Infrared Intensification and Hydrogen Bond ... - ACS Publications

Article Cite This: J. Phys. Chem. A XXXX, XXX, XXX−XXX

pubs.acs.org/JPCA

Infrared Intensification and Hydrogen Bond Stabilization: Beyond Point Charges Leonardo J. Duarte,† Arnaldo F. Silva,† Wagner E. Richter,‡ and Roy E. Bruns*,† †

Instituto de Química, Universidade Estadual de Campinas, CP 6154, Campinas CEP 13083-970, São Paulo, Brazil Departamento de Engenharia Química, Universidade Tecnológica Federal do Paraná, Campus Ponta Grossa, Av. Monteiro Lobato s/n, Jardim Carvalho, Curitiba 84016-210, Brazil

‡

Downloaded via UNIV AUTONOMA DE COAHUILA on July 20, 2019 at 12:33:36 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

S Supporting Information *

ABSTRACT: Infrared band intensification of the A−H bond stretching mode of A−H···B acid−base systems has long been known to be the most spectacular spectral change occurring on hydrogen bonding. A QTAIM/CCTDP model is reported here to quantitatively explain the electronic structure origins of intensification and investigate the correlation between experimental enthalpies of formation and infrared hydrogen bond stretching intensifications amply reported in the literature. Augmented correlation-consistent polarized triplezeta quantum calculations at the MP2 level were performed on complexes with HF and HCl electron acceptors and HF, HCl, NH3, H2O, HCN, acetonitrile, formic acid, acetaldehyde, and formaldehyde electron donor molecules. The A−H stretching band intensities are calculated to be 3 to 40 times larger than their monomer values. Although the acidic hydrogen atomic charge is important for determining the intensities of HF complexes relative to HCl complexes with the same electron donor, they are not important for infrared intensifications occurring on hydrogen bond formation for a series of bases with a common acid. Charge transfers are found to be the most important factor resulting in the intensifications, but dipolar polarization effects are also significant for each series of complexes. A mechanism involving intra-acid and intermolecular electron transfers as well as atomic polarizations is proposed for understanding the intensifications. The calculated sums of the intermolecular electron transfer and acid dipolar polarization contributions to the dipole moment derivatives for each series of complexes are highly correlated with their enthalpies of formation and H-bond intensifications. This could be related to increasing electron transfer from base to acid that correlates with the calculated hydrogen bonding energies and may be a consequence of the A−H bond elongation on complex formation having amplitudes similar to those expected for the A−H vibration.

■

INTRODUCTION Infrared spectroscopy has long been considered one of the most successful techniques for studying hydrogen bonding.1 The most notable spectral changes occur for the A−H stretching band, although other bands are also perturbed. The position of this band decreases by up to several hundred wave numbers, but by far, the most striking change occurs for the band intensity that can increase by a factor of 10 or even more. The symmetric O−H stretching intensity in the gasphase water molecule2 is only 3.0 ± 0.4 km mol−1, but in the water dimer, its intensity3 increases to 144 km mol−1 (estimated error of 20%).3 This spectral change provides a very sensitive probe of H-bonding in the water dimer. Although strong hydrogen bonds show a red frequency shift, blue shifts occur for weaker ones, and these are accompanied by intensity decreases.4 Iogansen5 has published a review of about 150 papers reporting correlations between experimental values of the formation enthalpies and the square root of the intensifications of the H-bond stretching mode for 138 donor−acceptor pairs © XXXX American Chemical Society

in CCl4, CH2Cl2, C6H6, and C2Cl4 solvents, HOD in liquid water at 11 different temperatures, and equimolar mixtures of chloroform-d with 15 different bases. Hydrogen bond stretching intensification has been investigated by our group,2,6 but a definitive chemically meaningful explanation for both the intensity enhancement and its relation with the enthalpy of formation has yet to be given. These intensities provide information on changes in electronic structures of the complexes and donor molecules as their acidic protons are displaced. In fact, the dominant change in the molecular geometry on H-bond formation is an elongation of the donor A−H bond in the complex. For this reason, the A−H stretching intensities can be expected to shed light on the electronic changes that are related to the stability of the Hbonds. One might expect that these same changes occur as the A−H donor bond lengthens on complex formation. This is not Received: April 2, 2019 Revised: June 11, 2019 Published: July 5, 2019 A

DOI: 10.1021/acs.jpca.9b03105 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

resulted in a root-mean-square error (RMSE) of 11.4 km mol−1 having an intensity range spanning 493 km mol−1.16 The counterpoise method was applied for complex optimizations to correct formation enthalpy values for basis set superposition error (BSSE).21,22 The infrared intensities were calculated by GAUSSIAN, which also provided the Hessian matrix. These intensities were also numerically calculated by the PLACZEK program23 using derivatives obtained from the AIM atomic charges and dipoles calculated by the AIMALL24 program. As in previous studies, the PLACZEK program creates 6N geometries (N being the number of atoms) generated by positive and negative displacements (±0.01 Å) of each atom along each Cartesian axis. Each of these geometries has its own QTAIM atomic charges and dipoles evaluated by AIMALL. In this way, the electronic structure analysis of the H-bond vibrations could be carried out with the charge, charge transfer, and dipolar polarization model.25

