New values for the absolute solvation free energy of univalent ions in aqueous solution

29 December 2000

Chemical Physics Letters 332 (2000) 597±602

www.elsevier.nl/locate/cplett

New values for the absolute solvation free energy of univalent ions in aqueous solution Josefredo R. Pliego Jr., Jose M. Riveros * Instituto de Quõmica, Universidade de S~ ao Paulo, Caixa Postal 26077, 05513-970 S~ ao Paulo, SP, Brazil Received 13 September 2000; in ®nal form 31 October 2000

Abstract The absolute solvation free energy of 30 univalent ions, mainly organic species, has been calculated from experimental and theoretical data on proton anities, aqueous acidity constants, solvation free energy of neutral species, and the new value for the absolute solvation free energy of the proton determined by Tissandier et al. [J. Phys. Chem. A 102 (1998) 7787]. Our new values reveal considerable di€erences with previous compilations, and should be taken into consideration for comparison with liquid simulation results and in the development of implicit solvation models. Ó 2000 Elsevier Science B.V. All rights reserved.

1. Introduction The calculation of the solvation free energy of neutral and ionic species is one of the most active research ®elds in theoretical chemistry. This important thermodynamic property is essential for modeling chemical processes in the liquid phase, and many semi-empirical and dielectric continuum models for computing this property have been developed in the past 20 years [1±11]. Due to the simplicity of these models, parameters such as the atomic van der Waals radii are adjusted in order to reproduce the experimental solvation free energy values. Thus, accurate values of this property are necessary for an adequate parametrization as well as for testing the performance of the model.

*

Corresponding author. Fax: +55-11-3818-3888. E-mail addresses: [email protected] (J.R. Pliego [email protected] (J.M. Riveros).

Jr.),

Values for the solvation free energy of several neutral and ionic species in aqueous solution have been compiled by several authors [3,12±15]. While this property can be obtained with good accuracy for neutral molecules, the problem is considerably more complicated for ions because the solvation free energies of ions cannot be measured directly. The usual procedure in the latter involves the use of electrode potentials or ionization constants. However, these methods yield values that are dependent on the absolute standard for the solvation free energy of the proton …DG0solv …H‡ ††. Unfortunately, the actual value of this quantity remains a controversial issue and subject to considerable uncertainty. Marcus has compiled solvation free energies of ions using DG0solv …H‡ † ˆ ÿ252:4 kcal molÿ1 [14], while Pearson [13] and Florian and Warshel [3] have adopted the value of DG0solv …H‡ † ˆ ÿ259:5 kcal molÿ1 : Recently, Tissandier et al. [16] have arrived at a new experimental value for DG0solv …H‡ †. Using the cluster-pair-based approximation and

0009-2614/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 0 ) 0 1 3 0 5 - 1

598

J.R. Pliego Jr., J.M. Riveros / Chemical Physics Letters 332 (2000) 597±602

Table 1 Solvation free energy calculated for anions …Aÿ † and cations …BH‡ † from aqueous ionization constants (pKa ), gas phase proton 0 ) and solvation free energy of neutralsa anities (DHPA HA

a

pKa (HA)b

0 DHPA …Aÿ †c

Gsolv …HA†d e

DGsolv …Aÿ †

HF HCl HCl HBr HBr HI HI HCN H2 O H2 O2 NH3 PH3 CH3 CN HCCH CH3 OH CH3 CH2 OH PhOH H2 S CH3 SH HCOOH CH3 COOH

3.18 )6.1 ) )8 ) )9 ) 9.22 ) 11.65 33 27e 25e 25e 15.5 15.5 9.99 7.05 10.33 3.75 4.76

371:5  0:2 333:40  0:03 ) 323:57  0:05 ) 314:36  0:07 ) 351:4  0:5 ) 376:4  0:8i 404:0  0:4 368:7  1:0j 372:9  2:1 378:0  0:6 381:6  0:7 378:6  0:8 347:2  1:0j 351:1  2:0 356:9  2:2 345  2 342  3

)7.5 )0.5e ) )0.7e ) ÿ0:9e ) ÿ4:7g ) ÿ8:7e )4.31 0.6e ÿ3:9k 0.0k )5.10 )5.05 ÿ6:5k ÿ0:7e ÿ1:3k ÿ6:2 ÿ6:7k

