A density functional theory study on the interaction between UO22+ and the carbamoylphosphoramidic acid ligand for uranium extraction from seawater

NUCLEAR CHEMISTRY, RADIOCHEMISTRY, NUCLEAR MEDICINE

A density functional theory study on the interaction between UO₂²⁺ and the carbamoylphosphoramidic acid ligand for uranium extraction from seawater

Xiao-Jing Guo，

Cheng Li，

Jiang-Tao Hu，

Hong-Juan Ma，

Hong-Liang Qian

Nuclear Science and Techniques

Vol.29, No.6

Article number 90

Published in print 01 Jun 2018

Available online 09 May 2018

DOI：10.1007/s41365-018-0422-0

38600

Phosphorylurea molecules, which are bidentate organophosphorous compounds containing both phosphoryl and carbonyl groups, are considered efficient extractants for UO₂². This study aims to explain the complexation of UO₂²⁺ with carbamoylphosphoramidic acid (CPO), a simple model for phosphorylurea, for ligand design for uranium recovery from seawater using density functional theory calculations (DFT), natural bond order analysis (NBO), and the quantum theory of atoms in molecules (QTAIM). The results showed that, when CPO acts as a monodentate ligand, the affinity of phosphoryl for UO₂²⁺ is stronger than that of carbonyl, and CPO coordinates to UO₂²⁺ through the phosphoryl oxygen atom. When CPO serves as a bidentate ligand, both the phosphoryl and carbonyl oxygen atoms connect to UO₂²⁺, and the U–O(carbonyl) bond plays a more important role than the U–O(phosporyl) bond in the interaction between UO₂²⁺ and CPO. This paradox may be caused by the significant charge transfer from the U–O(carbonyl) π bond orbital to the C–N σantibond orbital of the bidentate CPO. The NH spacer between the phosphoryl and carbonyl groups could ensure the delocalization of the electron system of the molecule. The bidentate binding motif is favored by entropy and opposed by enthalpy, while the monodentate binding motif is favored by enthalpy and opposed by entropy. Ultimately, the bidentate binding motif is more favorable than the monodentate one. As expected, the interaction between UO₂²⁺ and the deprotonated CPO is stronger than that between UO₂²⁺ and the neutral CPO. Comparing the interaction between UO₂²⁺ and CPO with that between UO₂²⁺ and N-phenylcarbamoylphosphoramidic acid (PhCPO), formed by replacing one hydrogen atom from the terminal nitrogen atom of CPO with a phenyl group, the phenyl substituent at the terminal nitrogen atom of PhCPO shows a slightly negative effect on the interaction between UO₂²⁺ and PhCPO.

Uranium extractionAdsorptionDensity functional theory

1. INTRODUCTION

Concerns about the energy crisis and greenhouse gas emissions prompted more and more countries to choose nuclear power as a clean energy source [1, 2]. Nuclear energy provides over 11% of the world's electricity as a continuous and reliable base-load power, without carbon dioxide emission. Uranium consumption is expected to continue to rise to meet the increasing nuclear energy demands in the foreseeable future. Provided that all uranium mines currently under development enter service as planned, the uranium market should be adequately supplied just until 2025 according to the World Nuclear Association report. However we could extend that by 6500 years if half of the uranium resources (estimated at 4.5 billion tons) in the ocean could be recovered [3].

Ligand design is a very important field in the development of effective adsorbents for uranium recovery from seawater. Phosphoryl-containing compounds show high affinity for UO₂²⁺. It has been reported that uranyl phosphates and arsenates constitute about one-third of the ~200 known uranium minerals [4]. This truly proves the strong affinity of phosphoryl for uranium. Phosphonate ligands are currently used to extract uranium in the TRUEX (transuranic extraction) and PUREX (plutonium and uranium recovery by extraction) processes [5, 6]. Several researchers such as Alexandratos et al. [7] and Yuan et al. [8] have also pointed out the high affinity of phosphonate ligands for UO₂²⁺. Another proof of the strong affinity of phosphoryl for UO₂²⁺ is the higher uranium sorption capacity of phosphoric acid-functionalized mesoporous carbon sorbents compared to amidoxime-functionalized materials, which are known to be efficient for uranium extraction from seawater [9]. Moreover, carbonyl could also bind to UO₂²⁺, therefore both the phosphoryl and carbonyl-containing ligands have been incorporated into mesoporous materials to be used as sorbents for UO₂²⁺[9, 10].

Bidentate organophosphorous compounds containing both phosphoryl and carbonyl are considered efficient extractants for UO₂²⁺; for example, carbamoylphosphine oxide (CMPO) is well-known, and often used in the TRUEX process [11]. The predominant connecting site of CMPO with UO₂²⁺ is the phosphoryl oxygen (OP) atom, while the carbonyl oxygen (OC) atom can connect with a proton and serve as an internal buffer [12]. Wang et al. [13] reported that CMPO coordinated as a bidentate chelating ligand through both the OP and OC atoms for 1:1-type complexes, and as monodentate ligand interacting with UO₂²⁺ through the OP atoms for 2:1-type complexes [13]. The N-diphenylphosphorylurea ligand, another group containing both phosphoryl and carbonyl, has also been shown to effectively bind to UO₂²⁺[1, 14]. Similar in structure to CMPO, phosphorylurea molecules have a NH spacer between the phosphoryl and carbonyl groups as opposed to the CH₂ spacer in the CMPO ligands. It has been said that the CH₂ spacer between the phosphoryl and carbonyl groups in a CMPO molecule does not ensure the electronic interactions between them, while replacing CH₂ with NH could ensure the delocalization of the electron system of the molecule to strengthen its affinity for UO₂²⁺[15]. Moreover, the replacement of CH₂ by NH makes the structure more rigid, and the resulting distances between the OP and OC atoms in phosphorylureas are shorter than those in the corresponding CMPOs, which probably enhance the binding abilities of phosphorylureas for UO₂²⁺[15].

While there are numerous studies about CMPOs, the interactions between UO₂²⁺ and phosphorylureas has not been fully explored in the literature yet. Matrosov et al.[14] proposed a bidentate binding motif for uranyl complexes with phosphorylureas, while Carboni et al.[1] proposed a monodentate coordination motif where UO₂²⁺ interacts with the OP atom. Additionally, replacing the alkyls at the phosphorous atom with aryls could alter the binding abilities of CMPOs for UO₂²⁺. It has been previously reported that replacing alkyls at the phosphorous atom with aryls in the CMPO series could enhance the binding abilities of the compounds [15]. Wang et al. [13] reported that the CMPO and diphenyl-N,N-diisobutylcarbamoyl phosphine oxide (Ph₂CPMO) ligands showed comparable U-ligand binding strengths. What if aryls connect to the terminal nitrogen atom? Since phosphorylureas containing phenyl at the terminal nitrogen atom have been incorporated into mesoporous materials intended as sorbents for UO₂²⁺[1, 9], more detailed knowledge of the interactions between UO₂²⁺ and phosphorylureas is needed. The information could help advance the disclosing of the structure-property relationships for ligand design for uranium recovery from seawater by showing the effects of electronic and structural differences on binding.