the only instance in which infrared intensity-related properties were shown to be ingrained in fundamental experimentally measured chemical information or indeed chemical reactivity. The research groups of Katritzky and Topsom have published many papers showing that the square roots of infrared intensities are linearly related to Hammett sigma constants and other reactivity parameters.7−9 It was also shown, by our group, that the experimental mean dipole moment derivatives of the chlorofluoromethanes have an almost perfect linear relationship with the ionization energies measured for 1s core electrons.10 Electronic structure changes for molecular vibrations are successfully described using the Quantum Theory of Atoms in Molecules (QTAIM),11−13 including some hydrogen bonding systems.14 Within this formalism, a charge, charge transfer, and dipolar polarization model has been used to accurately reproduce the theoretical infrared intensities of most molecules for which experimental atomic polar tensors have been determined.15 Indeed, QTAIM studies have already been carried out for some H-bonding complexes where electronic structure changes are interpreted using equilibrium atomic charge displacement (C), interatomic charge transfer (CT), and dipolar polarization (DP) as the proton is displaced from its equilibrium position.17 QTAIM also permits the partitioning of the total intensity into atomic contributions, which are very convenient to access information about the A−H:D−N′ model system, composed of the most relevant atoms of Hbond formation. With QTAIM, the importance of each atom in hydrogen bond intensification can be assessed. As these intensifications are correlated with the formation energies, the atomic intensity contributions could provide useful information as to the electronic structure changes that are important to understand the origins of H-bond stabilization. In this paper, QTAIM models are reported with the aim of explaining infrared hydrogen bond stretching intensification and its relation to hydrogen bond stability in terms of charge, charge transfer, and dipolar polarization atomic parameters. Taking computer demand and theoretical interest into consideration, the model systems used here involve small donors, HF and HCl, with nine different small bases, HF, HCl, NH3, H2O, HCN, acetonitrile, acetaldehyde, formaldehyde, and formic acid electron donor molecules. Although the experimental evidence of the proportionality between the enthalpy of formation and A−H stretching band intensification was observed in condensed phases for other more complex systems, one can expect that this behavior also exists for the simpler isolated gas-phase complexes as well.

■

A CHARGE, CHARGE TRANSFER, DIPOLAR POLARIZATION MODEL FOR INFRARED INTENSIFICATION Within the Quantum Theory of Atoms in Molecules (QTAIM), a charge, charge transfer, and dipolar polarization model (CCTDP), the dipole moment derivative with respect to the vibrational normal coordinate is the result of three contributions ∂pσ ∂Q

N

=

∑ i=1

∂σ qio i ∂Q

N

+

∑ i=1

σio

∂qi ∂Q

N

+

∑ i=1

∂mi , σ ∂Q

(1)

where σ = x, y, z, i is summed over all the atoms in the molecule, N, and qi and mi, σ represent the atomic charges and Cartesian atomic dipole components, respectively. The first term represents the sum of the dipole derivative contributions owing to equilibrium charge movements weighted by a factor measuring the importance of their atomic Cartesian displacements in the vibrational normal mode, the second gives a sum of the changes in the charges of the atoms as they vibrate weighted by their equilibrium Cartesian coordinates, and the last one contains the sum of changes in the atomic dipoles during the vibration. These terms are the charge (C), charge transfer (CT), and dipolar polarization (DP) contributions to the dipole moment derivative, respectively, so the intensity of the vibrational bands can be expressed as NAπ ijj ∂pσ yzz jj zz 3c 2 jk ∂Q z{ 2 li ∂p y o ij ∂pσ yz ij ∂pσ yz | o o Nπ o jj σ zz o o zz + jj z = 2m jj z + jjj jj ∂Q zzz } o j ∂Q zz j ∂Q zz o 3c o o o k { k { k {DPo C CT n ~ 2

A=

■

COMPUTATIONAL DETAILS The structures were optimized using the GAUSSIAN09 program18 at the second-order Møller−Plesset Perturbation Theory electron correlation (MP2) level,19 which provides accurate values of the system total energy at a reasonable computational cost. Augmented correlation-consistent polarized triple-zeta (aug-cc-pVTZ) basis sets were used as they are able to provide a precise treatment of long-range interactions.20 The QCISD correlation treatment-level calculations have been found to provide accurate intensity estimates for a wide range of molecular vibrations for hydrocarbons, chlorofluoromethanes, X2CY (X = F, Cl; Y = O, S), and the substituted benzenes among others. A comparison of experimental and theoretical values for 143 normal vibrations

(2)

for which NA is the Avogadro’s number and c is the velocity of light.26 On taking the square, one has A=

2 2 2 l ij ∂pσ yz ij ∂p yz o Nπ o oijj ∂pσ yzz + ijj ∂pσ yzz jj zz + 2jjj σ zzz + m j z j z j z j z j z 2o j z j z j z j ∂Q z 3c o ok ∂Q {C k ∂Q {CT k ∂Q {DP k {C n | o jij ∂pσ zyz jij ∂pσ zyz jij ∂pσ zyz jij ∂pσ zyz jij ∂pσ zyz o o jjj ∂Q zzz + 2jjj ∂Q zzz jjj ∂Q zzz 2jjj ∂Q zzz jjj ∂Q zzz } o o k {CT k {Ck {DP k {CTk {DPo ~

(3) B


Article


Table 1. AH Stretching CCTDP Intensity Contributions for the HF and HCl Proton Donors and Monomers (km mol−1) complex HF electron acceptor dimer NH3 H2O HCN acetonitrile acetaldehyde formaldehyde formic acid monomer rmsa HCl electron acceptor dimer NH3 H2O HCN acetonitrile acetaldehyde formaldehyde formic acid monomer rmsa

CxC

CTxCT

DPxDP

2CxCT

2CxDP

2CTxDP

total int.

