Impact of Lewis Base on Chemical Reactivity and Separation

Article pubs.acs.org/JPCA

Impact of Lewis Base on Chemical Reactivity and Separation Efficiency for Hydrated Fourth-Row Transition Metal (II) Complexes: An ONIOM DFT/MM Study Dingsheng He* and Ming Ma College of Chemistry and Chemical Engineering, Hunan Normal University, Changsha, 410081, P. R. China ABSTRACT: In this paper, two-layer ONIOM combinations of high-level quantum mechanics (QM) and inexpensive molecular mechanics (MM) are successfully used to investigate the structural characters of metal (M, all the transition metals in the fourth period)−H2O−Lewis base (A−) complexes. Global and local descriptors of chemical reactivity and selectivity from conceptual density functional theory are employed to show the properties of the active complexes of M(H2O)2A2 and to study the effect of the Lewis base for the separation of transition metal ions. It is shown that chemical potential, hardness, electrophilicity, as well as the dual and multiphilic descriptors are adequate for characterizing the global and local reactivity trends of the M(H2O)2A2 complex. It is found that the reactivity is well localized at the metallic center in M(H2O)2A2 and the dual descriptor (Δf M(r)) can also be used to characterize the directional attack of the electrophile and nucleophile except for the selectivity of the reaction. On the basis of the values of ωM and Δsk, and the sign of Δf M(r), the selectivity of the nucleophilic reagent (R−) for M(II) in M(H2O)2A2 (from high to low) follows this order: Cu(II) > Ni(II) > Co(II) > Fe(II) ≫ Mn(II) > Zn(II) > Cr(II). The Lewis base (A−) improves chemical reactivity and selectivity because of changing the reaction path and forming an intermediate, which possesses the higher antibonding character and the larger HOMO/LUMO gap. NBO or AIMALL analysis and Frontier orbital theory results presented here provided more theoretical support for the above reactivity and selectivity studies.

1. INTRODUCTION The concept of stability and reactivity is fundamental to understanding chemistry.1,2 The stability of reactants or products and reactivity in reactions is recognized as the cornerstone in modern organic synthesis, preparation of pharmaceuticals and new materials, separation science, and so on. It exerts considerable influence on the efficiency of chemical reactions. Consequently, the study of stability and reactivity for chemical reactions is of paramount significance. The efficiency of chemical reactions is determined by the preference of a reaction for a particular product and its associated reaction rate. Our experiments showed that the striking rate acceleration and high selectivity of chemical reactions were obtained when some specific Lewis base was added into the reaction between bidentate ligands and hydrated transition metal ions for the fourth period.3 More interestingly, the Lewis base used is of low usage concentration, at the range of 10−4 mol/L, serving like catalysts. These excellent characteristics promote us to explore the microscopic structure of the system that might have influenced both the stability and reactivity for chemical reaction. Generally speaking, the microscopic structure analysis provides the basis for understanding the impact of the structure on stability and reactivity. A lot of studies in the literature have demonstrated the ability of computational chemistry. It is well-known that molecular orbital theory (MOT) and density functional theory (DFT) are © 2014 American Chemical Society

strong tools, complementary to experiments. The orbital and electron density can help us to understand molecular structures and to predict reactivity. Apart from the Diels−Alder reaction and the catalytic system, there are a lot of other types of reactions and phenomena where DFT has been used and is being used until now. However, early studies are relatively less concerned with the molecules containing heavy transition metal ions because of the insurmountable computational costs required by the structural optimization. Substantial deduction of computational expenses can be achieved if hybrid methods are employed. These hybrid methods combine the accuracy of a QM method (accurate ab initio quantum mechanics) with the low expenditure of MM methods (molecular mechanics (MM) methods).3 The ONIOM method is a common hybrid method. It divides the system into two layers in this study, treating the high layer with the high-level QM (HQ = B3LYP/6-31 + G*), while the low layer can be treated with a less expensive method (MM (UFF)). Conceptual DFT has been generally used to examine the chemical reactivity and the site selectivity of molecular systems. The chemical potential μ, global hardness η, and electrophilicity index ω are global descriptors. They are used to test the Received: January 15, 2014 Revised: April 2, 2014 Published: April 2, 2014 2984

dx.doi.org/10.1021/jp500447m | J. Phys. Chem. A 2014, 118, 2984−2994

The Journal of Physical Chemistry A

Article

reactivity of chemical species. Fukui functions f kα, local electrophilicity indices ωk, local softness, and dual descriptor Δf are local descriptors. They can predict the selectivity of a chemical species in reaction.4,5 In this paper, we consider the practical separation process on how to enhance the separation efficiency of transition metals in the fourth period. In specifics, we consider the impact of the Lewis base, bis(2-ethylhexyl) sulfosuccinate (C20H37O7SNa, abbreviation OT, NaA, HA, and A−), and the bidentate ligand, 1-phenyl-3-methyl-4-benzoyl-pyrazolone-5 (abbreviation HPMBP, HR, and R−). Our task is to analyze the reaction characteristics of the Lewis base OT and provide the theoretical explanations for the impact of the base on separation efficiency.6 Namely, we will answer the following two questions: (1) Why can the Lewis base OT remarkedly improve the coordination reaction reactivity and selectivity of bidentate ligand for the transition metal ions in the fourth period? (2) How do we predict reactivity and selectivity based on the structure of the reactants and intermediates. With these questions answered, we should understand the characteristics of this system. Although in this study we only consider the reactions of two reactants (OT and HPMBP) with the transition metal ions in the fourth period, this paper presents the pathway for us to analyze and predict the reactivity and selectivity of other related reactions important to chemical synthesis, new materials, separation fields, and so on.

ω=

⎛ ∂E ⎞ 1 ⎜ ⎟ = − (I + A ) ⎝ ∂N ⎠ν 2

⎛ ∂ 2E ⎞ ⎛ ∂μ ⎞ η = ⎜ 2⎟ = ⎜ ⎟ = I − A ⎝ ∂N ⎠ν ⎝ ∂N ⎠ν

⎛ ∂μ ⎞ ⎛ ∂ρ(r ) ⎞ f (r ) = ⎜ ⎟ =⎜ ⎟ ⎝ ∂N ⎠ν(r) ⎝ ∂ν(r ) ⎠ N

η = εL − εH

(4)

1 2η

(5)

S=

(8)

f k− = qk (N ) − qk (N − 1)

(9)

ωk = ωf k+

(10)

where it is used to exhibit reactivity and selectivity for reactions involving electrophile−nucleophile interactions.15 On the basis of the literature and frontier molecular orbital energies, a parameter, ΔE, is defined as16−18 ΔE = LUMOreactant 1 − HOMOreactant 2

(11)

where the energy difference between the LUMO and HOMO, ΔE, is used to assess reactivity of a chemical reaction. Generally, the LUMO−HOMO gap is an indicator of the reactivity of the reactant molecules in the reaction. Because the LUMO−HOMO gap is approximated, the reactants with a smaller LUMO−HOMO gap are more reactive than those with a higher LUMO−HOMO gap. 2.2. Dual Descriptor Δf(r). Reference 13 proposed a dual descriptor (Δf(r)) as the index of selectivity to characterize both the nucleophilic and electrophilic reactions. It is expressed as

