Red-Shifting versus Blue-Shifting Hydrogen Bonds: Perspective from

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Red-Shifting versus Blue-Shifting Hydrogen Bonds: A Perspective from Ab Initio Valence Bond Theory Xin Chang, Yang Zhang, Xinzhen Weng, Peifeng Su, Wei Wu, and Yirong Mo J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b02245 • Publication Date (Web): 13 Apr 2016 Downloaded from http://pubs.acs.org on April 19, 2016

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The Journal of Physical Chemistry

Red-Shifting versus Blue-Shifting Hydrogen Bonds: A Perspective from Ab Initio Valence Bond Theory Xin Chang,1 Yang Zhang,1 Xinzhen Weng,1 Peifeng Su,1∗ Wei Wu,1 Yirong Mo2 1

The State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China 2 Department of Chemistry, Western Michigan University, Kalamazoo, MI 49008, USA Abstract Both proper, red-shifting and improper, blue-shifting hydrogen bonds have been well recognized with enormous experimental and computational studies. The current consensus is that there is no difference in nature between these two kinds of hydrogen bonds, where the electrostatic interaction dominates. Since most if not all the computational studies are based on molecular orbital (MO) theory, it would be interesting to gain insights into the hydrogen bonds with modern valence bond (VB) theory. In this work, we performed ab initio VBSCF computations on a series of hydrogen bonding systems where the sole hydrogen bond donor CF3H interacts with ten hydrogen bond acceptors Y (=NH2CH3, NH3, NH2Cl, OH-, H2O, CH3OH, (CH3)2O, F-, HF or CH3F). This series includes four red-shifting and six blue-shifting hydrogen bonds. In consistent with existing findings in literatures, VB-based energy decomposition analyses show that electrostatic interaction plays the dominating role and polarization plays the secondary role in all these hydrogen bonding systems, and the charge transfer interaction, which denotes the hyperconjugation effect, contributes only slightly to the total interaction energy. As VB theory describes any real chemical bond in terms of pure covalent and ionic structures, our fragment interaction analysis reveals that with the approaching of a hydrogen bond acceptor Y, the covalent state of the F3C−H bond tends to blue-shift, due to the strong repulsion between the hydrogen atom and Y. In contrast, the ionic state F3C- H+ leads to the red-shifting of the C−H vibrational frequency, owing to the attraction between the proton and Y. Thus, the relative weights of the covalent and ionic structures essentially determine the direction of frequency change. Indeed, we find the correlation between the structural weights and vibrational frequency changes. ∗

Author to whom correspondence should be addressed. Email: [email protected]. Tel: 86-592-2180413. 1

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Introduction A hydrogen bond donor X−H and a hydrogen bond acceptor Y can interact and form a hydrogen bonding complex X−H···Y, where X is often an electronegative atom or group and Y is an atom or group of excessive electrons such as lone pairs. 1-7 The existence of hydrogen bond has been extensively confirmed in literature, notably by the observation of the change of the stretching vibrational frequency of the X−H bond. It has been widely accepted that the nature of hydrogen bonding is primarily electrostatic, but there is also insignificant yet notable electron transfer (i.e., hyperconjugation) from Y to the antibonding orbital σXH*. It is the latter interaction that weakens the X−H bond to some extent and consequently red-shifts its vibrational frequency with increased intensity.8 In fact, hydrogen bonds are broadly characterized with the red-shift with enhanced intensity in IR spectra.9,10 However, since 1980’s, the so-called “improper, blue-shifting” hydrogen bonds, where the X−H bond lengths contract rather than elongate, and accordingly their stretching vibrational frequencies blue-shift with reduced intensity, have been identified in the gas and condensed phases.11-18 But we note that most of donors in blue-shifting hydrogen bonds are the C−H bond,4,12-14,16,19-26 and a current consensus is that there are no fundamental distinctions between the classical and improper hydrogen bonds.22,27-33 To interpret the cause of the blue-shifting phenomenon, several groups studied the behavior of hydrogen bond donors in electric field, and correlated the blue-shifting to the negative sign of the dipole moment derivative with respect to the stretching coordinate.21,29,30 But this correlation was later invalidated by Hobza et al.10 Recognizing that orbital interactions lengthen the hydrogen bond, Li et al proposed that the competition between the short-range Pauli repulsion and the long-range electrostatic attraction between the hydrogen bond donor and acceptor is the origin of both the red-shifting and blue-shifting hydrogen bonds.34 Alternatively, Alabugin et al considered the n(Y)σXH* hyperconjugation and the rehybridization and polarization of the X−H bond as the two major competing forces, and claimed that the rehybridization enhances the s-character of the hybrid orbital on X and results in the shortening of the X−H bond.35 This claim is in accord with Bent’s rule that the percent s character of A in the A-B bond increases when B gets more electropositive.36 Differently, Joseph and Jemmis showed that there is no obvious relationship between the s character on one atom and the bond length.37 Instead, they provided a unified theory for all hydrogen bonds, which states that the two 2