659.6 634.0 815.8 604.6 673.8 600.9 600.2 342.6 519.8 106.8

18.7 50.0 2.7 29.2 218.4 153.5 96.1 139.7 85.8 51.2

0.2 40.00 5.2 0.2 21.8 12.7 10.4 1.0 9.7 15.9

−220.9 356.2 −93.4 265.6 767.1 196.6 33.0 206.0 −422.3 556.1

−6.2 318.3 129.8 −21.3 −242.5 170.8 157.8 8.8 −141.9 323.2

1.4 89.4 −7.4 −4.7 −138.1 11.3 3.2 −17.8 57.6 48.2

452.8 1487.9 852.6 873.6 1300.5 1145.7 900.6 680.7 108.7 964.8

95.3 191.6 157.0 133.5 144.3 145.8 138.9 134.3 83.2 64.5

281.3 1331.4 503.6 669.0 967.6 879.9 608.3 621.5 118.7 683.8

326.7 1010.1 562.3 597.7 747.3 657.6 548.9 561.2 198.7 465.3

−209.2 −198.0 −279.1 −304.8 −329.1 −230.6 −224.2 −251.5 −239.8 46.0

−358.1 −521.9 −499.9 −682.3 −852.4 −529.4 −425.1 −533.0 −286.5 300.4

250.9 1864.3 567.9 587.1 865.4 1014.6 738.5 650.6 47.1 891.2

114.8 51.2 124.1 174.0 187.7 91.3 91.6 118.1 172.8 68.0

a

rms indicates the root-mean-square difference.

In a more compact form

This expression holds for normal coordinates for which all the atomic Cartesian coordinate variations must be taken into account. An analogous expression holds for dynamic atomic intensity contributions27 for which the portion of the intensity owing to the movement of only one atom of the normal coordinate is taken into account. This is particularly useful for studying hydrogen bonding since the sole movement of the hydrogen atom accounts for almost all of the A−H stretching intensity,16 ΔHA1/2 . For the H-bond calculations performed here, 90% or more of the total intensity is accounted for by only the hydrogen displacement of the normal vibration. More important than just reducing the computation time for the CCTDP parameters, the dynamic hydrogen intensity contribution permits a simple interpretation of the intensity behavior in terms of intra-acid and intermolecular charge transfer and acid and base polarizations,

A = (CxC + CTxCT + DPxDP + 2CxCT + 2CxDP + 2CTxDP)

(4)

with symbols referenced later in this manuscript. In vacuum, the enthalpy of hydrogen bond formation can be written by subtracting the sum of the monomer energies from the complex total energy: Complex Acceptor Donor Δf H = E Total − (E Total + E Total )

(5)

4

Iogansen defines the square root of the hydrogen bond intensification as 1/2 1/2 ΔA1/2 ≡ A Complex − ADonor

(6)

As such ΔA1/2 = ΔAx1/2 + ΔA1/2 + ΔAz1/2 y ÄÅ Å i NAπ ÅÅÅÅ jjjijj ∂pσ yzz ÅÅ∑ jjjj − = zz 3c 2 ÅÅÅÅ σ jjjjk ∂Q z{Complex ÇÅ k

ÉÑ Ñ ij ∂pσ yz yzzzÑÑÑÑ jj zz zzÑÑ jj ∂Q zz zzÑÑ k { Acid z{ÑÑÑ Ö

∂pz ∂z H

+ (DP)base

(7)

where the term on the right is the sum of the differences between the Cartesian components of the hydrogen bond stretching dipole moment derivative in the complex and the free acid molecule. The total hydrogen bond intensification is written as a sum of intensifications along the three Cartesian axes. ΔA1/2 =

=

ij ∂p yz Δjjj σ zzz j ∂Q z 3c k {

NAπ 3c

2

(9)

where CT and DP are defined in eq 2. The derivation of this equation can be found in the Supporting Information. The first term, qoH, is just the equilibrium charge on the hydrogen atom. The intra-acid charge transfer term is given by the change in the atomic charge of the A atom owing to a unitary displacement of the hydrogen atom multiplied by the A−H bond distance as can be verified in the Supporting Information derivation. The intermolecular charge transfer term contains the change in the atomic charges of the D and N′ atoms occurring for a unitary displacement of the H atom multiplied by their respective distances from the H atom. Finally, the (DP)acid and (DP)base terms contain derivatives of the point dipoles of the acid and base molecules, respectively.

