following section. We note that the most recent work by Jemmis and coworkers suggested that the polarization of the partially occupied σ*(Y−A) orbital is the driving force for the contraction of the Y−A bond.73,74 So far our focus has been on the correlations of vibrational frequency changes with the structural variations, electron density movement and contributions from different energy terms to binding energies at optimal geometries. To quantify the roles of each type of interactions in the frequency shifts, we employed the PES analyses based on BLW-ED computations and identify the forces governing the red- or blue-shifting phenomenon (Eq. 5). Fig. 5 shows the energy 20


Page 21 of 41

profiles along the variation of ∆R2 for four systems in which H2O is the common Lewis base. Two of the focused systems, a(F3CH···OH2) and c(F3CCl···OH2), exhibit a shrinking of the Y−A bond, while the rest, b(FH···OH2) and d(FCl···OH2), have stretched Y−A bond at the optimal geometries, as evidenced by the minimal positions of the total binding energy curves with respect to the zero point. Curves of frozen energy, polarization energy and charge transfer energy are all monotonic, predicting no minimal points at the viable range of ∆R2. Strikingly, the correlation between the deformation energy and ∆R2 is the only non-monotonic function. Therefore, the deformation energy most likely plays the dominating role for the overall shape of the binding energy curve although it is a destabilizing factor as any deformation of monomers necessarily offsets the binding energy. But the deformation energy experiences a minimum value at the origin (Table 3) for all complexes, indicating a favorable Y−A bond length after the engagement of the Lewis base. It should be noted that the dispersion energy changes little along ∆R2 in the interval investigated in this work (∆R2∈[-0.1, 0.1]) for each of the complexes, suggesting no contribution to the bond length variation. Energy profiles for all complexes are shown in the Supporting Information (Fig. S2).

1 ∆E(kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-3

(a) F3CH···OH2

16 ∆ECT 12

∆Epol

-7

8

-11

∆EF

∆Eb -15 -0.10 -0.05 0.00 0.05 ∆R2(Å)

4 0 -0.10

0.10

21


∆Edef

-0.05

0.00 0.05 ∆R2(Å)

0.10


10

40 (b) FH···OH2

∆E(kJ/mol)

0

30

∆Epol

-10 ∆EF

-20

20 ∆ECT

∆Edef 10

-30 ∆Eb -40 -0.10 -0.05 2

∆E(kJ/mol)

0.00 0.05 ∆R2(Å)

0 -0.10

0.10

0.00 0.05 ∆R2(Å)

0.10

0.00 0.05 ∆R2(Å)

0.10

12

∆Epol

10

-2 ∆ECT

-4

-0.05

14

(c) F3CCl···OH2

0

8

∆EF

∆Edef

6

-6

4

-8

∆Eb

-10 -0.10

0

-0.05

2 0.00 0.05 ∆R2(Å)

0 -0.10

0.10

15

∆Epol

∆EF

-10

∆ECT

-15

10

-20 -25

5

∆Eb

-30 -0.10 -0.05

-0.05

20

(d) FCl···OH2

-5 ∆E(kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 41

0.00 0.05 ∆R2(Å)

0 -0.10

0.10

∆Edef

0.00 ∆R2(Å)

0.10

Figure 5. Energy profiles along the variation of the Y−A bond length (Å) based on the DFT optimal geometries at the M062X-D3/cc-pVTZ level. Right curves represent the variation of the destabilizing deformation energy term while left curves are the profiles of frozen energy, 22


Page 23 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


polarization energy, charge transfer energy and the total binding energy.

One notable finding in Fig. 5 is that for blue-shifting systems (a and c) both the electron transfer and polarization energy terms change only slightly with respect to the bonding distance, where for red-shifting complexes (b and d) the changes are far more significant. Still, there is a monotonous decreasing (or enhancement) of the charge transfer energy which is actually found in all complexes studied, and indicates that the whole complex will be stabilized by charge transfer interactions between D and Y−A, and the Y−A bond gets longer with the gradual shortening of the distance between D and Y−A. This finding holds no matter whether the final bonding complex exhibits red- or blue-shifting of the Y−A stretching vibrational frequency. In order to gain insights into this monotone variation, the variation of σ*(Y−A) orbital energies of the free and distorted Lewis acid (d-acid), and the block-localized Lewis acid (BL-acid) along with the stretching of the Y−A bond were calculated and plotted in Fig. 6. It should be noted that only the BLW method so far can derive the orbitals energies of a monomer (i.e., BL-acid here) in the presence of others, which can be labeled with “in-situ”.100 The σ*(Y−A) orbital energy decreases as the Y−A bond stretches in both d- and BL-acid cases, suggesting a stronger acidity when the Y−A bond stretches for all systems (Fig. S3). Moreover, we found that the amount of electrons transferred from D to Y−A increases with the increasing Y−A bond length in all cases (Fig. S4), indicating a stronger charge transfer interaction due to the elongation of the Y−A bond.