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competing forces are the contraction of the X−H bond due to the enhanced electrostatic attraction between X and H in the presence of Y and the elongation of the X−H bond due to the electrostatic attraction between H and Y.37 Based on the block-localized wave function (BLW) method, Mo and coworkers demonstrated that in most cases, electrostatic interaction leads to the contraction and blue-shifting of a hydrogen bond, while the n(Y)σXH* hyperconjugation results in the lengthening and red-shifting of the hydrogen bond, and the competition between these two factors determines the final frequency change direction.38 They also showed that in a few cases, both factors could contribute to the red-shifting of hydrogen bonds.38 Thus, studies so far concur that there is no fundamental difference between red- and blue-shifting hydrogen-bonds, and there are competing interactions which decides the direction of frequency change. Yet, there is disagreement about the nature of the competing interactions, though the dominance of the attractive electrostatic interaction in hydrogen bonding is widely accepted. The possible candidates for the repulsive forces include electric fields, Pauli repulsion, the rehybridization and polarization etc.15,18,19,30,34,37-42 However, we note that most of the computational studies are based on molecular orbital (MO) theory, where a molecular wavefunction is built from MOs which are extended to the whole system, i.e., fully delocalized. Alternatively, valence bond (VB) theory uses a bottom-up strategy to build molecular wavefunction.43-46 It starts from atom-centered local orbitals, followed by the construction of bond functions using these atomic orbitals. At last, wavefunctions for electron-localized Lewis structures are built with bond functions. The overall molecular wavefunction is a linear combination of all possible Lewis structures. Furthermore, a real chemical bond is described with one covalent and two ionic structures. Accumulating VB studies so far have shown that VB theory is hopefully able to provide new insights into the nature of weak non-covalent interactions from a perspective very different from MO theory.47-50 Yet we are certain that studies with MO and VB theories should be complementary rather than conflicting. A notable recent example is the study of halogen bonds by Wang et al,51 who decomposed the total interaction energy into several individual interaction terms based on ab initio VB wavefunction and demonstrated that VB studies not only shed new light on the physical nature of non-covalent interaction, but also are consistent with MO results. Among a range of modern ab initio VB methods, valence bond self-consistent field (VBSCF) theory is the major one.52-54 Analogous to the CASSCF method, VBSCF incorporates 3



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the static correlation, but fails to take the dynamic correlation into account.46 Fortunately, as demonstrated by Li et al, the blue-shifting of hydrogen bonds can be well reproduced at the Hartree-Fock (HF) level of theory, confirming that the dynamic correlation is unimportant in the elucidation of the nature of blue-shifting phenomenon.34 In this work, we performed ab initio VBSCF computations of a series hydrogen bonding complexes, where the hydrogen bond donor is CF3H but the hydrogen bond acceptors Y include ten species, NH2CH3, NH3, NH2Cl, OH-, H2O, CH3OH, (CH3)2O, F-, HF or CH3F. Our focus is on the vibrational frequency change of the F3C−H bond, which may either red-shift or blur-shift, based on the nature of the approaching acceptor.