NAπ 2

= qHo + (CT)intra − acid + (CT)intermol + (DP)acid

ji ∂p zy ji ∂p zy ji ∂p zy Δjjj σ zzz + Δjjj σ zzz + Δjjj σ zzz j ∂Q z j ∂Q z j ∂Q z k {C k {CT k {DP (8) C


Article


■

RESULTS The intensity is the square of the dipole moment derivative as shown in eq 2. The square of the sum of the charge (C), charge transfer (CT), and dipolar polarization (DP) results in three squared contributions, C2, CT2, and DP2, and three cross terms, 2CxCT, 2CxDP, and 2CTxDP given in eq 4. These six intensity contributions for both the HF and HCl complexes are presented in Table 1 along with the total intensities in the last column. The HF complex intensities are 4 to 13 times larger than the monomer intensity of 108.7 km mol−1. For HCl, the complex intensifications are even larger with values ranging from 5 to 40 times larger than the monomer value of 47.1 km mol−1. These estimates are expected to be reasonably accurate as QCISD/cc-pVTZ quantum calculations predict an increase from 4 km mol−1 for the monomer to 163 km mol−1 in the water dimer,2 whereas the experimental values are 3 and 144 km mol−1 (±20%), respectively.3 It is easily seen from the values in Table 1 that charge transfer is the largest source of H-bond enhancement for the HCl complexes as their CTxCT, 2CXCT, and 2CTxDP rms differences are much larger than the values of the other contributions. The values of the dipole moment derivative contributions of eq 2 and given in Table S1 confirm this conclusion. The charge transfer derivative rms difference of 0.5324 e amu1/2 between the HCl complexes and the HCl monomer is five times larger than those for charge and dipolar polarization. Their dipole moment derivative values are all positive for charge transfer and all negative for polarization. Opposing signs for the charge transfer and dipolar polarization derivatives are common for a wide variety of molecular vibrations15,16 that have been described using a charge transfer and counterpolarization model. This behavior is only exhibited by the H2O and acetonitrile complexes for the less polarizable HF acid complexes. Also, the charge transfer direction in most of the complexes is opposite to the one in the monomer. Owing to these sign differences, the CTxCT contributions in Table 1 are relatively small, and the rms difference between complexes and HF monomer is only 51.2 km mol−1. The CxC contributions are largest for all the complexes and for HF owing to the large electronegativity difference between fluorine and hydrogen. However, the CxC rms difference is only 106.8 km mol−1, also indicating small variations between the complexes and HF monomer. The values in Table S1 clearly show that charge transfer is also the most important source of the large intensity values for the HF complexes. The largest dipole moment derivative rms difference occurs for the charge transfer term, 0.5571 e amu1/2, that is three times larger than the difference for polarization and five times the one for charge. The large variation in the charge transfer derivatives owing to sign changes is amplified by the large and relatively constant charge derivatives resulting in the large 2CxCT rms difference, 556.1 km mol−1, in Table 1. A similar behavior produces the 323.4 km mol−1 rms difference for the 2CxDP contribution, the second largest source of intensity enhancement. Table S2 contains formation enthalpy values, the A−H stretching intensifications, (ΔA1/2 ), and the dynamic hydrogen atom contributions, (ΔHA1/2 ), to the intensification for both groups (HCl and HF) of complexes. The intensifications are obtained by analyzing distortions of all atoms as specified by the normal coordinate, whereas the dynamic hydrogen contributions are determined by considering only the hydro-

gen atom displacement in this normal mode. Note that the hydrogen intensification contributions are about the same as the total intensity values, having an rms error of only 0.7 km1/2 mol−1/2. As such, the analysis of the relation between ΔfH and ΔA1/2can be carried out by simply displacing the hydrogen atom according to the H-bond stretching normal coordinate rather than having to include the displacements of all the other atoms. This simplifies the interpretation of the results as shown by Eqs. (S1)−(S4). Figure 1 contains a plot of the enthalpy of

Figure 1. The negatives of the hydrogen bond formation enthalpies plotted against the differences of the square roots of complex and monomer intensifications of the dynamic hydrogen contributions for the A−H stretching vibrations.

formation against differences in the square roots of the complex and monomer intensities, eq 6, owing to only the movement of the hydrogen atom participating in the H-bond. An almost identical graph is obtained if the total intensity was used instead of just the hydrogen atom displacement contribution. The linear correlations, with similar slopes, suggest that the enthalpies of formation of the HF and HCl complexes are also correlated. Figure S1 (Supporting Information) shows this relationship where R = 0.978. Therefore, the relative stabilizations within each series of complexes seem to only be dependent on the electronic structure changes of the bases on complex formation. This excellent agreement has never been reported before, as it was not included in Iogansen’s work, and it points to the conclusion that the infrared intensity enhancements of the HCl and HF complexes have a common source. Table 2 contains the charge, charge transfer, and dipolar polarization values of the dynamic hydrogen contributions to the dipole moment derivatives for the HF and HCl complexes. These dynamic hydrogen contributions correspond to unitary displacements of the hydrogen atom from equilibrium. The charge contributions for the HF adducts are about twice those for the HCl adducts. This occurs because fluorine is much more electronegative than chlorine. Charge transfer (CT) and dipolar polarizations (DP) are larger for the HCl adducts than for the HF complexes. Higher dipolar polarization contributions are expected for the HCl adducts as chlorine is much more polarizable than fluorine. D


Article


Table 2. Charge−Charge Transfer−Dipolar Polarization Contributions to the Dynamic Hydrogen Intensity Values to the Dipole Moment Derivatives (e) for HF and HCl Adductsa acid HF

HCl

base

charge

charge transfer

dipolar polarization

charge

charge transfer

dipolar polarization

dimer NH3 H2O HCN acetonitrile acetaldehyde formaldehyde formic acid monomer DAC average rms diff.

