Abstract
Clusters of the WNn (n = 1–9) forms are investigated theoretically using density functional theory methods. Geometry optimizations are undertaken under the constraint of well-defined point-group symmetries at the (U)B3LYP level employing a pseudopotential method in conjunction with double-zeta basis sets for W atom and 6–31G(d) basis sets for N atoms. In this article, different molecular properties such as total energies, relative stabilities as well as chemical bonding and equilibrium geometries of WNn (n = 1–9) clusters are systematically calculated and discussed. Theoretical results show that the lowest-energy WNn (n = 1–9) isomers prefer to interact with N2 units to N3 and N units, moreover, some circle-like low-lying stable WNn structures are considered, which turn out to be less stable than isomers with N2 units as the building blocks, furthermore, W atom is in favorable of chemisorption nitrogen rather than dissociative nitrogen, which is in good agreement with experimental observation. Comparisons theoretical results on geometry and stretching frequency with available experimental and theoretical data are made, a good agreement is obtained. In addition, natural population analyses are calculated in order to elucidate the charge distributions in the clusters.
Introduction
Transition metal fixation of N2 is very important in chemistry and is widely studied by theoretical and experimental methods [1–7] because transition metals activated N2 is extremely important in industry, consequently, transition metals are widely used in the industry. Various molecular properties of those clusters as diverse as equilibrium geometries and total energies [1–7]; magnetic moments [8, 9]; and static polarizabilities [10] have been intensively investigated and calculated inter alia. Clusters under study have varied from small metallic dimers [9] to quite large systems having 30 transition metal atoms or over [8]. The theoretical methods employed in those studies have ranged from the relatively simple Jellium model, which has indeed provided a reasonable description for many metallic clusters [11], to ab initio Hartree-Fock level with relativistic effective core potentials [3], density functional theory and post-Hartree-Fock methods [3, 8].
More recently, there has been a growing interest in synthesizing and studying relatively small metallic clusters containing a few non-metal atoms such as nitrogen and carbon [12, 13]. Due to its catalytic relevance of those clusters, cluster assembled materials involving nitrides, oxides and hydrogen of transition metals have been widely carried out in the prospect of developing new catalysts as well as in the study of the activation [1, 14]. In fact, a promoted catalyst of this metallic element has been used since the last decade for the N2 activation and the NH3 synthesis. Those types of clusters can be also regarded as very small prototypes of a single molecule adsorbed on the metal surface of a heterogeneous catalyst. Therefore, it is worthwhile pointing out that theoretical studies of increasingly growing metallic clusters with a few adsorbed atoms or molecules can characterize the variation of the chemisorption and catalytic properties from the microscopic level to the bulk catalyst.
With respect to the interaction between the N2 and transition metal cluster, some interesting types of small metallic clusters bearing non-metal atoms are those containing transition metal and nitrogen atoms [1, 4]. These systems are the series of adsorption complexes formed with the N2 molecule and monomers and dimers of the transitions metals: Sc, Ti, V, Cr, Co, and Ni [15]. Theoretical studies of those small systems are highly relevant for the catalytic processes involved in ammonia synthesis and nitrogen fixation [16]. A theoretical investigation on those clusters has been performed at the level of the density functional theory (DFT) [17] with the exchange and correlation potentials under both the local spin density approximation (LSDA) of Vosko-Wilk-Nussair (SVWN5) and the generalized gradient approximation (GGA) of Becke-Perdew-Wang (BPW91), and employing 6–311G* basis sets for all the atoms. Several the other experimental and theoretical investigations on nitride metallic clusters involving different transitions metals such as Ti, Zr and Nb [12]; Nb, Ta and Re [18]; and Y and La [19] as well as Fe, Cu and W [1, 20–22] have been synthesized and characterized. It has been found in the course of that study that the adsorbed N2 molecule was still characterized by a strong triple covalent bond that invariably remained unchanged after its adsorption on the transition metal clusters. On the other hand, the transition metal atoms had the d-orbitals partially unoccupied, with the energy cost to alter the atomic orbital populations being rather small. More importantly, the adsorption of the N2 molecule on the transition metal clusters changed noticeably the magnetic character of the metal atoms, with transitions from anti-ferromagnetism to ferromagnetism in the case of the Cr clusters. The variation of the magnetic properties of metallic clusters upon N2 adsorption has been observed in almost all the transition metal systems at varying degrees.