Methodology and Computational Details VBSCF method Modern chemistry theory originates from the concept of Lewis structure which is built with chemical bonds strictly localized between two atoms, plus single atom-centered lone pairs. Based on the solution of Schrödinger equations for hydrogen cation (H2+), Heitler and London elucidated the nature of chemical bond, which is formed by two nonorthogonal atomic orbitals. The extension of this finding to the general case of a Lewis structure leads to the Heitler-London-Slater-Pauling (HLSP) function as:43-46   Φ K = Aˆ φ1 (1)φ2 ( 2) Lφ N ( N )∏ [α (i ) β ( j ) − β (i )α ( j )]∏ α ( k )  , ( ij ) k  

(1)

where Â is an antisymmetrizer, and orbitals φi and φj form a chemical bond, and φk is singly occupied and does not form any bond with others. Thus, any Lewis structure can be well defined with a HLSP function. Considering that a molecule may not be well described by a single Lewis structure, Pauling and Wheland pioneered the resonance theory, suggesting that a complete description of a molecule requires a set of Lewis (resonance or VB) structures. In modern language, a many-electron wave function is expressed by the linear combination of VB structures, i.e.,

Ψ VB = ∑ C K Φ K ,

(2)

K

where {CK} is a set of coefficients for VB structure {ΦK}. The VB total energy and the structural coefficients can be obtained by solving the following secular equation: 4


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HC = EMC ,

(3)

where H, M and C are the Hamiltonian, overlap and coefficient matrix, respectively. In the VBSCF method, both sets of structural coefficients and orbitals {φi} shown in Eq. 1 are simultaneously optimized to minimize the total energy. Since the weights of VB structures are typically used to show the relative importance of individual VB structures, they can be useful in the understanding of the correlation between molecular structure and reactivity.55 By the Coulson-Chirgwin definition,56 weights of VB structures are expressed as

WK = ∑ CK CL M KL = CK2 + ∑ CK CL M KL ,

(4)

L≠ K

L

In the classical VB theory, a bond between two atomic orbitals φi and φj centered on atoms A and B, respectively, can be expressed as a combination of a covalent structure and two ionic structures

ΨAB = C1Φ(A : B) + C2Φ(A+ B− ) + C3Φ(A −B+ ) ,

(5)

where

{

}

Φ(A : B) = Aˆ [φi (1)φ j (2) + φi (2)φ j (1)][α (1)β (2) − β (1)α (2)] ,

(6a)

Φ(A + B− ) = Aˆ {φ j (1)φ j (2)[α (1) β (2) − β (1)α (2)]},

(6b)

Φ(A−B+ ) = Aˆ{φi (1)φi (2)[α (1)β (2) − β (1)α (2)]}.

(6c)

A covalent bond is characteristic of the strong bonding interaction between two neutral atoms with unpaired electrons, while an ionic bond results from the electrostatic attraction between two oppositely charged ions. In reality, however, any diatomic bond is neither purely covalent nor purely ionic, rather, a mixture of both, as shown in Eq. 5. For a polarized bond, one ionic structure is expected to have higher structural weight than the other.

VB-based energy decomposition analysis Numerous MO-based energy decomposition approaches have been developed and extensively applied to the elucidation of intermolecular interactions. These approaches including the symmetry-adapted perturbation theory (SAPT) method,57,58 and supramolecular methods.59-70 Here we describe an approach based on VB theory particularly designated for the study of 5



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hydrogen bonds, whose formation process can be modeled as a typical proton transfer reaction between hydrogen donor and acceptor. In the ten complexes F3C−H···Y studied in this work, each acceptor Y contains a lone pair. Thus, there would be four active electrons, including two electrons in the C−H bond and two electrons in the lone pair of Y molecule. These four active electrons are accommodated into three active orbitals centered on C, H and Y, respectively. These four active electrons and three active orbitals lead to six VB structures as shown in Fig. 1. Among these six VB structures, the di-ionic charge transfer state ΦCT3 in which two electrons on Y are transferred to the C-H bond is very unstable. Thus, the VB wavefunction for the hydrogen bonding complex, ΨHB, is essentially a linear combination of the five VB structures, where Φcov, Φion1 and Φion2 are the covalent and two ionic structures that describe the C-H bond with the existence of Y, and the remaining two structures ΦCT1 and ΦCT2 describe the transfer of an electron from Y to the C-H bond. Since charge transfer plays a minor role in the formation of hydrogen bond, it is expected that ΦCT1 and ΦCT2 make small contributions to ΨHB. Similar to all other energy decomposition schemes, we derive the energy terms with several intermediate states. First, we use the free monomers F3CH and Y as the reference state for the complex. As there is no interaction between monomers at this no-bonding state, the VB wave function, ΨL, is the combination of only three VB structures, Φcov, Φion1 and Φion2, and the corresponding VBSCF energy is Enb. In practice, as advised by Danovich et al,71 the energy at the 25 Å distance of CF3H and Y is approximated as Enb. Second, the distance between the monomers is changed from 25 Å to the equilibrium distance of the complex F3C−H···Y. At this step we freeze the wavefunction ΨL, i.e., all orbital coefficients and structural coefficients are unchanged without any further optimization, and Y acts as a spectator and interacts with CF3H eq via electrostatic and Pauli exchange repulsion. The subsequent energy is Efix , and the energy