(2)

(3)

f k+ = qk (N + 1) − qk (N )

where qk(N + 1), qk(N), and qk(N − 1) stand for the gross NBO population on atom k in a molecule with N + 1, N, and N − 1 electrons, respectively. High values of f(r) are related to a highly electrophilic/nucleophilic center. In other words, the Fukui function f(r) indicates the capacity of a molecular site to accept or donate electrons. A local electrophilicity index ωk is defined as

(1)

εL + εH 2

(7)

On the basis of population analysis, Yang and Mortier14 proposed the condensed forms of Fukui functions under the finite difference approximation. For systems with electron gain or donation, the condensed-to-atom Fukui function, respectively, is expressed as

where E is the total energy of the system, N is the number of electrons in the system, ν is the external potential, I is the first ionization potential, and A is electron affinity. Here, I = EN−1 − EN and A = EN+1 − EN, where EN+1, EN−1, and EN denote the total energies of the system with N + 1, N − 1, and N electrons, respectively. Furthermore, on the basis of Janak’s theorem,5,11 I and A can be replaced by εH and εL (the frontier molecular orbital energies for HOMO and LUMO), respectively. Chemical potential, μ, global hardness, η, and global softness, S, can thus be defined as μ=

(6)

To describe the region selectivity of a chemical reaction, the Fukui function4,13 is defined as

2. THEORETICAL BACKGROUND 2.1. General Definitions. The conceptual DFT reactivity index is a key concept associated with the reaction mechanism because it facilitates the comprehensive understanding of chemical reactions to develop new species and novel materials. On the basis of conceptual DFT,7−11 we used the chemical potential μ and global hardness η. They are defined as μ = −χ =

μ2 2η

Δf (r ) = f + (r ) − f − (r ) ≈ ρ LUMO (r ) − ρ HOMO (r )

(12)

One can notice that the sign of the dual descriptor is very important to characterize the reactivity of a site within a molecule. For a site with Δf(r) > 0, a nucleophilic attack governs the reaction at the site, whereas, for a site with Δf(r) < 0, an electrophilic attack governs the reaction at the site. For the kth atom in a molecule, the condensed dual descriptor is expressed as follows: Δfk (r ) = f k+ (r ) − f k− (r )

(13)

Condensed-to-atom softness can easily be computed on the basis of the following relation5,13 ⎛ ∂ρ(r ) ⎞ ⎛ ∂ρ(r ) ⎞ ⎛ ∂N ⎞ s (r ) = ⎜ ⎟ ⎜ ⎟ = S · f (r ) ⎟ =⎜ ⎝ ∂μ ⎠ν(r) ⎝ ∂N ⎠ν ⎝ ∂μ ⎠ν

Parr et al.12 have presented the electrophilicity index ω which evaluates the capability of an electrophile to accept the maximal number electrons if the electron sea provides enough electrons 2985

(14)


The Journal of Physical Chemistry A Δsk = S ·Δfk = S(f k+ − f k− )

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In the reference, two other reactivity descriptors, “relative electrophilicity” and “relative nucleophilicity”, have some conceptual similarity with the dual descriptor and also help to locate the preferable reactive sites.13 2.3. Atoms in Molecules.19−22 The gradient vector, ∇ρ, of the electron density is very important. We define the critical points in the charge density distribution where ∇ρ(r) = 0. There are four types of stable critical points: (3, −3) [nuclear critical point (NCP)], (3, −1) [bond critical points (BCPs)], (3, +1) [ring critical points (RCPs)], and (3, +3) [cage critical points (CCPs)]. We are particularly concerned with the properties evaluated at the BCPs, RCPs, and CCPs, e.g., the charge density ∇ρb and the Laplacian ∇2ρb evaluated at the BCP, respectively. Diagonalization of the Hessian matrix results in the coordinate invariant (ordered) eigenvalues λ1 < λ2 < λ3. λ1, λ2, and λ3 are the three curvatures of the density at the critical point. λ1 and λ2 are negative and perpendicular to the bond path (by convention, |λ1| > |λ2|), whereas the third, λ3, is positive and lies along the bond path. The ellipticity, ε, is a measure of the accumulation of charge in the two directions perpendicular to the bond path at a BCP: ε = λ1/λ 2 − 1

Figure 1. Schematic description of the structure of the ligands: red spheres, oxygen atoms; yellow sphere, sulfur atom; blue spheres, nitrogen atoms; gray and large spheres, carbon atoms; gray and small spheres, hydrogen atoms. (a) Manoxol OT (abbreviation OT or NaA or HA, A− is the residual after H+ is ionized from hydroxyl; OT contains 66 atoms) and (b) HPMBP (1-phenyl-3-methyl-4-benzoylpyrazolone-5, abbreviation HR, R− is the residual after H+ is ionized from hydroxyl).

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The above parameters are used to analyze the bonding interactions. For other concepts and terminologies on AIMAll theory, we should consult the refs 21 and 22.

3. COMPUTATIONAL DETAILS For M(H2O)42+ and MR2, the single-layer ONIOM is used in the calculation. Figure 1 displays the structure of A− and R− anions. All the computational studies were performed at the DFT/B3LYP level with the Gaussian 03 package.23,24 After optimizations, no imaginary frequency in the optimized conformations was found. In calculations, the mixed basis set (economic basis set) has been used. The 3-21G basis set was used for the hydrogen, carbon, and nitrogen atoms, the 631+G* basis set for the oxygen atom in the ligand molecule, the 6-311+G* basis set for the S atom, and the 6-31G* basis set for all the transition metal ions (M(II)). In this way, the mixed basis set meets the needs of accurate calculations for thermodynamic data. For M(H2O)42+, M(H2O)2A2, and MR2, various spin states have been tested. Table 1 shows that the high multiplicities are most stable for Sc(II)(2S + 1 = 2), Ti(II)(2S + 1 = 3), V(II)(2S + 1 = 4), Cr(II)(2S + 1 = 5), Mn (II)(2S + 1 = 6), Fe(II)(2S + 1 = 5), Co(II)(2S + 1 = 4), Ni(II)(2S + 1 = 3), Cu(II)(2S + 1 = 2), and Zn(II)(2S + 1 = 1). We employed the most stable spin state for each of the complexes in the present study. For M(H2O)2A2, we have finished the computations with both single-layer and two-layer ONIOM methods. Figure 2 illustrates the basic concept of the two-layer ONIOM (high:low). For the high layer containing a metal ion, two H2O molecules, and two groups (−SO3), a total of 15 atoms, our calculation at the UB3LYP/6-31+G* level has been completed (for Zn(H2O)2A2, RB3LYP), whereas for the low layer containing 122 atoms, the low cost molecular mechanics (MM) level, UFF, is used. Reference 6 demonstrated that solvent molecules (water) have little impact on the DFT reactivity indices. Consequently, we employ a rather simplified, gas-phase-like model, where the Lewis base is represented by one single molecule interacting

directly with complex ions. Similar models of this kind have also been proposed elsewhere in the literature.17,18 Natural bond orbital (NBO) analysis was performed at the B3LYP level of theory using NBO program 5.0,25 providing information about orbital occupancies, percentage bonding, nonbonding, and antibonding character of each MO and orbital energies for the donor and acceptor orbitals. To characterize the topological properties of complexes, atoms in molecules (AIM) analysis was carried out using AIMAll (version 13.05.06).26

