EâH (E = N and P) Bond Activation of PhEH2 by a Trinuclear Yttrium

Article pubs.acs.org/Organometallics

E−H (E = N and P) Bond Activation of PhEH2 by a Trinuclear Yttrium Methylidene Complex: Theoretical Insights into Mechanism and Multimetal Cooperation Behavior Gen Luo,†,‡ Yi Luo,*,† and Zhaomin Hou*,†,‡ †

State Key Laboratory of Fine Chemicals, School of Chemical Engineering, Dalian University of Technology, Dalian 116024, PR China ‡ RIKEN Center for Sustainable Resource Science and Organometallic Chemistry Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan S Supporting Information *

ABSTRACT: E−H (E = N and P) bond activation of PhEH2 by a trinuclear yttrium methylidene complex to give a μ3-EPh species has been investigated through DFT calculations. It has been revealed that the reaction involves three major steps, i.e., activation of one of the two E−H bonds, intramolecular isomerization, and the subsequent activation of the second E−H bond. The first E−H bond activation is a mono-metal-assisted σ-bond metathesis (σ-BM) process, while the second E−H bond activation is achieved by the cooperation of three metal sites. The effect of the phenyl group in PhEH2 has also been examined. It has been found that the phenyl group in PhNH2 showed a significant steric effect for the N−H activation, but in the case of PhPH2, such steric effect was not observed. The relatively low energy barriers and significant exergonic feature lead us to predict that the trinuclear yttrium methylidene complex should be also effective for activation of NH3 and PH3. In addition, a general behavior of the activation of CX (X = O and S) and E−H (E = C, N, and P) bonds by multialkyl-bridged trinuclear rare-earth complexes has been described, which could be beneficial for further studies on the chemical transformations at multimetallic frameworks.

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INTRODUCTION Transition-metal-mediated E−H (E = N and P) bond activation as a synthetic elementary step has received intense attention because of its great importance in the transformation of amines and phosphines to value-added compounds in the fields of medicine, agrochemicals, and materials.1,2 In past decades, significant progress has been achieved experimentally in N−H/P−H bond activation by transition metal complexes.3,4 A deep understanding of the mechanisms of N−H/ P−H bond activation by transition metal complexes is of great importance to establish an effective strategy for functionalization of amines and phosphines. In this context, theoretical studies have successfully revealed the related mechanisms and effectively promoted the design and development of new reactions.5,6 Recently, several mechanisms mediated by mononuclear transition metal complexes were well-established based on both experimental and theoretical studies,3−6 i.e., E− H bond cleavage by oxidative addition to low-valent metal center,3d,e,4a,d,5a,b,e,h,6d σ-bond metathesis with metal−alkyl/ hydride bond, 4b,c,5f,6a,c,e,g or metal−ligand cooperation.3a−c,5d,g,6b Compared to mononuclear complexes, a multimetallic system may work more efficiently for bond activation owing to the cooperation of multiple metal centers,7 although the knowledge of cooperative mechanisms is still rather limited.8 In such systems, each metal center could be allotted © XXXX American Chemical Society

a part as a binding site and an activation site and therefore facilitate chemical transformations. Experimentally, it has been demonstrated that multinuclear complexes are capable of activating N−H/P−H bonds.9−11 However, in contrast to mononuclear systems, the related mechanistic studies of N−H/ P−H bond activation by multimetallic complexes still remain rather unexplored.12 Given the importance of N−H/P−H bond activation, in-depth mechanistic understandings of the related reactions mediated by multinuclear complexes are in great demand, may establish new activation modes, and may inspire us to develop new reactions or catalysts. In addition to the metal-mediated N−H/P−H activation mechanism, we are also interested in the multimetal cooperating behavior in the chemical transformation mediated by multinuclear rare-earth metal complexes which often exhibit high reactivity toward the activation of chemical bonds.13−15 Our previous computational studies have revealed the mechanisms of carbon-based σ- and π-bond activation by trinuclear rare-earth metal complexes, which demonstrated the important role of multimetallic cooperation in achieving related chemical transformations.16−18 For instance, the studies on an Special Issue: Organometallic Actinide and Lanthanide Chemistry Received: June 13, 2017

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DOI: 10.1021/acs.organomet.7b00443 Organometallics XXXX, XXX, XXX−XXX