To the best of our knowledge, no theoretical investigation on this series of interesting WNn (n = 1–9) clusters has been systematically performed. Therefore, the computational investigation on the WNn (n = 1–9) clusters by DFT methods is reported herein as the paper in a series of publications devoted to these types of compounds [23]. The present investigation includes the determination of the clusters equilibrium geometries and the calculation of their total energies, fragmentation energies and natural population analyses. The calculated properties have been employed in interpreting different chemical properties of the clusters such as their relative stability, the nature of their bonding, formation and their internal charge distributions.
Computational details
The application of ECP, by means of which only the valence electrons are explicitly treated theoretically, provides a reasonable method to reduce difficulties in calculations of clusters containing heavy atoms, which are caused by a large number of two-electron integrals of heavy metal atom of the investigated systems. LanL2DZ basis sets, which include the scalar relativistic effects, become widely used in computational chemistry, particularly in the investigation of some compounds or clusters containing heavy metal elemental atoms [2, 24–26]. The standard LanL2DZ basis sets of ECP theory consistent within the third row transition metals. This method (at B3LYP/LanL2DZ level) results in bond length of W2 cluster with spin S = 0 a value of 2.182 Å, which deviates to theoretical finding, R(W-W) = 2.039 [27], by less than 7%. The photoelectron spectra of the anionic CunN–1 (n = 2–4) clusters are calculated at the (U)B3LYP/LanL2DZ level, showing a good agreement with the available experimental results [2]. All-electron B3LYP/6–31G(d) calculation of N-N bond length of N2, namely 1.106 Å, is in good agreement with available experimental and computational data (1.133Å [2] and 1.098Å [10]). Therefore, the combination of DFT methods with ECP’s can provide a feasible and accurate approach to the study of the WNn (n = 1–9) clusters as shown below.
Present calculations were undertaken at the level of the DFT theory with the hybrid Becke (B3) exchange and the Lee, Yang and Parr (LYP) [28, 29] correlation (B3LYP) functionals in combination with 6–31G(d) basis sets for N and LanL2DZ double-zeta basis sets for W as implemented in the Gaussian code [30]. In order to optimized WNn (n = 1–9) geometries, geometrical optimizations were systematically carried out and were followed by the evaluation of their harmonic vibrational frequencies in order to attest the clusters stability and make sure that all optimized geometries are stable. Spin-polarized calculation for the WNn (n is odd) clusters while spin unpolarized calculation for the WNn (n is even) clusters were taken into accounts. The spin contamination for transition-metal nitrogen clusters is negligiable.
Results and discussion
Equilibrium geometries, total energies and stabilities
WN
Since the ground-state atomic tungsten and N have six unpaired electron (5d56s1) and three unpaired electron (2p3), respectively, various spin multiplicities have been taken into accounts. The linear WN molecule with doublet, quartet and sextet spin state is performed. Based upon theoretical results of WN cluster summarized at Table 1, one notices that W-N bond length in WN cluster increases from 1.655 Å to 2.965 Å as spin S goes from S = 1/2 to S = 7/2. W and N interact with σ chemical bonding. WN cluster with doublet, sextet and octet spin states is 1.25, 3.85 and 5.76 eV higher in total energies than quartet spin state. Consequently, it should be pointed out that WN cluster with quartet spin state is the most stable structure; furthermore, the W-N bond length in WN molecule with quartet spin state is 1.665Å which is in good agreement with experimental result (1.741 Å) [31], this finding gives a firm supporting to our calculation. The corresponding electronic state of the most stable WN cluster is 4Σ character. The sharp 1059.cm–1 is assigned to WN isolated in solid argon [23]. However, the harmonic fundamental for doublet WN isomer is 1028.0 cm–1, furthermore, W-N bond length in quartet WN is 1.665 Å, which is in good agreement with the gas-phase value (1.667Å) [24A] and theoretical result(1.678Å) [23].