0.7682 0.7580 0.77747 0.7681 0.8093 0.7676 0.7667 0.7692 0.7530 0.7705 0.0245

−0.1250 0.2844 0.0600 0.2092 0.4954 0.1506 0.0337 0.1404 −0.3058 0.1048 0.4930

0.0014 0.2087 0.0701 −0.0346 −0.1486 0.1026 0.1055 0.0377 −0.1028 0.0267 0.1817

0.3149 0.4143 0.3728 0.3610 0.3759 0.3858 0.3735 0.3660 0.2975 0.3624 0.0753

0.5363 1.1986 0.7344 0.8291 1.0096 0.9024 0.7576 0.8023 0.3554 0.7917 0.5244

−0.3486 −0.2247 −0.3478 −0.4163 −0.4438 −0.2994 −0.2999 −0.3629 −0.4288 −0.3542 0.1076

a

DAC = dynamic atomic contributions.

Figure 2. Theoretical formation enthalpy values graphed against complex−monomer differences in the charge and the sum of the charge transfer and dipolar polarization contributions to the dynamic hydrogen atom dipole moment derivatives for (a) HF complexes and (b) HCl complexes.

The small rms difference and large average value for the fluorine charges of the HF complexes in the last two lines of Table 2 show that even though the equilibrium charge contributions are large, they are relatively constant, having important intensity effects on both the monomer and the complexes but not much on the hydrogen bond intensifications. In the HCl complexes, the values of the chlorine charges are also similar to the one in the monomer. As a result, the charge contribution to intensification in Table 1 is also much smaller than that owing to charge transfer. Figure 2a,b shows graphs of the hydrogen bond formation enthalpies against the differences in the charge derivatives and the sum of the charge transfer and dipolar polarization derivatives induced by the displacement of only the hydrogen atom of these complexes. As can be seen for both the HF and HCl complexes, the changes in the charge transfer and dipolar polarization sums vary linearly with the formation enthalpies. Although the changes in the charge contributions to the dipole moment derivatives also seem to be linearly related with the formation enthalpies, they have almost vertical regression lines, showing almost constant values compared with the more ample variations found for the charge transfer and dipolar

polarization sum. The equilibrium atomic charges for the monomers and complexes are given in Table S3. It is noteworthy that the dominant charge transfer derivative changes alone do not correlate as strongly as the charge transfer and dipolar polarization sum. All the HCl complexes are calculated to have important charge transfer and counterpolarization cancellations of dipole moment derivatives, whereas the dipolar polarization contributions are small for the HF complexes and have the same direction as the charge transfer except for the HCN and CH3CN bases that contain triple bonds as neighbors to the acidic hydrogens. Charge Transfer and Dipolar Polarization Mechanism for Hydrogen Bonding Intensity Enhancement. Equations S4 and S9 simplify the analysis of the underlying electronic factors contributing to infrared intensity enhancements which might correlate with hydrogen bond stability. These equations contain terms describing contributions to the change in dipole moment along the z axis for a unitary displacement of the H atom in this direction, that is, contributions to the pzz polar tensor element. The results for the individual terms in Eq. S4, including the terms for the nearest neighbor atom(s), are presented in Table S4 for both the H-bonded complexes and the HF and HCl monomers. The E


Article


Figure 3. Charge, charge transfer and dipolar polarization contributions (in units of e) for the HF monomer and dimer that explain the intensity enhancement of the hydrogen stretch on complexation inhe HF dimer. The directions of arrows to the right point to positive poles of the dipole moment.

Figure 4. Charge, charge transfer, and dipolar polarization contributions to the dipole moment derivatives of the HF complexes with HF, H2O, and NH3 bases. Note that the intermolecular charge transfer and net polarizations are proportional to the base strengths in the HF < H2O < NH3 series (in units of e). The directions of arrows to the right point to positive poles of the dipole moment. On the left, dotted arrows for inter-molecular charge transfer and full for acid (intra-molecular) charge transfer. One dipolar polarization arrow is omitted since its magnitude is almost zero.

individual dynamic hydrogen contributions to the A−H stretching normal coordinates can be obtain multiplying the values in this table by their appropriate L matrix elements

1. The equilibrium charge of the hydrogen atom in HF is very positive, resulting in a large positive charge contribution, 0.753 e (Figure 3a). Counteracting this effect, a negative intramolecular electron transfer occurs for this vibration, that is, the hydrogen atom becomes less positive (gains electronic charge) when the H−F bond stretches contributing −0.305 e to the dipole moment derivative. This causes a partial cancellation between charge and charge transfer effects in the HF monomer (Figure 3b). The dipolar polarization

( ). The terms in Eq. S4 are expressed as intra-acid and ∂z H ∂Q

intermolecular charge transfers and acid and base polarizations in eq 9. Dynamic effects occurring in both the monomer and complex contribute to the intensity enhancements and can be conveniently analyzed with the aid of eq 9. We take the HF monomer and dimer as archetypes: F


Article


Table 3. Charge Transferred from Base to Acid (e) and Base-Induced Polarization (eu) in the Acid for the HF and HCl Complexesa complex

electron transfer

acid polarization

complex

electron transfer

acid polarization

(HF)2 NH3···HF H2O···HF HCN···HF acetonitrile···HF acetaldehyde···HF formaldehyde···HF formic acid···HF

−0.012 −0.067 −0.027 −0.030 −0.035 −0.038 −0.034 −0.030

0.111 0.334 0.201 0.187 0.219 0.239 0.215 0.199

(HCl)2 NH3···HCl H2O···HCl HCN···HCl acetonitrile···HCl acetaldehyde···HCl formaldehyde···HCl formic acid···HCl

−0.015 −0.069 −0.018 −0.020 −0.025 −0.033 −0.026 −0.021

0.109 0.544 0.271 0.251 0.312 0.358 0.300 0.277

a

The (−) sign indicates that the charge is transferred to the acid (HF and HCl).