In this research, the binding of UO₂²⁺ with carbamoylphosphoramidic acid (CPO), a simple phosphorylurea model, (Fig. 1), as well as N-phenylcarbamoylphosphoramidic acid (PhCPO), (Fig. 1) was quantified by applying density functional theory (DFT) calculations. We focused on the stable structures, their bonding characteristics, and the relative stabilities of various uranyl complexes. The difference in calculated properties was interpreted in terms of the electronic and structural differences between various uranyl complexes. Based on the results, we explained the following: (1) which is the interacting site of CPO with UO₂²⁺, and why, (2) what are the roles of the U–OP and U–OC bonds in the interaction between UO₂²⁺ and CPO, and (3) whether the binding strength of UO₂²⁺ with CPO is affected by incorporating a phenyl group into CPO at the terminal nitrogen atom.

Figure 1.

The molecular skeletons of carbamoylphosphoramidic acid (CPO) and N-phenylcarbamoylphosphoramidic acid (PhCPO)

2. COMPUTATIONAL METHODS

We performed DFT calculations using the Gaussian-09 C1 package[16] at the B3LYP level of theory[17, 18]. The spin-orbit coupling effects were not considered during the calculations. The Stuttgart RSC 1997 effective core potential (ECP) was used for uranium. This potential includes the 60 electrons in the core for uranium atoms to take scalar relativistic effects into consideration. The remaining 32 electrons are described by the associated valence basis set [19-21]. It has been reported that the additional diffuse functions to the oxygen and hydrogen atoms can significantly affect the U, d, f, and p populations of (UO₂)₂(OH)₂(H₂O)₆²⁺, while the additional polarization function does not [22]. Diffuse functions are very important, and often necessary to use when negatively charged ligands are involved [23]. Additionally, for the complexes with phenyl rings, dispersion effects must be non-negligible. Therefore, in this paper, we used the 6-31++G* basis set for carbon, nitrogen, oxygen and hydrogen atoms. This level of theory accurately yields the main features of actinyl complexes [13, 24, 25]. No symmetry constraint was applied during the calculations. Harmonic vibrational frequency calculations at the same level verified that each structure was a minimum with zero imaginary frequency. As discussed in our previous papers, aqueous environments influence the binding motif of the relatively stable isomers for some uranyl complexes [26, 27]. Moreover, since we were interested in the structural information for uranyl complexes with CPO and PhCPO in solution, all the structures were fully optimized with solvation effects, via a polarizable conductor calculation model (CPCM), similar to the conductor-like screening model (COSMO) method [28, 29] using the "SCRF=COSMO" keyword in the Gaussian 09 program package. NBO analysis [30] was performed using the NBO 6.0 program [31]. QTAIM analysis [32] was employed to analyze the U–ligand bonds using the Multiwfn 3.3.5 software [33].

The extent of protonation/deprotonation in aqueous solution was determined by the acid dissociation constant (pK_a). We directly calculated the pKa of CPO using the above computational methods but at a higher basis set of 6-311++G(d,p).

The pK_a for the $CPO ⇌ {DCPO}^{-} + H^{+}$ reaction is given by:

p K_{a} = \frac{Δ G_{aq}^{*}}{2.303 R T} = \frac{G_{aq, {DCPO}^{-}}^{*} + G_{aq, H^{+}}^{*} - G_{aq, CPO}^{*}}{2.303 R T}

(1)

where $G_{aq, CPO}^{*}$ and $G_{aq, {DCPO}^{-}}^{*}$ are the standard free energy of CPO and deprotonated CPO (DCPO) in aqueous solutions, respectively. The free energy of a proton in aqueous medium is calculated as:

G_{aq, H^{+}}^{*} = G_{g, H^{+}}^{°} + Δ G_{aq, H^{+}}^{*} + Δ G^{1 atm \to 1 M},

(2)

where $G_{g, H^{+}}^{°} = H_{g, H^{+}}^{°} - T S_{g, H^{+}}^{°}$ is the gas-phase free energy of the proton at 298.15 K obtained using $H_{g, H^{+}}^{°} = \frac{5 R T}{2} = 1.48 kcal / mol$ and $S_{g, H^{+}}^{°} = 26.05 cal / (mol \cdot K) . Δ G_{aq, H^{+}}^{*} = - 265.9 kcal / mol$ is the aqueous-phase solvation free energy of the proton, as reported in the literature [34-36]. $Δ G^{1 atm \to 1 M}$ is a correction term for the change in the standard state of 1 atm to 1 mol/L, calculated as $R T log (24.4) = 1.89 kcal / mol$ . The symbols * and $°$ refer to the standard state: 1 mol/L and 1 atm, respectively.

Also, the pK_a for the ${DCPO}^{-} ⇌ {DDCPO}^{2 -} + H^{+}$ reaction is given by:

p K_{a} = \frac{Δ G_{aq}^{*}}{2.303 R T} = \frac{G_{aq, {DDCPO}^{2 -}}^{*} + G_{aq, H^{+}}^{*} - G_{aq, {DCPO}^{-}}^{*}}{2.303 R T}

(3)

where $G_{aq, {DCPO}^{-}}^{*}$ and $G_{aq, {DDCPO}^{2 -}}^{*}$ are the standard free energy of DCPO and deprotonated DCPO (DDCPO) in aqueous solution, respectively.

The effect of explicit water on the calculated pK_a^’s was assessed by adding two explicit water molecules hydrogen-bonded directly to the site being protonated/deprotonated as shown in Fig 2.

Figure 2.

(Color online) Arrangement of the explicit water molecules near the OH and O^- groups in CPO.

3. RESULTS AND DISCUSSION

UO₂²⁺ is known to coordinate with five water molecules forming a pentahydrate complex [UO₂(H₂O)₅]²⁺ in aqueous solution. Since the literature about the structures of uranyl complexes with CPO is scarce, we optimized UO₂(H₂O)₅²⁺ and UO₂(CO₃)₃^4- in aqueous solution to check the reliability of our theoretical methods. (See Figure S1 and Table S1). Additionally, using similar methods and calculation setups, we recently studied the coordination of uranyl hydrates [37], and successfully predicted the structures of uranyl complexes with amine, amidoximate, and carboxyl groups both in gas phase and aqueous solution [26, 27]. The structural properties after optimization agree well with other calculation results and experiments [38-40].