Based upon natural population analysis, the final nature population distribution shows that charges in WN molecule transfer from 5d of W atom to 2p of N atom because the electronegativity of N atom is bigger than that of W atom. The charge-transfer of the most stable WN molecule with quartet spin state is bigger than those with doublet and sextet spin states. This observation is similar to our previous theoretical result of CuN molecule [2], and the 5d orbitals of W atom in WN molecule, which plays the same rule of Cu in CuN cluster, do not behave as core orbitals but actually play important roles in chemical bonding.
WN2
The possible WN2 clusters with C2v, C ∞v, Cs and D ∞h symmetries (Table 1) are taken into considerations and selected as the candidates of the ground-state configuration. The nonlinear C2v WN2 cluster with spin states being considered are shown at Fig. 1 and Table 1, W-N bond lengths of C2v WN2 cluster increase while N-N bond length decreases, together with the steadily drops of the stability, as the spin S goes from S = 0 to S = 2 monotonously. On the other hand, the singlet C2v WN2 is the most stable structure. As for Cs WN2 cluster, frequency analysis on Cs WN2 cluster shows that only singlet Cs WN2 is the stable structure; however, the singlet Cs WN2, which is 0.52 eV higher in total energy than the singlet C2v WN2 cluster, is less stable than C2v WN2 (S = 0) isomer. In addition, our theoretical result of W-N bond length (1.804Å) in C2v WN2 (S = 0) isomer is in good agreement with 1.717Å at the BP86 level [23]. Charges in C2v WN2 transfer from W atom to N atoms.
Linear WN2 isomers with well defined C ∞v and D ∞h symmetries are considered. For C ∞v WN2 cluster, the total energy of C ∞v WN2 increases as spin S goes from S = 0 to S = 2, together with pronounced drops of the stability, reflecting the higher stability of C ∞v WN2 with singlet spin state as compared with C ∞v WN2 with triplet and quintet spin states. Based upon the natural populations, one finds that charges in C ∞v WN2 molecule transfer from W and N(2) atoms to N(1) atom, furthermore, the charges localized on N(1) atom are mainly transferred from W atom, the N(2) in C ∞v WN2 isomer does little contribution to charge-transfer.
The Linear D ∞h WN2 cluster considering of different states is performed. Unfortunately, harmonic frequency analysis on D ∞h WN2 cluster indicates that the D ∞h isomer with triplet spin state has an imaginary frequency, which is a transition state. However, the D ∞h isomers with singlet and quintet spin states turn out to be the stable structures. W-N stretching harmonic frequency of the singlet D ∞h WN2 is determined as 710.3 cm–1, which is much lower than 845.2 cm–1 of C2v WN2 isomer with singlet spin configuration, reflecting that this calculation is in good agreement with experimental measurement [1]. Furthermore, the singlet D ∞h isomer is more stable than that of the quintet state. However, it is less stable than C ∞v WN2, demonstrating that W in linear WN2 molecule is in favorable of chemisorptions of nitrogen rather than dissociative nitrogen.
By comparison the calculated total energies of C2v, C ∞v, D ∞h and Cs symmetries, it has been noticed that the linear WN2 clusters are less stable than C2v isomer. Therefore, the singletWN2 is the most stable structure, which is selected as the ground state, the corresponding electron state is 1A1 character, indicating that N2 unit in neutral WN2 isomer is in favorable of chemisorptions on W atom, in the other word, the dissociation of nitrogen is less stable with respect to the N2 molecular chemisoption on W atom.
