Effect of Microhydration on Dissociation of Trifluoroacetic Acid - The

Article pubs.acs.org/JPCA

Effect of Microhydration on Dissociation of Trifluoroacetic Acid Parvathi Krishnakumar†,§ and Dilip Kumar Maity*,†,‡,§ †

Theoretical Chemistry Section and ‡Human Resource Development Division, Bhabha Atomic Research Centre, Mumbai 400085, India § Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai 400094, India ABSTRACT: First-principle-based electronic structure calculations were carried out on microhydrated trifluoroacetic acid clusters (CF3COOH, tfa) to understand its molecular level interaction with water and subsequent ionic dissociation to form CF3COO− ion. From several geometrical inputs, the global minimum energy structure of hydrated cluster, tfa·nH2O (n = 1−7), was obtained adopting dispersion-corrected density functional, namely, ωB97X-D, and a set of correlated atomic basis function, aug-cc-pVDZ. It was predicted that tfa requires at least six H2O molecules to dissociate. Energy parameters of these hydrated clusters were improved by applying MP2 as well as CCSD(T) methods. A linear variation was observed for calculated solvent stabilization energy profile with the number of solvent H2O molecules present in the hydrated cluster. However, the calculated interaction energy profile showed the characteristic feature indicating the formation of contact ion-pair on the addition of six H2O molecules to tfa. On the basis of energy decomposition analysis, it was observed that the major interaction between tfa and H2O molecules was of electrostatic nature. On successive addition of water molecules, the electrostatic component of the interaction between solute and solvent molecules depicted a sudden increase when moving from penta- to hexahydrated cluster. This observed nature of energy profile coincided with the formation of hydronium ion in the case of hexahydrated cluster. The formation of H3O+ was manifested in simulated IR spectra of tfa·6H2O and tfa·7H2O clusters. A large red shift in IR peak positions corresponding to O−H stretching of tfa was predicted on microhydration.

1. INTRODUCTION Unlike a strong acid, a weak acid does not dissociate completely in aqueous medium. Depending on the extent of dissociation of an acid in aqueous medium, the bulk strength of an acid is defined in terms of pKa value. Thus, macroscopic or bulk strength of an acid may be correlated with the ease of proton transfer from acid to the neighboring solvent water molecule. Proton transfer of an acid (X-H) naturally depends on the bond strength of the acidic proton. The proton-transfer process involves polarization of X-H bond induced by solvent water molecules, followed by contact ion pair (Xδ−···Hδ+···δ−OH2) formation. Contact ion pair leads to the formation of a solventseparated ion pair that subsequently transforms to two separate solvated ions. This process generates hydrated proton (hydronium ion, H3O+), which remains in either Zundel (H3O+·H2O) or Eigen (H3O+·3H2O) form, and its interconversion has also been reported based on ultrafast spectroscopy.1−6 Depending on the strength of an acid, several molecules of water are needed to form stable contact ion pair in an acid molecule and make proton transfer possible. Molecular level description of acid−water interaction is important in understanding many physicochemical processes because proton transfer constitutes a major class of chemical transformations. Clusters of acid and water molecules have been an important area of research for both experimentalists and theoreticians. The interaction of acid and water molecules occurs through the formation of different size molecular © 2014 American Chemical Society

clusters having ring-like structures stabilized by H bonds. A few theoretical studies have been reported on the number of H2O molecules needed to form contact ion-pair of hydrofluoric acid, hydrochloric acid, sulfuric acid, nitric acid, perchloric acid, and formic acid.7−12 At the experimental front, IR spectroscopic studies have been effectively used to determine the minimum size of hydrated cluster of a few acids that can form a stable contact ion pair.13−16 Off late, a few theoretical and experimental studies have been reported on water clusters of carboxylic acids, namely, formic acid, acetic acid, trifluoroacetic acid (tfa), and oxalic acid.17−24 A theoretical study has also been reported predicting contact ion pair complex as the global minimum leading to ionic dissociation of formic acid (pKa = 3.75).12 tfa is the most abundant halogenated acid in the atmosphere, produced mainly from the degradation of hydrochlorofluorocarbons (HCFCs). Because of the presence of water vapor in the atmosphere, the formation of its water cluster is inevitable. Its removal in the gas phase proceeds mainly in the wet deposition because it is inert toward reaction with hydroxyl radical (•OH), the major chlorofluorocarbon scavenger from atmosphere. Isolated firstprinciple-based theoretical reports are available in the literature on stable structures of tfa·nH2O (n ≤ 5) clusters and infrared Received: March 25, 2014 Revised: July 9, 2014 Published: July 9, 2014 5443

dx.doi.org/10.1021/jp502976e | J. Phys. Chem. A 2014, 118, 5443−5453

The Journal of Physical Chemistry A

Article

Table 1. Comparison of Theoretical Geometrical Parameters and Peak Positions (in cm−1) in IR Spectra of Trifluoroacetic Acid (CF3COOH) and Water (H2O) Molecules in Gas Phase with Available Experimental Valuesa CF3COOH

H2O

method

rC−F (Å)b

rC−C (Å)

rCO (Å)

rC−O (Å)

rO−H (Å)

νC−F (cm−1)

νCO (cm−1)

νO−H (cm−1)

rO−H (Å)

∠HOH (degree)

MP2 ωB97X-D M062X B3LYP exptc

1.349 1.337 1.334 1.345 1.325

1.544 1.547 1.542 1.550 1.546

1.212 1.197 1.194 1.200 1.192

1.349 1.333 1.333 1.341 1.342

0.974 0.967 0.969 0.972 0.960

1182 1216 1248 1162 1240

1819 1898 1928 1850 1792

3736 3821 3798 3735 3587

0.966 0.961 0.962 0.965 0.957

103.84 104.74 104.78 104.77 104.51

νO−H (cm−1)

sym

3804 3881 3867 3795 3657

νO−H (cm−1)

asym

3937 3992 3977 3905 3756

a

Basis sets adopted for theoretical results are aug-cc-pVDZ for all atoms. bThese values are calculated keeping all three C−F bonds to be of same length. cRefs 30 and 31.

