Theoretical Studies for Trimethyl Phosphate Complexes with HNO3

Theoretical Studies for Trimethyl Phosphate Complexes with HNO3 and Water as a CO2-Soluble Extractant. Yongho Kim,* Chea-Yong Park, and Hakwon Kim...
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Ind. Eng. Chem. Res. 2005, 44, 3389-3395

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Theoretical Studies for Trimethyl Phosphate Complexes with HNO3 and Water as a CO2-Soluble Extractant Yongho Kim,* Chea-Yong Park, and Hakwon Kim Department of Chemistry and Institutes of Natural Sciences, Kyung Hee University, Yongin-City, Kyunggi-Do, 449-701, Korea

We have calculated structures and energies for the hydrogen-bonded complexes of tri-n-butyl phosphate with nitric acids and water molecules, which might have crucial role in the PUREX process for the reprocessing of spent nuclear fuel and the treatment of nuclear wastes in the nuclear industry. The structure and H-bond strengths for the TMP-(HNO3)x(H2O)y, complexes with x + y ) 1-3 have been calculated. Short and strong hydrogen bonds are formed between phosphoryl oxygen and the proton of nitric acid. The hydrogen bonds between water and the phosphoryl oxygen are weaker and longer. The more H-bond donors are bound to the phosphoryl oxygen, the weaker and the longer H-bonds become. Weak hydrogen bonds between methyl and water might contribute to the stability of the clusters. Solvent effect seems very important to the relative stability of complexes. We have calculated the solvation free energies of TMP complexes using the dielectric continuum approach in order to model the solvent effect of trin-butyl phosphate and supercritical-CO2 approximately. The TMP-(HNO3)(H2O)2 and TMP(HNO3)2(H2O)(II) are two most stable complexes, which agree well with experimental results. Introduction Hydrogen-bonded complexes of organic phosphates play an important role in a variety of chemical processes. Organic phosphates can be used as model systems for understanding biological processes and also have industrial applications, such as extractants in a number of solvent extraction processes. In particular, tri-n-butyl phosphate (TBP) has been known as an extractant for the uranyl and plutonyl extraction in the PUREX (Plutonim-Uranium-Extraction) process for the reprocessing of spent nuclear fuel and the treatment of nuclear wastes in the nuclear industry.1-3 In this process, uranium oxides (UO2) in the spent fuel are dissolved in strong nitric acid solutions and oxidized to uranyl ions (UO22+), and the subsequent solvent extractions (in dodecane) with TBP as the active extracting reagent remove uranium as UO2(NO3)2(TBP)2 complexes into the organic phase. Recently, for the green process of nuclear waste treatment, supercritical fluid extraction (SFE) technology has been utilized for the extraction of some radioactive metal ions.4,5 Owing to the markedly reduced generation of waste, this new supercritical CO2 (sc-CO2) technology has drawn attention as a green nuclear process. TBP also has been used as an extracting reagent in sc-CO2 extraction technology because it forms the CO2-soluble complex with nitric acid to make solid uranium dioxides dissolved in sc-CO2. However, the chemical nature of the TBP-nitric acid complex and the mechanism of UO2 dissolution in sc-CO2 with the TBP-nitric acid solution is not well-known. Recent molecular dynamics studies suggest that hydronium ions or hydrogen from HNO3 or H2O are bonded to the oxygen of the PdO bond in TBP.6,7 Ferraro et al.8 have performed infrared studies for the TBP-HNO3 complexes in n-octane. In this paper, two extracted species, TBP-HNO3 and TBP-(HNO3)2, were * To whom correspondence should be addressed. Fax: +8231-203-5773. E-mail: [email protected].