WN3
Equilibrium geometries of WN3 with C ∞v, C2v, C3v and Cs symmetries are optimized. Specifically, the Cs WN3 isomer can be described as the slightly distorted C3v WN3 isomer, W atom interacts with three N atoms simultaneously with nonequivalent W-N bond lengths. As can be seen from the findings related to geometries of examined systems, which is tabulated as Table 1 and illustrated on Fig. 1, the W-N bond length (R) of Cs WN3 is obviously exhibits dependence on the spin of this species considered. The W-N bond distance (R) in Cs WN3 cluster increases steadily as spin S varies from doublet to sextet state. On the contrary, W-N bond length (R0) and total energy of Cs WN3 are not sensitive to the spin variation. Based upon theoretical results of total energies, it is found that the quartet Cs WN3 is the most stable structure, the electron state of the most stable Cs WN3 cluster is corresponding to 4A” character.
After one N atom is capped on the C ∞v WN2 isomer, C ∞v isomer is yielded. The quartet WN3 is a transition state and geometry optimization on C ∞v isomer with sextet spin state fails to converge. Fortunately, C ∞v WN3 with doublet state is found to be the stable structure, however, it is less stable than the quartet Cs isomer.
Cs WN3(B) structure, which is depicted as one N capped on C ∞v WN2 isomer, is displayed in Fig. 1. It is worth pointing out that Cs WN3(B) structure apparently distorts the geometry of C ∞v WN3 isomer. W in Cs WN3(B) isomer interacts with one N and N2 units, respectively. Theoretical result on Cs WN3(B) proves that Cs WN3(B) is the stable isomer. As can be seen from the finding related to the final equilibrium geometry correlation with spin of this species considered, which is provided at Table 1, an elongation of W-N2 bond length as well as the steadily drops of total energies of Cs WN3(B) isomer are found. It is important to be pointed out that the doublet Cs WN3(B) isomer is the most stable structure.
The C2v WN3 isomer is yielded after one N atom caps on the bottom of C2v WN2 isomer. This interesting geometry can be seen as the circle-like structure with W atom interacting with two N atoms directly. Unfortunately, the C2v WN3 with doublet and sextet spin states turns out to be unstable structures, however, the C2v WN3 with quartet spin state is verified to be the most stable structure.
Based upon calculated results on total energies, it is worthwhile mentioning that Cs WN3(B) is the most stable structure. Therefore, W in neutral WN3 clusters prefers to bound N2 and N units rather than N3 units, in the other word, N3 unit in WN3 cluster is not the favorable building block.
WN4
Equilibrium geometries of WN4 clusters with C4v, C2v, C3v, Cs, and D ∞h symmetries are optimized at the (U)B3LYP/GEN level of this species considered. Our theoretical calculation shows obviously that the C ∞v WN4 isomer is not a thermodynamically stable structure. Fortunately, the linear D ∞h WN4 isomers with singlet and triplet spin states turn out to be the stable structures. However, the D ∞h WN4 with quintet spin state has two imaginary frequencies, which is corresponding to the second-order saddle point. Based upon the calculated geometry of D ∞h WN4 isomer (Table 1), it indicates that the W-N bond length increase from 1.983 to 2055 Å monotonously while charge-transfer between W and N atom decreases as the spin S varies from S = 0 to S = 2, reflecting that the electrostatic interactions between N(1) and W (or between N(3) and W) become weak along with the elongation of W-N(1) or W-(3) bond lengths. In addition, the charges in D ∞h WN4 isomer mainly transfer from W atom to N((1) and N(3) atoms. W-N and N-N bonds interact each other with π chemical bonding. Total energy calculation reveals that triplet D ∞h WN4 isomer is the most stable structure, the corresponding electron state is 3Σg. Two of N2 units in linear D ∞h WN4 isomer can be seen as the basic building blocks, furthermore, the W atom preferentially reacting with two N2 molecules is an evidence for molecular chemisoption of nitrogen being energetically more stable than dissociative nitrogen. Similar to C ∞v WN2 isomer, charges in D ∞h WN4 isomer are transferred from N(2), N(4) and W atoms to N(1) and N(3) atoms.