spectral properties.21−23 Experimental studies on clusters of tfa and water, tfa·nH2O (n ≤ 3) have been reported based on pulsed nozzle Fourier transform microwave spectroscopy.20 Assignments of the observed microwave emission lines have also been made to H-bonded ring structures of tfa and water molecules with the support from ab initio quantum-chemical results. To the best of our knowledge, no report is available in the literature on the hydrated cluster of trifuoroacetic acid (pKa = 0.52), where contact ion pair is the most stable structure leading to the dissociation of proton. In what follows, we report the results based on a systematic study on microhydrated clusters of tfa following first-principle-based electronic structure calculations. The fully optimized ground-state structure, binding characteristics, various energy parameters, and IR spectra of tfa·nH2O clusters (n = 1−7) are presented, elucidating the minimum number of water molecules required for acid dissociation of CF3COOH to form a stable contact ion pair. Physical origin of interaction between tfa and water is also explained based on various energy components calculated. Spectral signature depicting acid dissociation of CF3COOH and the formation of hydronium ion is reported through calculated IR spectra of tfa·nH2O clusters. Shifts of IR bands due to interaction with solvent water molecules and solute tfa are calculated and discussed.

all equilibrium structures are also calculated to verify the nature of optimized structure and to generate IR spectrum under harmonic approximation. MP2 method has also been applied to reoptimize the most stable structures obtained at DFT level. Decomposition of interaction energy of the hydrated clusters has been performed following localized molecular orbital (LMO)-based approach to identify the physical origin of interaction. LMO-based scheme is known to handle monomer units of the cluster in a better way than the Morokuma or reduced variational space (RVS) procedures.26,27 Energy decompositions are carried out at DFT as well MP2 level of theory. All of these molecular electronic structure calculations are carried out following GAMESS suit of quantum-chemistry program.28 Visualization of structure and IR spectrum are done by MOLDEN program system.29

3. RESULTS AND DISCUSSION 3.1. Structure. Selected geometrical parameters for the minimum energy equilibrium structure of CF3COOH and H2O molecules calculated applying different DFT functionals and MP2 methods adopting aug-cc-pVDZ basis sets are supplied in Table 1 and compared with the reported measured values. Computed unscaled harmonic stretching frequencies are also tabulated for comparison with the measured experimental data for selected modes.30,31 Note that structure of CF3COOH is calculated with symmetry restriction to keep all C−F bond lengths same. Calculations are also carried out without applying any symmetry restriction that results in two different types of bond lengths for C−F bonds in CF3COOH. The C−F bond that is syn to CO bond is shorter by 0.008 Å and the other two C−F bonds are longer by 0.005 Å than those in the structure calculated by the previously mentioned symmetry restriction applying ωB97X-D functional. However, the structure obtained by applying symmetry restriction is 0.04 kcal/mol less stable than that of the structure, predicted without any symmetry restriction at this level of theory. Other DFT functionals and MP2 method also predict that the structure obtained on symmetry restriction is less stable by 0.04 kcal/mol at most. It is worth mentioning that no variation in other geometrical parameters and harmonic stretching frequency is observed calculated by these two different ways. Table 1 suggests that popular DFT functional, B3LYP, performs well for H2O as well as CF3COOH molecules in terms of geometrical parameters and IR frequency. However, it is known that this functional does not perform well for hydrogen-bonded systems because it cannot treat dispersion interactions properly. The overall performance of other DFT functionals considered at present and MP2 method is observed to be similar for these small isolated molecules. Table 2

2. THEORETICAL METHODS To choose a suitable level of theory for electronic structure, we carried out calculations of isolated water and tfa molecules applying several DFT functionals and MP2 method and compared them with available experimental data. For the calculation of cluster geometry, Dunning-type correlation consistent atomic basis functions augmented with diffuse functions (aug-cc-pVDZ) have been adopted. Correlated popular density functional like B3LYP, a functional that treats dispersion correction accurately, ωB97X-D, and a modern DFT functional that is known to account noncovalent interactions, and MO62X have been tried for benchmark studies. It is noted that dispersion-corrected DFT functional, namely, ωB97X-D, predicts geometrical parameters of hydrated cluster close to MP2 as well as experimental data. Rotational constants (A, B, C) calculated under rigid-rotor approximation for mono-, di-, and trihydrated clusters of tfa have also been compared with the reported experimental values. Again, it is noted that DFT functional ωB97X-D performs very well against measured values.25 The search for minimum energy structures of different size tfa·nH2O clusters has been performed by applying this particular DFT functional following Newton−Raphson algorithm with different possible initial guess structures. Hessians of 5444