23



0.6

(a) F3CH···OH2

Energy of σ* (a.u)

Energy of σ* (a.u)

0.53 0.48 0.43 0.38

d-acid BL-acid

0.10 0.08

(c) F3CCl···OH2

Energy of σ* (a.u)

0.12

(b) FH···OH2

0.5

0.4 d-acid BL-acid

0.3 -0.10 -0.05 0.00 0.05 0.10 ∆R2 (Å)

0.33 -0.10 -0.05 0.00 0.05 0.10 ∆R2 (Å)

Energy of σ* (a.u)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 41

d-acid BL-acid

0.06 0.04 0.02 0.00 -0.10 -0.05 0.00 0.05 0.10 ∆R2 (Å)

0.04 (d) FCl···OH2 0.02 d-acid 0.00 BL-acid -0.02 -0.04 -0.06 -0.08 -0.10 -0.10 -0.05 0.00 0.05 0.10 ∆R2 (Å)

Figure 6. Correlation between the σ* orbital energy (in a.u) of the d- and BL-acids in the complexes formed with H2O and ∆R2 (in Å)

Similar to the charge transfer interaction, the polarization energy also monotonously decreases along ∆R2 for almost all systems, suggesting that the stretching of the Y−A bond is energetically preferred due to the polarization effect. Compared with the charge transfer curve, the variation of polarization energy is less significant. In other words, the polarization effect plays the secondary role in the elongation of the Y−A bond. One exception is once again the F3CCl…OH2 complex, where the polarization energy increases slightly as the Y−A bond gets longer, though the maximum change in the our defined interval is only 0.4 kJ/mol. Most importantly, the polarization energy essentially changes little and remains nearly a constant (-1.5 24


Page 25 of 41

kJ/mol) in an interval around the origin (from -0.02 Å to 0.02 Å), indicating a negligible contribution to the bond length variation. We thus still can claim that the polarization interaction generally tends to elongate the Y−A bond for all red- or blue-shifting H- and X-bonds. Theoretically, polarization interaction is the reorganization of electron density within each monomer, due to the electronic field imposed by the other monomer. This reorganization is accomplished by mixing occupied molecular orbitals with unoccupied molecular orbitals within each monomer, and of particular, partially fills the initially vacant σ*(Y−A) (here our definition of the antibonding orbital as a virtual orbital dominantly on the Y−A bond is different from the one by Jemmis and coworkers based on the NBO analyses where antibonds are localized and partially occupied). Indeed, we found that the HUMO-LUMO gap of the d-acid decreases with the elongation of the Y−A bond for all Lewis acids studied (Fig. 7). This suggests that a more significant orbital mixing within the electron accepter correlates with higher polarization energy.

16

16

F3CH

(a)

FH

∆HL(eV)

14

F3CCl

12

F3CH

(b)

FH

14

∆HL(eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


F3CCl

12 10

10

FCl

FCl 8

8

-0.10 -0.05

0.00 0.05 ∆R2 (Å)

-0.10 -0.05

0.10

0.00 0.05 ∆R2 (Å)

0.10

Figure 7. Correlation between the HOMO-LUMO energy gap (in eV) in different distorted Lewis acids in the complexes formed with H2O (a) and H3N (b), and ∆R2 (in Å).

Differently, the frozen energy keeps increasing along ∆R2 (Fig. 5). This means that the frozen interaction energy between the Lewis acid and base, resulted from both the electrostatic and Pauli repulsive interactions, tends to destabilize the complex as the Y−A bond length 25



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Page 26 of 41

increases. Therefore, the frozen energy is the only energy component which contributes to the shrinking of the Y−A bond, and necessarily responsible for the blue-shifting phenomenon. This finding is consistent with our previous study of blue-shifting H-bonds using the BLW method,78 and is also in line with the electrostatic explanation of blue-shifting H-bond based on ab initio VB computations by Chang et al.,101 who showed that blue shifts stem from the repulsion between the Lewis base and hydrogen atom, which is included in the covalent state in terms of the resonance theory, while red-shifts are mainly ruled by the attraction between the Lewis base and the proton, which is considered in an ionic state which also contributes to the overall molecular wavefunction. In addition, a similar electrostatic explanation based on the “attraction vs repulsion” model was also supported by Wang et al., based on the electron population analysis within MO theory.79 This competition between attraction and repulsion is buried in our frozen energy term, which is the sum of both the electrostatic interaction and the Pauli exchange repulsion. Yet in this work, the continuous shrinking of the Y−A bond caused by the frozen energy term strongly indicates the “absence” of the elongating (i.e., repulsive) effect. A reasonable assumption from the correlation between ∆EF and ∆R2 is that, the Pauli exchange repulsion, which is a quantum mechanical effect and included in the frozen energy, may also tend to shorten the Y−A bond,77 and lead to the overall shrinking effect of the frozen energy term. At this point we have reached a unified theory for the variation of Y−A bond length and the corresponding stretching vibrational frequency shifts for both H- and X-bonds. In summary, the polarization and charge transfer interactions tend to elongate the Y−A bond and contribute to the red-shift of its stretching vibrational frequency, while the frozen energy is the only energy component which prefers the shrinking of the Y−A bond and thus is responsible for the blue-shift of the Y−A stretching vibrational frequency. The consistent behavior of each energy component to the variation of Y−A bond suggests that their roles do not change with different types of non-covalent interactions, but are fundamentally ruled by the physical nature of themselves. Of course, the magnitude of the role of each energy term may vary in different systems. Importantly, the overall variations of the Y−A bond length and the corresponding stretching vibrational 26