identified in organic phase, and the infrared spectra revealed that the HNO3 molecules in TBP-(HNO3)2 are spectrally nonequivalent. They suggested that the predominant structure of TBP-(HNO3)2 involves the chain HNO3 dimer, and only one HNO3 molecule is directly bound to the phosphoryl oxygen. The water peaks were also observed in the IR spectrum. The TBP-nitric acid complex is prepared by shaking TBP with a concentrated nitric acid solution. Because water is present in the nitric acid solution, the complex is expected to have a general formula of TBP-(HNO3)x(H2O)y, where x and y can vary depending on the relative amounts of TBP and nitric acid used in the preparation. Two types of the complexes, one with x ) 0.7 and the other with x ) 1.8, were also reported in the literature for direct dissolution of uranium dioxide in sc-CO2.5,9-11 To understand the factor of dissolution of uranium oxides in sc-CO2, the molecular level structures of the TBP(HNO3)x(H2O)y complex should be probed. The behavior of solute in supercritical fluid solution is complicated due to the heterogeneity of solvent density, so many studies have been performed to understand this unique solvent environment. Kauffman12 has reviewed their research on rotational diffusion and photoisomerization kinetics of diphenylpolyenes in polar liquids and supercritical fluids. To examine the influence of solvent polarity on chemical reactivity, they have investigated the solvation and exciplex formation kinetics of 1-[9anthryl]-3-[4-N,N-dimethylaniline]propane (ADMA) in various organic liquids and supercritical fluids and reported that the ADMA peak energy in sc-CO2 is quite close to that in n-hexane. In this paper, we report our theoretical studies on the structure and the hydrogenbond strength of trimethyl phosphate (TMP) complexes with nitric acid and water molecules, TMP-(HNO3)x(H2O)y, x + y ) 1-3, to model the CO2-soluble complex, TBP-(HNO3)x(H2O)y. TMP is a good model of TBP in which three butyl groups are replaced by three methyl groups to reduce enormous computational cost. Butyl

10.1021/ie0492597 CCC: $30.25 © 2005 American Chemical Society Published on Web 03/29/2005

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group is so flexible that there would be no problem in steric hindrance to phosphoryl oxygen due to the replacement. We have calculated the solvation free energies of TMP complexes using the dielectric continuum approach implemented in the AMSOL program13 in order to model the solvent effect of tri-n-butyl phosphate and sc-CO2 approximately. Computational Methods All electronic structure calculations were done using the GAUSSIAN 98 quantum mechanical packages.14 Geometries for TMP, HNO3, and TMP-(HNO3)x(H2O)y complexes with x + y ) 1-3, were optimized initially at the Hartree-Fock (HF) level of theory using the 6-31G(d,p) basis sets. Frequencies were calculated at this level and scaled by 0.8929 for the zero-point energies and enthalpies.15 The vibrational modes were assigned by checking normal mode eigenvectors and monitoring the vibrational motion using the GaussView program. The final structures for TMP, HNO3, and TMP-(HNO3)x(H2O)y complexes with x + y ) 1-3 were optimized at the MP2/6-31G(d,p) level starting from the HF structures. The formation energy for the hydrogen-bonded complex was calculated from the difference in energies between the complex and the monomers. These energies correspond to hydrogen bond strengths. The basis set superposition error (BSSE) is important in the calculation of the formation energies,16 so it was corrected by the Boys and Bernardi counterpoise correction scheme.17 The fragment relaxation energy (i.e., the energy associated with the transition from the optimized geometry of monomer to the geometry that the monomer has in the dimer)18,19 were also considered in addition to the correction of the BSSE as described previously.20 Solvation free energies were calculated by the AM1/ SM5.2R21 method incorporated in the AMSOL program13 using the geometries optimized at the MP2 level. The free energy of solvation in this approach is based on two terms: the first is a generalized Born approximation term that accounts for electronic polarization of the continuum-dielectric solvent (i.e., for the electronic polarization of the solvent molecules and for the resulting feedback of this effect on the solute charge distribution). The second is a solvent-accessible surface area term that accounts for the free energy of formation, dispersion interactions, and first-solvation-shell effects such as solvent structure changing and the nonelectrostatic part of hydrogen bonding. The solvation model SM5.2R is parametrized for water and organic solvents to be used with accurate gas-phase geometries at 298 K, 1 atm. We have used the solvent parameters of trin-butyl phosphate to model experimental results.5,9-11 Kauffmann12 has studied quadrupolar solvent-dipolar solute interaction in solvation and reactivity in sc-CO2. They found that the large quadrupolar moment of CO2 coupled with its small size is responsible for its solvation properties, and the solvent effect of n-hexane on spectroscopic properties is quite similar to that of sc-CO2. These results suggest that n-hexane can be used to model sc-CO2, so the solvent parameters of n-hexane were used to calculate the solvation free energy of scCO2. Since we are using a dielectric continuum approach for the solvation, specific solvent effects of CO2 such as weak hydrogen bonds, the effect of temperature and pressure for the supercritical condition, and the effect of quadrupolar moment cannot be explicitly considered.