4. RESULTS AND DISCUSSION 4.1. The Coordination Reaction Mechanism of M(II) Ions in the Presence of OT. The experiments have shown that a striking rate acceleration and higher selectivity can be obtained when Lewis base OT is added into the reaction between 1-phenyl-3-methyl-4-benzoyl-pyrazolone-5 and the hydrated transition metal ions in the fourth period. We have carefully investigated the structural characteristics of the complex containing OT by DFT computations. In the presence of OT, the coordination reaction mechanism of M(II) ions is generally supposed as follows:27 HA org = HA aq (17) HA aq = Haq + + A aq −

(18)

HR org = HR aq

(19)

+

HR aq = Haq + R aq 2986

−

(20)



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Table 1. Comparison of Energy for Different Spin States of Different Transition Metals in M(H2O)2A2 M(II)

charge:(2S + 1)/energy (au)

Sc (d1) Ti (d2) V (d3) Cr (d4) Mn (d5) Fe (d6) Co (d7) Ni (d8) Cu (d9) Zn (d10)

0:2/−4324.072 09 0:3/−4412.782 72 0:4/−4507.317 55 0:5/−4607.773 04 0:6/−4714.291 23 0:5/−4826.950 17 0:4/−4945.978 27 0:3/−5071.487 22 0:2/−5203.607 16 0:1/−5342.460 21



0:1/−4412.732 56 0:2/−4507.245 30 0:3/−4607.706 38 0:4/−4714.226 76 0:3/−4826.905 75 0:2/−4945.917 75 0:1/−5071.426 29

0:1/−4607.657 06 0:2/−4714.170 97 0:1/−4826.844 07

answer, we shall carefully analyze the reaction trend for the above reactions from the different chemical theories. First, we consider the order M(H 2O)4 2 + → M(H 2O)2 A 2 → MR 2

4.2. Analysis of the Reaction Trend of M(H2O)42+ → M(H2O)2 → MR2. 4.2.1. Reactivity Indices and Structural Parameters. Table 2 indicates the reactivity difference between the M(H2O)2A2 complexes through the comparison of their DFT reactivity indices and FMO (frontier molecule orbital) energies.28 If the Fukui function f +M possesses a larger value, it reflects that the M atoms can accept more electrons in a nucleophilic attack. Similarly, if f −M possesses a large value, it shows that the M atom can donate more electrons in a electrophilic attack. Thus, the Fukui functions provide information about the site reactivity within a molecule. In Table 2, we notice that (i) Δf M(r) < 0 for d1 → d3 and Δf M(r) > 0 for d4 → d10. When Δf M(r) > 0, the process is driven by a nucleophilic attack on atom M and this atom acts as an electrophilic species; conversely, when Δf M(r) < 0, the process is driven by an electrophilic attack over atom M and it acts as a nucleophilic species. This result indicates that M(H2O)2A2 (M = d1 → d3) is preferentially reacting with an electrophilic reagent but for M = d4 → d10 it is preferential to react with a nucleophilic reagent. This implies that the low oxidation states (M(II)) can be changed to the higher oxidation states (M = d1 → d3), whereas M(II)(d4 → d10) is relatively stable for M(H2O)2A2. This conclusion is consistent with the experimental results. Table 2 shows that the nucleophilic reagent (R−) does not react with M(H2O)2A2 (M = d1 → d3) and easily reacts with M(H2O)2A2 (M = d4 → d10). (ii) For the M(H2O)2A2 molecules containing Cu(II), Ni(II), Co(II), and Fe(II), respectively, they always have a larger electrophilicity index ω and smaller global hardness η, confirming that all the M(H2O)2A2 (M = Cu(II), Ni(II), Co(II), and Fe(II)) complexes are more reactive than the M(H2O)2A2 complexes (M = Zn(II), Mn(II), Cr(II), V(II), Ti(II), and Sc(II)). (iii) The LUMO energies of the M(H2O)2A2 (M = Cu(II), Ni(II), Co(II), and Fe(II)) molecules are lower than those of the M(H2O)2A2 molecules (M = Zn(II), Mn(II), Cr(II), V(II), Ti(II), and Sc(II)). The lower energy for the LUMO is more significant, justifying that Cu(II), Ni(II), Co(II), and Fe(II) ions in M(H2O)2A2 serve mainly as electron acceptors in the nucleophilic reaction and more easily accept electrons than the other transition metal ions in the fourth period. (iv) Because ωM and Δsk well incorporate the global and local properties that are related to the reactivity and the selectivity of chemical systems, on the basis of the values of ωM or Δsk and the sign of

Figure 2. Two-layer ONIOM.

M(H 2O)4aq 2 + + 2A aq − = M(H 2O)2 A 2aq + 2H 2Oaq (21) −

M(H 2O)2 A 2aq + 2R aq = MR 2aq + 2H 2Oaq + 2A aq

−

(22)

MR 2aq = MR 2org

(23)

Equations 21 and 22 indicate that the coordination reaction of M(II) ions occurs through the two steps in the presence of OT. If reaction eqs 21 and 22 are summed together, the total reaction equation is the following: M(H 2O)4aq 2 + + 2R aq − = MR 2aq + 4H 2Oaq

(25)

(24)

where aq and org stand for aqueous phase and organic phase, respectively. On the basis of eqs 21, 22, and 24, M(H2O)2A2 is an intermediate product. Figure 3 shows that the Lewis base

Figure 3. The description of the reaction mechanism for eqs 21, 22, and 24.

(A−) in the above reactions alters the reaction pathway. From the above equations, we can understand why the usage concentration of OT in the organic phase is such a low value. Equation 24 also indicates that the coordination reaction of M(II) hydrated ions only contains one step in the absence of OT. Simultaneously, we can understand why OT can accelerate the coordination reaction and obviously improve the selectivity of reaction in comparison with the absence of OT. To find the 2987



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Table 2. Calculated DFT Reactivity Indices and the Frontier Molecular Orbital Energies (au) for M(H2O)2A2 at the B3LYP/ Oniom global properties (in gas phase)

local properties (in gas phase)

M (3dn)

HOMO

LUMO

μ

η

ω

f +M

ωM

ΔSM

Δf M(r)

Sc(II) (d1) Ti(II) (d2) V(II) (d3) Cr(II) (d4) Mn(II) (d5) Fe(II) (d6) Co(II) (d7) Ni(II) (d8) Cu(II) (d9) Zn(II) (d10)