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3855 3821 2562 1910

3805 3737 2530 1752

3865.1 3835.1 2533.7 1733.3

2471 1085 716 499

2484 1090 724 497

2501 1103 730 504

2463 1085 719 488

2498.8 1082.6 718.5 493.4

2044 993 621 428

2063 1000 628 465

2073 1010 633 477

2046 993 624 411

2075.2 993.8 622.5 414.8

compares calculated rotational constants at different levels under rigid-rotor approximation with the reported measured values.20 Values calculated considering ωB97X-D DFT functional are within 1% error of experimental values for mono- and dihydrated clusters. For trihydrated cluster, calculated error in rotational constants is predicted to be higher. However, overall error is less at ωB97X-D level compared with MP2 or other DFT functionals. Literature data suggest that ωB97X-D functional is a good candidate to produce accurate energy parameters for hydrogen-bonded systems.32,33 On the basis of these observations, the present systems are treated applying this particular DFT functional that treats dispersion correction rather accurately. Energy parameters are improved by further applying MP2 and CCSD(T) methods on minimum energy structures calculated at the ωB97X-D/aug-cc-pVDZ level of theory. It is worth mentioning that basis set superposition error (BSSE) in mono-, di-, and trihydrated clusters is calculated by applying counter-poise-based super molecule approach. The BSSE energy is calculated as 0.4, 0.6, and 0.8 kcal/mol for mono-, di-, and trihydrated clusters of tfa, respectively, following the ωB97X-D/aug-cc-pVDZ method. Optimized structures of H2O and CF3COOH along with the global minimum energy structures predicted for hydrated cluster of tfa, tfa·nH2O (n = 1−5), are given in Figure 1. Selected bond lengths of isolated solute and solvent molecules as well as the hydrated clusters are also supplied in the Figure. Bond length and bond angle in free H2O molecule are calculated as 0.961 Å and 104.76° at the ωB97X-D/aug-ccpVDZ level, and these data compare well with the measured values of 0.9575 Å and 104.51° respectively. Computed geometrical parameters of free tfa in the gas phase are also noted to be fairly close to the experimental data. The largest deviation in bond length is predicted for C−F bond, and it is 0.017 Å longer than the reported experimental data when the calculation is carried out without any symmetry restriction. It is to be noted that the present calculated O−H bond distance in free tfa at ωB97X-D/aug-cc-pVDZ level is the same as the earlier value calculated applying MP2/6-311++G(2df,2pd) level.20 To predict the most stable structures for the hydrated clusters of tfa (tfa·nH2O), we considered several possible initial geometrical configurations for optimization. Note that solvent H2O molecules in starting geometries of these clusters for optimization are arranged in such a way that CF3COOH dissociates to form CF3COO− with the addition of minimum number of H2O molecules. The oxygen atom of solvent H2O molecule is predicted to be connected to the dissociating H atom of tfa in the equilibrium structures of all of these hydrated clusters. Only one equilibrium structure is obtained for the monohydrated cluster, and the most stable one is shown as 1wa in Figure 1. Note that the addition of the first solvent H2O molecule to tfa increases its CO distance (rCO) by 0.01 Å and O−H bond distance (rO1H) by 0.024 Å. The present calculated value of rO1H compares well with the previous reported value.20 The calculated distance (rHO2) between the transferring H atom and O atom of the neighboring solvent H2O molecule is 1.713 Å, which is less than that observed in case of formic acid.12 The present calculated value is very close to previous reported values at B971 and MP2 levels.21 Note that C−O bond (rCO1) of tfa is also shortened significantly on adding a water molecule to tfa. The most favored structure for dihydrated cluster of tfa is displayed as 2w-a in Figure 1 with bond distance parameters. Note that four minimum energy structures are obtained for the

Ref 20. a

3771 3737 2506 1711 tfa tfa·H2O tfa·2H2O tfa·3H2O

3848 3811 2549 1905

expta B3LYP MO62X

C/MHz

ωB97X-D MP2 expta B3LYP MO62X

B/MHz

ωB97X-D MP2 expta B3LYP A/MHz

MO62X ωB97X-D MP2 system

Table 2. Comparison of Rotational Constants (A, B, and C in MHz) for Hydrated Clusters of Trifluoroacetic Acid, tfa·nH2O (n = 1−3) Calculated at Different Levels of Theory and the Available Experimental Data


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Figure 1. Fully optimized equilibrium structures calculated applying ωB97X-D functional with aug-cc-pVDZ set of correlated basis function for (A) H2O and (B) CF3COOH and for the most stable structure of (1w-a) CF3COOH·H2O, (2w-a) CF3COOH·2H2O, (3w-a) CF3COOH·3H2O, (4w-a) CF3COOH·4H2O, and (5w-a) CF3COOH·5H2O. A few selected structures of tetra- and pentahydrated clusters and their relative stability (including zero-point energy correction) with respect to the lowest energy structure are displayed as ΔE value in kilocalories per mole. C, O, F, and H atoms are shown as gray, red, yellow, and blue balls, respectively.

Table 3. Selected Mulliken Atomic Charge, Bond-Length, and Bond-Order Parameters of tfa·nH2O (n = 1−7) Clusters Calculated at ωB97X-D/aug-cc-pVDZ Level of Theorya bond length (in Ǻ )

atomic charge (au)

bond order

system

O1

H

O2

rCO

rO1···H

rH···O2

CO

O1···H

H···O2

tfa·1w tfa·2w tfa·3w tfa·4w tfa·5w tfa·6w tfa·7w

−0.38 −0.39 −0.39 −0.41 −0.47 −0.78 −1.11

+0.24 +0.29 +0.32 +0.39 +0.42 +0.43 +0.64

−0.33 −0.34 −0.51 −0.62 −0.60 −0.17 −0.39

1.207 1.217 1.213 1.217 1.222 1.226 1.228

0.992 1.009 1.016 1.036 1.064 1.415 1.564

1.713 1.592 1.561 1.481 1.419 1.057 1.012

1.73 1.64 1.60 1.56 1.50 1.55 1.53

0.90 0.82 0.78 0.72 0.67 0.24 0.11

0.05 0.06 0.07 0.05 0.10 0.60 0.36

a O1 and O2 are oxygen atoms of tfa O−H bond and the nearest H2O molecule, respectively. H refers to the transferring proton of trifluoroacetic acid.