change from the first step to this step is defined as the frozen energy eq ∆E Fro = Efix − E nb ,

(7)

If the geometrical relaxation is neglected, the term denotes the frozen electronic density interaction, containing both electrostatic and Pauli repulsion energy.51 Third, we consider the relaxation of the coefficients of the VB structures and the VB orbitals in ΨL and perform VBSCF computation at the optimal geometry of the complex but with three VB structures Φcov, Φion1 and Φion2. Subsequently, we obtain the total VBSCF energy ELeq . 6


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The energy variation in this process is defined as the polarization energy eq , ∆E Pol = ELeq − Efix

(8)

Obviously, this polarization reflects the impact of the spectator Y on the electron density of CF3H. As the last step, we consider the charge transfer between CF3H and Y, and perform VBSCF computation with five VB structures including ΦCT1 and ΦCT2, leading to the VBSCF eq energy E HB . The energy reduction due to the participation of these two charge transferred states

is defined as the charge transfer energy eq ∆E CT = E HB − ELeq ,

(9)

In brief, here we propose a VB-based energy decomposition scheme where the total interaction energy at the VBSCF level is a sum of three terms: ∆E int = ∆E Fro + ∆E Pol + ∆E CT .

(10)

VB-based fragment interaction analysis Since the molecular wavefunction is a superposition of covalent and ionic structures as shown in eqs. 2 and 6, we individually explore the interaction of the hydrogen bond acceptor Y with the covalent and ionic states of F3C−H. The strategy here is to separate the molecule to two fragments. For the covalent state, the fragments are CF3 and H radicals, and they interact with Y and forms complexes C1 and C2. For the ionic state F3C-H+, the fragments are the anion CF3and the proton, and their complexation with Y leads to I1 and I2. The fragmentation scheme is shown in Fig. 2. By studying the interaction between Y and fragments of CF3H separately, we expect to gain critical clues to better understand the causes of the red-shifting and blue-shifting of hydrogen bonds.

Computational details All geometry optimizations are performed at the MP2/6-311++G(d,p) level of theory with Gaussian 09.72 The zero-point energy (ZPE) correction is not considered. VB calculations are performed with our XMVB program at the VBSCF/6-311G(d,p) level.73 While all valence electrons are involved in the VB calculations, only three active VB orbitals are used to accommodate four active electrons and construct VB structures as shown in Fig. 1. All other 7



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electrons are doubly occupied in fragment orbitals. At this point we need note the significant differences of our present VBSCF approach from the popular GVB method.74,75 In GVB, all orbitals are extended to the whole complex (i.e., fully delocalized) and subject to strong orthogonality constraint, but in our present computations, all orbitals are strictly localized on three groups, namely CF3, H and Y, and there is no orthogonality constrain imposed on them.