Figure 1. Structure of trimethyl phosphate optimized at the MP2/ 6-31G(d,p) level. Bond lengths are in Å, and angles are in degree.

Results and Discussion The structures of TMP have recently been calculated at the MP2/6-31G(d) level and MP2/6-31G(d,p) level by Singh and co-workers.22 There are two possible hydrogenbonding sites, one to the phosphoryl oxygen and the other to the ester oxygen of TMP. The optimized structure of TMP is shown in Figure 1, which has C3 symmetry along the PdO bond axis. We have also calculated other conformers, but their energies are all higher. Pushlenkov et al.23 have studied the structure of the ternary system TBP-HNO3-H2O by infrared spectroscopy and reported that the ester oxygen of TBP is not hydrogen bonded with nitric acid. They have also reported that water in this ternary system is hydrogen bonded to the phosphoryl oxygen or nitrate oxygen. Viswanathan and co-workers24 have reported that the hydrogen bond to the phosphoryl oxygen is about 3 kcal/ mol stronger than that to the ester oxygen when a water molecule is attached. The TMP-(HNO3)x complexes with x ) 1-3 were also studied by Kim et al.20 showing that the hydrogen bond between nitric acid and the phosphoryl oxygen is very strong. We have also calculated hydrogen bonds attached to the ester oxygen, which turns out to be much weaker than those to the phosphoryl oxygen. Therefore, we have only considered H-bonded complexes bound to the phosphoryl oxygen in this study. The optimized structures at the MP2 level for the TMP-(HNO3)x(H2O)y complexes with x + y ) 1-3 are shown in Figures 2 - 4. Figure 2 shows the optimized structures of TMP-(HNO3)x complexes with x ) 1-3. The structures and the hydrogen bond strengths have been discussed in a previous paper.20 The H-bonds between the phosphoryl oxygen and nitric acids are typical short and strong hydrogen bonds. As seen in Figure 2, the H-bond becomes longer as more nitric acids are bound to the phosphoryl oxygen. Figure 3 shows the optimized structures of TMP-(H2O)y complexes with y ) 1-3. The hydrogen bond length between water and the phosphoryl oxygen in TMP-H2O is 1.909 Å as shown in Figure 3A. This H-bond length is slightly shorter than those of normal hydrogen bonds between oxygen atoms (e.g., the hydrogen bond between water and formaldehyde), which is about 2 Å.25 The distance between the water oxygen and the methyl proton is only 2.357 Å. This is smaller than the van der Waals distance

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Figure 2. Structure of TMP-(HNO3)y, y ) 1-3, optimized at the MP2/6-31G(d,p) level. Bond lengths are in Å. N1, N2, and N3 denote the first, second, and third nitric acid added to TMP, respectively. The PdO bond length is denoted in italics.

between these two atoms, 2.6 Å,26 which strongly suggests the formation of a weak hydrogen bond. Various types of C-H‚‚‚O hydrogen bonds have been reviewed, and generally the interaction with about 2.4 Å of distance can be considered as a weak hydrogen bond.27 It is interesting to note that the bond length in the weak H-bond of TMP-H2O is shorter than that of TMP-HNO3, suggesting that the water oxygen is more basic than the nitrate oxygen. In the optimized structure of TMP-(H2O)2 as shown in Figure 3B, the phosphoryl oxygen and two water molecules, W1 and W2, make a triangle. The H-bond lengths between the phosphoryl oxygen and protons of W1 and W2 groups are 1.843 and 2.210 Å, respectively. The former is shorter and the latter longer than that of TMP-H2O. The H-bond length between W1 and W2 is in between. These mean that the second water molecule tends to form stronger H-bond with the first water rather than the phosphoryl oxygen. There are two weak H-bonds between water oxygens and methyl protons. Figure 3C shows the optimized structure of TMP-(H2O)3. Only two water