−0.276 −0.278 −0.277 −0.279 −0.278 −0.238 −0.279 −0.282 −0.275 −0.277

−0.053 −0.051 −0.057 −0.058 −0.059 −0.094 −0.108 −0.132 −0.160 −0.049

−0.164 −0.164 −0.167 −0.169 −0.169 −0.166 −0.193 −0.207 −0.218 −0.163

0.224 0.228 0.220 0.220 0.220 0.143 0.171 0.149 0.116 0.228

0.060 0.059 0.063 0.065 0.065 0.096 0.109 0.144 0.204 0.058

0.749 0.497 0.340 0.347 0.423 0.350 0.533 0.544 0.532 0.347

0.045 0.029 0.022 0.022 0.027 0.034 0.058 0.078 0.109 0.020

−0.152 −0.038 −0.142 0.711 0.980 1.173 1.604 1.799 2.459 0.758

−0.068 −0.017 −0.062 0.313 0.431 0.336 0.550 0.537 0.569 0.346

Δf M(r), the selectivity of R− for M(II) in M(H2O)2A2 (from high to low) follows this order:

products should have a larger η and smaller ω. However, because during any chemical reaction there is structural and electronic reordering, the external potential hardly remains constant. Generally speaking, the dual descriptor (Δf M(r)) not only provides useful information on chemical reactions between a nucleophile and an electrophile but also helps to identify the electrophilic/nucleophilic behavior of a specific site within a molecule. For complicated molecules containing many atoms, especially containing transition metals, we recommend the dual descriptor (Δf M(r)), Δsk, and ωM to characterize the site reactivity and selectivity within a molecule. Figure 5 shows the isosurface at 0.0004 au of the dual descriptor for the M(H2O)2A2 molecules (M = Ni and Ti), respectively. As already shown, molecular sites with Δf(r) > 0 are expected to be electrophilic, whereas molecular centers with Δf(r) < 0 are expected to be nucleophilic. The zone with Δf(r) > 0 is represented in blue and the areas with Δf(r) < 0 in red. Thus, Figure 5 can be seen as a map of the nucleophilic/ electrophilic behavior of the different sites within the molecule. From Figure 5, we get the following information: (i) For Ni(H2O)2A2, the blue areas (Δf(r) > 0) are localized over the metallic center (Ni), thus indicating its aptitude to accept a nucleophilic attack. However, it has three blue areas indicating the nucleophilic attack from three different directions toward Ni(II) (only two blue areas are indicated in Figure 5b). One is driven by a nucleophilic attack directly on the Ni atom, and the other two are directly on O1 or O3 in water molecules which coordinate to Ni(II). This fact also shows that Δf k is used successfully to characterize the directional attack of the electrophile and nucleophile except for the selectivity of the reaction. Figure 5a and b demonstrates that the nucleophilic attack is a main reaction and has a good stereoselectivity. The Δf(r) functions calculated for M(H2O)2A2 (M = Cu, Co, Fe, and Mn) are the same as those for Ni(H2O)2A2 in Figure 5a and b. (ii) Considering Ti(H2O)2A2, the blue and red areas do not emerge highly and concentratedly within the specific site of the molecules indicating the worst selectivity. For M(H2O)2A2 (M = Cr, V, Sc, and Zn), their Δf(r) functions are the same as those in Figure 5c and d. 4.2.2. Frontier Orbital Theory and Secondary Orbital Interactions. On the basis of the frontier orbital theory, the most important molecular orbitals are the highest filled orbital (HOMO) of one reactant and the lowest unfilled orbital (LUMO) of the other reactant. We consider the two orbitals which are the closest orbitals in energy. A fundamental assumption of perturbation molecular orbital theory (PMO) is that interactions are strongest between

Cu(II) > Ni(II) > Co(II) > Fe(II) ≫ Mn(II) > Zn(II) > Cr(II)

This selectivity order does not contain the Sc(II), Ti(II), and V(II) because they are not stable. (v) In eqs 4, 5, 6, 10, and 15, it indicates that the structural parameters of central metal ions and ligands determine the DFT reactivity indices and the FMO (frontier molecule orbital) energies and solvent do not exhibit a distinct effect on them. Figure 4 indicates a good correlation between [ϕLUMO(M(H2O)2A2) − ϕHOMO(R−)] and Δsk or ωM. This verifies that

Figure 4. Linear correlation between the ωM or ΔSM descriptors and the gap energy (ΔE = ϕLUMO(M(H2O)2A2) − ϕHOMO(R−)) (M = Cu, Ni, Co, Fe, and Mn).

the metal elements (M = Mn, Fe, Co, Ni, and Cu) in M(H2O)2A2 should possess a stable oxidation state for satisfying a good correlation. Only in the condition of the stable oxidation state for M, the gap energy for [ϕLUMO(M(H2O)2A2) − ϕHOMO(R−)] is the function of perturbation when the R− anions approach M(H2O)2A2. For the metal elements in Table 2 (d5 → d9), they have a stable oxidation state (+2), whereas, for Cr, V, Ti, and Sc elements in M(H2O)2A2, their high oxidation states (Cr(III), V(V or IV), Ti(III), and Sc(III)) are stable. A more reactive species (reactant or product) possesses a smaller η and larger ω, and conversely, a more stable species has a larger η and smaller ω. It is expected that the needed 2988



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Figure 5. Δf(r) calculated at two-layer ONIOM combinations of high-level QM (HQ = B3LYP/6-31+G*) and MM (UFF). Isosurfaces at 0.0004 au of the dual descriptor (total electronic density) in blue are the electrophilic regions, and those in red are the nucleophilic regions. (a and b) For Ni(H2O)2A2 (transparent and mesh); (c and d) for Ti(H2O)2A2 (transparent and mesh).

ϕHOMO(A−) ≈ 0.575σO5 − 0.579σO4 − 0.573σO6

orbitals that are close in energy. Frontier orbital theory suggests that these strong initial interactions guide the course of reaction as it proceeds to completion. Let us illustrate these ideas. Figure 6 is the PMO description of the interaction between A− and

(26)

On the basis of NBO, ϕHOMO(A−) has primarily (>99.8%) nonbonding character (lone electron pair in O5, O4, and O6 atoms, respectively), reflecting the highly concentrated electronic density on the oxygen atoms in S−O bonds from A−, whereas ϕLUMO(M(H2O)42+) (M = Zn, Cu, Ni, Co, Fe, and Mn) in Table 3 has a higher antibonding character than that of M(H2O)42+ (M = Cr, V, Ti, and Sc). The antibonding character from ϕLUMO(M(H2O)42+) shows a repulsion between the electrons in antibonding orbitals (π*) from ϕLUMO(M(H2O)42+) and the electrons from ϕHOMO(A−). When A− anions continually approach M(H2O)42+, it is important to consider the proximity that can be achieved by the orbitals within the limits of the geometry of the reacting molecules. The proximity affects and alters the charge density distributions and the energy in the two reactant molecules. This results in the strong interaction between M(H2O)42+ and A−. As a result, the strong interaction activates the reactant molecules. In other words, the activation means that the M−O bond is weakened in M(H2O)42+ and the partial overlap between ϕLUMO(M(H2O)42+) and ϕHOMO(A−) takes place. If the ϕLUMO(M(H2O)42+) fully accepts the electrons from the ϕHOMO(A−) molecular orbital, the repelling from the electrons between ϕLUMO(M(H2O)42+) and ϕHOMO(A−) should attain the maximum. In the end, the old bonds rupture and the new bonds form. The strong interactions give rise to the formation of M(H2O)A2. However, the repelling between ϕLUMO(M-

Figure 6. The PMO description of the interaction between A− anion and M(H2O)42+.