Results and Discussions VB analysis for hydrogen bonding interaction at the optimized geometries Table 1 lists the optimal hydrogen bond distances and the vibrational frequencies of the C−H bond at the MP2/6-311++G(d,p) level. Due to the sensitivity of the C−H bond length with its corresponding stretching frequency, we reported the data with four decimals. Among the ten acceptors, OH- and F- are ionic and interact with F3CH strongly, and thus cause the strong red-shifting of the stretching vibrational frequency of the F3C−H bond. Apart from these two ionic acceptors, we observe the slight variation of the F3C−H bond distances ranging from 1.0848 Å to 1.0882 Å, and the vibrational frequency shifts vary from -12.8 (red-shifting) to 41.8 cm-1 (blue-shifting). In general, we expect that the bond distance would correlate with its frequency, as a shorter bond tends to vibrates with higher stretching frequency. Fig. 3 plots the correlation between these two properties for the neutral hydrogen bonding complexes. Indeed, we observe a clear line relationship. With the optimal geometries, we performed VB-based energy decomposition analysis and Table 2 lists the energy contributions to the total interaction energies. In accord with the bond distance and vibrational frequency changes in Table 1, both F- and OH- form very strong hydrogen bonds with CHF3, and their interaction energies are very close and ten times more than the other neutral hydrogen bonding systems. These neutral systems are typical hydrogen bonding complexes with interaction energies varying from -2.1 to -4.4 kcal/mol. The VBSCF computed interaction energies are close to the results from other computational studies. For example, the VBSCF interaction energy of CF3H···FH is -2.08 kcal/mol, slightly lower than the values of -2.59 and -2.60 kcal/mol at the M05-2X/6-311+G(d,p) and MP2/6-31+G* levels, respectively.37,38 Furthermore, for comparison, the MP2/6-311++G(d,p) computed total interaction energies with and without the BSSE correction are shown in the last two columns of Table 2. In general, it is shown that the MP2 values are close to the corresponding VB ones. As 8


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such, VBSCF is qualified for the hydrogen bonding description. Energy decomposition results shown in the first four columns of Table 2 exhibit that both red-shifting and blue-shifting hydrogen bonds have the very same origins. First, in all systems, the frozen energy term, which is composed of both electrostatic interaction and Pauli exchange repulsion, dominates the total interaction energy. Since the Pauli exchange is always repulsive, the negative values of the frozen interaction energies indicate the attraction between the hydrogen bond donor and acceptors. Apart from the complexes with anions OH- and F-, both polarization and charge transfer effects are comparable but only a small fraction of the frozen interaction. Third, there is no obvious correlation between interaction energies and directions of frequency shifting. All these energy decompositions results are pretty similar to numerous published studies in literature, and in accord with the general view that there is no fundamental difference between red-shifting and blue-shifting hydrogen-bonds. However, the uniqueness of the present study is the computations in terms of resonance structures, i.e., the structural weights from VBSCF computations, as shown in Table 3. Table 3 shows that the weights of the [F3C−H Y] structure and the [F3C- H+

Y]

structure, namely Wcov and Wion1, together account for about 95% of the total VB wave function. For example, in the complex of F3C−H···NH3, the weights of Φcov and Φion1 are 70.0% and 25.0%, respectively. In consistent with the insignificant charge transfer interactions, the weights of the VB structures corresponding to the charge transfer interaction, ΦCT1 and ΦCT2, are very small, contributing less than 1.0% to the total VB wavefunction in neutral complexes. For the anions OH- and F-, these two charge-transferred structures contribute 1~2% to the total wavefunction. For the comparison of free F3CH, the contributions of the covalent structure (F3C−H) and ionic structures (F3C-···H+ and F3C+···H-) to the C−H bond are 72.2%, 21.1% and 6.7%, respectively. Therefore, the formation of the hydrogen bond between F3CH and Y reduces the covalent characteristics of the C−H bond but increases the ionic characteristics (C-···H+, in consistent with the high electronegativity of the F3C group). This trend indicates the gradual polarization of the C−H bond. Interestingly, it is found that blue-shifting hydrogen bonds tend to retain relatively large portion of Φcov and small portion of Φion1 while the red-shifting hydrogen bonding complexes exhibit the opposite trends. VB-based fragment interaction analysis of the states F3C− −H···Y and F3C-H+···Y 9



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VBSCF computations in the above show that the major contributing VB structures are [F3C−H Y] structure (Φcov) and the [F3C- H+