molecules among three can make hydrogen bonds to the phosphoryl oxygen. The third water molecule links two water molecules, which are directly H-bonded to phosphate group, to form a cyclic water trimer on top of the TMP. The H-bond lengths among water molecules are quite similar, which are about 2.1 Å. The optimized structures of mixed complexes, TMP(HNO3)(H2O), TMP-(HNO3)(H2O)2, TMP-(HNO3)2(H2O)(I), and TMP-(HNO3)2(H2O)(II), are shown in Figure 4. In the structure of TMP-(HNO3)(H2O) shown in Figure 4A, the H-bond between the phosphoryl oxygen and the nitric acid is still quite short, which is a short and strong H-bond. The weak H-bond of methyl proton with W1 is 2.344 Å in length, which is clearly shorter than 2.4 Å. The optimized structure of TMP(HNO3)(H2O)2 is shown in Figure 4B, where only two H-bonds are formed to the phosphoryl oxygen. The second water molecule, W2, acts as a hydrogen bond donor to W1 and N1 and links them to make a cyclic conformation by forming double hydrogen bonds. The length of the weak hydrogen bond between the methyl proton and the W2 oxygen is quite short, 2.271 Å, which is comparable to the normal H-bond length. This weak H-bond might have a considerable effect on the stability of the complex. Two optimized structures for TMP(HNO3)2(H2O), namely, TMP-(HNO3)2(H2O)(I) and TMP-(HNO3)2(H2O)(II), are obtained as shown in Figure 4C,D, respectively. In TMP-(HNO3)2(H2O)(I) the water molecule is directly bound to the phosphoryl oxygen, whereas in TMP-(HNO3)2(H2O)(II) the water molecule links two nitric acids. In TMP-(HNO3)2(H2O)(I), the H-bonds from two nitric acids (N1 and N2) to the phosphoryl oxygen are still quite short. There is also a weak H-bond between water molecule and a methyl proton, which is 2.324 Å long. This bond is even shorter than the H-bond between the W1 and hydroxyl oxygen of nitric acid, which implies the considerable role of the weak H-bond in the stability of the cluster. In TMP(HNO3)2(H2O)(II) as shown in Figure 4D, the H-bonds from N1 and N2 to the phosphoryl oxygen are slightly shorter than corresponding H-bonds in TMP-(HNO3)2(H2O)(I). The water molecule acts as hydrogen bond donors toward both nitric acids, and there is also a weak hydrogen bond between the methyl proton and the water oxygen. Potential energies, zero-point vibrational energies (ZPE), enthalpy, and solvation free energies of nitric acid, water, trimethyl phosphate (TMP), and TMP(HNO3)x(H2O)y complexes with x + y ) 1-3 are listed in Table 1. Formation energies, enthalpies, and free energies in solution for various hydrogen-bonded complexes are listed in Table 2. We have obtained the enthalpies and free energies of dissociation for a water molecule and a nitric acid from TMP complexes using the information in Table 2, and the results are summarized in Table 3. The dissociation enthalpies for the first, second, and third water of TMP-(H2O)y complexes become smaller as more water is added. Similarly, the dissociation enthalpies for nitric acids become smaller as more nitric acids are added. Note that the dissociation enthalpies of the third water in TMP-(H2O)3 and the third nitric acid in TMP-(HNO3)3 are quite similar. The dissociation enthalpy of a water in TMP-(HNO3)(H2O) is smaller than that of the second water in TMP(H2O)2. This is probably due to the fact that the second water in TMP-(H2O)2 are doubly hydrogen bonded including the weak hydrogen bond as shown in Figure

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Figure 3. Structure of TMP-(H2O)x, x ) 1-3, optimized at the MP2/6-31G(d,p) level. Bond lengths are in Å. W1, W2, and W3 denote the first, second, and third water molecule added to TMP, respectively. The PdO bond length is denoted in italics.