Page 27 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


frequency are determined by the competition between the frozen interaction and the sum of both polarization and charge transfer interactions. The parabolas which best fit the data points in the extremal region of ∆R2 for all energy components were obtained (Table S5), and the regression coefficients were all greater than 0.97, indicating that parabola is a suitable function for the approximation of all energy terms. Most importantly, values of first-order derivatives (Eq. 5) at the origin (∆R2=0) were computed and listed in Table 3, aiming at providing an objective evaluation of the contribution of each energy component to the variation of the Y−A bond length and subsequently the shifting of the vibrational frequency. At first we examined the derivative of the binding energy curve at the origin point. Negative values (also see Fig. 1a) were found for all red-shifting cases, while positive values (Fig. 1b) were obtained in all blue-shifting cases. Second, the zero-contribution of the deformation and dispersion interactions is confirmed by the values of their first-order derivatives at origin, which equal to zero in all cases. Third, negative values of the first-order derivative of the charge transfer energy curve are obtained at the origin for all cases, proving that the elongation and the accompanied red-shifting are preferred by charge transfer interactions between monomers. The elongation of the Y−A bond is further enhanced by the polarization interactions as negative values of the first-order derivative of the polarization energy curve, i.e., “the polarization forces” are also found in most of the cases except complexes F3CCl…NH3 and F3CCl…OH2 which have zero values for the first-order derivative of the polarization energy curve at the origin. In other words, the polarization force plays a little role in shifting the position of the minimal point in these two complexes. The magnitude of the first-order derivative of the charge transfer energy curve is greater than that of the energy curve of polarization interactions in all cases, indicating that “the charge transfer force” has a more significant impact on energetics (i.e., stability) and structure (i.e., the elongation of the Y−A bond) than the polarization effect. Finally, robust positive values of the forces from the frozen energy term at the origin were found in all complexes, confirming that the frozen energy is the only energy component contributes to the shrinking of the Y−A bond and the corresponding blue-shifting of 27



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Page 28 of 41

vibrational frequency. Here we emphasize that conclusions obtained by applying the PES analysis explain the variation of Y−A bond lengths when the distance between D and Y falls in the van der Waals region. If the interacting Lewis acid and base are at long range, both the polarization and charge transfer interactions would fade to zero, leaving only the frozen interaction governing the stability and variations of the Y−A bond and its accompanied stretching vibrational frequency. Since the frozen interaction is primarily composed of the Pauli exchange which is a kind of short-range interaction and thus fades to zero as well and the electrostatic interaction which is the only long-range interaction, and blue-shifts (or red-shifts in a few cases) occurs at long-range distances,78 the primary driving force in the frozen energy term is the electrostatic interaction.

Table 3. Derivatives of all BLW energy components with respect to ΔR2 at the origin point (ΔR2=0). Complex

Bond Type

Δ‫ܨ‬ୢୣ୤

Δ‫ܨ‬୊

Δ‫ܨ‬ୢ୧ୱ୮

Δ‫ܨ‬୮୭୪

Δ‫ܨ‬େ୘

Δ‫ܨ‬ୠ

F3CH···NH3

Hydrogen

0.0

12.7

0.0

-6.0

-10.9

-4.2

F3CH···OH2

Hydrogen

0.0

11.2

0.0

-2.5

-5.8

2.9

FH···NH3

Hydrogen

0.0

120.5

0.0

-95.2

-169.2

-143.9

FH···OH2

Hydrogen

0.0

78.1

0.0

-62.4

-102.7

-87

F3CCl···NH3

Halogen

0.0

19.3

0.0

0.0

-6.0

13.3

F3CCl···OH2

Halogen

0.0

16.7

0.0

0.0

-2.9

13.8

FCl···NH3

Halogen

0.0

248.8

0.0

-65.0

-300.0

-116.2

FCl···OH2

Halogen

0.0

17.7

0.0

-12.9

-50.5

-45.7

Conclusions By performing geometrical optimizations and vibrational frequency calculations using both 28