Figure 5. Plots of the (a) hydrogen bond enthalpy of formation versus the charge transferred on complexation and (b) hydrogen bond enthalpy of formation versus the sum of the hydrogen and halogen atomic dipole moments along the z axis.

51.37 kJ mol−1, respectively, from Table S2) and the total electron transfer for the dynamic hydrogen contributions to the dipole moment derivatives (−0.1250, 0.0600, and 0.2844 e, respectively, from Table 2). Figure 4 illustrates a charge transfer−dipolar polarization mechanism for the HF complexes. The equilibrium hydrogen charge contributions are almost constant. Although the intramolecular charge transfer shows relatively small variations for the three complexes, the intermolecular charge transfer increases with base strength by a factor of six, from 0.070, 0.202, to 0.424 e. These results are consistent with the simple additive model summing the constant effective charge of the A−H bond and the effective charge for the H−D bond that increases with increasing H-bond intensification.14 Indeed, Rozenberg14 provides evidence of linear correlations between both the Hbonding intensifications and stabilization energies with the QTAIM electron density at the H−D bond critical point. The net dipolar polarization contributions in Figure 4 also vary significantly as base strength increases, 0.002, 0.071, and 0.209 e, reinforcing the charge transfer changes. The dipolar polarization values of the bases are almost constant, 0.058, 0.071, and 0.062 e, even though they form a very diverse group of molecules. On the other hand, the HF acid polarization ranges from −0.056 e for the dimer to +0.147 e for the ammonia complex. The sums of the intermolecular charge transfer and acid dipolar polarizations for the HF, H2O, and NH3 complexes with HF are 0.014, 0.202, and 0.571 e and are highly correlated with the formation enthalpy values. The sums of the intermolecular charge transfer and acid polarizations for

contribution of −0.102 e is smaller and also of opposite sign to the charge, resulting in a total dipole moment derivative of 0.346 e. 2. The formation of the (HF)2 dimeric complex leads to the donation of electrons from the donor to the acceptor unit as can be verified in Table S3. This donation contributes more electron density to the fluorine atom rather than the hydrogen atom as quantified in Figure 3c. When the HF bond stretches, intramolecular electron transfer is smaller in the complex than in the free acid molecule, −0.195 e. Also, intermolecular electron transfer occurs from the electron donor molecule to the acid, +0.070 e, owing to the HF bond length increase. The acid and base dipolar polarizations essentially cancel one another, resulting in a total dipole moment derivative of 0.645 e. The total effect is that, after complexation, the charge contribution does not change significantly, but the net charge transfer decreases by almost a third of the value found for the monomer, producing a total dipole moment derivative almost twice as large in the complex (Figure 3d). The net polarization is almost zero for the complex reinforcing the intensification. It seems reasonable to assume that the intermolecular charge transfers are proportional to the capacities of the Lewis bases to donate electrons to the acids and that they would correlate with chemically relevant quantities such as basicities and heats of reaction. That is indeed confirmed by the respective order of −ΔfH for HF···HF < H2O···HF < NH3···HF (17.71, 33.56, and G


Article


shows that H-bond intensification is a result of charge transfer and dipolar polarization contributions to the dipole moment derivatives for series of bases with common electron acceptors. Although the charges have important contributions for both the complexes and the monomer intensities, they make small contributions to intensity enhancements for bases with the same electron acceptor. Electronic structure changes for the acid−base reactions are strongly correlated with changes occurring for their A−H stretching vibrations. This seems reasonable considering that the change in the A−H bond length on H-bond formation is expected to be comparable to the A−H vibrational amplitudes. This provides a theoretical basis for the experimental observations of the strong correlations between hydrogen bond enthalpies of formation and infrared proton stretching intensification. Similar important observations are expected to be found regarding other chemically relevant quantities, such as gas-phase basicities and proton affinities. Models containing only atomic charges have been shown to be inadequate to explain the intensity values for a wide variety of molecular vibrations.5,14,24,30 Recently, our group proposed a simple model that quantitatively reproduces the variations in the out-of-plane CH bending intensities of substituted benzenes for which charge contributions are found to be negligible and dipolar polarization changes provide the only important intensity source.31,32 It is very important to draw attention to the fact that one of the simplest reaction mechanisms, an acid−base reaction, cannot be properly represented without polarization (which is obtained through atomic dipoles). This is especially troublesome, as most force fields28,29 currently used in mechanistic simulations rely solely on static charge models.