Figure 4. Structure of mixed complexes, TMP-(HNO3)(H2O), TMP-(HNO3)(H2O)2, TMP-(HNO3)2(H2O)(I), and TMP-(HNO3)2(H2O)(II), optimized at the MP2/6-31G(d,p) level. Bond lengths are in Å. W and N denote water and nitric acid, respectively. The PdO bond length is denoted in italics.

3B. The dissociation enthalpy of the nitric acid in TMP(HNO3)(H2O) is larger than that of the second nitric acid in TMP-(HNO3)2, which indicates that the H-bond strength of the nitric acid is reduced less when the preexisting H-bond is with water. These results imply that the H-bond between nitric acid and phosphoryl oxygen is so strong that it predominates over the H-bond with water. Therefore, the electron density on the phosphoryl oxygen, once used to make the preexisting H-bond with water, would be rearranged to maximize the H-bond strength with nitric acid. The change in the partial charge of the phosphoryl oxygen can be used to

understand the reorganization of electron density. When a nitric acid is added to TMP-(H2O) to form TMP(HNO3)(H2O), the negative partial charge calculated by Mulliken population analysis is changed from -0.79 to -0.89, whereas it is changed from -0.85 to -0.93 when TMP-(HNO3)2 is formed form TMP-(HNO3). The electron density is rearranged more when a nitric acid is added to TMP-(H2O). The dissociation enthalpy of the third nitric acid in TMP-(HNO3)3 is 3.4 kcal/mol, which is much smaller than that of the second nitric acid and comparable to that of water in TMP-(HNO3)(H2O). Note that this

Ind. Eng. Chem. Res., Vol. 44, No. 10, 2005 3393 Table 1. Potential Energies, Zero-Point Vibrational Energies, Enthalpy, and Net Solvation Energies for Nitric Acid, Water, Trimethyl Phosphate (TMP), and TMP-(HNO3)x(H2O)y Complexes, x + y ) 1-3a MP2/6-31G(d,p)

ZPEb

enthalpy (298 K)

∆Gsol (298 K)c

-280.176011 -76.219786 -760.375605 -836.611258 -912.849881 -989.089405 -1116.811077 -1397.006831 -1397.008190 -1193.050359 -1040.577843 -1320.773202 -1600.967241

0.026922 0.020711 0.128840 0.152438 0.176842 0.200201 0.180205 0.208182 0.208412 0.204597 0.156814 0.185161 0.213430

-280.145191 -76.195600 -760.236492 -836.445564 -912.657260 -988.870299 -1116.613014 -1396.776161 -1396.777509 -1192.825468 -1040.406287 -1320.570581 -1600.730027

-3.2 (-1.7) -7.7 (-0.2) -8.3 (-4.7) -11.7 (-3.3) -14.5 (-2.2) -18.0 (-2.1) -8.4 (-2.2) -6.0 (-1.5) -6.1 (-1.7) -12.0 (-1.5) -4.0 (-3.0) -1.1 (-2.1) -0.2 (-2.1)

HNO3 H2O TMP TMP-H2O TMP-(H2O)2 TMP-(H2O)3 TMP-(HNO3)(H2O) TMP-(HNO3)2(H2O)(I) TMP-(HNO3)2(H2O)(II) TMP-(HNO3)(H2O)2 TMP-HNO3 TMP-(HNO3)2 TMP-(HNO3)3

a Energies are in hartree except for the solvation free energies. b Zero-point energies were calculated at the HF/6-31G(d,p) level and scaled by 0.8929. c Net solvation free energies in TBP calculated by the AM1/SM5.2R method using the structures optimized at the MP2/ 6-31G(d,p) level. Numbers in parentheses are the solvation energy in n-hexane. In kcal/mol.