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Figure 2. Fully optimized most stable equilibrium structures calculated applying ωB97X-D functional with aug-cc-pVDZ set of correlated basis function for (6w-a) HCOOH.6H2O and (7w-a) HCOOH·7H2O clusters. A few selected structures of hexa- and heptahydrated clusters and their relative stability (including zero point energy correction) with respect to the lowest energy structure are displayed as ΔE value in kilocalories per mole. C, O, F, and H atoms are shown as gray, red, yellow, and blue color balls, respectively.

trihydrated cluster. Unlike formic acid, an equilibrium structure is also obtained showing ionization of tfa and formation of contact ion-pair in the case of tetrahydrated cluster of tfa, and the structure is displayed as 4w-b in Figure 1. However, this particular structure is 11.8 kcal/mol less stable than the global minimum energy structure, 4w-a. In the case of pentahydrated cluster of tfa, eight minimum energy structures are obtained having two structures, showing the formation of contact ion pair. The most stable structure (5w-a) and other two structures (5w-b and 5w-c) showing ionization of tfa are displayed in Figure 1. Note that 5w-b and 5w-c are less stable than 5w-a by 7.0 and 7.7 kcal/mol, respectively. One can easily notice that in 5w-a O1−H bond is stretched by 0.028 Å and H−O2 bond is compressed by 0.062 Å compared with those in 4w-a. Six equilibrium structures are obtained in tfa·6H2O cluster, and the global minimum energy structure is displayed as 6w-a in Figure 2. It is interesting to note that this structure shows dissociation of tfa and formation of hydronium ion (H3O+). Calculated bond distance parameter rO1H is increased significantly to 1.415 Å, and rHO2 is decreased to 1.057 Å, indicating transfer of proton from tfa to the nearest neighboring solvent H2O molecule. One can easily notice that the other two OH bonds in the hydronium ion are shorter than rHO2. One more structure (6w-b) is also obtained showing the formation of contact ion pair in tfa·6H2O cluster. However, this particular structure is 1.7 kcal/mol less stable than 6w-a and has all three O−H bonds of H3O+ ion nearly of same length. In the case of heptahydrated cluster of tfa, eight equilibrium structures are predicted and six structures show the formation of contact ion pair. A charge-separated ion pair of tfa forming H3O+ ion is obtained as the global minimum energy structure in the case of tfa·7H2O cluster, shown as 7w-a in Figure 2. Supplied bond distances (rO1H = 1.564 Å) suggest that the proton of CF3COOH is now transferred to the solvent H2O molecule

dihydrated cluster. Calculated geometrical parameters suggest additional increase in CO and O−H (rO1H) bond lengths in tfa for the dihydrated cluster. The distance between the dissociating H atom of tfa and O atom of solvent H2O molecule (rHO2) is computed to be reduced notably. Moreover, the distance between carbonyl O atom of tfa and H atom of second solvent H2O molecule is also reduced on addition of the second solvent water molecule to tfa. Present rO1H and rHO2 values of the dihydrated cluster are less than previous MP2 values.20,21 Five equilibrium structures of trihydrated cluster of tfa are calculated, and the global minimum energy structure is displayed in Figure 1 as 3w-a. The formation of ring structure due to H bonding is observed as the main growth motif in the cluster, as discussed in mono- and dihydrated clusters. These ring structures are formed due to hydrogen bonding interactions between solute tfa and solvent water molecules as well as inter water hydrogen bonding. Data supplied in Table 3 suggest that O−H bond distance in tfa (rO1H) is increased by 0.048 Å compared with that in free tfa. The distance between the dissociating H atom and O atom of the neighboring solvent H2O molecule (rHO2) is reduced by ∼0.152 Å compared with tfa·H2O cluster, suggesting the initiation of dissociation process. CO bond of tfa is also observed to be shortened. In the case of tetrahydrated cluster of tfa, six equilibrium structures are predicted, and the global minimum energy structure, 4w-a, is depicted in Figure 1. As in case of hydrated formic acid, a new growth motif is obtained in this cluster. However, this new open book structure is less stable than the global minimum structure, 4w-a, by 1.2 kcal/mol. Note that the relative stability of different equilibrium structures is calculated incorporating zero-point energy correction. Such structures (open book) are also obtained in higher hydrated tfa clusters. Bond-length parameters in 4w-a indicate that rO1H is lengthened by 0.02 Å and rHO2 is shortened by 0.08 Å compared with bonds in the 5447



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Table 4. Calculated Solvent Stabilization Energy (Estab) and Solvent Interaction Energy (Eint) of tfa·nH2O (n = 1-7) Clusters Applying Different Theoretical Methods and Adopting aug-cc-pVDZ Basis Set −Estab (kcal/mol)

a

system

ωB97X-D

tfa·H2O tfa·2H2O tfa·3H2O tfa·4H2O tfa·5H2O tfa·6H2O tfa·7H2O

11.6 24.1 32.8 44.4 54.0 62.3 78.2

MP2a 11.6 23.8 32.5 44.0 53.9 62.5 78.4

−Eint (kcal/mol) CCSD(T)

ωB97X-D

11.6 23.6 32.3 43.7 53.6 60.8 77.2

12.3 22.1 25.2 32.2 39.6 96.2 150.3

(11.5) (23.8) (32.4) (43.8) (53.4) (62.6) (77.4)

MP2a 12.0 21.5 24.5 31.4 39.0 93.6 147.3

(12.1) (21.7) (24.7) (31.7) (39.3) (95.4) (148.9)

CCSD(T) 12.1 21.4 24.4 31.1 38.7 92.2 143.5

Values in the parentheses refer to data calculated applying aug-cc-pVTZ basis set.