M(H2O)42+. The conclusion from Figure 6 is that an electrophile (M(H2O)42+) will undergo a greater stabilizing attraction on approaching A−. NBO analysis indicates that the HOMO electrons for A− are mainly localized on the O atoms (from the S−O bond in A−). When the A− anion approaches M(H2O)42+, the perturbation takes place. Because the LUMO of M(H2O)42+ is the low energy, empty orbital, it is a better acceptor of the electrons from the HOMO of attacking A− anions. According to NBO analysis,29,30 the HOMO of A− is a strong mixture of σO (NBO) with approximate composition: 2989



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Table 3. Comparison of the LUMO of M(H2O)42+, M(H2O)2A2, and MR2 (in the Gas Phase) LUMO for M(H2O)42+

LUMO for M(H2O)2A2

LUMO for MR2

M (3dn for M)

bonding (%)

nonbonding (%)

antibonding (%)

bonding (%)

nonbonding (%)

antibonding (%)

bonding (%)

nonbonding (%)

antibonding (%)

Sc(II) (d1) Ti(II) (d2) V(II) (d3) Cr(II) (d4) Mn(II) (d5) Fe(II) (d6) Co(II) (d7) Ni(II) (d8) Cu(II) (d9) Zn(II) (d10)

0.000 0.002 0.004 0.013 0.000 0.000 0.000 0.001 0.001 0.001

1.000 0.994 0.993 0.961 0.735 0.707 0.697 0.731 0.703 0.742

0.000 0.004 0.003 0.026 0.264 0.293 0.303 0.268 0.296 0.256

0.007 0.003 0.002 0.019 0.005 0.013 0.006 0.016 0.017 0.008

0.685 0.868 0.968 0.245 0.640 0.233 0.606 0.187 0.152 0.711

0.308 0.128 0.031 0.736 0.355 0.754 0.388 0.797 0.831 0.281

0.183 0.169 0.144 0.139 0.140 0.141 0.143 0.145 0.022 0.150

0.356 0.364 0.197 0.201 0.199 0.200 0.205 0.206 0.937 0.534

0.461 0.466 0.658 0.659 0.661 0.660 0.653 0.649 0.041 0.316

Table 4. Comparison of the Gap between the LUMO and HOMO Energy for Two Reactants ϕLUMOM(H2O)42+ − ϕHOMO(A−) for eq 21 ϕLUMO(M(H2O)2A2 − ϕHOMO(R−) for eq 22 ϕLUMO(M(H2O)42+) − ϕHOMO(R−) for eq 24 M

3dn for M

ΔE (au)

ΔE (au)

ΔE (au)

Sc(II) Ti(II) V(II) Cr(II) Mn(II) Fe(II) Co(II) Ni(II) Cu(II) Zn(II)

3d1 3d2 3d3 3d4 3d5 3d6 3d7 3d8 3d9 3d10

−0.2508 −0.2651 −0.3031 −0.3094 −0.2845 −0.3254 −0.3352 −0.3780 −0.4153 −0.2823

0.0070 0.0103 −0.002 92 0.0126 −0.000 82 −0.0351 −0.0417 −0.0544 −0.0953 0.0147

−0.2952 −0.3095 −0.3475 −0.3538 −0.3289 −0.3698 −0.3796 −0.4224 −0.4593 −0.3263

(H2O)42+) (M = Zn, Cu, Ni, Co, Fe, and Mn) and ϕHOMO(A−) is stronger than that between ϕLUMO(M(H2O)42+) (M = Cr, V, Ti, and Sc) and ϕHOMO(A−) because of the different antibonding character in ϕ LUMO (M(H 2 O) 4 2+ ) and the electronic configuration and number of d electrons in the transition metal ions. From the above analysis, we also see why M(H2O)2A2 (M = Zn, Cu, Ni, Co, Fe, and Mn) is more easily generated than the formation of other M(H2O)2A2 molecules (M = Cr, V, Ti, and Sc). For M(H2O)2A2 in Table 3, the LUMOs for Cu(II), Ni(II), and Fe(II) possess high antibonding character, whereas the other transition metals in the fourth period have relative low antibonding character. For MR2, the LUMOs from V(II)(d3) to Ni(II)(d8) have almost the same values of antibonding character. The residual transition metals (d1, d2, d9, and d10) have lower antibonding character. This implies that the MR2 molecules containing the transition metals (d1, d2, d9, and d10) are relatively stable compared with the MR2 molecules having higher antibonding character. Let us consider an interesting example. In Table 3, ϕLUMO(Cu(H2O)2A2) and ϕLUMO(Zn(H2O)2A2) possess 83.1 and 28.1% antibonding character, respectively. When the R− anion approaches M(H2O)2A2, the repelling from the electrons between ϕLUMO(Cu(H2O)2A2) and ϕHOMO(R−) is the strongest compared with ϕLUMO(Zn(H2O)2A2). According to the above analysis, we can arrive at the similar conclusion that Cu(H2O)2A2 is more reactive than Zn(H2O)2A2 and CuR2 is more easily generated than ZnR2. For M(H2O)42+ in Table 4, the gap energies for [ϕLUMO(M(H2O)42+) − ϕHOMO(A−)] are negative. This shows that the energy of ϕLUMO(M(H2O)42+) is lower than that of ϕHOMO(A−) and the reaction between M(H2O)42+ and A− can easily take

place. For M(H2O)2A2, the gap energies between [ϕLUMO(M(H2O)2A2) − ϕHOMO(R−)] are negative for M = Cu(II), Ni(II), Co(II), and Fe(II), whereas they are positive for M = Zn(II), Cr(II), Ti(II), and Sc(II). The positive gap energy indicates that the reaction between M(H2O)2A2 and R− is forbidden, and the negative gap energy shows that the reaction between M(H2O)2A2 and R− is not forbidden. In other words, the negative gap energy reflects that the electrons in ϕHOMO(R−) should enter into ϕLUMO(M(H2O)2A2) with lower energy (M = Cu(II), Ni(II), Co(II), and Fe(II)), whereas the positive gap energy reflects that the electrons in ϕHOMO(R−) should enter into ϕLUMO(M(H2O)2A2) with higher energy (M = Zn(II), Cr(II), Ti(II), and Sc(II)), compared with ϕHOMO(R−). Especially, for Mn(II) and V(II), the gap energies are −0.00082 au (−2.15 kJ/mol) and −0.00292 au (−7.67 kJ/ mol), respectively. This indicates that the smaller gap energy goes against the reactions between M(H2O)2A2 (M = Mn(II) and V(II)) and R−. Table 4 also indicates that the energy gap between the LUMO and HOMO for Cu in eq 22 is about one-fourth that for Cu in eqs 21 and 24, respectively. Undoubtedly, the falloff of the gap energy and the repelling from the electrons between ϕLUMO(M(H2O)2A2) and ϕHOMO(R−) give the better explanations for the difference of the reaction rate and the selectivity in eq 22. For eq 24 in Table 4, the negative values show that the R− anions can react with all the hydrated metal ions in the fourth period and the reaction selectivity for eq 24 is very poor. We must remember that the gap energies between the LUMO and HOMO in Table 4 are computed on the basis of the optimized structures of the reactant molecules. When A− or R− approaches M(H2O)42+, the perturbation gives rise to the changes of the gap energies between LUMO and HOMO for 2990