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the regular DFT and BLW method and comparing their results in D···Y−A complexes, we confirmed that the charge transfer interactions from the Lewis base D to the acid YA tend to elongate the Y−A bond and contribute to the accompanied decrement of the stretching vibrational frequency, as “turning off” the charge transfer interaction always results in reduced Y−A bond lengths. This conclusion is in accord with the general view in literature and supported by the BLW-ED analyses of the complexes constructed with the same Lewis acid but different Lewis bases (NH3 and H2O). The matchup between the variations in Y−A bond lengths and strengths of charge transfer interactions of the complexes in the same group suggests that a higher value of charge transfer energy is accompanied with a longer Y−A bond, leading to a reduction in its stretching vibrational frequency. Notably, the same pattern of electron density variation caused by the charge transfer or polarization interactions has been observed from the electron density difference (EDD) maps with the BLW method. The “double faced adhesive tape” shape of the overall electron density variation caused by charge transfer interactions has been rediscovered in both red- and blue-shifting cases. The increment of electron density in the region of the lone pair orbital of D, and the reduction of electron density around Y due to polarization have been identified in the EDD maps. This pattern of electron density movement due to polarization clearly suggests that any polarization is essentially a preparation step for the subsequent electron transfer between monomers, as verified in the EDD maps for the charge transfer. Significantly, a nodal plane in the Y−A bond area has been found in each of the EDD maps representing the electron density variation caused by both the charge transfer and polarization interactions, implying a likely electron flow to the σ*(Y−A) orbital and an elongation of the Y−A bond due to both the charge transfer and polarization interactions. This was verified by orbital energy analyses. We examined the HOMO-LUMO gap of each acid Y−A which serves as the H- or X-bond acceptor, and also the energy of the anti-bond orbital σ*(Y−A) which would accept electrons from the donor D. It is found that the HOMO-LUMO gap decreases with the stretching of the Y−A bond, indicating a more effective orbital mixing (i.e., polarization) within the acid due to the electrostatic field 29



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imposed by the adjacent Lewis base. This is considerably different from the previous view that the presence of the Lewis base moves the electron density from Y to A and thus increases the electrostatic attraction between Y and A and subsequently shortens the Y−A bond.76,79 With the elongation of Y−A bond, the σ*(Y−A) orbital energy decreases, and thus electron transfer from D to this anti-bond orbital is enhanced. We further investigated the correlation between the stability of a complex and the variation of its Y−A bond length using the PES analysis based on BLW-ED approach. Monotonous decreasing curves have been found in both of the ∆Epol vs ∆R2 and ∆ECT vs ∆R2 correlations. This indicates that both polarization and charge transfer interactions play stabilizing roles when the Y−A bond is stretched. The roles of polarization and charge transfer in the elongation of Y−A bond length and the accompanied red-shifting are ruled by the physical nature of these interactions, and irrelevant to the type of non-covalent interactions. Deformation and dispersion interactions, however, do not contribute to the variation of Y−A bond lengths, because their first-order derivatives at the origin of the energy curve are zero. The shrinking of the Y−A bond is only preferred by the frozen energy term, because only ∆EF decreases as the Y−A bond length decreases. Note that the frozen energy term is composed of the electrostatic and Pauli repulsion energies, and only the electrostatic interaction is long-range. As blue shift is a long range phenomenon, electrostatic interaction is the primary cause for the blue shifts of H- and X-bonds, and there is no essential difference between H- and X-bonds. The overall variations of the Y−A bond length and the accompanied stretching vibrational frequency are determined by the competition between the frozen energy and the sum of polarization and charge transfer interactions.

Supporting Information: Detailed structural information and computational results. This material is available free of charge via the Internet at http://pubs.acs.org. Acknowledgements: CW acknowledges the support from Natural Science Foundation of China (NO.21603274), the fundamental research funds for the central Universities (NO. 15CX02053A) 30


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and the talent introduction fund of China University of Petroleum (No. 2014010575). SS acknowledges support from the ISF (grant number 1183/13). This work was supported by a grant from the Faculty Research and Creative Activities Award (FRACAA), Western Michigan University (WMU).

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Crystal

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Molecular 31


Structure

of


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Cimino,

P.;

Pavone,

M.;

Barone,

V.

Halogen

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TOC Graphics

(a) Elongation

∆Eb

(b) Shrinking

∆Eb

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-0.1

0.0 ∆R2

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0.0 ∆R2

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A Unified Theory for the Blue- and Red-Shifting Phenomena in

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