and forming a new covalent bond H−O2 with water molecule. Breaking and making of these two bonds may be reflected in the values of calculated bond orders in these hydrated clusters. Table 3 also lists calculated bond distance and bond-order indices34 of these two bonds and CO bond along with their bond lengths. Note that calculated bond-order values remain almost the same until pentahydrated cluster showing insensitivity to the addition of solvent water molecules. However, a large variation in bond-order values is observed after adding one more water molecule to the tfa·5H2O cluster. Change in values for both the breaking (0.67 to 0.24) and making (0.10 to 0.60) of bonds in the tfa·6H2O cluster refers to the transfer of H atom from O1 to O2 atoms. Similarly, bond lengths of these two bonds do depict such sudden variation on going from penta- to hexahydrated cluster. In this whole process of H-atom transfer in these hydrated clusters, because carbonyl oxygen atom takes active part in forming cyclic hydrogen-bonded structures, CO bond-length and bondorder indices are also included in the Table. However, no regular variation is observed in these two calculated parameters. 3.3. Solvent Stabilization and Interaction Energy. Solvent-induced stabilization energy of these clusters, tfa·nH2O, may be expressed as Estab = Etfa·nH2O − (nEH2O + Etfa), where Etfa·nH2O is the energy of the cluster tfa·nH2O. EH2O and Etfa correspond to the energy of a single H2O and tfa. By definition, stabilization energy represents stabilization of tfa due to interactions of solvent water molecules and tfa. This energy term (Estab) accounts for interaction of tfa with solvent H2O molecules as well as interactions due to H bonding among water molecules. Stabilization energy of tfa·nH2O clusters calculated applying ωB97X-D/aug-cc-pVDZ method is supplied in Table 4. These energy parameters are improved by doing the single-point energy calculations at MP2/aug-ccPVDZ, MP2/aug-cc-pVTZ and CCSD(T)/aug-cc-pvDZ levels, and the values are listed in the Table. The variation of solvent stabilization energy (Estab) versus n, number of water molecules in tfa·nH2O cluster calculated at ωB97X-D and MP2 levels adopting aug-cc-pVDZ set of atomic basis functions, is shown in Figure 3a. Note that Estab changes linearly on addition of solvent H2O molecules, and this is understandable because the value corresponds to internal energy that increases with the increase in size of the hydrated cluster. It is interesting to examine that the two lines calculated at two different levels of theory overlap throughout the cluster size studied at present. A similar feature is also observed in the case of data obtained from MP2/aug-cc-pVTZ and CCSD(T)/aug-cc-pvDZ levels of theory, as displayed in Figure 3b. The plotted energy profiles do not display any characteristic feature to indicate the

(rHO2 = 1.012 Å), indicating dissociation of the acid and formation of CF3COO− and H3O+ ions. The previous discussions on the structural aspects of the hydrated clusters suggest that tfa may dissociate under the influence of water molecules only when no fewer than six water molecules are present in the immediate neighborhood of the acid molecule surrounding O−H bond. On the basis of theoretical studies, a previous report has shown that seven water molecules are able to ionize formic acid, leading to HCOO− and H3O+ ions.12 Similarly, theoretical study on hydrated clusters of oxalic acid has revealed that the formation of an ion pair of oxalic acid needs five molecules of water.24 A previous study on nitric acid suggests that to form stable ionpair structure of nitric acid, four solvent water molecules are sufficient.8 In the same way, sulfuric acid ion-pair structure of HSO4−H3O+(H2O)n has lower energy than the hydrogenbonded neutral structure, H2SO4(H2O)n, if five or more solvent water encapsulate the acid.7 Literature reports indicate that only three H2O molecules are able to dissociate perchloric acid.9 It is also reported that four water molecules are required to ionize HCl, while three solvent water molecules are enough to dissociate HBr and HI.10,13,14 In hydrated clusters of all these acids, the global minimum energy structures are predicted to be multi cyclic. 3.2. Atomic Charge and Bond Order. Atomic charges are computed for the global minimum energy structures of hydrated tfa clusters, tfa·nH2O (n = 1−7), by applying the definition suggested by Mulliken. Calculated atomic charges over O1, H, and O2 atoms in these hydrated clusters are listed in Table 3. Respective values in the case of monohydrated cluster, tfa·H2O, are about −0.38, +0.24, and −0.33 au Note that O1 refers to oxygen atom of tfa O−H bond and O2 refers to oxygen atom of the solvent H2O molecule, to which the proton is transferred. On stepwise addition of solvent water molecules to tfa, a little change in atomic charge on O1···H··· O2 atoms in tfa·nH2O cluster is observed up to n = 5, and a large change is noted for hexa-hydrated cluster of tfa. As shown in Table 3, atomic charge on O1 is increased from −0.47 au to −0.78 au, and the same for O2 atoms is decreased to −0.17 au from −0.60 au However, the change of atomic charge on transferring H atom is only from +0.42 au to +0.43 au for hexahydrated cluster. The change of atomic charge on all three atoms is observed to be significant for heptahydrated cluster, though. This change coincides with the formation of chargeseparated ion-pair in hydrated clusters of tfa (O1δ−−Hδ+− O2δ‑) as the most stable structures for hexa- and heptahydrated cluster. In this process of tfa and solvent H2O molecules interaction, the proton transfers from tfa to H2O molecule. This is only possible by rupturing the covalent O1−H bond in tfa 5448



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number of solvent water molecules (n) in Figure 3a,b. One may easily notice that stabilization and interaction energy are very close to dihydrated clusters, but when intermolecular H bond among solvent water molecules starts building up, hydration energy exceeds interaction energy. Calculated interaction energy is significantly smaller than Estab for the hydrated cluster of size n = 3−5. The interaction energy profile shows a sharp increase for hexa- and heptahydrated clusters of tfa. This increase in Eint values over Estab may be explained from the definition of these two energy parameters. In the case of hexaand heptahydrated clusters of tfa, the O−H bond of tfa is close to dissociation limit. However, by definition of Estab, the energy of tfa with equilibrium O−H bond length is considered. This makes Estab lower than Eint, where energy of the system with actual geometrical parameters is calculated. It is worth mentioning that a very small variation is observed in interaction energy for all of these hydrated clusters at DFT, MP2, and CCSD(T) levels of theory. (See Table 4 and Figure 3.) The difference between the two energy parameters, Estab and Eint, for hydrated clusters up to n = 5 should be the measure of inter water hydrogen bonding energy. The two intersecting energy curves do indicate the formation of charge-separated ion pair of trifuoroacetic acid in the case of hexahydrated cluster. In other words, interaction energy profiles clearly point out that six solvent H2O molecules are enough to dissociate tfa to form a contact ion pair. 3.4. Energy Decomposition Analysis. To understand the physical origin of interaction between solute tfa and solvent water molecules, we carried out energy decomposition analysis (EDA) of interaction for all hydrated clusters of tfa. EDA can extract various energy components such as electrostatic, exchange repulsion, polarization, and dispersion from the total interaction energy in clusters following a super molecule approach. This is often useful to understand physical insight of interactions, thus leading to the development of force-field (FF) methods. FF methods employ different functional forms of energy to model total interaction in terms of different sources of interaction. An algorithm based on LMO-based energy decomposition analysis (LMOEDA) is applied to reveal sources of Kohn−Sham interaction energy. In this procedure, changes in the exchange and correlation functionals on going from monomer (tfa and H2O) to super molecule (tfa·nH2O) are considered to describe the exchange and dispersion terms. Only the global minimum energy structures of each size hydrated clusters, tfa·nH2O (n = 1−7), are employed for EDA calculation, and computed values of different energy components are provided in Table 5. It can be easily noticed