ÿ103:2  0:6 ÿ70:7  0:5 ÿ74:7  2:0f ÿ63:7  1:5 ÿ68:3  2:0f ÿ56:0  1:5 ÿ59:4  2:0f ÿ72:0  0:7 ÿ105:0  0:5h ÿ97:7  0:9 ÿ91:8  1:5 ÿ59:8  1:8 ÿ71:2  2:6 ÿ72:4  1:6 ÿ94:0  0:9 ÿ91:0  1:0 ÿ68:6  1:1 ÿ70:7  2:1 ÿ72:6  2:3 ÿ74:6  2:1 ÿ70:7  3:0

BH‡

pKa …BH‡ †b

0 DHPA …B†l

DGsolv …B†

DGsolv …BH‡ †

H3 O‡ CH3 OH‡ 2 CH3 CH2 OH‡ 2 …CH3 †2 C@OH‡ …CH3 CH2 †2 OH‡ NH‡ 4 CH3 NH‡ 3 …CH3 †2 NH‡ 2 …CH3 †3 NH‡ CH3 CH2 NH‡ 3 C6 H5 NH‡ 3 ‡ pyridineH

) )3 )4 )7.5 )3 9.25 10.66 10.73 9.80 10.65 4.87 5.23

) 181:7  0:5 184:2  1:0j 193:7  0:5 198:1  0:5 203:5  0:5 215:4  1:0 222:5  0:5 226:4  2:0n 217:5  2:0n 209:5  2:0n 219:9  2:0n

) )5.10 )5.05 ÿ3:81k ÿ1:75k )4.31 )4.57 ÿ4:28k ÿ3:23k ÿ4:51 ÿ4:9e ÿ4:7k

ÿ110:4  0:7m ÿ90:8  1:5 ÿ86:9  1:8 ÿ71:4  0:7 ÿ71:1  1:5 ÿ84:9  0:7 ÿ75:2  0:7 ÿ67:9  0:7 ÿ61:7  2:1 ÿ73:0  2:1 ÿ73:5  2:1 ÿ63:4  2:1

Units of kcal molÿ1 , 25°C. Unless otherwise stated, solvation free energies were calculated by Eqs. (8) and (9) using the data presented in this table. b Ref. [26]. c Ref. [27]. d Ref. [15]. e Ref. [13]. f Obtained from di€erences of solvation free energy between OHÿ and Xÿ ions compiled by Tissandier et al. [16]. See text. g Ref. [3]. For formic acid, we have used a theoretical calculation based on the interative Langevin dipoles model (ILD). h Ref. [18]. i Ref. [28]. j Ab initio calculation at MP4/6-311+G(2df,2p)//HF/6-31+G(d,p) level and additivity approximation. k Ref. [31]. l Ref. [29]. m See text. n Theoretical data from [30] (ab initio calculation at MP2/6-311+G(d,p)//HF/6-31G* level).

J.R. Pliego Jr., J.M. Riveros / Chemical Physics Letters 332 (2000) 597±602

thermodynamic properties of ion±water clusters, they have shown the previous values to be inconsistent with the cluster data, and have derived a value of DG0solv …H‡ † ˆ ÿ264:0  0:1 kcal molÿ1 . This new value is considerably more negative than previous ones, and has a signi®cant e€ect on the absolute solvation free energies presently available for several ions. However, this new value is consistent with the absolute solvation free energy for the hydroxide ion obtained by Monte Carlo liquid simulations using an intermolecular potential developed from ab initio calculations on hydroxide ion±water clusters [17,18]. In addition, it is also consistent with a recent theoretical determination of the solvation free energy of the proton by Tawa et al. [19]. In this Letter, this new data is used to derive new experimental values for the solvation free energy of 30 univalent ions. 2. Calculation of the experimental solvation free energy Tabulated standard solvation free energies …DG0solv † are often associated with the process: gas (1 atm) ! solution …1 mol lÿ1 † [14]. An alternative de®nition can be de®ned as suggested by BeinNaim [20], DGsolv , and refers to the process: gas …1 mol lÿ1 † ! solution …1 mol lÿ1 †. We have adopted this latter de®nition …DGsolv †, but the two quantities are linked by the equation [18]: ~ †; DGsolv ˆ DG0solv ÿ RT ln…RT