The C2v WN4 isomer, which can be seen as the distortion of linear D ∞h WN4 isomer, is obtained. Subsequently, harmonic vibrational frequency analysis reveals that the linear quintet D ∞h WN4 isomer is a transition state, however, singlet and triplet states turn out to be the stable structures. Similar to D ∞h WN4 isomer, the W-N bond lengths and natural populations of W and N atoms in C2v WN4 isomer are associated with spin S, bond lengths of C2v WN4, which are shorter than those of D ∞h WN4 isomer, increases from 1.922 to 2.001 Å along with the increasing of charge-transfer from W to N(1) or N(3) atoms and decreasing of charge-transfer from W to N(2) and N(4) atom, as spin S goes from S = 0 to S = 2, indicating that the electrostatic interactions between W and N(1) (or W and N(3)) in the triplet state is stronger than those of the singlet state. It obviously shows that the triplet C2v WN4 cluster is the most stable structure, furthermore, it less stable than the triplet D ∞h WN4 isomer. W-N and N-N are σ chemical bonding. Additionally, most of the charges obtained from W atom localize at N(1) and N(3) atoms.
As for C3v, Cs, and C4v isomers, the C3v WN4 is considered the one candidate of ground state, which can be seen as W inserting into N4 units, with W atom interacting with three N atoms simultaneously with equivalent W-N bond lengths. The final geometry optimization on C3v WN4 isomer proves that the singlet state is the only stable structure. Furthermore, N-N bond length is longer than free N-N bond length, the C3v WN4 isomer is 6.46 eV higher in total energy than the D ∞h WN4 isomer, consequently, it is less stable than the D ∞h WN4 isomer. WN4 with C4v symmetry, which can be described as W capped on the planar N4 units, is yielded, W in C4v WN4 interacts with four N atoms directly with equivalent W-N bond lengths. N-N bond lengths in C4v WN4 isomer are longer than the free N-N bond length. Harmonic vibrational frequency analysis proves that the singlet state is the low-lying stable structure. The circle-like Cs isomer is taken into account, the calculated results on harmonic vibrational frequency analysis demonstrate that Cs isomer with quintet and triplet spin states have one imaginary frequency. However, the singlet Cs isomer turns out to be a stable structure. Similar to C4v and C3v isomers, N-N bond lengths in Cs isomer are longer than free N-N bond length of N2 molecule, furthermore, singlet Cs isomer is 2.65 eV higher than triplet D ∞h isomer. In general, all of the three structures with singlet spin state turn out to be the stable structures. However, they are less stable than triplet D ∞h isomer. Therefore, the triplet D ∞h isomer is the lowest-energy structure, which is selected as the ground state, the corresponding electron state is 3Σg. Based upon the results show above, we can prefer that W prefers to interact with N2 units and does not favor to interact with N4 units directly
WN5
WN5 with C2v symmetry, which is obtained by capped one N on the C2v WN4 cluster and is composed of one N atom and two N2 units, has been considered. Theoretical results show that C2v WN5 with sextet spin state is a transition state, however, doublet and quartet C2v WN5 isomers turn out to be the stable structures. Based upon the calculated result, it indicates that W-N(2)(or W-N(4)) bond length is dependence on the spin S of this species considered, furthermore, an elongation of W-N(3) or W-N(4) bond length is found when spin S goes from S = 1/2 to S = 5/2. W interacts with N(2)-N(3) and N(4)-N(5) units directly with π chemical bonding. However, the bond lengths of N(2)-N(3) and N(3)-N(4) units are longer than that of isolate N2 unit, W-N(1) bond length is shorter than W-N(2), however, W-N bond lengths in C2v WN5 isomer is slightly longer than W-N bond length [31].