When UO₂²⁺ interacts with CPO/PhCPO, aqua groups are added to the equatorial plane of UO₂²⁺, resulting in a penta-coordinated pattern in the equatorial plane of UO₂²⁺. As stated in the introduction section, both phosphoryl and carbonyl show affinity for UO₂²⁺. CPO/PhCPO could serve as a monodentate ligand coordinating with UO₂²⁺ through either the OP or OC atom referred to as binding motifs I and II. In addition, both the OP and OC atoms could bind to UO₂²⁺ forming a bidentate binding motif referred to as III. Therefore, [UO₂(H₂O)₄(L)]²⁺ containing monodentate ligands and [UO₂(H₂O)₃(L)]²⁺ containing bidentate ligands were studied as 1:1 ligand/metal stoichiometric complexes (where L=CPO or PhCPO, hereinafter), while [UO₂(H₂O)₃(L)]²⁺ containing two monodentate ligands, [UO₂(H₂O)₂(L)₂]²⁺ containing one monodentate and one bidentate ligand, and [UO₂(H₂O)(L)₂]²⁺ containing two bidentate ligands were studied as 2:1 ligand/metal stoichiometric complexes. Moreover, the corresponding complexes with deprotonated CPO or PhCPO: [UO₂(H₂O)₄(DL)]⁺, [UO₂(H₂O)₃(DL)]⁺, [UO₂(H₂O)₃(DL)₂], [UO₂(H₂O)₂(DL)₂], and [UO₂(H₂O)(DL)₂] were investigated (DL=DCPO or DPhCPO, and represent the deprotonated CPO or PhCPO, hereinafter).

3.1 Structural and vibrational properties.

3.1.1 Complexes with 1:1 ligand/metal stoichiometry.

According to the optimized geometries and zero-point energies for [UO₂(H₂O)₄(L)]²⁺ in Figure S2(a), binding motif I is favored over II. This indicates that the e a) presents the most energetically stable geometries of [UO₂(H₂O)₄(L)]²⁺ where the monodentate ligands coordinate to UO₂²⁺ through the OP atoms and [UO₂(H₂O)₃(L)]²⁺ for the 1:1 ligand/metal stoichiometric complexes. As shown in Table 1(a), the U–O(CPO) distances are slightly shorter than the U–O(PhCPO) distances for [UO₂(H₂O)₄(L)]²⁺ and [UO₂(H₂O)₃(L)]²⁺, which indicates that the interaction between UO₂²⁺ and CPO is slightly stronger than that between UO₂²⁺ and PhCPO. These results also imply that the phenyl substituent at the terminal nitrogen atom of PhCPO shows a slightly negative effect on the interaction between UO₂²⁺ and PhCPO. It is generally known that the donation of electrons to the U center by the equatorial ligands weakens the U=O bond. The U=O bond lengths for uranyl complexes with CPO are almost the same as those for the complexes with PhCPO, which indicates that the charge transfers from equatorial ligands to the U centers for uranyl complexes with CPO and PhCPO are similar. The calculated symmetric and asymmetric vibrational frequencies of uranyl for the most energetically stable [UO₂(H₂O)₄(L)]²⁺ and [UO₂(H₂O)₃(L)]²⁺ are presented in Table 2(a). The stronger U=O bonds are accompanied by higher uranyl stretching vibrational frequencies. In accordance with the U=O bond lengths, the uranyl stretching vibrational frequencies for uranyl complexes with CPO and PhCPO are similar. These results indicate that the phenyl substitute at the terminal nitrogen atom has an insignificant effect on the binding ability of PhCPO for UO₂²⁺. Specifically, for [UO₂(H₂O)₃(L)]²⁺, the distances between U and the OP atoms of the bidentate ligands are longer than those between U and the OC atoms. These results indicate that the U–OC bonds play a more important role than the U–OP bonds in the interactions between UO₂²⁺ and the bidentate CPO/PhCPO. This is opposite to the fact that the electron-donating abilities of the OP atoms are stronger than those of the OC atoms for CPO/PhCPO, which will be discussed in Sect. 3.3.

Calculated U=O, U–OP and U–OC distances (Å) of most energetically stable (a) [UO₂(H₂O)₄(L)]²⁺ and [UO₂(H₂O)₃(L)]²⁺ (L=CPO or PhCPO) and (b) [UO₂(H₂O)₄(DL)]⁺ and [UO₂(H₂O)₃(DL)]⁺ (DL=DCPO or DPhCPO). OP and OC represent the phosphoryl and carbonyl oxygen atoms.

		[UO₂(H₂O)₄(L)]²⁺		[UO₂(H₂O)₃(L)]²⁺				[UO₂(H₂O)₄(DL)]⁺		[UO₂(H₂O)₃(DL)]⁺
		L=CPO	L=PhCPO	L=CPO	L=PhCPO			DL=DCPO	DL=DPhCPO	DL=DCPO	DL=DPhCPO
(a)						(b)
	U=O	1.767	1.767	1.769	1.768		U=O	1.774	1.773	1.775	1.774
	U–OP	2.343	2.355	2.380	2.396		U–OP	2.260	2.260	2.303	2.306
	U–OC	/	/	2.353	2.368		U–OC	/	/	2.352	2.361

Calculated frequencies (cm^-1) of the symmetrical and asymmetrical stretching modes of U=O for the most energetically stable (a) [UO₂(H₂O)₄(L)]²⁺ and [UO₂(H₂O)₃(L)]²⁺ (L=CPO or PhCPO) and (b) [UO₂(H₂O)₄(DL)]⁺ and [UO₂(H₂O)₃(DL)]⁺ (DL=DCPO or DPhCPO).

		[UO₂(H₂O)₄(L)]²⁺		[UO₂(H₂O)₃(L)]²⁺				[UO₂(H₂O)₄(DL)]⁺		[UO₂(H₂O)₃(DL)]⁺
		asym	sym	asym	sym			asym	sym	asym	sym
(a)						(b)
	L=CPO	953	897	948	892		DL=DCPO	938	872	932	873
	L=PhCPO	953	895	950	891		DL=DPhCPO	938	872	934	874

The calculated pK_a1 and pK_a2 values for CPO are 1.49 and 13.59 respectively, while the pK_a1 and pK_a2 values become 1.87 and 12.26 when two explicit water molecules are added near the OH and O^- groups in CPO as shown in Fig.2. According to the pK_a values, CPO could very likely lose one proton forming DCPO in seawater, while DDCPO is difficult to form. Thus, we also studied the uranyl complexes with DCPO and DPhCPO. In addition, according to the optimized geometries and zero-point energies in Figure S3(a), binding motif I is favored over II for [UO₂(H₂O)₄(DL)]⁺. The most energetically stable geometries of [UO₂(H₂O)₄(DL)]⁺ where the monodentate ligands coordinate to UO₂²⁺ through the OP atoms and [UO₂(H₂O)₃(DL)]⁺ with binding motif III are presented in Fig. 3(b). As shown in Tables 1(b) and 2(b), the U=O bond lengths and the uranyl stretching vibrational frequencies for the uranyl complexes with DCPO and DPhCPO are very similar. The U–O (DCPO/DPhCPO) distances are all shorter than the corresponding U–O (CPO/PhCPO) distances, while the U=O bond lengths for uranyl complexes with DCPO/DPhCPO are longer than the corresponding values for uranyl complexes with CPO/PhCPO as shown in Table 1. Additionally, uranyl stretching vibrational frequencies decrease with the deprotonation of CPO/PhCPO (Table 2). These results indicate that the interactions of UO₂²⁺ with DCPO/DPhCPO are stronger than those with CPO/PhCPO. It is reasonable to assume that positively charged UO₂²⁺ interacts strongly with the negatively charged DCPO/DPhCPO compared with the neutral CPO/PhCPO. According to the distances between U and the oxygen atoms of the bidentate DCPO/DPhCPO, the U–OP bonds play a more important role than the U–OC bonds in the interactions between UO₂²⁺ and the bidentate DCPO/DPhCPO for [UO₂(H₂O)₃(DL)]⁺. This is different for [UO₂(H₂O)₃(L)]²⁺ where the U–OC bonds play a leading role in the interactions between UO₂²⁺ and the bidentate CPO/PhCPO since the deprotonation of CPO/PhCPO causes more electrons to gather at the phosphoryl group thus causing the bonds between U and the OP atoms of DCPO/DPhCPO to be stronger.