…1†

where R~ ˆ 0:082053 K . The chemical potential of a species X in the liquid phase can be expressed as: ÿ1

lsol …x† ˆ lg …x† ‡ DGsolv …x† ‡ RT ln ‰XŠ;

…2†

where lg …x† is the chemical potential of X in the gas phase at 1 mol lÿ1 of concentration, and ‰XŠ is the concentration of X in solution. The chemical potential of X in the gas phase using the 1 atm standard state, l0g …x†, is related to lg …x† by, ~ †: lg …x† ˆ l0g …x† ‡ RT ln…RT

…3†

For species HA and BH‡ in aqueous solution, we can de®ne

‡ HAsol ! Aÿ sol ‡ Hsol

599

DGa …HA†

…4†

and DGa …HA† ˆ DG0bas …Aÿ † ‡ DG0solv …H‡ † ‡ DGsolv …Aÿ † ÿ DGsolv …HA†:

…5†

ÿ

In Eq. (5), DG0bas …A † stands for the gas phase basicity of Aÿ . This property can be obtained from 0 the gas-phase proton anity of Aÿ …DHPA …Aÿ †† through the approximation [21,22]: 0 …Aÿ † ÿ 7:5 kcal molÿ1 : DG0bas …Aÿ †  DHPA

…6†

Since DGa …HA† ˆ 2:303RT pKa …HA†;

…7†

the solvation free energy of ion Aÿ can then be calculated by combining these equations and assuming that DG0solv …H‡ † ˆÿ264:0  0:1 kcal molÿ1 , 0 …Aÿ † DGsolv …Aÿ † ˆ 2:303RT pKa …HA† ÿ DHPA

‡ DGsolv …HA† ‡ 271:5 kcal molÿ1 : …8† Similarly, for BH‡ DGsolv …BH‡ † ˆ ÿ2:303RT pKa …BH‡ † 0 …B† ‡ DGsolv …B† ‡ DHPA

ÿ 271:5 kcal molÿ1 :

…9† ÿ

Solvation free energies for di€erent A and BH‡ ions were then calculated from the values of pKa , proton anity and solvation free energy of neutral species available in the literature [3,13±15,23±31]. For the H3 O‡ and OHÿ ions, we have used a di€erent procedure that is described in Section 3 Our results are presented in Table 1. The error in the calculated values was estimated from the combined uncertainties in proton anities and in other properties. We have also assumed an uncertainty of 0:5 kcal molÿ1 in Eq. (6). For Clÿ , Brÿ and Iÿ , we have also adopted another procedure. We have taken the di€erence between the standard solvation free energy of these ions and the standard solvation free energy of the hydroxide ion as reported by Tissandier et al. [16] that were based on the standard solvation free energy of the corresponding salts and hydroxide

600

J.R. Pliego Jr., J.M. Riveros / Chemical Physics Letters 332 (2000) 597±602

Table 2 Comparison between the present and previous absolute solvation free energies …DGsolv †a Ion

This workb

Pearson

Fÿ Clÿ Brÿ Iÿ CNÿ OHÿ HOÿ 2 NHÿ 2 PHÿ 2 CH2 CNÿ HCCÿ CH3 Oÿ CH3 CH2 Oÿ PhOÿ HSÿ CH3 Sÿ HCOOÿ CH3 COOÿ H3 O‡ CH3 OH‡ 2 CH3 CH2 OH‡ 2 …CH3 †2 C@OH‡ …CH3 CH2 †2 OH‡ NH‡ 4 CH3 NH‡ 3 …CH3 †2 NH‡ 2 …CH3 †3 NH‡ CH3 CH2 NH‡ 3 C6 H5 NH‡ 3 PyridineH‡

ÿ103:2  0:6 ÿ74:7  2:0f ÿ68:3  2:0f ÿ59:4  2:0f ÿ72:0  0:7 ÿ105:0  0:5g ÿ97:7  0:9 ÿ91:8  1:5 ÿ59:8  1:8 ÿ71:2  2:6 ÿ72:4  1:6 ÿ94:0  0:9 ÿ91:0  1:0 ÿ68:6  1:1 ÿ70:7  2:1 ÿ72:6  2:3 ÿ74:6  2:1 ÿ70:7  3:0 ÿ110:4  0:7 ÿ90:8  1:5 ÿ86:9  1:8 ÿ71:4  0:7 ÿ71:1  1:5 ÿ84:9  0:7 ÿ75:2  0:7 ÿ67:9  0:7 ÿ61:7  2:1 ÿ73:0  2:1 ÿ73:5  2:1 ÿ63:4  2:1