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Organometallics

here not only enrich the activation models of N−H/P−H bonds at the molecular level but also provide a deeper understanding of the cooperative effect of multiple metal centers.

intramolecular C−H bond activation of a trinuclear multimethyl complex elucidated that the cooperation of trimetallic centers makes the C−H bond activation kinetically easier in comparison with that of bimetallic or monometallic center(s).16 In carbon-based π-bond (CO and CS) activation, it was also revealed that the multimetal cooperative effect is essential in facilitating the intramolecular isomerization and bond activation processes.17,18 These findings prompted us to wonder about the mechanism of other atom-based bond activations such as those of N−H and P−H bonds by multinuclear rare-earth metal complexes, which would enrich the chemistry of chemical bond activation by multinuclear rareearth metal complexes. Recently, Zhang and co-workers reported that E−H (E = N and P) bond activation of PhEH2 could be achieved by trinuclear methylidene complexes (Scheme 1),18,19 which provided a good reaction model for

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COMPUTATIONAL DETAILS

The reaction of [L3Y3(μ2-Me)3(μ3-Me)(μ3-CH2)] (L = PhC[NC6H4(iPr-2,6)2]2) (1a) with PhEH2 (E = N and P) was considered as a computational model reaction for the current calculations. Due to the huge molecular size (more than 250 atoms), the two-layer ONIOM (TPSSTPSS:HF) approach was used in the geometrical optimizations. Ph and C6H4(iPr-2,6)2 parts in PhC[NC6H4(iPr-2,6)2]2 ligands were included in the outer layer, and the remaining part of the system comprises the inner layer (see Figure S1). The inner layer was calculated at the relatively higher level. In the higher-level calculations, the TPSSTPSS functional20,21 was applied, and the 6-31G(d) basis set for nonmetal atoms and the effective core potentials (ECPs) of Hay and Wadt with double-ζ valence basis set (LanL2DZ)22 for Y atoms were utilized. The outer layer was involved in lower-level calculations. In the lower-level calculations, the Hartree−Fock method was utilized, and the LanL2MB basis set was used for all atoms. Each optimized structure was subsequently analyzed by harmonic vibration frequencies at the same level of theory to characterize of a minimum (Nimag = 0) or a transition state (Nimag = 1) and to obtain the thermodynamic corrections to Gibbs free energy. To obtain more reliable relative energies, single-point energy calculations were carried out by using pure DFT method (single-layer) on the basis of optimized structures. In such single-point calculations, the M06-L functional,23 which often shows good performance in treatment of transition-metal systems,24 was used together with the CPCM model25 for considering the toluene solvation effect. The Stuttgart/Dresden ECP together with associated basis sets26 were used for Y atoms, and the 6-31G(d,p) was used for the nonmetal atoms. The theoretical method adopted here has been successfully applied for similar systems in our previous studies.17,18 The free energies in solution, including corresponding energy corrections obtained from gas-phase calculation, were used to analyze the reaction mechanism. All calculations were performed with Gaussian 09 software package.27

Scheme 1. E−H (E = N and P) Bond Activation by Trinuclear Rare-Earth Methylidene Complexes18,19

computational investigation of the N−H/P−H activation by multinuclear rare-earth metal complex. In this study, the mechanisms of the activation of N−H and P−H bonds by a trinuclear yttrium methylidene complex have been investigated by DFT calculations. The structural information of the key transition states and intermediates as well as the energy profiles are clarified, and some new insights have been obtained. The general behavior of chemical transformation in several multinuclear systems has been also described. The results reported

Figure 1. Computed free energy profile (kcal/mol) for the reaction of 1a with PhNH2. All the energies are relative to the energy sum of 1a and PhNH2. L = PhC[NC6H4(iPr-2,6)2]2. B


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Figure 2. Optimized structures (distances in Å) of stationary points involved in the reaction of 1a with PhNH2. The PhC[NC6H4(iPr-2,6)2]2 ligands. Some H atoms are omitted for clarity.

Figure 3. Computed free energy profile (kcal/mol) for the reaction of 1a with PhPH2. All the energies are relative to the energy sum of 1a and PhPH2. L = PhC[NC6H4(iPr-2,6)2]2.