Figure 3

(Color online). Optimized structures of most energetically stable (a) [UO₂(H₂O)₄(L)]²⁺ and [UO₂(H₂O)₃(L)]²⁺ (L=CPO or PhCPO) and (b) [UO₂(H₂O)₄(DL)]⁺ and [UO₂(H₂O)₃(DL)]⁺ (DL=DCPO or DPhCPO).

3.1.2 Complexes with 2:1 ligand/metal stoichiometry.

Three kinds of 2:1 ligand/metal stoichiometric uranyl complexes, [UO₂(H₂O)₃(L)₂]²⁺, [UO₂(H₂O)₂(L)₂]²⁺, and [UO₂(H₂O)(L)₂]²⁺ were examined. The two ligands (CPO or PhCPO) bind to UO₂²⁺ in a monodentate style for [UO₂(H₂O)₃(L)₂]²⁺, and serve as bidentate ligands for [UO₂(H₂O)(L)₂]²⁺. While one ligand coordinates to UO₂²⁺ in binding motif I, the other acts as a bidentate ligand for [UO₂(H₂O)₂(L)₂]²⁺. Similar to the case of uranyl complexes with 1:1 ligand/metal stoichiometry, binding motif I is favored over II for uranyl complexes with 2:1 ligand/metal stoichiometry according to the optimized geometries and zero-point energies for [UO₂(H₂O)₃(L)₂]²⁺, and [UO₂(H₂O)₂(L)₂]²⁺ in Figure S2(c) and (d). Figure 4(a) presents the most energetically stable geometries of [UO₂(H₂O)₃(L)₂]²⁺, [UO₂(H₂O)₂(L)₂]²⁺, and [UO₂(H₂O)(L)₂]²⁺. The monodentate CPO/PhCPO coordinate to UO₂²⁺ through the OP atoms, which proves again that the electron-donating ability of the OP atom is stronger than that of the OC atom of CPO and PhCPO. As shown in Table 3(a), the distances between U and the oxygen atoms of monodentate CPO and PhCPO are very similar for [UO₂(H₂O)₃(L)₂]²⁺ and [UO₂(H₂O)₂(L)₂]²⁺. The U–OP and U–OC bonds between UO₂²⁺ and the bidentate CPO are shorter than the corresponding bonds between UO₂²⁺ and the bidentate PhCPO for [UO₂(H₂O)₂(L)₂]²⁺, while the U–OP bonds between UO₂²⁺ and the bidentate CPO are longer than those between UO₂²⁺ and the bidentate PhCPO for [UO₂(H₂O)(L)₂]²⁺. These might be explained by the numerous hydrogen bonds between the hydrogen atoms of CPO/PhCPO and the oxygen atoms of H₂O in the equatorial plane of uranyl. Additionally, the U=O bond lengths for [UO₂(H₂O)₃(CPO)₂]²⁺, [UO₂(H₂O)₂(CPO)₂]²⁺, and [UO₂(H₂O)(CPO)₂]²⁺ are almost the same as those for [UO₂(H₂O)₃(PhCPO)₂]²⁺, [UO₂(H₂O)₂(PhCPO)₂]²⁺, and [UO₂(H₂O)(PhCPO)₂]²⁺ respectively, which indicates that the charge transfer from the equatorial ligands to the U centers for uranyl complexes with CPO and PhCPO are similar. The calculated frequencies of the symmetrical and asymmetrical stretching modes of U=O for the most energetically stable [UO₂(H₂O)₃(L)₂]²⁺, [UO₂(H₂O)₂(L)₂]²⁺, and [UO₂(H₂O)(L)₂]²⁺ are presented in Table 4(a). Similarly to the case of uranyl complexes with 1:1 ligand/metal stoichiometry, the uranyl stretching vibrational frequencies for uranyl complexes with CPO and PhCPO are comparable for [UO₂(H₂O)₃(L)₂]²⁺, [UO₂(H₂O)₂(L)₂]²⁺, and [UO₂(H₂O)(L)₂]²⁺, which indicates that the phenyl substitute at the terminal nitrogen atom of PhCPO shows only an insignificant effect on the binding ability of PhCPO for uranyl. Specifically, the U–OP bonds are longer than the U–OC bonds between UO₂²⁺ and the bidentate CPO/PhCPO for [UO₂(H₂O)₂(L)₂]²⁺ and [UO₂(H₂O)(L)₂]²⁺. These results indicate that the U–OC bonds play a more important role than the U–OP bonds in the interactions between UO₂²⁺ and the bidentate CPO/PhCPO.

Calculated U=O, U–OP and U–OC distances (Å) for the most energetically stable (a) [UO₂(H₂O)₃(L)₂]²⁺, [UO₂(H₂O)₂(L)₂]²⁺, and [UO₂(H₂O)(L)₂]²⁺ (L=CPO or PhCPO) and (b) [UO₂(H₂O)₃(DL)₂], [UO₂(H₂O)₂(DL)₂], and [UO₂(H₂O)(DL)₂] (DL=DCPO or DPhCPO). OP and OC denote the phosphoryl and carbonyl oxygen atoms.

		[UO₂(H₂O)₃(L)₂]²⁺		[UO₂(H₂O)₂(L)₂]²⁺		[UO₂(H₂O)(L)₂]²⁺				[UO₂(H₂O)₃(DL)₂]		[UO₂(H₂O)₂(DL)₂]		[UO₂(H₂O)(DL)₂]
		L=CPO	L=PhCPO	L=CPO	L=PhCPO	L=CPO	L=PhCPO			L=DCPO	L=DPhCPO	L=DCPO	L=DPhCPO	L=DCPO	L=DPhCPO
(a)								(b)
	U=O	1.768	1.766	1.772	1.771	1.773	1.773		U=O	1.781	1.781	1.781	1.781	1.783	1.782
	U–OP1^a	2.353	2.356	2.378	2.374	2.423	2.403		U–OP1^a	2.321	2.309	2.332	2.339	2.360	2.352
	U–OC1^a					2.382	2.386		U–OC1^a					2.384	2.394
	U–OP2^a	2.348	2.342	2.416	2.420	2.412	2.399		U–OP2^a	2.303	2.298	2.339	2.335	2.342	2.338
	U–OC2^a			2.371	2.390	2.390	2.395		U–OC2^a			2.395	2.405	2.408	2.425

Calculated frequencies (cm^-1) of the symmetrical and asymmetrical stretching modes of U=O for the most energetically stable (a) [UO₂(H₂O)₃(L)₂]²⁺, [UO₂(H₂O)₂(L)₂]²⁺, and [UO₂(H₂O)(L)₂]²⁺ (L=CPO or PhCPO) and (b) [UO₂(H₂O)₃(DL)₂], [UO₂(H₂O)₂(DL)₂], and [UO₂(H₂O)(DL)₂] (DL=DCPO or DPhCPO).