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Table 5. Some Significant Donor−Acceptor (O → M or M → O) Natural Bond Orbital Interactions and Their Second-Order Perturbation Stabilization Energies (E(2), in kcal/mol)a donor NBO → acceptor NBO in M(H2O)2A2 M

LP O → LP* M

LP O → RY* M

CR O → LP* M

BD O−S → LP* M

LP M → RY* O

CR M → BD* O−S

total

Sc(II) Ti(II) V(II) Cr(II) Mn(II) Fe(II) Co(II) Ni(II) Cu(II) Zn(II)

213.77 185.48 175.48 195.2 127.24 152.26 164.21 181.93 176.05 138.66

4.20 0 0.20 0 1.13 1.35 2.77 3.61 3.29 6.89

9.63 4.14 8.27 4.88 3.22 3.88 4.03 4.43 4.43 4.31

0 0 0.47 0 0 0 0.69 1.30 2.81 4.24

0.62 0.57 2.17 0.27 4.10 4.58 6.84 7.19 7.68 7.02

0.65 0 3.26 0.83 0.78 2.10 2.62 1.83 2.44 0.34

228.87 190.19 189.85 201.18 136.47 164.17 181.16 200.29 196.70 161.46

a

LP denotes an occupied lone pair. RY* denotes a Rydberg orbital. CR denotes a one-center core pair. The unstarred and starred labels corresponding to Lewis and non-Lewis NBOs,respectively.

the bond critical point (BCP). The above parameters are listed in Table 6. Generally speaking, closed shell interactions (e.g., ionic, van der Waals, hydrogen bonding, etc.) are shown by the positive values of ∇2ρb (∇2ρb > 0), low ρb (0.20 au), and |λ1|/λ3 > 1.19,22 On the basis of Table 6, it is observed that the low ρb ( 0) or covalent dominant (H < 0). Table 6 lists the values and the signs of the total electronic energy density (H). The sign (H < 0) indicates that the interaction for M−O bonding (M = Mn, Fe, Co, Ni, Cu, and Zn in M(H2O)2A2) possesses the “covalence” of the interaction in nature. This conclusion is not in contradiction with the electrostatic interaction in the closed-shell interaction for M−O bonding. On the basis of inorganic chemistry, Lewis acids (or acceptors) and Lewis bases (or donors) may interact to give a donor−acceptor complex. The new bond formed is called a dative bond, but it is not really different from any other polar covalent bond. According to the Pauling electroneutrality principle, the dative bond (M−O) in M(H2O)2A2 is a polar covalent bond and not a typical ionic bond or a typical covalent bond. Conversely, for M(H2O)2A2 (M = Sc, Ti, V, and Cr) in Table 6, ∇2ρb > 0, ρb < 0.1 au, and Hb > 0; this indicates that the M−O interaction is electrostatic dominant (ionic bond) for M(H2O)2A2. For V(II), Cr(II), Mn(II), and Ni(II) in Table 6, they have five M−O bonding interactions. The fifth polar covalent bond is an M−O44 bond. The M−O44 bond has a longer bond length and a lower value of the charge density and ∇2ρb in comparison with that of other M−O bonds, respectively. It indicates that the M−O44 bond is relatively a weaker bond.

these reactant molecules because the electron density distributions and structure in the reactant molecules are altered. Consequently, the reactant molecules are not in equilibrium. The possible nuclear motions also influence the stability of reactant molecules. 4.3. NBO Analysis.30,31 For each donor NBO and acceptor NBO, the stabilization energy, E(2), related to delocalization (“2e-stabilization”) is estimated. Table 5 displays the stabilization interaction energies (E(2)) for the different interactions in M(H2O)2A2. For M(H2O)2A2, the strongest donor−acceptor interaction occurs between LPO → LP* M. It indicates that the occupied lone electron pairs from oxygen atoms enter into the empty valence orbitals of M2+ ions and form the coordination bond. Through the coordination bond, the stable coordination compounds M(H2O)2A2 are generated. Second, Table 5 exhibits the very weaker interactions of LPM → RY* O and CR M → BD* O−S, respectively, because of the * donation from 3d-dominated nM orbitals of M into aligand acceptor orbitals of the adjacent ligand (for example, RY* O * back-bonding is and BD* O−S). The formation of nM → aligand to diminish the accumulation and repulsion of negative charge around the M2+ ion because of the formation of the coordination bond (LPO → LP* M) and to increase the stability of M(H2O)2A2. However, it is shown in Table 5 that * back-bonding for Mn(II) → Cu(II) the strength of nM → aligand is higher than that of Sc(II), Ti(II), V(II), and Cr(II) complexes. This is because the M2+ ions (M = Mn, Fe, Co, Ni, and Cu) possess more d-electrons to form the nM → a*ligand back-bonding. On the basis of coordination chemistry, nM → a*ligand back-bonding influences the stability of the M(H2O)2A2 complexes. The above structural characteristics of M(H2O)2A2 are beneficial to the separation of fourth-row transition metal ions based on eqs 21 and 22. Meanwhile, the probability of separation for the different metal ions can also been forecasted on the basis of M(H2O)2A2 in solvent extraction and liquid membrane separation. 4.4. AIM Analysis of Interatomic Bonding for M(H2O)2A2. 4.4.1. Dative Bond between the Metal Ion and Oxygen Atoms from Ligands. Figure 1 shows the structure of bis(2-ethylhexyl) sulfosuccinate anion (A−). The electron density (ρb), its Laplacian (∇2ρb), and the total electronic energy density (H), which is composed of the electronic potential energy density (V) and the electronic kinetic energy density (G), are used to analyze the structural characteristics at 2991



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Table 6. Analysis of the Bond Critical Points (BCPs) for M−O in M(H2O)2A2 bond (M−O)

dM−O (Å)

ρb (×10−2)

∇2ρb (×10−1)

Vb (×10−2)

Gb (×10−2)

Hb (×10−3)

|λ1|/λ3

Sc−O1 Sc−O2 Sc−O3 Sc−O4 Ti−O1 Ti−O2 Ti−O3 Ti−O4 V−O1 V−O2 V−O3 V−O4 V−O44 Cr−O1 Cr−O2 Cr−O3 Cr−O4 Cr−O44 Mn−O1 Mn−O2 Mn−O3 Mn−O4 Mn−O44 Fe−O1 Fe−O2 Fe−O3 Fe−O4 Co−O1 Co−O2 Co−O3 Co−O4 Ni−O1 Ni−O2 Ni−O3 Ni−O4 Ni−O44 Cu−O1 Cu−O2 Cu−O4 Cu−O5 Zn−O1 Zn−O2 Zn−O3 Zn−O4

4.0789 3.9767 4.2000 3.8767 3.9866 3.9368 4.0519 3.8463 3.9668 3.9361 3.9741 3.8966 4.2698 3.8473 3.7838 3.9436 3.7665 4.7879 4.0455 3.8567 4.0647 3.8266 4.6639 3.9045 3.7406 3.9370 3.6589 3.7776 3.6901 3.8394 3.6487 3.7775 3.7072 3.8238 3.7074 4.2325 3.686 3.606 3.805 3.600 3.810 3.562 3.930 3.705