Y] structure (Φion1). Thus, in this subsection, the fragment

interactions in these two states are analyzed. For the covalent structure, we analyze the interaction of the acceptor Y with the radicals of CF3 and H, and resulting complexes are named C1 and C2 as shown in Fig. 2. For the ionic structure, the interaction of Y with either F3C- or H+ is decomposed. The two subsequent complexes of Y with ions are called I1 and I2. Here we investigated three typical complexes with Y = NH3, H2O and HF. F3CH···NH3 concerns a red-shifting hydrogen bonds while the other two are blue-shifting. All geometries of C and I adopt their parent’s optimal geometry. Results for the covalent and ionic states are shown in Tables 4 and 5, respectively. For the covalent states, the interaction between the hydrogen bond acceptor Y and hydrogen atom is repulsive in the order of NH3 > H2O > HF, and dominated by the frozen energy term. Both the polarization and charge transfer stabilization energies are trivial, except Y = NH3, which has a considerable charge transfer energy, -1.2 kcal/mol, suggesting that NH3 is a better Lewis base than H2O and HF. Overall, the H···Y interaction is mainly due to the Pauli repulsion. In sharp contrast, interactions of Y with the CF3 radical are attractive, and again dominated by the frozen energy term. This implies that there is favorable electrostatic attraction between Y and the CF3 radical, as there is quite long distance between two interacting parts and electrostatics is the only long-range interaction. In C2 complexes, both the polarization and charge transfer stabilization energies are negligible, and the total interaction decreases again in the order of NH3 > H2O > HF. The combination of the repulsion to H and the attraction to CF3 exerted by Y results in the compression of the F3C−H bond, accompanied by the blue-shifting of its stretching vibrational frequency, though the H···Y repulsive interaction is stronger than the CF3···Y attractive interaction. We note that this tendency is true for both red-shifting and blue-shifting hydrogen bonding systems. For the ionic states, however, things are completely different from the above analyses. On one hand, acceptors have strong attraction with H+ in the order of Y = NH3 > H2O > HF. Not only the frozen interaction but also charge transfer interaction play considerable roles in the stability of complexes H+···Y. Interestingly, the decreasing of the interaction energy in H+···Y along Y = NH3, H2O and HF is mainly attributed to the weakening of the charge transfer interaction. On the other hand, F3C- and Y are repulsive, even though they are quite far away. 10


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This repulsion is overwhelmingly from the frozen interaction, likely dominated by the long-range electrostatic interaction. The combination of the H+···Y attraction and the F3C-···Y repulsion generates a force to stretch the F3C−H bond, accompanied by the red-shifting of its stretching vibrational frequency. Fragment interaction analyses of three typical hydrogen bonding systems reveal the contrast behaviors of the covalent and ionic structures of the F3C−H bond at the presence of a hydrogen bond acceptor Y, which point to a novel perspective from the ab initio VB theory for the hydrogen bond vibrational frequency shifting; the covalent state (Φcov) tends to red-shift but the ionic state (Φion1) is responsible for the blue-shifting. The competition between the covalent state and the ionic state determines the final direction of the frequency changes. We verify this hypothesis with the ten complexes studied in this work (Table 3), and define ∆Wcov and ∆Wion1 as the structural weight changes from the non-interacting state to the optimal bonding state F3CH···Y. Obviously, the relative changes ∆Wcov and ∆Wion1 are expected to be the indicators for frequency changes. Table 6 lists the ratios of ∆Wcov versus ∆Wion1 and the products of these two changes, along with the shifting directions. Indeed, we observe that for red-shifting hydrogen bonds, the values of |∆Wcov/∆Wion1| are large (≥0.56), or more obviously the values of |∆Wcov⋅∆Wion1| are even larger than 7.8. But for blue-shifting hydrogen bonds, both the |∆Wcov/∆Wion1| and |∆Wcov⋅∆Wion1| values are small with ≤0.50 or ≤6.1, respectively. As such, it is shown that the blue-shifting hydrogen bonds keep the relatively larger covalent character of C-H bond compared to the red-shifting ones.

Conclusion With the finding of blue-shifting hydrogen bonds, numerous theoretical studies have been conducted with a general conclusion that there is no fundamental difference in nature between red-shifting and blue-shifting hydrogen bonds. Rather, there are competing forces which decides the direction of frequency changes.15,18,19,30,34,37-42 But we note that these studies are based on MO theory. Any perspective from ab initio VB theory will supplement our understanding of the nature of hydrogen bonds. In this work, we performed VBSCF computations of hydrogen bonding complexes 11