		[UO₂(H₂O)₃(L)₂]²⁺		[UO₂(H₂O)₂(L)₂]²⁺		[UO₂(H₂O)(L)₂]²⁺				[UO₂(H₂O)₃(DL)₂]		[UO₂(H₂O)₂(DL)₂]		[UO₂(H₂O)(DL)₂]
		asym	sym	asym	sym	asym	sym			asym	sym	asym	sym	asym	sym
(a)								(b)
	L=CPO	948	887	940	884	938	879		L=DCPO	918	853	917	857	912	855
	L=PhCPO	954	893	941	881	937	878		L=DPhCPO	914	848	919	856	914	853

Figure 4.

(Color online) Optimized structures of most energetically stable (a) [UO₂(H₂O)₃(L)₂]²⁺, [UO₂(H₂O)₂(L)₂]²⁺, and [UO₂(H₂O)(L)₂]²⁺ (L=CPO or PhCPO) and (b) [UO₂(H₂O)₃(DL)₂], [UO₂(H₂O)₂(DL)₂], and [UO₂(H₂O)(DL)₂] (DL=DCPO or DPhCPO).

Moreover, UO₂²⁺ binds to the monodentate DCPO/DPhCPO through the OP atoms in binding motif I for [UO₂(H₂O)₃(DL)₂] and [UO₂(H₂O)₂(DL)₂] (Figure S3(c) and (d)). The most energetically stable geometries of [UO₂(H₂O)₃(DL)₂], [UO₂(H₂O)₂(DL)₂] and [UO₂(H₂O)(DL)₂] are presented in Figure 4(b). As shown in Table 3(b), the U=O bond lengths for uranyl complexes with DCPO and DPhCPO are very similar, and so are the uranyl stretching vibrational frequencies in Table 4(b). As expected, the interactions between UO₂²⁺ and DCPO/DPhCPO are stronger than those between UO₂²⁺ and CPO/PhCPO according to the U–O and U=O bond lengths in Table 3 and the uranyl stretching vibrational frequencies in Table 4. Comparing the U–OP and U–OC bond lengths, we can conclude that the U–OP bonds play a more important role than the U–OC bonds in the interactions between UO₂²⁺ and the bidentate DCPO/DPhCPO for [UO₂(H₂O)₂(DL)₂] and [UO₂(H₂O)(DL)₂]. These results are in accordance with the results for the uranyl complexes with 1:1 ligand/metal stoichiometry.

3.2 Thermodynamic properties.

3.2.1 Complexes with 1:1 ligand/metal stoichiometry.

Changes in the enthalpies (ΔH) and Gibbs free energies (ΔG) that accompany the formation of uranyl complexes with 1:1 ligand/metal stoichiometry are listed in Table 5. The energies are calculated based on the most energetically stable geometries for uranyl complexes. As shown in Table 5(a), the ΔH and ΔG values that accompany the formation of UO₂(H₂O)₄(CPO)²⁺ and UO₂(H₂O)₃(CPO)²⁺ are slightly more negative than those accompanying the formation of UO₂(H₂O)₄(PhCPO)²⁺ and UO₂(H₂O)₃(PhCPO)²⁺ respectively, which indicates that the phenyl substituent on the terminal nitrogen atom of PhCPO exerts a slightly negative effect on the interaction between UO₂²⁺ and PhCPO. Additionally, in batch experiments, the steric hindrance effect on uranyl adsorption with PhCPO functionalized materials could be stronger than that on uranyl adsorption with CPO functionalized materials. The ΔG values for the complexation reactions between uranyl and CPO/PhCPO are negative for the formation of UO₂(H₂O)₃(L)²⁺ and positive for UO₂(H₂O)₄(L)²⁺. These results indicate that the bidentate binding motif is favored over the monodentate one, which is consistent with the results of Matrosov et al [14]. However, the results are different than those of Carboni et al. [9] obtained based on enthalpies. Specifically, comparing the ΔH and ΔG values, the entropy exerts a negative effect on the interaction between uranyl and monodentate CPO/PhCPO for UO₂(H₂O)₄(L)²⁺ and a positive effect on the interaction between uranyl and bidentate CPO/PhCPO for UO₂(H₂O)₃(L)²⁺. The entropy was also suggested to play a significant role in the complexation of uranyl with the H₂PO₄⁻ anion where the complexation was favored by entropy and opposed by enthalpy [41].

Calculated changes in enthalpies and Gibbs free energies (ΔH and ΔG, kcal/mol) that accompany the formation of (a) [UO₂(H₂O)₄(L)]²⁺ and [UO₂(H₂O)₃(L)]²⁺ (L=CPO or PhCPO) and (b) [UO₂(H₂O)₄(DL)]⁺ and [UO₂(H₂O)₃(DL)]⁺ (DL=DCPO or DPhCPO) at 298.15 K.

		ΔH		ΔG				ΔH		ΔG
		L=CPO	L=PhCPO	L=CPO	L=PhCPO			L=DCPO	L=DPhCPO	L=DCPO	L=DPhCPO
(a)						(b)
	UO₂(H₂O)₅²⁺ + L → UO₂(H₂O)₄(L)²⁺ + H₂O	-3.4	2.0	1.3	3.3		UO₂(H₂O)₅²⁺ + DL^- →UO₂(H₂O)₄(DL)⁺ + H₂O	-15.0	-12.7	-12.0	-9.3
	UO₂(H₂O)₅²⁺ + L → UO₂(H₂O)₃(L)²⁺ + 2H₂O	-2.3	1.0	-7.8	-5.0		UO₂(H₂O)₅²⁺ + DL^- → UO₂(H₂O)₃(DL)⁺ + 2H₂O	-15.9	-13.1	-22.3	-17.3

The ΔH and ΔG values for the complexation reactions between uranyl and DCPO/DPhCPO in Table 5(b) also indicate that binding motif III is favored by entropy and opposed by enthalpy, while binding motif I is opposed by entropy and favored by enthalpy. As expected, the deprotonated ligands show a higher affinity for UO₂²⁺ than the neutral ones. The attachment of phenyl at the terminal nitrogen atom brings a slightly negative effect on the interaction between UO₂²⁺ and DCPO.