Table 2. Formation Energies, Enthalpies, and Free Energies in Solution for Various Hydrogen-Bonded Complexesa: TMP + xHNO3 + yH2O f TMP-(HNO3)x(H2O)y

TMP-H2O TMP-(H2O)2 TMP-(H2O)3 TMP-(HNO3)(H2O) TMP-(HNO3)2(H2O)(I) TMP-(HNO3)2(H2O)(II) TMP-(HNO3)(H2O)2 TMP-HNO3 TMP-(HNO3)2 TMP-(HNO3)3

∆E

∆(E + ZPE)

∆Hf (298 K)

∆Gf,sol (298 K)b

-5.92 -11.60 -16.15 -15.28 -21.40 -22.39 -22.00 -10.72 -18.34 -23.01

-4.11 -7.47 -10.36 -12.94 -18.40 -19.24 -17.35 -10.06 -16.76 -20.60

-4.42 -8.38 -11.48 -12.80 -17.81 -18.79 -17.87 -9.70 -16.07 -19.47

-0.1 (-2.8) 0.8 (-5.5) 2.0 (-8.3) -2.0 (-8.4) -1.3 (-11.0) -2.4 (-12.2) -3.0 (-12.5) -2.2 (-6.3) -2.4 (-10.0) -1.7 (-11.8)

a Energies are in kcal/mol. The formation energy was calculated from the difference in energies between the complex and monomers. b Formation free energies in TBP. Numbers in parentheses are the formation energy in n-hexane.

nitric acid can still form an H-bond with the phosphoryl oxygen. The dissociation enthalpy of a water in TMP(HNO3)2(H2O)(I) is about 1 kcal/mol smaller than that in TMP-(HNO3)2(H2O)(II). The water molecule in TMP(HNO3)2(H2O)(I) forms H-bonds directly to the phosphoryl and hydroxyl oxygen in addition to the weak hydrogen bond with a methyl proton as shown in Figure 4C. On the other hand, the water molecule in TMP(HNO3)2(H2O)(II) is not directly bound to the phosphoryl oxygen, but it connects two nitric acids by forming two H-bonds to nitrate oxygens as shown in Figure 4D. It is interesting to note that the dissociation enthalpy of the second water in TMP-(HNO3)(H2O)2 is 5.07 kcal/ mol, which is quite large. This water molecule, which is most important in the stability of the complex, is bound to TMP in a different way as shown in Figure 4B,C. It is not directly H-bonded to the phosphoryl oxygen but connects a nitric acid and the first water by forming bridged H-bonds, similar to the structure as shown in Figure 4D. It also forms a weak hydrogen bond with a methyl proton. It is interesting to note that its strength is even larger than those of the third nitric acid in TMP-(HNO3)3 and the water in TMP-(HNO3)(H2O). A similar type of hydrogen bond is formed in TMP(H2O)3 as shown in Figure 3C with 3.10 kcal/mol of bond strength, although there is no weak hydrogen bond with a methyl proton in it. The titration experiments to characterize the TBP(HNO3)x(H2O)y complexes were performed in the TBP phase (organic phase);5,9,10 therefore, solvent effect

would be important in the stabilities of hydrogen-bonded complexes in solution, so it should be considered properly. The solvation free energy is calculated at the AM1/ SM5.2R21 using the geometry optimized at the MP2/631G(d,p) level. The solvent parameters for TBP were used to model the solvent effect. To model the structure and energies of the complexes in sc-CO2, the solvent effect should also be considered properly. Since the solvent parameters of sc-CO2 are not available, we have used the solvent parameters of n-hexane to model the solvent effect of sc-CO2;12 therefore, the solvation free energies in sc-CO2 are in crude approximation at current stage. The formation free energies in TBP phase are obtained using the solvation free energies of monomers and complexes, and they are listed in Table 2. Among the quaternary complex, TMP-(HNO3)x(H2O)y with x + y ) 3, the most stable complex in terms of the formation free energy is TMP-(HNO3)(H2O)2 with -3.0 kcal/mol followed by TMP-(HNO3)2(H2O)(II) with -2.4 kcal/mol. This means that these two complexes would exist most abundantly in solution. This result agrees with the experimental observation that two types of complexes, one with x ) 0.7 and the other with x ) 1.8, are present in water present TBP solution.5,9,10 This trend is maintained in n-hexane, which implies that TMP-(HNO3)(H2O)2 and TMP-(HNO3)2(H2O)(II) might also exist most abundantly in sc-CO2. The dissociation free energies are listed in Table 3. The dissociation free energies of the first, second, and third water for TMP-(H2O)y complexes with y ) 1-3 are 0.1, -0.9, and -1.2 kcal/mol in TBP, respectively. These results mean that TMP-(H2O)2 and TMP-(H2O)3 hardly exist in TBP. When TMP is added in a concentrated nitric acid solution, the TMP-(HNO3) complex is formed preferably in TBP since the H-bond strength of nitric acid is predicted to be 2.1 kcal/mol larger than that of water in terms of dissociation free energy. It is unfavorable to form the TMP-(HNO3)(H2O) complex by adding a water molecule to TMP-(HNO3). In TMP(HNO3)2 the dissociation free energy of the second nitric acid is 0.3 kcal/mol, so it can be formed preferentially to TMP-(HNO3)(H2O). The next water molecule stabilizes the TMP-(HNO3)(H2O) complex to form TMP(HNO3)(H2O)2 by about 1.0 kcal/mol; however, it does not stabilize the TMP-(HNO3)2 complex to form TMP(HNO3)2(H2O)(II). As a result, TMP-(HNO3)(H2O)2 is slightly more stable in terms of the free energy in the TBP solution than TMP-(HNO3)2(H2O)(II). These re-