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F3C−H···Y (Y = NH2CH3, NH3, NH2Cl, OH-, H2O, CH3OH, (CH3)2O, F-, HF and CH3F). Among these systems, there are six blue-shifting cases and four red-shifting complexes. The uniqueness of VB theory lies in the use of resonance structures in molecular wavefunction. Thus, the chemical bonding can be studied in terms of several important resonance structures. VB-based energy decomposition analysis reaches conclusion similar to previous studies, i.e., hydrogen bonding is dominated by electrostatic interaction while the polarization interaction plays the secondary role. Of significance, VB-based fragment interaction analysis reveals that with the approaching of the hydrogen bond acceptor Y, the covalent structure of the F3C−H bond tends to be squeezed and this becomes shorter, accompanied by the blue-shifting of its vibrational frequency, but the ionic structure of the F3C−H bond will be stretched, resulting in the elongation of the C−H bond and the red-shifting of the vibrational frequency. The competition between the covalent and ionic structures thus decides the direction of frequency changes. As demonstrated, a clear correlation of the changes of the structural weights of the covalent and ionic structures with the frequency change directions is observed.

Acknowledgement This project is supported by the Natural Science Foundation of China (Nos. 21373165, 21120102035, 21273176, 21290190, 21573176), the Fundamental Research Funds for the Central Universities, China (No. 20720150037), and the National Foundation of Fundamental Training for Basic Science (NFFTBS), China (No. J1310024). YM acknowledges the support from the short-term Bairen Program of Fujian Province.

12


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Table 1. Major geometrical parameters (Å) and the vibrational frequency of the C−H bond (cm-1) in hydrogen bonding systems at the MP2/6-311++G** level. System

d(C···Y)

d(H···Y)

d(C−F)

d(C−H)

v

∆v

F3CH

/

/

1.338

1.0877

3223.4

/

F3CH···NH2CH3

3.302

2.255

1.344

1.0882

3206.8

-16.6

F3CH···NH3

3.379

2.292

1.343

1.0875

3221.2

-2.2

F3CH···NH2Cl

3.374

2.288

1.341

1.0867

3233.9

10.5

F3CH···OH-

2.751

1.624

1.374

1.1296

2589.9

-633.5

F3CH···OH2

3.281

2.197

1.341

1.0854

3259.9

36.5

F3CH···OHCH3

3.177

2.182

1.342

1.0854

3258.2

34.8

F3CH···O(CH3)2

3.169

2.146

1.341

1.0858

3250.7

27.3

F3CH···F-

2.654

1.517

1.364

1.1368

2500.8

-722.6

F3CH···FH

3.362

2.277

1.340

1.0852

3267.1

43.7

F3CH···FCH3

3.280

2.196

1.341

1.0848

3273.0

49.6

13



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Page 14 of 28

Table 2. VB-based energy decomposition analysis at the VBSCF/6-311G(d,p) level (kcal/mol). System

∆EFro

∆Epol

∆ECT

int ∆EVB

int ∆E MP2 (BSSE) *

int ∆EMP2 (no - BSSE) *

F3CH···NH2CH3

-1.8

-0.8

-0.7

-3.3

-4.2

-5.6

F3CH···NH3

-3.0

-0.7

-0.7

-4.4

-4.1

-5.4

F3CH···NH2Cl

-1.4

-0.5

-0.3

-2.2

-2.9

-4.5

F3CH···OH-

-13.5

-12.3

-6.5

-32.3

-26.4

-30.1

F3CH···OH2

-2.9

-0.5

-0.4

-3.8

-3.5

-4.6

F3CH···OHCH3

-2.3

-0.7

-0.4

-3.4

-3.9

-5.0

F3CH···O(CH3)2

-1.9

-0.7

-0.5

-3.1

-3.8

-5.2

F3CH···F-

-12.4

-13.0

-7.5

-32.9

-27.8

-30.9

F3CH···FH

-1.7

-0.2

-0.2

-2.1

-1.9

-2.5

F3CH···FCH3

-1.8

-0.3

-0.3

-2.4

-1.4

-2.9

* computed at the MP2/6-311++G** level.

14


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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 3. The weights (%) of VB structures at the equilibrium geometries at the VBSCF/6-311G(d,p) level. System

Wcov

Wion1

Wion2

WCT1

WCT2

F3CH···NH2CH3

70.1

24.8

4.6

0.4

0.1

F3CH···NH3

70.0

25.0

4.5

0.4

0.1

F3CH···NH2Cl

70.9

23.7

5.0

0.3

0.1

F3CH···OH-

57.9

36.1

4.3

1.1

0.6

F3CH···OH2

70.6

24.3

4.8

0.2

0.1

F3CH···OHCH3

70.5

24.3

4.8

0.3

0.1

F3CH···O(CH3)2

70.4

24.5

4.7

0.3

0.1

F3CH···F-

57.0

36.9

4.3

1.2

0.6

F3CH···FH

71.5

22.8

5.5

0.2

0.0

F3CH···FCH3

71.4

23.1

5.3

0.1

0.1

15



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Page 16 of 28

Table 4. Fragment interaction analysis for the covalent state of [F3C−H VBSCF/6-311G(d,p) level. ∆EFro ∆Epol ∆ECT ∆Eint