3.2.2 Complexes with 2:1 ligand/metal stoichiometry.

Based on the most energetically stable geometries of uranyl complexes with 2:1 ligand/metal stoichiometry, we collected the ΔH and ΔG values for the formation of [UO₂(H₂O)₃(L)₂]²⁺, [UO₂(H₂O)₂(L)₂]²⁺, and [UO₂(H₂O)(L)₂]²⁺ (L=CPO or PhCPO) in Table 6(a). The ΔH values that accompany the formation of [UO₂(H₂O)₃(CPO)₂]²⁺, [UO₂(H₂O)₂(CPO)₂]²⁺, and [UO₂(H₂O)(CPO)₂]²⁺ are negative, while those accompanying the formation of [UO₂(H₂O)₃(PhCPO)₂]²⁺, [UO₂(H₂O)₂(PhCPO)₂]²⁺, and [UO₂(H₂O)(PhCPO)₂]²⁺ are positive. The ΔG values are negative if the forming complexes contain bidentate ligands (UO₂(H₂O)₂(L)₂²⁺ and UO₂(H₂O)(L)₂²⁺), however they are positive for (UO₂(H₂O)₃(L)²⁺). Based on these results, we could reach the same conclusions we reached for uranyl complexes with 1:1 ligand/metal stoichiometry. First, the phenyl substituent on the terminal nitrogen atom of PhCPO exerts a slightly negative effect on the binding strengths of [UO₂(H₂O)₃(PhCPO)₂]²⁺, [UO₂(H₂O)₂(PhCPO)₂]²⁺, and [UO₂(H₂O)(PhCPO)₂]²⁺. Second, the entropy causes a negative effect on the interactions between UO₂²⁺ and the monodentate CPO/PhCPO, while it gives a positive effect on the interactions between UO₂²⁺ and the bidentate CPO/PhCPO.

Calculated changes in enthalpies and Gibbs free energies (ΔH and ΔG, kcal/mol) that accompany the formation of (a) [UO₂(H₂O)₃(L)₂]²⁺, [UO₂(H₂O)₂(L)₂]²⁺ and [UO₂(H₂O)(L)₂]²⁺ (L=CPO or PhCPO) and (b) [UO₂(H₂O)₃(DL)₂], [UO₂(H₂O)₂(DL)₂], and [UO₂(H₂O)(DL)₂] (DL=DCPO or DPhCPO) at 298.15 K.

		ΔH		ΔG				ΔH		ΔG
		L=CPO	L=PhCPO	L=CPO	L=PhCPO		L=DCPO	L=DPhCPO	L=DCPO	L=DPhCPO
(a)						(b)
	UO₂(H₂O)₅²⁺ + 2L → UO₂(H₂O)₃(L)₂²⁺ + 2H₂O	-5.7	1.4	2.2	7.8		UO₂(H₂O)₅²⁺ + 2DL^- → UO₂(H₂O)₃(DL)₂ + 2H₂O	-27.0	-22.4	-19.6	-13.6
	UO₂(H₂O)₅²⁺ + 2L → UO₂(H₂O)₂(L)₂²⁺ + 3H₂O	-4.5	1.3	-3.7	-0.8		UO₂(H₂O)₅²⁺ + 2DL^- → UO₂(H₂O)₂(DL)₂ + 3H₂O	-25.8	-21.3	-29.0	-22.6
	UO₂(H₂O)₅²⁺ + 2L → UO₂(H₂O)(L)₂²⁺ + 4H₂O	-3.7	2.8	-13.9	-8.6		UO₂(H₂O)₅²⁺ + 2DL^- → UO₂(H₂O)(DL)₂ + 4H₂O	-27.9	-22.1	-40.1	-32.2

The ΔH and ΔG values that accompany the formation of [UO₂(H₂O)₃(DL)₂], [UO₂(H₂O)₂(DL)₂], and [UO₂(H₂O)(DL)₂] (DL=DCPO or DPhCPO) are summarized in Table 6(b). Considering all the calculation results, we could reach several conclusions. First, binding motif III is favored over I, and binding motif I is favored over II for uranyl complexes with CPO/PhCPO. In addition, binding motif III is favored by entropy and opposed by enthalpy, while binding motif I is opposed by entropy and favored by enthalpy. Second, the attachment of phenyl at the terminal nitrogen atom exerts a slightly negative effect on the interactions between UO₂²⁺ and PhCPO. Lastly, as expected, the deprotonated ligands show a higher affinity for uranyl than the neutral ligands.

3.3 Electronic structures

3.3.1 Natural bond orbital (NBO) analysis.

As discussed above, binding motif I is favored over II for uranyl complexes with CPO/PhCPO, which indicates that the electron-donating ability of the OP atom is stronger than that of the OC atom. Paradoxically, for the complexes showing binding motif III where the bidentate CPO/PhCPO coordinate to UO₂²⁺ through both the OP and OC atoms, the distance between U and the OP atom is longer than that between U and the OC atom, which indicates that the U–OC bonds play a more important role than the U–OP bonds in the interactions between UO₂²⁺ and the bidentate CPO/PhCPO. In order to provide insights into the bonding nature of the U center with the OP and OC atoms, NBO analysis was conducted to investigate the natural charges, Wiberg bond indices (WBIs)^[42], donor-acceptor charge transfer, and hybridization of the U–O bonds in the complexes of interest. First, the natural charges of the free and bonded ligands in Table S2 are used to calculate the charge transfer (ΔQ) from the ligands to UO₂²⁺ and the adjacent water molecules as shown in Table 7. As expected, similarly with the interaction energies, the bidentate ligands in [UO₂(H₂O)₃(L)]²⁺ with binding motif III lose more electrons than the monodentate ligands in [UO₂(H₂O)₄(L)]²⁺ with binding motifs I and II. Comparing the WBIs of the U–O bonds in Table 7, the U–OP bonds in [UO₂(H₂O)₄(L)]²⁺ with motif I show a higher degree of covalent character than the U–OC bonds in [UO₂(H₂O)₄(L)]²⁺ with motif II. For [UO₂(H₂O)₃(L)]²⁺, the WBIs of the U–OC bonds are larger than those of the U–OP bonds, which indicates that the U–OC bonds show a higher degree of covalent character than the U–OP bonds, and the U–OC bonds play a more important role than the U–OP bonds in the interactions between UO₂²⁺ and the bidentate CPO/PhCPO.

The charge transfer (ΔQ) from ligands to UO₂²⁺ and adjacent water molecules and Wiberg bond indices (WBIs) of U–OP and U–OC bonds for uranyl complexes with 1:1 ligand/metal stoichiometry showing different binding motifs. OP and OC denote the phosphoryl and carbonyl oxygen atoms.