)107 )77 )72 )63 )77 )106 )101 )95 ÿ67 ÿ75 )73 )95 ) ÿ72 )76 ) ) )77 )104 )83 ) )64 )64 )79 )70 )63 )56 ) )68 )59

c

Florian and Warsheld

Marcuse

ÿ107  6 ÿ78  7 ) ) ÿ75  5 ÿ110  5 ) ) ) ) ) ÿ98  5 ÿ94  5 ÿ75  5 ÿ76  5 ÿ76  5 ÿ80  5 ÿ82  5 ÿ105  5 ÿ87  5 ÿ81  6 ) ) ÿ81  5 ÿ73  5 ÿ66  5 ÿ59  5 ) ÿ68  5 ÿ58  5

)103.0 )73.4 )67.0 )58.0 )63.2 )107.2 ) ) ) ) ) ) ) ) )62.7 ) ) ) ) ) ) ) ) )83.3 ) ) ) ) ) )

a

Units of kcal molÿ1 ; 25°C. Recommended values calculated in this work. c Ref. [13]. d Ref. [3]. e Ref. [14]. Based on conventional standard solvation free energy (see text). f Obtained from di€erences of solvation free energy between OHÿ and Xÿ ions as compiled by Tissandier et al. [16]. See Eq. (10) in the text. g Taken from [18]. b

with alkaline metals. Then, based on the solvation free energy of the hydroxide ion of ÿ105:0 kcal molÿ1 [18], we have determined the DGsolv of these halides by DGsolv …Xÿ † ˆ DGsolv …OHÿ † ‡ ‰DG0solv …Xÿ † ÿ DG0solv …OHÿ †Š: …10† These results are included in Table 1 with an assumed uncertainty of 2:0 kcal molÿ1 .

3. Solvation free energy of the H3 O‡ and OHÿ ions The solvation free energy of H3 O‡ can be obtained from a three-step process: vaporization of H2 O, formation of the H3 O‡ ion in the gas phase, and solvation of the H3 O‡ species. DGsolv …H3 O‡ † ˆ DGsolv …H‡ † ‡ DG0bas …H2 O† ÿ DGvap …H2 O†:

…11†

J.R. Pliego Jr., J.M. Riveros / Chemical Physics Letters 332 (2000) 597±602

For the vaporization of water, we have taken the value of 2:0 kcal molÿ1 [15], while its basicity was calculated by Eq. (6) using the experimentally determined proton anity of 165:0  0:5 kcal molÿ1 [29]. This value is in excellent agreement with the theoretical ab initio G2(MP2) value of 164:5 kcal molÿ1 [25]. By comparison, the experimental proton anity at 0 K reported by Ng et al. [24] with theoretical correction for 298.15 K leads to a value of 167:2 kcal molÿ1 [25]. Pearson has previously used a value of 167 kcal molÿ1 for the proton anity of H2 O while Coe [23] has calculated a value of 163:2  2:2 kcal molÿ1 from the thermodynamic data of ion±water clusters. For the hydroxide ion, we have shown [18] that DGsolv …OHÿ † ˆ ÿ105:0 kcal molÿ1 based on the ionic product of water, the basicity of the OHÿ ion, and the new value for the solvation free energy of the proton reported in [16]. This value is included in Table 1, and we have assumed an uncertainty of 0:5 kcal molÿ1 due to the basicity of OHÿ . 4. Results and discussion The relevant data used in Eqs. (8) and (9), as well as the calculated solvation free energies for cations and anions are summarized in Table 1. The uncertainties are also indicated but they are probably rather optimistic. Table 2 shows a comparison of our data with those compiled by Pearson [13], by Florian and Warshel [3], and with the conventional values tabulated by Marcus [14]. Since Pearson reports solvation data as DG0solv , his values have been transformed to DGsolv by using Eq. (1). Marcus has compiled tables of conventional and absolute values of DG0solv . However, the absolute data are based on the old value of the proton solvation free energy. Thus, the conventional data of Marcus have been transformed to absolute values using DG0solv …H‡ † ˆ ÿ264:0 kcal molÿ1 and Eq. (1) to convert to DGsolv values. The values for pKa in the range of 0±16 are usually accurate and we have adopted more recent values of proton anities than those in Pearson's ÿ and CH3 CH2 OH, compilation. For PHÿ 2 , PhO