the eight HF complexes have a 0.92 correlation coefficient with the intensifications and 0.95 for the enthalpy values in Table 3. The intermolecular charge transfer−acid dipolar polarization mechanism shown in Figure 4 is also valid for the HCl complexes. As chlorine is much more polarizable than fluorine, the polarization contributions to the dipole moment derivatives are much larger. The sums of the intermolecular charge transfer and acid polarizations have a 0.94 correlation with the intensifications and 0.97 with the stabilization enthalpies. Finally, it should be mentioned that the charge transfer derivative becomes more negative as the hydrogen bond stabilization decreases as is shown in Figure 4. This behavior was also found in ref 4. In addition, the inclusion of atomic polarization in the CCTDP model reinforces the electron transfer trend. Although no blue shift hydrogen bonds are included in this paper, there is no reason to suspect that the CCTDP model will not provide a unified explanation of the decreased intensities as well. Complex Formation. The electronic charge transferred from the Lewis base to the acid is an important source of hydrogen bond stabilization.28 Because this charge transfer depends on the capacity of the Lewis base to donate electrons to the acid, the enthalpy of formation of the resulting complex is expected to be proportional to the base strength. Table 3 contains values of the electronic charge transferred from the base to the acid for the HF and HCl complexes. This is the net charge on the acid. It is clear that stronger bases transfer more electronic charge to both HF and HCl. Figure 5a contains a graph of the negative enthalpy of formation against the charge transferred from base to acid. With the exception of the HF and HCl dimers, there appears to be linear relationships between these quantities. In any case, the results in Figure 5a provide a very strong argument that electron donation plays a key role in complex stabilization. However, electron transfer, alone, could not account for the linearity between the formation enthalpy and the hydrogen bond intensification. Only its sum with the dipolar polarization reproduces this linearity. As such, one might expect that the change in atomic polarizations on complex formation would also provide important contributions to the stabilization. The HF and HCl atomic polarizations (z-component sums of atomic dipoles) have been included in Table 3. Figure 5b shows the hydrogen bond formation enthalpies as a function of the atomic polarizations of the HF and HCl acids on complex formation. The atomic polarization values are a sum of the z-components of the atomic dipoles of the hydrogen and halogen atoms. The linear relationships are indeed impressive with correlation coefficients of 0.98 and 0.95 for HF and HCl, respectively. One can expect polarization changes occurring in the A−H bond to be very important for energy changes on H-bond formation. The polarization changes occurring for the base are not as systematic as those of the acids.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.9b03105. Derivation of eq 8: a charge, charge transfer, dipolar polarization model for infrared intensification; charge− charge transfer−dipolar polarization contributions to the dipole moment derivatives with respect to normal coordinates (e amu1/2) for HF and HCl adducts; hydrogen bond formation enthalpy, −ΔfH (in kJ mol− 1), differences in the square roots of the complex and monomer intensities of the A−H stretching mode, ΔA1/2, and the corresponding dynamic hydrogen atom differences, ΔHA1/2 (in km1/2 mol−1/2); equilibrium atomic charges (e) for all monomers and complexes studied in the paper (using the A−H···D-N′ notation, we show only the charges of the A, H, and D atoms, as in most cases they experience the most dramatic changes); individual charge, charge transfer, and dipolar polarization contributions of Eq. S4 (e); linear dependence of the enthalpies of formation for HCl and HF complexes; and atomic Cartesian coordinates of the equilibrium geometries of the hydrogen bond complexes (PDF)

■

CONCLUDING REMARKS Although infrared intensities have long been known to be sensitive probes of hydrogen bonds, their very large intensifications on hydrogen bond formation have not been explained in the literature for lack of a reliable model for describing the electronic behavior owing to molecular vibrations. The QTAIM/CCTDP model has been proven to be very accurate for estimating intensity values, and its use here

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Roy E. Bruns: 0000-0002-8234-1129 H


Article

The Journal of Physical Chemistry A Notes

G. A.; Nakatsuji, H.; Li, X.; Caricato, M.; Marenich, A.; Bloino, J.; Janesko, B. G.; Gomperts, R.; Mennucci, B.; Hratchian, H. P.; Ortiz, J. V.; et al. Gaussian 09; Gaussian, Inc, 2016. (19) Møller, C.; Plesset, M. S. Note on an approximation treatment for many-electron systems. Phys. Rev. 1934, 46, 618−622. (20) Dunning, T. H., Jr. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 1989, 90, 1007. (21) Boys, S. F.; Bernardi, F. The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors. Mol. Phys. 1970, 19, 553−566. (22) Simon, S.; Duran, M.; Dannenberg, J. J. How does basis set superposition error change the potential surfaces for hydrogenbonded dimers? J. Chem. Phys. 1996, 105, 11024. (23) Gomes, T. C. F.; Silva, J. V., Jr.; Vidal, L. N.; Vazquez, P. A. M.; Bruns, R. E. Implementaçaõ computacional do modelo Carga-Fluxo de Carga-Fluxo de Dipolo para cálculo e interpretação das intensidades do espectro infravermelho. Quim. Nova 2008, 31, 1750−1754. (24) Keith, T. A. AIMAll (Version 17.11.14), TK Gristmill Software, Overland Park KS, USA, 2017 (aim.tkgristmill.com) (25) Silva, A. F.; Richter, W. E.; Meneses, H. G. C.; Bruns, R. E. Atomic charge transfer-counter polarization effects determine infrared CH intensities of hydrocarbons: a quantum theory of atoms in molecules model. Phys. Chem. Chem. Phys. 2014, 16, 23224−23232. (26) Overend, J. Infrared Spectroscopy and Molecular Structure; Elsevier: Amsterdam, 1955. (27) Silva, A. F.; Richter, W. E.; Bassi, A. B. M. S.; Bruns, R. E. Dynamic atomic contributions to infrared intensities of fundamental bands. Phys. Chem. Chem. Phys. 2015, 17, 30378−30388. (28) Terrabuio, L. A.; Luiz, R.; Haiduke, A. A quantum theory atoms in molecules investigation of Lewis base protonation. Int. J. Quantum Chem. 2017, 197−207. (29) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; et al. A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules. J. Am. Chem. Soc. 1995, 117, 5179−5197. (30) Brooks, B. R.; Brooks, C. L., III; MacKerell, A. D., Jr.; Nillson, L.; Patrella, R. J.; et al. CHARMM: The Biomolecular Simulation Program. J. Comput. Chem. 2009, 30, 1545−1614. (31) Richter, W. E.; Silva, A. F.; Bruns, R. E. Atomic Polarizations Necessary for Coherent Infrared Intensity Modeling with Theoretical Calculations. J. Chem. Phys. 2017, 146, 134107. (32) Duarte, L. J.; Bruns, R. E. Atomic Polarizations, Not Charges, Determine CH Out-of-Plane Bending Intensities of Benzene Molecules. J. Phys. Chem. A 2018, 122, 9833−9841.