Figure 3. Plot of calculated stabilization energy, Estab, and interaction energy, Eint, in kilocalories per mole versus n, number of water molecules for CF3COOH·nH2O clusters at (a) ωB97X-D/aug-ccpVDZ (blue and black lines) and MP2/aug-cc-pVDZ (red and magenta lines) and (b) MP2/aug-cc-pVTZ (red and magenta lines) and CCSD(T)/aug-cc-pVDZ (blue and black lines) level of theory. Energy calculations are carried out on geometry optimized at ωB97XD/aug-cc-pVDZ level.

formation of an ion pair for any size of hydrated cluster studied at present. To look for an alternative energy parameter that can show some characteristic feature for the dissociation of acid, we calculated interaction energy. Interaction energy (Eint) between tfa and cluster of water molecules in the hydrated cluster, tfa· nH2O, may be defined as Eint = Etfa·nH2O − (E(H2O)n + Etfa) where, Etfa·nH2O refers to the energy of the cluster tfa·nH2O. E(H2O)n and Etfa correspond to the energy of (H2O)n and tfa, respectively. For evaluation of E(H2O)n, solute part (tfa) is deleted from the optimized geometry of the cluster, followed by a single-point energy calculation. Following a similar procedure for the evaluation of Etfa, the (H2O)n part is removed from the optimized geometry of the hydrated cluster, followed by a single-point energy calculation. Thus, Eint essentially represents the net interaction of tfa with (H2O)n systems in these hydrated clusters. Interaction energy of the tfa·nH2O (n = 1−7) clusters is calculated by applying ωB97X-D/aug-cc-pVDZ method and tabulated in Table 4. These energy values are further improved by doing the single-point energy calculations at MP2/aug-ccPVDZ, MP2/aug-cc-pVTZ, and CCSD(T)/aug-cc-pvDZ levels, and the values are given in the Table. Calculated interaction energy (Eint) for tfa·nH2O clusters applying different theoretical procedures (DFT, MP2, and CCSD(T)) is plotted against the

Table 5. Energy Components of Interaction Between tfa and Water in Hydrated Clusters of tfa Obtained from Localized Molecular Orbital Based Energy Decomposition Analysis energy component (kcal/mol)

5449

cluster size (n)

exchange (−Eex)

dispersion (−Edisp)

electrostatic (−Eelec)

1 2 3 4 5 6 7

10.7 16.8 19.0 22.3 26.6 30.3 30.8

5.9 7.9 8.5 9.4 12.3 14.1 15.9

73.8 118.4 135.1 168.4 208.8 436.5 511.1



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the global minimum energy structure of each size of tfa·nH2O clusters (n = 1−7), isolated H2O, and CF3COOH molecules is calculated. From the calculated frequency and IR intensity, vibrational spectra are simulated applying Lorentzian line shape with peak half-width of 10 cm−1. On the basis of the previously reported experimental values of stretching frequency of H2O (νsym = 3657 cm−1, νasym = 3756 cm−1) and calculated harmonic data (ωsym = 3881 cm−1, ωasym = 3992 cm−1) at ωB97X-D/augcc-pVDZ level, 0.94 is considered to be the scaling factor at present. Scaled frequencies for free water are thus calculated as 3645 and 3753 cm−1, respectively, for symmetrical stretching (ωsym) and asymmetrical stretching (ωasym). Present calculated scaled stretching frequencies of C−F, CO and O−H bond in free tfa are 1143, 1783, and 3592 cm−1, respectively. The calculated scaled stretching frequency for O−H bond of tfa is reasonably close to the reported experimental data of 3587 cm−1 in gas phase.30,31 Frequencies of hydrated clusters of tfa are also calculated with the same scaling factor, and selected IR frequencies (>1500 cm−1) of these clusters, tfa·nH2O (n = 1− 7), are supplied in Table 6. Simulated IR spectrum of isolated free water molecule is presented in Figure 5a, pointing the strong IR peak at 3753 cm−1 for the asymmetric stretching mode. Frequencies due to symmetric stretching and bending in H2O are computed at 3645 and 1530 cm−1, respectively. The IR spectrum of free tfa molecule in the gas phase is displayed in Figure 5b, showing the peak at 3592 cm−1 corresponding to O−H stretching mode and the same at 1783 cm−1 for CO stretching. The peak at 1357 cm−1 in the IR spectrum is for C−C stretching mode, and large intensity peaks around 1100 cm−1 correspond to different stretching modes of C−F bonds. Calculated scaled frequencies of these two molecules as well as for hydrated clusters are supplied in Table 6. Figure 5c reports simulated IR spectrum of monohydrated cluster of tfa in the range of 1000−4000 cm−1. The strongest IR band at 3142 cm−1 corresponds to O−H stretching of tfa, and IR peak at 1746 cm−1 is due to CO stretching. Thus, on hydration of tfa by a single H2O molecule, a large red shift of 450 cm−1 for O−H stretching mode is noted. A red shift of 37 cm−1 is also seen for CO stretching mode. It is interesting to observe that while symmetric stretching of H2O gets red-shifted by 90 cm−1, a blue shift of 38 cm−1 is seen for the asymmetric stretching mode. A weak band is also observed

that the electrostatic component is largely dominant over the other energy components. This is understandable from the calculated atomic charges of O1, H, and O2 atoms of the hydrated clusters, as supplied in Table 3. It is interesting to note that variation of exchange and dispersion components is very small for the entire size of hydrated clusters studied, as displayed in Figure 4. However, the calculated energy profile of