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Table 3. Enthalpy and Free Energy Change for Dissociating Water and Nitric Acid from the Complexesa TMP-(H2O) f TMP + H2O TMP-(H2O)2 f TMP-(H2O) + H2O TMP-(H2O)3 f TMP-(H2O)2 + H2O TMP-(HNO3)(H2O) f TMP-HNO3 + H2O TMP-(HNO3)(H2O)2 f TMP-(HNO3)(H2O) + H2O TMP-(HNO3)2(H2O)(I) f TMP-(HNO3)2 + H2O TMP-(HNO3)2(H2O)(II) f TMP-(HNO3)2 + H2O TMP-HNO3 f TMP + HNO3 TMP-(HNO3)2 f TMP-HNO3 + HNO3 TMP-(HNO3)3 f TMP-(HNO3)2 + HNO3 TMP-(HNO3)(H2O) f TMP-(H2O) + HNO3 TMP-(HNO3)(H2O)2 f TMP-(H2O)2 + HNO3 TMP-(HNO3)2(H2O)(I) f TMP-(HNO3)(H2O) + HNO3 TMP-(HNO3)2(H2O)(II) f TMP-(HNO3)(H2O) + HNO3 a

∆Hd (298 K)

∆Gd,sol (298 K)b

4.42 3.96 3.10 3.10 5.07 1.74 2.72 9.70 6.37 3.40 8.38 9.49 5.01 5.99

0.1 (2.8) -0.9 (2.6) -1.2 (2.9) -0.2 (2.1) 1.0 (4.2) -1.1 (0.9) 0.0 (2.2) 2.2 (6.3) 0.3 (3.7) -0.7 (1.7) 1.9 (5.5) 3.8 (7.0) -0.6 (2.6) 0.5 (3.8)

Energies are in kcal/mol. b Dissociation free energies in TBP. Numbers in parentheses are the dissociation energy in n-hexane.