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS L.J.D. and A.F.S. thank São Paulo’s FAPESP for the award of a Ph.D. fellowship 2017/22741-3 and postdoctoral grant number 2014/21241-9, and R.E.B. acknowledges FAPESP for funding through the award 2018/08861-9 and Brazil’s CNPq for research fellowship, 304518/2014-0.

■

REFERENCES

(1) Pimentel, G.; McClellan, A. The Hydrogen Bond; W.H. Freeman and Company: San Francisco, 1960. (2) Silva, A. F.; Richter, W. E.; Terrabuio, L. A.; Haiduke, R. L. A.; Bruns, R. E. Quantum theory of atoms in molecules/charge-charge flux-dipole flux models for fundamental vibrational intensity changes on H-bond formation of water and hydrogen fluoride. J. Chem. Phys. 2014, 140, No. 084306. (3) Kuyanov-Prozument, K.; Choi, M. Y.; Vilesov, A. F. Spectrum and infrared intensities of OH-stretching bands of water dimers. J. Chem. Phys. 2010, 132, No. 014304. (4) Joseph, J.; Jemmis, E. D. Red-,blue-, or no-shift in hydrogen bonds: A unified Explanation. J. Am. Chem. Soc. 2007, 129, 4620− 4632. (5) Iogansen, A. V. Direct proportionality of the hydrogen bonding energy and the intensification of the stretching ν(XH) vibration in infrared spectra. Spectrochim. Acta, Part A 1999, 55, 1585−1612. (6) Terrabuio, L. A.; Richter, W. E.; Silva, A. F.; Bruns, R. E.; Haiduke, R. L. A. An atom in molecules study of infrared intensity enhancements in fundamental donor stretching bands in hydrogen bond formation. Phys. Chem. Chem. Phys. 2014, 16, 24920−24928. (7) Angelelli, J. M.; Katritzky, A. R.; Pinzelli, R. F.; Topsom, R. D. Infrared intensities as a quantitative measure of intramolecular interactionsXVI. Tetrahedron 1972, 28, 2037−2050. (8) Katritzky, A. R.; Topson, R. D. Some Applications of Infrared Intensities to the Study of Intramolecular Interactions in Organic Chemistry. In Vibrational Intensities in Infrared and Raman Sprctroscopy, 1st Edition; Person, W. B., Zerbi, G., Eds. Elsevier Scientific Publishing Company: New York, 1982; 337−355. (9) Katritzky, A. R.; Topsom, R. D. Infrared Intensities: A Guide to Intramolecular Interactions in Conjugated Systems. Chem. Rev. 1977, 77, 639−658. (10) Guadagnini, P. H.; Oliveira, A. E.; Bruns, R. E.; De Barros Neto, B. Core electron energies, infrared intensities, and atomic charges. J. Am. Chem. Soc. 1997, 119, 4224−4231. (11) Bader, R. F. W. Atoms in Molecules; A Quantum Theory, Clarendon Press: Oxford, 1990. (12) Popelier, P. L. A. Atoms in Molecules: An Introduction; Prentice Hall, 2000. (13) Matta, C. F.; Boyd, R. J. The Quantum Theory of Atoms in Molecules. From Solid State to DNA and Drug Design; Wiley − VCH: Weinheim, Germany, 2007. (14) Rozenberg, M. The hydrogen bond − practice and QTAIM theory. RSC Adv. 2014, 4, 26928. (15) Haiduke, R. L. A.; Bruns, R. E. An atomic charge-charge fluxdipole flux atom-in-molecule decomposition for molecular dipolemoment derivatives and infrared fundamental intensities. J. Phys. Chem. A. 2005, 109, 2680−2688. (16) Silva, A. F.; Richter, W. E.; Meneses, H. G. C.; Faria, S. H. D. M.; Bruns, R. E. How Accessible Is Atomic Charge Information from Infrared Intensities? A QTAIM/CCFDF Interpretation. J. Phys. Chem. A 2012, 8238−8249. (17) Silva, A. F.; Richter, W. E.; Bruns, R. E. Quantum Theory of Atoms in Molecules/Charge−Charge Flux−Dipole Flux interpretation of fundamental vibrational intensity enhancements on H-bond formation of water trimer. Chem. Phys. Lett. 2014, 610-611, 14−18. (18) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, I


Infrared Intensification and Hydrogen Bond ... - ACS Publications

Recommend Documents