	[UO₂(H₂O)₄(L)]²⁺, motif I		[UO₂(H₂O)₄(L)]²⁺, motif II		[UO₂(H₂O)₃(L)]²⁺, motif III
	L=CPO	L=PhCPO	L=CPO	L=PhCPO	L=CPO	L=PhCPO
ΔQ	0.297	0.375	0.331	0.354	0.496	0.505
U–OP^a	0.545	0.462	/	/	0.403	0.390
U–OC^a	/	/	0.5000	0.475	0.446	0.455

Second, the second order perturbation energies (E⁽²⁾) corresponding to the donor-acceptor charge transfer in complexes larger than 5 kcal/mol are listed in Table 8. The OP atom is a stronger electron donor than the OC atom. This is reflected in the smaller U–OP distance in [UO₂(H₂O)₄(L)]²⁺ with motif I compared to the U–OC distance in [UO₂(H₂O)₄(L)]²⁺ with motif II. The E⁽²⁾ corresponding to the charge transfer from the lone pairs of OP to the U orbitals are larger than those from the lone pairs of OC. Specifically, there are significant charge transfers from the BD (1) U–OP orbital to the BD*(1) P–N orbital in [UO₂(H₂O)₄(L)]²⁺ with motif I and from the BD (1) U–OC orbital to the BD*(1) N–C orbital in [UO₂(H₂O)₄(L)]²⁺ with motif II. The corresponding E⁽²⁾ values are 7.16 and 11.02 kcal/mol respectively. The weaker charge transfer from the BD (1) U–OP orbital to the BD*(1) P–N orbital compared to that from the BD (1) U–OC orbital to the BD*(1) N–C orbital is compensated by the stronger charge transfer from the lone pairs of OP compared to that from the lone pairs of OC to the U orbitals for [UO₂(H₂O)₄(L)]²⁺. Altogether, the charge transfer between the U center and CPO/PhCPO in [UO₂(H₂O)₄(L)]²⁺ with binding motif I is stronger than that in [UO₂(H₂O)₄(L)]²⁺ with binding motif II. As for [UO₂(H₂O)₃(L)]²⁺ with a bidentate CPO/PhCPO, the E⁽²⁾ corresponding to the charge transfer from the lone pairs of OP to the U orbitals are slightly larger than that from the lone pairs of OC to the U orbitals. Moreover, there is a significant charge transfer from the BD (2) U–OC orbital to the BD*(1) C–N orbital, and the corresponding E⁽²⁾ is 11.83 kcal/mol. However, there is no other E⁽²⁾ corresponding to the charge transfer involving the OP orbital higher than the chosen 5 kcal/mol threshold. This may be the reason for the stronger U–OC bond compared to the U–OP bond in [UO₂(H₂O)₃(L)]²⁺ containing a bidentate CPO/PhCPO ligand.

(a) Donor and acceptor orbitals, and the stabilization interaction energies E⁽²⁾ (kcal/mol). (b) The hybrid atomic orbitals of the U–O bonds for uranyl complexes with 1:1 ligand/metal stoichiometry showing different binding motifs. OP and OC denote the phosphoryl and carbonyl oxygen atoms.

Donor		Acceptor	E(2) (kcal/mol)
[UO₂(H₂O)₄(L)]²⁺ L=CP O, motif I
	LP (1) OP	LV (3) U	9.67
	LP (2) OP	LV (3) U	9.80
	BD (1) U–OP	BD*(1) P–N	7.16
	LP (1) OP	BD*(1) U–O	7.32
[UO₂(H₂O)₄(L)]²⁺ L=CPO, motif II
	LP (1) OC	RY (1) U	13.87
	LP (1) OC	BD*(1) U–O	6.14
	BD (1) U–OC	BD*(1) N–C	11.02
[UO₂(H₂O)₃(L)]²⁺ L=CPO, motif III
	LP (1) OP	LV (2) U	6.37
	LP (1) OP	LV (3) U	5.00
	LP (1) OP	BD*(1) U–O	9.48
	LP (1) OC	LV (2) U	9.93
	LP (1) OC	LV (3) U	5.03
	LP (1) OC	BD*(1) U–O	5.10
	BD (2) U–OC	BD*(1) C–N	11.83

BD: bonding orbital; BD*: antibonding orbital; LP: lone-pair. RY: Rydberg orbital; LV: lone vacancy. For BD and BD*, (1) and (2) are the σand π orbitals respectively.

The hybrid form in Table 9 also offers some hints. For example, in [UO₂(H₂O)₃(L)]²⁺ with a bidentate CPO/PhCPO ligand, the U–OP bond contains 7% uranium character, composed of 52% 6d orbital and 28% 5f orbital, while, the U–OC bond contains 8% uranium character, composed of 52% 6d orbital and 29% 5f orbital. These results indicate that the uranium character of the U–OC bond is stronger than that of the U–OP bond, and the contribution of the 6d/5f orbitals to the U–OC bond is also higher than that to the U–OP bond in [UO₂(H₂O)₃(L)]²⁺ with a bidentate CPO ligand, while the contribution of the 6d/5f orbitals to the U–OC bond in [UO₂(H₂O)₄(L)]²⁺ with motif II is lower than that to the U–OP bond in [UO₂(H₂O)₄(L)]²⁺ with motif I.

The hybrid atomic orbitals of U–OP and U–OC bonds for uranyl complexes with 1:1 ligand/metal stoichiometry showing different binding motifs. OP and OC denote the phosphoryl and carbonyl oxygen atoms.

	U–OP	U–OC
[UO₂(H₂O)₄(L)]²⁺	92%O + 8%U	/
L=CPO, motif I	U: 50% 6d, 37% 5f
[UO₂(H₂O)₄(L)]²⁺	92%O + 8%U	/
L=CPO, motif II	U: 50% 6d, 36% 5f
[UO₂(H₂O)₃(L)]²⁺	93%O + 7%U	92%O + 8%U
L=CPO, motif III	U: 52% 6d, 28% 5f	U: 52% 6d, 29% 5f

3.3.2 Quantum theory of atoms in molecules.

Quantum theory of atoms in molecules is a useful tool for studying the interactions between atoms in a molecule based on electron densities and properties at the bond critical point (BCP) [36]. BCP is the (3, -1) saddle point on the electron density curvature being a minimum in the direction of the atomic interaction line and maximum in the two directions perpendicular to it. Based on the values of electron densities and their Laplacians at BCPs, interactions can be divided into shared (covalent bonds) and closed shell interactions (ionic bonds, hydrogen bonds and van der Waals interactions). The electron densities at BCP ρ(r) larger than 0.1 eÅ^-3 and the large negative Laplacians represent shared interactions, while ρ(r) in the 0.001–0.040 eÅ^-3 range and small positive Laplacians indicate closed shell interactions [43].

The electron densities and their Laplacians for the critical points of U–OC and U–OP bonds are shown in Table 10. In all cases, the Laplacian is positive, which indicates closed shell interactions. The U–OP bond in [UO₂(H₂O)₄(L)]²⁺ (L=CPO, motif I) has a larger ρ(r) value, and a less positive value of the Laplacian than the U–OC bond in [UO₂(H₂O)₄(L)]²⁺ (L=CPO, motif II), which indicates that the U–OP bond shows a higher degree of covalent character for [UO₂(H₂O)₄(L)]²⁺ (L=CPO, motif I) compared to the U–OC bond for [UO₂(H₂O)₄(L)]²⁺ (L=CPO, motif II). Depending on the values of the electron densities and their Laplacians at BCPs, the U–OP bond shows a lower degree of covalent character than the U–OC bond for [UO₂(H₂O)₃(L)]²⁺ (L=CPO, motif III). These results are consistent to the U-O bond lengths and NBO analysis results.