5.841 6.235 4.755 7.360 6.139 6.058 5.341 7.112 5.678 5.717 5.717 6.211 3.568 6.772 7.259 6.010 7.477 2.582 5.855 6.988 5.508 7.420 2.817 6.927 8.046 6.279 9.018 7.751 8.295 6.907 8.847 7.416 7.951 6.857 8.129 4.131 8.679 9.320 7.325 9.475 7.531 10.32 6.403 8.582

+2.951 +3.451 +2.561 +3.965 +3.672 +3.918 +3.277 +4.369 +3.938 +4.033 +3.734 +4.340 +2.393 +4.471 +4.850 +3.839 +4.971 +0.752 +2.751 +3.898 +2.648 +4.168 +0.857 +3.226 +4.426 +3.160 +5.162 +4.167 +4.873 +3.699 +5.231 +3.971 +4.291 +3.468 +4.322 +1.651 +3.963 +4.500 +3.172 +4.596 +3.096 +4.460 +2.687 +3.509

−6.367 −7.549 −5.042 −9.506 −7.803 −8.195 −6.512 −9.788 −7.975 −8.321 −7.596 −9.127 −4.653 −9.648 −10.78 −8.194 −11.17 −2.734 −7.311 −9.704 −6.929 −10.49 −3.052 −9.360 −11.93 −8.714 −13.95 −12.32 −13.84 −10.89 −14.97 −12.51 −13.75 −11.31 −13.99 −5.818 −1.519 −1.675 −1.232 −1.708 −1.269 −1.968 −1.006 −1.522

+6.872 +8.088 +5.722 +9.709 +8.492 +8.995 +7.353 +10.36 +8.911 +9.264 +8.465 +9.989 +5.318 +10.41 +11.45 +8.896 +11.80 +2.308 +7.098 +9.725 +6.774 +10.45 +2.597 +8.713 +11.50 +8.308 +13.43 +11.37 +13.01 +10.07 +14.02 +11.22 +12.24 +9.988 +12.40 +4.972 +1.255 +1.400 +1.013 +1.429 +1.021 +1.542 +0.839 +1.200

+5.050 +5.390 +6.800 +2.030 +6.890 +8.000 +8.410 +5.720 +9.360 +9.430 +8.690 +8.620 +6.650 +3.930 +6.700 +7.020 +6.300 −4.260 −2.130 +0.210 −1.550 −0.400 −4.550 −6.470 −4.300 −4.060 −5.200 −9.500 −8.300 −8.200 −9.500 −12.90 −15.10 −13.20 −15.90 −8.460 −2.642 −2.750 −2.197 −2.798 −2.474 −4.267 −1.674 −3.226

0.196 0.176 0.178 0.176 0.182 0.156 0.161 0.173 0.106 0.098 0.144 0.104 0.089 0.140 0.138 0.140 0.138 0.194 0.183 0.167 0.181 0.170 0.204 0.195 0.178 0.181 0.178 0.166 0.151 0.154 0.168 0.135 0.147 0.149 0.149 0.167 0.182 0.180 0.196 0.179 0.209 0.207 0.203 0.206

with that of R−. Because the formation and strong perturbation interactions of molecular orbitals only occur between orbitals that are close in energy, reaction eq 21 more easily takes place than reaction eq 24. Again considering reaction eq 22, M(H2O)2A2 is an intermediate. On the basis of the lower HOMO energy for the A− anion, the higher antibonding character for the LUMO of M(H2O)2A2 and the gap energies between [ϕLUMO(M(H2O)2A2) − ϕHOMO(R−)] constitute the base of separation for the different transition metals in this study. In this way, these reactions generally occurred with high chemo-, region-, and stereoselectivity. Consequently, the criterion of selecting a Lewis base for enhancing chemical reactivity and selectivity is to consider the decrease of the HOMO energy in comparison with that of the original ligand and whether this Lewis base can form an intermediate which

5. ANALYSIS OF CHARACTERS FOR THE LEWIS BASE (A−) BASED ON ITS HOMO-LOWERING STRATEGY On the basis of eqs 21 and 24, the anions A− and R− are electron pair donors, respectively. From an orbital-based perspective, this definition focuses direct attention on onecenter donor (LP) and acceptor (LP*) NBOs of the valence shell. Most important are the valence-shell vacancies (“LP*” NBOs) that characterize strong Lewis acids. Whereas filled valence LP-type NBOs are ubiquitous features of all anions, the corresponding unfilled LP*-type NBOs typically occur only in open-shell transition metal species. In this study, the energies of HOMO for A− and R− are −0.0977 and −0.0537 au, respectively. Relatively, the energy decrease of the HOMO for A− is beneficial for the electron pair to enter into the LUMO of M(H2O)42+ from the HOMO of A− in comparison 2992