sults suggest that the role of water molecule is very important to the relative stability of complexes, and the relative abundance of the complexes would be changed depending on the relative amount of water and nitric acid present in solution. This study shows that TMP(HNO3)(H2O)2 and TMP-(HNO3)2(H2O)(II) would be two most stable complexes in terms of the dissociation free energy, which agree quite well with experimental results.5,9,10 The calculated PdO stretching frequency of TMP at the HF/6-31G(d,p) level is 1251 cm-1, which agrees quite well with the experimental value (1275 cm-1).8 This frequency is reduced to 1228 and 1203 cm-1 in TMP(H2O) and TMP-(HNO3), respectively. These results are correlated with the change in the PdO bond length of complexes, which is the shortest (1.485 Å) in TMP and the longest (1.499 Å) in TMP-(HNO3). Comparing hydrogen bond strengths in Table 2 with PdO bond lengths, one can see that the stronger the hydrogen bond is, the longer the PdO bond becomes. The calculated symmetric and asymmetric NOO stretching frequencies of HNO3 are 1437 and 1763 cm-1, respectively, which are slightly larger than experimental values (i.e., 1300 and 1680-1640 cm-1, respectively). Ferraro et al.8 have monitored the NOO asymmetric stretch with increasing the concentration of nitric acid and found that the intensity of the 1648 cm-1 band (NOO asymmetric stretch) in a dilute solution of nitric acid is lowered and new bands at 1620 and 1672 cm-1 appear as more nitric acid is added. They argued from these results that the second HNO3 molecule is not directly bound to the phosphoryl group, since it has larger asymmetric stretch band (1672 cm-1). The calculated NOO asymmetric stretching frequency of TMP-(HNO3) is 1742 cm-1 and that of the free HNO3 is 1763 cm-1, which is about 20 cm-1 higher. This is consistent with the experimental observation that the hydrogen bond to the phosphoryl oxygen reduces the NOO asymmetric stretch of HNO3. There are two NOO asymmetric stretching frequencies in the TMP-(HNO3)2 complex, which are 1746 and 1754 cm-1. The second NOO asymmetric stretch is about 10 cm-1 higher than the first. Although the change is small the second HNO3 bound to the phosphoryl oxygen has larger frequency as well. Considering the errors involved in the experimental and theoretical frequencies it is not possible to remove the presence of the TMP complex with two nitric acids directly bound to phosphoryl group completely. We have also calculated the dissociation free energies in n-hexane to model sc-CO2. Although dielectric continuum approach of sc-CO2 solvation is currently in

crude approximation since appropriate parameters (perhaps including the effect of quadrupolar moment) are not developed yet and specific solvent effects cannot be considered explicitly, it can provide us with some insight of CO2 solvation originated from the electronic polarization of the solvent molecules and the resulting feedback of this effect on the solute charge distribution. Since n-hexane is a dipolar solvent that gives similar spectroscopic properties as sc-CO2 does,12 it can be used to model the solvent effect of sc-CO2 as a dielectric continuum. Net solvation energies and formation free energies in n-hexane are listed in parentheses of Table 1 and 2, respectively. Interestingly, the net solvation energy of H2O is increased (destabilized) more than that of HNO3 comparing solvation energies of n-hexane from those of TBP. The same trend is observed for TMPH2O and TMP-HNO3 complexes. As shown in Table 2, the decrease in formation free energies of HNO3 complexes becomes much larger than that of H2O complexes due to the low dielectric constant. Although these results should be interpreted with care, the data in n-hexane are consistent with those in the TBP solution, namely, TMP-(HNO3)(H2O)2 is the most stable complex in terms of formation free energy followed by TMP-(HNO3)2(H2O)(II). Conclusions We have calculated the energies and structures for the hydrogen-bonded clusters between TMP, water, and nitric acids. The hydrogen bond between TMP and nitric acids are fairly strong. Although three nitric acids can be hydrogen-bonded directly to the phosphoryl oxygen of the TMP, only two waters can make hydrogen bonds directly. While the H-bond dissociation enthalpy of the TMP-(HNO3)x complexes with x ) 1, 2, and 3 at 300 K are 9.7, 6.3, and 3.4 kcal/mol, respectively, those of the TMP-(H2O)y complexes with y ) 1, 2, and 3 at 300 K are 4.4, 4.0, and 3.1 kcal/mol, respectively. The strength of each additional H-bond becomes smaller as nitric acids and water are attached to the TMP consecutively. The weak hydrogen bond between water and a methyl proton takes important role to the stability of the complexes. Solvent effect seems very important to the relative stability of complexes in terms of dissociation free energy in solution. n-Hexane is used as a dielectric continuum model of sc-CO2. TMP-(HNO3)(H2O)2 and TMP-(HNO3)2(H2O)(II) are two most stable complexes not only in TBP but also in n-hexane in terms of the free energy in solution, which agree quite well with experimental results.

Ind. Eng. Chem. Res., Vol. 44, No. 10, 2005 3395

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Received for review August 14, 2004 Revised manuscript received February 18, 2005 Accepted February 24, 2005 IE0492597