601

we have determined the proton anity from ab initio calculations at the MP4/6)311+G(2df,2p)// HF/6)31+G(d,p) level of theory, and additivity approximations. An error of 1:0 kcal molÿ1 is assumed in these values. For trimethylamine, ethylamine, aniline and pyridine, we have also used the results from the theoretical calculations of Hillebrand et al. [30] performed at MP2/ 6)311+G(d,p)//HF/6)31G(d) level. An error of 2:0 kcal molÿ1 is estimated in these cases since no thermal corrections have been included. The solvation free energy of the neutrals is mainly experimental data with some exceptions: HCl, HBr, HI and HCOOH. The ®rst three were taken from an estimate by Pearson [13] and probably subject to considerable error. In fact, a signi®cant di€erence is obtained for DGsolv of the respective anions using Eqs. (8) and (10). We believe this di€erence to be due to DGsolv …HX†; which is much too positive. Other possible sources of error are pKa values lower than zero. In summary, the DGsolv …Xÿ † obtained from Eq. (10) are more accurate and represent our recommended values. For the HCOOH, the solvation free energy was taken from the Interactive Langevin Dipoles Model calculation of Florian and Warshel [3]. As expected, our calculated solvation free energies for anions are less negative than those reported by Pearson and by Florian and Warshel, while our values for cations are more negative. Nevertheless, the di€erences are variable (Table 2). For cations, an important di€erence is observed for the H3 O‡ ion: our recommended value stands at ÿ110:4  0:7 kcal molÿ1 as opposed to ÿ104 kcal molÿ1 reported by Pearson [13], and 105  5 kcal molÿ1 by Florian and Warshel [3]. These di€erences re¯ect the new value for the solvation free energy of the proton and the smaller basicity of water used in this work. The DGsolv for OHÿ in the Pearson row is very close to our value, di€ering by only 1 kcal molÿ1 . This is unexpected in view of the di€erent value of DG0solv (H‡ ) that we are using. Indeed, the calculation of the solvation free energy of the OHÿ ion with the data used by Pearson leads to DGsolv …OHÿ † ˆ ÿ109 kcal molÿ1 , close to the Florian and Warshel value. Thus, the standard solvation free energy reported by Person should be 107 kcal molÿ1 , instead of 104 kcal molÿ1 .

602

J.R. Pliego Jr., J.M. Riveros / Chemical Physics Letters 332 (2000) 597±602

When we compare our solvation data with that of Marcus, we observe excellent agreement for Fÿ , Clÿ , Brÿ , Iÿ , OHÿ and NH4 ‡ . However, signi®cant di€erences (about 8 kcal molÿ1 are noticeable for the CNÿ and HSÿ ions. The values for Clÿ and HSÿ ions di€er among themselves only by 4 kcal molÿ1 , an expected behavior due to the similarity between these two ions. On the other hand, the values of Marcus for these ions di€er by 10 kcal molÿ1 . This di€erence seems unusually large, and is probably due to a substantial error in the conventional data of Marcus. In summary, we think that the absolute solvation free energies of the univalent ions reported in this work are the most accurate to date. We particularly emphasize that these new values are of timely relevance for present day theoretical calculations based on liquid simulations that make use of ab initio ion±water potentials and for the development of implicit solvation models. Acknowledgements The authors wish to thank the support of the S~ ao Paulo Science Foundation (FAPESP) and the Brazilian Research Council (CNPq). References [1] C.J. Cramer, D.G. Truhlar, Chem. Rev. 99 (1999) 2161. [2] D.J. Giesen, G.D. Hawkins, D.A. Liotard, C.J. Cramer, D.G. Truhlar, Theor. Chem. Acc. 98 (1997) 85. [3] J. Florian, A. Warshel, J. Phys. Chem. B 101 (1997) 5583. [4] J.B. Foresman, T.A. Keith, K.B. Wiberg, J. Snoonian, M.J. Frisch, J. Phys. Chem. 100 (1996) 16098. [5] M. Cossi, V. Barone, R. Cammi, J. Tomasi, Chem. Phys. Lett. 255 (1996) 327.

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