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(4) Parr, R. G.; Yang, W. Density Functional Approach to the Frontier-Electron Theory of Chemical Reactivity. J. Am. Chem. Soc. 1984, 106, 4049−4050. (5) Chandra, A. K.; Nguyen, M. T. Fukui Function and Local Softness as Reactivity Descriptors. Chemical Reactivity Theory; CRC Press/Taylor Francis Group: Boca Raton, FL, 2009; pp 163−178. (6) He, D.; Ma, M. Quantum chemical study of extraction characteristics of kinetic synergist OT in liquid membrane using HPMBP as carrier. Sep. Purif. Technol. 2013, 107, 289−296. (7) Parr, R. G.; Yang, W. Density Functional Theory of Atoms and Molecules; Oxford University Press: Oxford, U.K., 1989. (8) Geerlings, P.; De Proft, F.; Langenaeker, W. Conceptual Density Functional Theory. Chem. Rev. 2003, 103, 1793−1873. (9) Noorizadeh, S.; Maihami, H. A theoretical study on the regioselectivity of Diels - Alder reactions using electrophilicity index. J. Mol. Struct.: THEOCHEM 2006, 763, 133−144. (10) Noorizadeh, S. Is there a minimum electrophilicity principle in chemical reactions? Chin. J. Chem. 2007, 25, 1439−1444. (11) Janak, J. F. Proof that ∂E/∂ni = εi in density-functional theory. Phys. Rev. B 1978, 18, 7165−7168. (12) Parr, R. G.; Szentpály, L. V.; Liu, S. B. Electrophilicity Index. J. Am. Chem. Soc. 1999, 121, 1922−1924. (13) (a) Morell, C.; Grand, A.; Toro-Labbe, A. New Dual Descriptor for Chemical Reactivity. J. Phys. Chem. A 2005, 109, 205−212. (b) Roy, R. K.; Krishnamurti, S.; Geerlings, P.; Pal, S. Local Softness and Hardness Based Reactivity Descriptors for Predicting Intra- and Intermolecular Reactivity Sequences: Carbonyl Compounds. J. Phys. Chem. A 1998, 102, 3746−3755. (14) Yang, W.; Mortier, W. J. The use of global and local molecular parameters for the analysis of the gas-phase basicity of amines. J. Am. Chem. Soc. 1986, 108, 5708−5711. (15) (a) Chattaraj, P. K.; Sarkar, U.; Roy, D. R. Electrophilicity Index. Chem. Rev. 2006, 106, 2065−2091. (b) Roy, R. K. On the Reliability of Global and Local Electrophilicity Descriptors. J. Phys. Chem. A 2004, 108, 4934−4939. (c) Roy, R. K.; Usha, V.; Paulovic, J.; Hirao, K. Are the Local Electrophilicity Descriptors Reliable Indicators of Global Electrophilicity Trends? J. Phys. Chem. A 2005, 109, 4601−4606. (16) Houk, K. N.; Strozier, R. W. On Lewis Acid Catalysis of DielsAlder Reactions. J. Am. Chem. Soc. 1973, 95, 4094−4096. (17) Yamabe, S.; Dai, T.; Minato, T. Fine Tuning [4 + 2] and [2 + 4] Diels-Alder Reactions Catalyzed by Lewis Acids. J. Am. Chem. Soc. 1995, 117, 10994−10997. (18) García, J. I.; Martínez-Merino, V.; Mayoral, J. A.; Salvatella, L. Density Functional Theory Study of a Lewis Acid Catalyzed DielsAlder Reaction. The Butadiene + Acrolein Paradigm. J. Am. Chem. Soc. 1998, 120, 2415−2420. (19) Jenkins, S.; Morrison, I. Characterization of Various Phases of Ice on the Basis of the Charge Density. J. Phys. Chem. B 1999, 103, 11041−11049. (20) Cremer, D.; Kraka, E. Chemical Bonds without Bonding Electron Density-Does the Difference Electron-Density Analysis Suffice for a Description of the Chemical Bond? Angew. Chem., Int. Ed. Engl. 1984, 23, 627−628. (21) Wiberg, K. B.; Bader, R. F. W.; Lau, C. D. H. Theoretical analysis of hydrocarbon properties. 1. Bonds, structures, charge concentrations, and charge relaxations. J. Am. Chem. Soc. 1987, 109, 985−1001. (22) (a) Bader, R. F. W.; Slee, T. S.; Cremer, D.; Kraka, E. Description of conjugation and hyperconjugation in terms of electron distributions. J. Am. Chem. Soc. 1983, 105, 5061−5068. (b) Matta, C. F.; Boyd, R. J. The Quantum Theory of Atoms in Molecules; Wiley-VCH: Weinheim, 2007. (23) Foresman, J. B.; Frisch, E. Exploring chemistry with electronic structure methods, 2nd ed.; Gaussian, Inc.: Pittsburgh, PA, 1996. (24) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; et al. Gaussian 03, revision B.04; Gaussian, Inc.: Pittsburgh, PA, 2003.

has a higher antibonding character and a negative gap energy between this intermediate and the original ligand, whereas the quantum chemical computation and analysis can finish this task.

6. CONCLUSIONS In this paper, the following conclusions are in order: (i) Two-layer ONIOM combinations of high-level QM (HQ = B3LYP/6-31+G*) and low-level MM (UFF) methods are suitable for the structural optimization of the M(H2O)2A2 molecules containing the transition metals in the fourth period. (ii) The chemical potential μ, hardness η, and electrophilicity index ω indicate that the Cu(II), Ni(II), Co(II), and Fe(II) in M(H2O)2A2 are more reactive than other transition metals in the fourth period, reacting with the nucleophilic reagent (R−). (iii) The dual descriptor of local reactivity of the M(H2O)2A2 species shows unambiguously that the electrophilic activity is mainly localized at the metallic center, Cu(II), Ni(II), Co(II), and Fe(II). The dual descriptor (Δf M(r)) and multiphilic descriptor Δsk or ωM are recommended to characterize the site reactivity and selectivity within the M(H2O)2A2 molecule. The selectivity of R− for M(II) in M(H2O)2A2 (from high to low) is Cu(II) > Ni(II) > Co(II) > Fe(II) ≫ Mn(II) > Zn(II) > Cr(II)

This constitutes the separation base of M(H2O)2A2 with the nucleophilic reagent (R−). (iv) For enhancing the chemical reaction reactivity and selectivity in this study, the Lewis base should possess a lower energy of the HOMO in comparison with that of the original ligand and can form an intermediate which has higher antibonding character and larger gap energy. (v) For M(H2O)2A2 (M = Sc, Ti, V, and Cr), the M−O interaction is electrostatic dominant (ionic bond). For the M− O bonding in M(H2O)2A2 (M = Mn, Fe, Co, Ni, Cu, and Zn), it is the dative bond (a polar covalent bond). (vi) NBO analysis verifies that for M(H2O)2A2 the strongest donor−acceptor interaction occurs between LPO → LP* M and the strength of nM → a*ligand back-bonding for Mn(II) → Cu(II) is stronger than that of Sc(II), Ti(II), V(II), and Cr(II) in M(H2O)2A2.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (21275052).

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REFERENCES

(1) Chattaraj, P. K. Chemical Reactivity Theory; CRC Press/Taylor Francis Group: Boca Raton, FL, 2009. (2) Martínez-Araya, J. I.; Salgado-Morán, G.; Glossman-Mitnik, D. Computational Nanochemistry Report on the OxicamsConceptual DFT Indices and Chemical Reactivity. J. Phys. Chem. B 2013, 117, 6339−6351. (3) Morokuma, K.; Wang, Q.; Vreven, T. Performance Evaluation of the Three-Layer ONIOM Method: Case Study for a Zwitterionic Peptide. J. Chem. Theory Comput. 2006, 2, 1317−1324. 2993



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(25) Glendening, E. D.; Badenhoop, J. K.; Reed, A. E.; Carpenter, J. E.; Bohmann, J. A.; Morales, C. M.; Weinhold, F. NBO 5.0 program; Theoretical Chemistry Institute, University of Wisconsin: Madison, WI, 2001. (26) Keith, T. A. AIMAll (version 13.05.06); TK Gristmill Software: Overland Park, KS, 2011 (aim.tkgristmill.com). (27) Chang, T.; Huang, G.; Ji, L. A Study of Kinetics to Extract Copper by a Mixed System of Extractants of Hydroxyoxime KindsOsmotic Agent T. Acta Sci. Nat. Univ. Sunyatseni 1982, 3, 58−63. (28) Liu, S. B.; Ess, D. H.; Schauer, C. K. Density Functional Reactivity Theory Characterizes Charge Separation Propensity in Proton-Coupled Electron Transfer Reactions. J. Phys. Chem. A 2011, 115, 4738−4742. (29) Zhou, P. P.; Qiu, W. Y.; Liu, S. B.; Jin, N. Z. Halogen as halogen-bonding donor and hydrogen-bonding acceptor simultaneously in ring-shaped H3N•X(Y)• HF(X= Cl, Br and Y=F, Cl, Br) Complexes. Phys. Chem. Chem. Phys. 2011, 13, 7408−7418. (30) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Intermolecular Interactions from a Natural Bond Orbital, Donor-Acceptor Viewpoint. Chem. Rev. 1988, 88, 899−926. (31) Weinhold, F.; Landis, C. R. Discovering Chemistry With Natural Bond Orbitals; John Wiley & Sons, Inc.: Hoboken, NJ, 2012.

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