Figure 4. Plot of calculated (a) electrostatic (Eelec), (b) exchange (Eex), and (c) dispersion (Edisp) energy components in kilocalories per mole at ωB97XD/aug-cc-pVDZ level for the hydrated clusters CF3COOH· nH2O against the number of solvent water units (n) present in the clusters. Electrostatic energy profile calculated at MP2/aug-cc-pVDZ level of theory labeled d.

the electrostatic component against the size (n) of the cluster has a characteristic feature showing slow increase until n = 5 and then a sudden increase for hexahydrated cluster of tfa. The sharp change of electrostatic component connotes the formation of contact ion pair in hexahydrated cluster of tfa.35 3.5. IR Spectra. Water clusters encapsulating tfa (CF3COOH) are stable due to the formation of a hydrogen bond between tfa and neighboring H2O molecules as well as among water molecules. Peak positions in IR spectra due to O−H stretching modes of H2O and CF3COOH molecules are expected to shift compared with that of free water and tfa due to H-bonding interactions. The frequency of normal modes for

Table 6. Scaled (scaling factor = 0.94) IR Frequency of Free H2O, Free CF3COOH (tfa), and Selected IR Frequency (>1500 cm−1) of tfa·nH2O Clusters (n = 1−7) Calculated Applying ωB97X-D/aug-cc-pVDZ Method frequency shift (in cm−1)a −1 b

system

calculated frequency (ν) (in cm )

ΔνCO

ΔνO···H

ΔνH···OH2

H2O tfa tfa·H2O tfa·2H2O tfa·3H2O tfa·4H2O tfa·5H2O tfa·6H2O

1530, 3645, 3753 1783, (3592) 171, 1521, 1746, (3142), 3555, 3715 188, 1537, 1561, 1732, (2808), 3270, 3449, 3706, 3711 301, 1539, 1559, 1594, 1718, (2699), 3333, 3395, 3446, 3646, 3712, 3715 317,1537, 1545, 1608, 1700, (2354), 3301, 3372, 3386, 3453, 3478, 3704, 3714, 3718 319,1537, 1545, 1648, (1969), 3269, 3305, 3349, 3427, 3453, 3524, 3593, 3711, 3713, 3718 (454), 1534, 1543, 1558, 1568, 1575, 1586, 1631, 1669, 2033, 2730, 2827, 3125, 3146, 3244, 3316, 3367, 3704, 3705, 3707, 3717, 3719 (214),1540, 1546, 1559, 1571, 1572, 1603, 1625, 1666, 1692, 2283, 2528, 2800, 3124, 3145, 3330, 3389, 3418, 3449, 3475, 3491, 3557, 3706, 3710, 3720

−37 −51 −65 −83 −135 −114

−450 −784 −893 −1238 −1623 −3138

+17 +130 +146 +148 +1863

−117

−3378

+2629

tfa·7H2O a

Frequency shifts are calculated with respect to free trifluoroacetic acid. Frequency shifts for stretching of forming the H bond between O atom of immediate solvent H2O molecule with the transferring H atom of tfa (ΔνH···OH2) are calculated in reference to monohydrated cluster. bFrequency data shown in bold faces, bold faces and underlined, and bold faces and in parentheses refer to CO stretching, stretching of breaking O−H bond of tfa, and forming O−H bond with the neighboring H2O, respectively. 5450



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Figure 5. Simulated IR spectra calculated at ωB97X-D/aug-cc-pVDZ level of theory for (a) H2O, (b) CF3COOH, (c) CF3COOH·H2O, (d) CF3COOH·2H2O, (e) CF3COOH·3H2O, (f) CF3COOH·4H2O, (g) CF3COOH·5H2O, (h) CF3COOH·6H2O, and (i) CF3COOH·7H2O based on harmonic oscillator approximation. Plotted IR spectra are scaled by a factor 0.94 to account anharmonicity.

at 171 cm−1 for the H bond between O atom of H2O and transferring H atom of tfa. In dihydrated cluster, a red shift of 784 cm−1 is obtained compared with the isolated tfa molecule for stretching mode of O−H bond. IR bands higher than 3000 cm−1 in Figure 5d are due to H-bonded and free O−H bonds in solvent H2O molecules. The peak at 3449 cm−1 is due to the stretching mode of H bond between carbonyl O atom and H atom of solvent H2O, while the same at 3270 cm−1 refers to inter water H bonding in the hydrated cluster. A weak band at 3706 cm−1 is assigned to stretching of free O−H bond of water molecules. Band due to the formation of H bond between O atom of solvent H2O and transferring H atom of tfa is predicted at 188 cm−1 that is blue-shifted by 17 cm−1 compared with monohydrated cluster. IR band due to CO stretching mode of tfa in this dihydrated cluster is observed at 1732 cm−1, which is red-shifted by 51 cm−1.

Calculated IR spectrum of trihydrated cluster is depicted in Figure 5e showing IR band at 2699 cm−1, which corresponds to O−H stretching of tfa. IR band for this rupturing O−H bond is red-shifted by 893 cm−1, and the IR peak due to formation of hydrogen bond between O atom of solvent H2O and transferring H atom of tfa is blue-shifted by 130 cm−1. Band for CO stretching mode of tfa is calculated at 1718 cm−1, suggesting a red shift of 65 cm−1. A strong band predicted at 3395 cm−1 refers to stretching mode of H bond between carbonyl O atom and H atom of H2O. IR peaks observed beyond 3500 cm−1 are due to stretching of free O−H bond of H2O units, and bands in the 3300−3500 cm−1 range are assigned to O−H bonds of water that are H-bonded either to tfa or to another H2O. O−H stretching of tfa (2354 cm−1) is further red-shifted on addition of another solvent water molecule to trihydrated cluster of tfa. IR spectrum of the most stable structure of tfa·4H2O cluster is displayed in Figure 5f. A very weak band appeared at 317 cm−1 is due to the newly 5451