System [F3C−H NH3] (Φcov) H···NH3

4.6

-0.0

-1.2

3.4

F3C···NH3

-1.9

-0.2

-0.2

-2.3

H···H2O

3.9

-0.6

0.00

3.3

F3C···H2O

-1.7

-0.2

-0.1

-2.0

H···HF

2.7

-0.0

-0.2

2.5

F3C···HF

-1.0

-0.1

0.00

-1.1

[F3C−H OH2] (Φcov)

[F3C−H FH] (Φcov)

16


Y] at the

Page 17 of 28

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 5. Fragment interaction analysis for the ionic state of [F3C- H+ VBSCF/6-311G(d,p) level. ∆EFro

∆Epol

∆ECT

∆Eint

H+···NH3

-32.5

-6.2

-43.1

-71.8

F3C-···NH3

20.8

-2.9

0.0

17.8

H+···H2O

-32.2

-2.8

-15.8

-50.8

F3C-···H2O

14.1

-0.1

0.0

14.0

H+···HF

-16.8

-3.1

-2.9

-22.8

F3C-···HF

10.3

-0.9

0.0

9.4

System [F3C- H+

[F3C- H+

[F3C- H+

NH3] (Φion1)

OH2] (Φion1)

FH] (Φion1)

17


Y] at the


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 18 of 28

Table 6. Comparison of the ratio of ∆Wcov versus ∆Wion1 with the frequency change direction. Shifting |∆Wcov/∆Wion1| |∆Wcov⋅∆Wion1|*

*

F3CH···NH2CH3

0.57

7.8

red

F3CH···NH3

0.56

8.6

red

F3CH···NH2Cl

0.50

3.4

blue

F3CH···OH-

0.95

214.5

red

F3CH···OH2

0.50

5.1

blue

F3CH···OHCH3

0.48

5.3

blue

F3CH···O(CH3)2

0.50

6.1

blue

F3CH···F-

0.96

240.2

red

F3CH···FH

0.41

1.2

blue

F3CH···FCH3

0.40

1.6

blue

Unit is in %⋅%

18


Page 19 of 28

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


Figure 1. The six VB structures for the description of bonding in F3C−H···Y.

19



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

Figure 2. Schemes for the fragment interactions between the hydrogen bond acceptor and either the covalent state or the ionic state of the hydrogen bond donor.

20


Page 20 of 28

Page 21 of 28

3280 3270

Frequency (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


3260 3250 Free F3C−H

3240 3230 3220 3210 3200 1.084

1.085

1.086

1.087

1.088

1.089

d(C−H) (Å) Figure 3. Correlation between the bond distance and the stretching vibrational frequency of the C−H bond in hydrogen bonding systems F3C−H···Y (Y = NH2CH3, NH3, NH2Cl, H2O, CH3OH, (CH3)2O, HF or CH3F).

21



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

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ed.; Gaussian, Inc.: Wallingford CT, 2010. (73) Song, L.; Mo, Y.; Zhang, Q.; Wu, W. XMVB: A Program for Ab Initio Nonorthogonal Valence Bond Computations. J. Comput. Chem. 2005, 26, 514-521. (74) Goddard III, W. A. Wavefunctions and correlation energies for two-, three-, and four electron atoms. Phys. Rev. 1968, 48, 1008-1017. (75) Bobrowicz, F. W.; Goddard III, W. A. In Methods of Electronic Structure Theory, Modern Theoretical Chemistry; Plenum: New York, 1977; Vol. 3, p 79-127.

27



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TOC graphic

Blue-shift CF3  H

Attractive

Y

Repulsive

Red-shift Repulsive

CF3

-

H+

Attractive

Y

28


Page 28 of 28

Red-Shifting versus Blue-Shifting Hydrogen Bonds: Perspective from

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