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RESULTS AND DISCUSSION

transition state, TS1N, leading to a more stable intermediate BN with a relative free energy of −16.4 kcal/mol. This process has a low energy barrier of 8.0 kcal/mol and yields a PhNH moiety and a new μ2-CH3 group. As shown in Figure 2, although four μ2-CH3 groups exist in BN, only the newly formed C5 methyl group is located at the same side (above the Y1−Y2−Y3 plane) as the PhNH group, and the remaining μ2-CH3 groups (C2, C3, and C4 groups) are located at the equatorial positions to support the trimetal platform. Therefore, the second N−H activation should take place between the PhNH moiety and the C5 methyl group. Starting from BN, successive multimetal cooperating intramolecular isomerization could take place to prepare for the second N−H bond activation. As displayed in Figures 1 and 2, the PhNH group in BN can easily change its

Reaction Mechanism of [L3Y3(μ2-Me)3(μ3-Me)(μ3-CH2)] (1a) with PhNH2 or PhPH2. The calculated energy profile for the reaction of PhNH2 with 1a and the corresponding optimized structures were shown in Figures 1 and 2, respectively. As shown in Figure 1, the reaction of PhNH2 with 1a starts with the coordination of N atom of PhNH2 to the Y1 center of 1a to form an adduct AN (d(Y1···N) = 2.69 Å). This step is slightly exergonic by 0.8 kcal/mol. Due to the coordination of PhNH2, the Y1−C1 bond in AN became weaker in comparison with that in 1a, as suggested by the bond length (2.48 Å in 1a vs 2.63 Å in AN, Figure 2). Subsequently, AN could undergo the N−H bond activation via a proton-transfer C


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Organometallics coordination fashion from terminal (μ1) to μ2-form in CN (d(Y1···N) = 2.29 Å and d(Y2···N) = 2.69 Å), and the C5 methyl group in CN can change its coordination fashion from μ2- (d(Y2···C5) = 2.65 Å and d(Y3···C5) = 2.50 Å) to μ1-form in DN (d(Y3···C5) = 2.44 Å), being ready for further detaching by accepting a proton. During these transformations, the coordination fashions of C1−C4 methyl groups remain unchanged to keep the Y1−Y2−Y3 triangle framework (also see Wiberg bond indexes in Table S1). Obviously, the intramolecular isomerization processes (from BN to DN) assisted by the cooperation of multimetal centers are reversible with low energy barriers (less than 4 kcal/mol via TS2N and TS3N). After forming DN, the second N−H bond activation occurs via a trimetal-cooperating proton-transfer transition state, TS4N, (vide inf ra) to give a more stable complex, 2aN, which is equivalent to the product obtained experimentally. This step has a low energy barrier of 3.0 kcal/mol and in accompanied by methane elimination. On the basis of the above result, it is easily concluded that the reaction mainly involves three processes: the first N−H bond activation, the multimetal cooperating intramolecular isomerization, and the second N−H bond activation. The whole reaction of PhNH2 with 1a has an overall energy barrier of 8.0 kcal/mol and is significantly exergonic by 55.7 kcal/mol. It is also worth noting that the first N−H activation is the rate-determining step; the following steps are almost barrierless in the current trinuclear system. Usually, the deprotonation of the first N−H bond of primary amines is easier than the second N−H activation by a mononuclear complex due to the stronger acidity of RNH2 than that of [RNH]−.3 In the current trinuclear system, the origin of the driving force for promoting the second E−H activation is the formation of a thermodynamically stable trimetal− supported product. Obviously, the cooperation of the metal centers is the precondition for the intramolecular isomerization, and the second E−H activation could occur in a facile manner in kinetics. It is noteworthy that during the reaction the μ3-CH2 (C5 group) acts as an H-acceptor participating in the N−H activation and that the three metal centers are more likely to act as a reaction platform to facilitate the transformations. Therefore, the cooperation between the C5 group and yttrium centers could also be of great importance for accomplishment of such reaction. The P−H bond activation of PhPH2 by 1a was also calculated. The free energy profile and optimized structures were shown in Figures 3 and S2, respectively. It was found that the activation of PhPH2 undergoes a similar reaction mechanism to the PhNH2 activation, which generally involves three processes. As illustrated in Figure 3, coordination complex AP undergoes the first P−H bond activation via TS1P with an energy barrier of 15.6 kcal/mol, leading to intermediate BP. The subsequent reversible intramolecular isomerization of BP to DP is feasible (less than 6 kcal/mol of ΔG⧧ values), showing again the cooperation of three yttrium centers. Finally, the second P−H activation could take place to provide the trinuclear yttrium phosphinidene product 2aP, accompanied by an elimination of CH4. Being similar to the case of N−H bond, the first P−H activation via TS1P is the rate-determining step with an energy barrier of 15.6 kcal/mol, and the whole reaction is significantly exergonic by 43.5 kcal/ mol. Geometric Structures and Wiberg Bond Indexes Analysis of Important Transition States. For a better