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molecule (rHO2) reduces slowly. On the addition of the sixth H2O molecule, rO1H increases and rHO2 decreases, largely suggesting breaking of O1···H and making of H··O2 bonds. Similar variation in atomic charge over O1 and O2 atoms in this process of proton transfer in tfa is also observed. Physical origin of interactions between trifuoroacetic acid and water molecules in these clusters is analyzed, and electrostatic interaction is observed to play major role. Because of weakening, IR band for O1−H stretching is red-shifted, having the largest shift for heptahydrated cluster. H−O2 bond becomes stronger on successive addition of H2O molecules and gets blue-shifted. In this proton dislocation process, IR band due to CO stretching of tfa also gets red-shifted. All of these observations point to the fact that six water molecules can dissociate tfa, forming CF3COO− in the gas phase. On successive addition of solvent H2O molecules, the barrier for this dissociation process reduces and becomes free dissociation when six water molecules surround the solute tfa molecule.

formed hydrogen bond between O atom of solvent H2O and transferring H atom of tfa. IR peak observed at 1700 cm−1 is due to CO stretching mode of tfa, and this is red-shifted by 83 cm−1 compared with free tfa. The band predicted at 3301 cm−1 is assigned to stretching mode of the H bond between carbonyl O atom and H atom of water and peak positions beyond this band represents stretching vibrations of inter water hydrogen-bonded O−H bond and free O−H bond of solvent H2O molecules. In the case of pentahydrated cluster of tfa, the calculated red shift of the peak position due to O−H stretching of tfa in IR spectrum is 1623 cm−1. Because of shortening of H-bond length between O atom of H2O and transferring H atom of tfa, the corresponding IR band is blue-shifted by 148 cm−1. The peak due to CO stretching is also predicted to be red-shifted, as can be seen from Table 6. Peaks in the region of 3200−3700 cm−1 (see Figure 5g) are due to O−H bonds; those are Hbonded either to another solvent molecule or to tfa in this pentahydrated cluster. One can easily notice that the calculated red shift for O−H stretching mode in tfa is systematically larger from monohydrated to pentahydrated cluster. Similarly, because of the formation of hydrogen bond between carbonyl O atom and H atom of nearest solvent H2O molecule, calculated red shift for CO stretching mode in tfa is systematically larger from monohydrated to pentahydrated cluster. At the same time, because of the formation of new hydrogen bond between transferring H atom and O atom of nearest solvent H2O, a blue shift in the IR peak position is observed in these hydrated cluster, and the shift is systematically larger from dihydrated to pentahydrated cluster. Calculated IR spectrum for the global minimum energy structure of hexahydrated cluster is shown in Figure 5h. Note that the proton of tfa is transferred to the solvent H2O molecule in this structure. Listed bond-length parameters of selected bonds (see Table 3) support solvent-induced dissociation of tfa and transfer of hydrogen atom to the neighboring solvent H2O molecule. IR peaks at 2033 and 2730 cm−1 are assigned to O−H asymmetric stretching of H3O+. The peak at 2827 cm−1 refers to the symmetric stretching of O−H bonds in H3O+, indicating a large blue shift in the newly formed O−H bond in this system. Bands past 3600 cm−1 refer to water O−H bonds that are not H-bonded. Peaks in the range of 3000−3500 cm−1 are because of H-bonded O−H bonds of water. Stretching of CO and C−O bonds of tfa in this cluster is coupled to bending motions of H3O+ unit. Unlike smaller clusters, calculated CO stretching frequency does not follow the same trend in this case; it is red-shifted, though. A weak band at 454 cm−1 assigned to the stretching of the rupturing O−H bond in tfa undergoes a huge red shift of 3138 cm−1. In the case of heptahydrated cluster, symmetric stretching of O−H bonds in H3O+ is at 2800 cm−1, and bands at 2283 and 2528 cm−1 in Figure 5i are assigned to asymmetric modes of O−H bonds in H3O+. Bands beyond 3700 cm−1 refer to water O−H bonds that are not H-bonded, and bands due to Hbonded O−H bonds of water are predicted in 3000−3700 cm−1 range. A weak band at 214 cm−1 is observed that refers to stretching of the rupturing O−H bond in tfa. Salient features of theoretical results presented in the previous sections may be summarized as follows. On successive addition of each H2O molecule to isolated trifuoroacetic acid, O−H bond of −COOH group (rO1H) slowly becomes longer and weaker until pentahydrated cluster. The distance between H atom of the acid and O atom of the neighboring H2O

4. CONCLUSIONS Structure and energy for hydrated tfa clusters, tfa·nH2O (n = 1−7), are reported. Dispersion-corrected DFT functional, namely, ωB97X-D, is applied with aug-cc-pVDZ as basis set for structure calculations. The minimum energy structure is determined from different possible initial guess structures of each hydrated cluster. The minimum energy configuration is obtained through Newton−Raphson-based algorithm of geometry optimization. It is predicted that in the case of hexahydrated cluster, the most stable structure has ion pair form indicating dissociation of tfa. Calculated Mulliken atomic charges over two O atoms involved in proton transfer also confirms the formation of charge-separated species. Although calculated solvent stabilization energy increases linearly with the addition of solvent H2O molecules to tfa, interaction energy increases largely from penta- to hexahydrated cluster. These energy parameters calculated applying MP2 as well CCSD(T) methods also show this feature. The decomposition analysis of the interaction energy between solute tfa and solvent H2O molecules is done for each of the hydrated clusters using LMOEDA approach and electrostatic interaction is observed to have major contribution. IR spectra for the most stable structures of each size hydrated clusters are simulated, and the variation in peak positions is in accordance with the extent of ionization of O−H bond in tfa. In the case of tfa, a minimum of six water molecules are needed for ionization and to form CF3COO−.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank BARC computer centre for providing generous computing time. P.K. wishes to thank Homi Bhabha National Institute for research fellowship.

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REFERENCES

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Effect of Microhydration on Dissociation of Trifluoroacetic Acid - The

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