Electron densities (ρ(r), eÅ^-3) and Laplacians of the electron densities (▽²ρ(r), eÅ^-5) for the selected bond critical points for uranyl complexes with 1:1 ligand/metal stoichiometry showing different binding motifs. OP and OC denote the phosphoryl and carbonyl oxygen atoms.

complex	Bond	ρ(r)	▽²ρ(r)
[UO₂(H₂O)₄(L)]²⁺ L=CPO, motif I	OP–U	0.069	0.287
[UO₂(H₂O)₄(L)]²⁺ L=CPO, motif II	OC–U	0.068	0.294
[UO₂(H₂O)₃(L)]²⁺ L=CPO, motif III	OP–U	0.062	0.258
	OC–U	0.066	0.279

3.4 Substitution reactions between UO₂(CO₃)₃^4- and CPO

As uranium in seawater mainly exists as the very stable uranyl tri-carbonate complex, we also studied the coordination of substitution complexes from UO₂(CO₃)₃^4- and CPO. The geometry with monodentate binding motif was identified to be energetically more stable than the geometry with bidentate binding motif for [UO₂(CO₃)₂(CPO)]^2- (substitution complex with 1:1 ligand/U stoichiometry). [UO₂(CO₃)₂(CPO)₂]^2- and [UO₂(CO₃)(CPO)₂]^2- correspond to complexes with 2:1 ligand/U stoichiometry. All the optimized structures for [UO₂(CO₃)₂(CPO)₂]^2- and [UO₂(CO₃)(CPO)₂]^2- were depicted in Figure S4, and the relatively stable isomers are presented in Figure 5. [UO₂(CO₃)₂(CPO)₂]^2- is a six-coordinated complex with two monodentate CPO ligands. One CPO acts as monodentate ligand, and the other serves as bidentate ligand in [UO₂(CO₃)(CPO)₂]^2-. The ΔG values for the substitution reactions leading to [UO₂(CO₃)₂(CPO)]^2-, [UO₂(CO₃)₂(CPO)₂]^2-, and [UO₂(CO₃)(CPO)₂]^2- are all positive, as shown in Table 11. These results indicate that [UO₂(CO₃)₂(CPO)]^2-, [UO₂(CO₃)₂(CPO)₂]^2- and [UO₂(CO₃)(CPO)₂]^2- are difficult to form from UO₂(CO₃)₃^4- and CPO in aqueous solution at 298.15 K. Also, CPO shows weaker coordinating ability to uranyl than CO₃^2-.

Calculated changes in Gibbs free energies (ΔG, kcal/mol) that accompany the formation of [UO₂(CO₃)₂(CPO)]^2-, [UO₂(CO₃)₂(CPO)₂]^2-, [UO₂(CO₃)(CPO)₂]^2-, [UO₂(CO₃)₂(DCPO)]^3-, [UO₂(CO₃)₂(DCPO)₂]^4-, and [UO₂(CO₃)(DCPO)₂]^2- at 298.15 K.

Reactions	ΔG
[UO₂(CO₃)₃]^4- + CPO → [UO₂(CO₃)₂(CPO)]^2- + CO₃^2-	13.8
[UO₂(CO₃)₂(CPO)]^2- + CPO → [UO₂(CO₃)₂(CPO)₂]^2-	9.5
[UO₂(CO₃)₂(CPO)]^2- + CPO → [UO₂(CO₃)(CPO)₂]^2- +CO₃^2-	35.0
[UO₂(CO₃)₃]^4- + CPO → [UO₂(CO₃)₂(DCPO)]^3- + HCO₃^-	-13.8
[UO₂(CO₃)₂(DCPO)]^3- + CPO + H₂O → [UO₂(CO₃)₂(DCPO)₂]^4- +H₃O⁺	47.5
[UO₂(CO₃)₂(DCPO)]^3- + CPO → [UO₂(CO₃)(DCPO)₂]^2- + HCO₃^-	-8.3

Figure 5.

(Color online) Optimized structures of most energetically stable (a) [UO₂(CO₃)₂(CPO)]^2-, [UO₂(CO₃)₂(CPO)₂]^2-, and [UO₂(CO₃)(CPO)₂]^2- and (b) [UO₂(CO₃)₂(DCPO)]^3-, [UO₂(CO₃)₂(DCPO)₂]^4-, and [UO₂(CO₃)(DCPO)₂]^2-.

As shown above, CPO could very likely deprotonate in seawater. We further examined the substitution reactions from UO₂(CO₃)₃^4- and CPO leading to the formation of [UO₂(CO₃)₂(DCPO)]^3-, [UO₂(CO₃)₂(DCPO)₂]^4-, and [UO₂(CO₃)(DCPO)₂]^2-. All optimized geometries are presented in Figure S5 and the relatively stable isomers are shown in Figure 5. [UO₂(CO₃)₂(DCPO)]^3- shows a monodentate binding motif with DCPO coordinating to UO₂²⁺ through the OP atoms. [UO₂(CO₃)₂(DCPO)₂]^4- and [UO₂(CO₃)(DCPO)₂]^2- are six- and five- coordinated complexes respectively. The calculated changes in the Gibbs free energy for the substitution reactions leading to [UO₂(CO₃)₂(DCPO)]^3- and [UO₂(CO₃)(DCPO)₂]^2- are negative as shown in Table 11. This implies that CPO could deprotonate to replace CO₃^2- in UO₂(CO₃)₃^4- to form [UO₂(CO₃)₂(DCPO)]^3- and [UO₂(CO₃)(DCPO)₂]^2-. [UO₂(CO₃)₂(DCPO)₂]^4- is thermodynamically unfavorable in the reaction between [UO₂(CO₃)₂(DCPO)]^3- with CPO mainly due to steric hindrance.

4. CONCLUSION

In this study, we examined the geometrical and electronic structures, and the thermodynamic stabilities of uranyl complexes with CPO or PhCPO using DFT calculation methods. When CPO/PhCPO serves as a monodentate ligand, UO₂²⁺ interacts with the OP atom indicating that the electron-donating ability of OP is stronger than that of the OC atom. However, when CPO acts as a bidentate ligand, the U–OC bond plays a leading role in the interaction between UO₂²⁺ and CPO/PhCPO. This may be caused by the significant charge transfer from the U–OC bond orbital to the C–N antibond orbital. Additionally, the uranium character of the U–OC bond is stronger than that of the U–OP bond, and the U–OC bond shows a higher degree of covalent character. However, for [UO₂(H₂O)₃(DL)]²⁺ (DL= DCPO/DPhCPO), the U–OP bonds play a leading role in the interaction between UO₂²⁺ and DCPO/DPhCPO, because the deprotonation of CPO/PhCPO causes more electrons to gather at the phosphoryl group resulting in stronger bonds between U and the phosphoryl oxygen atoms of DCPO/DPhCPO. The deprotonated CPO/PhCPO shows a higher affinity for UO₂²⁺ than the neutral CPO/PhCPO as expected. According to the ΔG values, the bidentate binding motif is favored over the monodentate binding motif for uranyl complexes with CPO/PhCPO. Anchoring a phenyl substituent at the terminal nitrogen atom of CPO exerts a slightly negative effect on the interaction between UO₂²⁺ and PhCPO. The entropy exerts a positive effect on the interaction between UO₂²⁺ and CPO/PhCPO if CPO/PhCPO acts as a bidentate ligand. However, if CPO/PhCPO serves as a monodentate ligand, the entropy exerts a negative effect.

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