understanding of the geometric features and the interatomic interactions of the proton-transfer transition states, the core structures of TS1 and TS4 were illustrated in Figure 4. In the

Figure 4. Structures of optimized transition states for E−H (E = N and P) activations. The values of angle, bond distance (d, unit: Å), and Wiberg bond index (WBI) are given below the corresponding structures. PhC[NC6H4(iPr-2,6)2]2 ligands and some H atoms are omitted for clarity.

first N−H activation transition state, TS1N, the atoms of Y1, C5, H1, and N construct a four-center structure, as suggested by the interatomic distances, viz., d(Y1···C5) = 2.89 Å, d(C5··· H1) = 1.49 Å, d(H1···N) = 1.29 Å, d(N···Y1) = 2.45 Å, d(Y1··· H1) = 2.42 Å, and the angle 61.1° for C5···Y1···N. All of these geometric features are similar to those involved in the reactions of metal-mediated C−H σ-bond metathesis (σ-BM) transition states.28,29 Similar geometric features were also found in the first P−H bond activation transition state, TS1P, as suggested by the Y1···H1 distance (2.30 Å) and the C5···Y···P angle (71.3°). During the first N−H or P−H bond activation process, only one metal atom (Y1) has an interaction with E−H (E = N and P) bond, and the other two metal atoms (Y2 and Y3) act as part of a metalloligand to support the C5 methylene group. In this sense, these transition states (TS1 N and TS1 P ) demonstrate a mono-metal-assisted σ-BM event. As to the second N−H bond activation transition state, TS4N, the atoms of Y3, N, H2, and C5 also construct a four-center structure with a σ-BM feature. In contrast to TS1N, the WBIs of 0.27 for Y1− N, 0.31 for Y2−N, and 0.20 for Y3−N in TS4N, suggesting that the N atom has interaction with three metal centers simultaneously. Thus, the N−H activation event shown here is assisted by the cooperation of three metal centers, i.e., a multimetal cooperating N−H σ-BM event, which is similar to previously reported intramolecular C−H activation featured by multimetal cooperating σ-BM mechanism.16 This mechanism also works for the P−H activation in the current system (TS4P). It is noted that the N···H interaction is stronger but that the C5···H interaction is weaker in TS4N in comparison D


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Figure 5. HOMOs of transition states TS1N, TS4N, TS1P, and TS4P (left, isovalue = 0.03) and their schematic representations (right). Atomic orbital contributions are reported in parentheses.

Figure 6. Energy profiles for the E−H bond activation of RNH2 and RPH2 (R = Ph and H) and selected optimized structures with geometric parameters (distances in Å). PhC[NC6H4(iPr-2,6)2]2 ligands and some H atoms are omitted for clarity.

with those in TS1N as suggested by their bond distances and WBIs (Figure 4). The similar feature is also observed in the case of the P−H bond (see the corresponding bond distances and WBIs in TS4P in comparison with those in TS1P, Figure 4). Therefore, TS4 for the second E−H (E = N and P) bond activation could be viewed as an early transition state compared with TS1 for the first E−H bond activation. Such biased bond

activation modes are also manifested through the atomic contributions in their frontier molecular orbitals (vide inf ra). Frontier Molecular Orbitals Analysis of TS1 and TS4. The frontier molecular orbitals of the transition states, TS1N, TS4N, TS1P, and TS4P, were analyzed and can be gleaned in Figure 5. As shown in this figure, the HOMOs of all the transition states are mainly contributed by the H-donor E (E = N or P) atom and the H-acceptor C atom. For instance, the E


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Figure 7. Activation of C = X (X = O and S) and E−H (E = C, N, and P) bonds at multimethyl-bridged trinuclear rare-earth complexes. Cp′ = η5C5Me4SiMe3; L = PhC[NC6H4(iPr-2,6)2]2.

N−H/P−H Bond Activation of NH3 and PH3. The results show that NH3 and 1a could form a more stable complex, A′N, than that in the case of PhNH2 (AN, Figure 6a). In the case of NH3, the formation of complex A′N is exergonic by 6.5 kcal/ mol, while the formation of AN is exergonic by only 0.8 kcal/ mol relative to 1a and PhNH2. Such difference mainly derives from the steric hindrance of phenyl in PhNH2. Due to the small size of N atom, when PhNH2 is close to 1a to give complex AN, the steric repulsion between phenyl in PhNH2 and the PhC[NC6H4(iPr-2,6)2]2 ligand could exist, as manifested by the Y···N distances in AN and A′N. As illustrated in Figure 6c, the Y···N distance in AN is 2.69 Å, while this distance was significantly shortened to 2.51 Å in A′N. In the case of NH3, the activation of the first N−H bond needs to overcome an energy barrier of 15.8 kcal/mol (via TS1′N), which significantly higher than that in PhNH2 case (8.0 kcal/mol via TS1N). Similarly, the energy barrier of the second N−H bond in the case of NH3 is also higher than that in the case of PhNH2 by more than 5 kcal/mol. This result is consistent with the analysis of frontier molecular orbitals in that the phenyl group plays an important role in stabilizing transition states during N−H bond activation processes. In the case of P−H activation, due to the relatively large size of P atom, there is almost no steric repulsion between phenyl of PhPH2 and the PhC[NC6H4(iPr-2,6)2]2 ligand, as

total orbital contributions of the H-donor N (or P) atoms and the H-acceptor C5 atoms are 53.8, 46.2, 74.8, and 59.1% for TS1N, TS4N, TS1P, and TS4P, respectively. Obviously, the orbital contributions of C5 and N atoms involved in protontransfer processes in TS4 are unbalanced (32.6 vs 13.6% in TS4N and 41.7 vs 17.4% in TS4P), which are different from the first E−H activation transition states TS1 (29.1 vs 24.7% in TS1N and 37.3 vs 37.5% in TS1P). The HOMOs of TS4 are more concentrated on C5 atoms, corresponding to the feature of earlier transition state for the second E−H activation previously mentioned. It is also worth noting that the phenyl of substrate has a significant contribution to the HOMOs in the N−H bond activation processes (more than 10%), especially in TS1N (up to 29.1%). As for P−H bond activation, by contrast, the phenyl substitution contributed less to the HOMOs in comparison with N−H activation processes. This result suggests that the phenyl group should play an important role in stabilizing the transition states of N−H activations but have relatively less influence on P−H activation processes. The difference of the phenyl effect on N−H and P−H activation is probably because the p−π conjugation is more effective in PhNH2 than that in PhPH2. In order to verify the phenyl effect on the energy, the activations of nonsubstituent substrates NH3 and PH3 by 1a were investigated (Figure 6). F


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Organometallics suggested by the Y···P distances in AP (3.05 Å) and A′P (3.04 Å). The differences of P−H activation energy barriers between PhPH2 and PH3 are less than 3 kcal/mol, which is also in agreement with the analysis of frontier molecular orbitals that the phenyl has relatively less influence on P−H bond activation processes. Moreover, the relatively low energy barriers (15.8 kcal/mol for NH3 and 18.5 kcal/mol for PH3) and the significant exergonic feature (48.6 kcal/mol for NH3 and 32.9 kcal/mol for PH3) indicate that trinuclear yttrium methylidene complex 1a should be also effective for activation of NH3 and PH3. Behavior of Reactivity in Trinuclear Complexes. Although the cooperation effect of multinuclear complexes are of great current interest and many related reactions have been explored experimentally, knowledge of their cooperative mechanisms are still limited. To have a better understanding of the multimetal cooperation behavior, the activation of various substrates including CX (X = O and S) and E−H (E = C, N, and P) bonds by multimethyl-bridged trinuclear rare-earth complexes were summarized in Figure 7. As reported previously, the CO double bond of a ketone could be activated by a trinuclear scandium methylidene complex via a CH22−/O2− exchange process (Figure 7a).17 During this process, the bonding mode of the leaving group CH2 changes in the order of μ3 → μ2 → μ1. Concomitantly, the bonding mode of the incoming group O atom follows a reverse trend of μ1→ μ2 → μ3. Similarly, during the CS double bond activation of CS2 by a trinuclear yttrium phosphinidene cluster, the change of coordination manner of the PhP unit (the leaving group) follows the order of μ3 → μ2 → μ1 before PhPCS release, and the incoming group (S atom) follows a reverse order of μ1 → μ2 → μ3 (Figure 7b).18 In the case of C−H activation (Figure 7c), the leaving methyl group (C1 group) first changes its coordination manner from μ2 to μ1 before liberation, and the C2 methyl group changes its coordination mode from μ2 to μ3.16 In addition, a similar behavior of the leaving group and the incoming group was also found during the E−H (E = N and P) bond activation by a trinuclear yttrium complex studied in this work (Figure 7d): The binding mode of leaving C-group undergoes the sequential change of μ3 → μ2 → μ1, and the coordination manner of the incoming group PhE varies in the manner of μ1 → μ2 → μ3. As mentioned above, these results give us a general sense that the coordination manner of incoming group (or atom) follows the order μ1 → μ2 → μ3, and that of the leaving group (or atom) generally follows a reverse trend μ3 → μ2 → μ1 in trinuclear system. Generally, the edge-bridging and face-capping groups have stronger bonding interactions than that of a terminal one with the metal centers in multinuclear complexes. It is understandable that the change in the coordination manner of a leaving group (from μ2 or μ3 to μ1) makes it more capable of detaching from the metal center. The detailed change of coordination manners summarized in this study could provide a hint for further investigation of the reaction mechanisms in multinuclear systems and may add better understanding to heterogeneous chemical transformations at metal surfaces.

cooperating intramolecular isomerization, and (3) the second E−H bond activation. The analysis of the geometrical features and the bond situation of the proton transfer transition states suggest that the first E−H bond activation is a mono-metalassisted σ-bond metathesis (σ-BM) process, while the second E−H bond activation is a multimetal cooperating σ-BM event. It is also found that the second E−H bond activation transition states could be viewed as early transition states in comparison with their corresponding first E−H bond activation. The frontier molecular orbital analysis indicates that phenyl group plays an important role in stabilizing transition states for the case of PhNH2, while it has relatively less influence in the reaction of PhPH2. Such phenyl effects were also verified by calculating the model reactions of NH3 and PH3 substrates. The results suggest that the phenyl group has a significant steric effect during the PhNH2 activation and almost no steric effect in the PhPH2 case. The relatively low energy barriers and the significant exergonic feature indicates that the trinuclear yttrium methylidene complex could also be capable of activating NH3 and PH3. Moreover, a comparison of the activation of different substrates at trinuclear rare-earth frameworks suggests that the bonding model of the incoming group (or atom) follows the order of μ1 → μ2 → μ3, and that of the leaving group (or atom) generally follows a reverse trend μ3 → μ2 → μ1. These findings could add better understanding to the multimetal cooperating transformations and are helpful for further studies on multinuclear metal complex systems.

CONCLUSION The detailed mechanisms of E−H (E = N and P) bond activation of PhEH2 by a trinuclear yttrium methylidene complex have been investigated by DFT calculations. The results show that the reaction mainly involves three processes: (1) the first E−H bond activation, (2) the multimetal

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.organomet.7b00443. Structures and tables of Wiberg bond indexes and energies (PDF) Cartesian coordinates of all optimized stationary points(XYZ)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Gen Luo: 0000-0002-5297-6756 Yi Luo: 0000-0001-6390-8639 Zhaomin Hou: 0000-0003-2841-5120 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partly supported by the NSFC (Nos. 21429201 and 21674014) and a Grant-in-Aid for Scientific Research (S) from the JSPS (No. 26220802). We also thank the RICC (RIKEN Integrated Cluster of Clusters) and the Network and Information Center of the Dalian University of Technology for part of the computational resources.

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REFERENCES

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