The C3v WN5 isomer with spin states is taken into account. Theoretical results apparently indicate that only quartet C3v WN5 cluster is the stable structure. Specifically, this structure can be seen as W interacting with three N atoms with equivalent bond lengths and one N2 unit directly. Furthermore, W-N(2) bond length in C3v WN5 isomer is shorter than those of W-N(3) bond lengths. However, the quartet C3v WN5 is less stable than doublet C2v WN5.
The benzene-like circle WN5 isomers with C2v(B) with S = 3/2 and 5/2 have a imaginary frequency, which are transition states; however, doublet C2v WN5(B) isomer turns out to be a stable structure. W-N(1) or W-N(2) bond length in circle WN5 (S = 1/2) is shorter than those in C2v WN5 isomer, on the contrary, N(1)-N(3) or N(2)-N(4) bond length in circle WN5 is longer than those in the C2v and C3v isomers. In addition, W and N in circle WN5 isomer interact with a small π bonding, N(1)-N(2) and N(3)-N(4) have the large π chemical bonding (Figure 3). Similar to C3v WN5 isomer, C2v WN5(B) is less stable than doublet C2v WN5 isomer.
Based upon calculated total energies of WN5 clusters, it should be mentioned that doublet C2v WN5 is the lowest-energy geometry, which actually is the most stable structure and ground state. In analogy to the C2v WN2 and D ∞h WN4 isomers, this finding reflects that W has a tendency to interact with more N2 units, in the other word, WN5 prefers to chemisoption nitrogen also.
WN6
Initial configurations of WN6 clusters, maintaining D4 h, D4d, C3v, and C2v symmetries, are considered as the possible candidates of the ground state geometry. The C2v geometry with N(1)WN(4) bond angle, namely 90°, is taken to be the initial geometry, however, the final equilibrium geometry with singlet and triplet spin states is linear structure with D ∞h symmetry, which turns out to be the stable structure. Unfortunately, WN6 with quintet spin state fails to convergence. Specifically, this structure can be described as W atom interacts with two N3 units. In addition, N-N units bind together with σ bonds, furthermore, N(1)-N(2) bond length is longer than N(2)-N(3) bond length. However, N(1)WN(4) block bonds together with π chemical bonding.
The NH3-like C3v WN6 isomer is optimized, however, theoretical result shows that singlet WN6 isomer is the only stable structure. C3v WN6, with N(1)WN(3) bond angle of 97.2°, can be seen as W interacting with three N2 units with equivalent bond lengths simultaneously, which looks like a big pyramid. The calculated total energy shows that the pyramid-like C3v WN6 isomer is lower in total energy than those of C2v WN6 isomer, therefore, C3v WN6 with singlet spin state is the lowest-energy structure, and it is selected as the ground state. The corresponding electron state is 1A1. Based upon this finding, one can find that W atom in WN6 isomers prefers to interact with N2 units, in the other word, W is in favor of chemisorptions of nitrogen rather than dissociative nitrogen, this theoretical observation is in good agreement with experimental result [1]. Furthermore, this result gives a firm supporting to our prediction and theoretical result in turn, which is completely different from the results for tungsten bulk crystals [32].
WN7
The possible WN7 isomers with C2v and Cs symmetries are taken into considerations. For the C2v WN7 isomer, the geometry can be described as one N atom capped on the top of D ∞h WN6 isomer, W atom interacts directly with one N and two N3 units simultaneously. N(1)WN(4) is a π chemical bond and N-N units are σ chemical bond. W-N(1), W-N(7), and N(1)-N(2) as well as N(2)-N(3) bond lengths increase monotonously when S goes from 1/2 to 5/2. Charges mainly transfer from W, N(2), and N(5) atoms to N(1) and N(4) atoms (near W atom), however, the obtained charges localized on N(3) and N(6) atoms are very small. Harmonic vibrational frequency analysis on C2v WN7 isomer indicates that C2v WN7 with quartet spin state is a transition state. Based upon the calculated results of total energy summary at Table 1, it obviously shows that the doublet C2v WN7, together with N(1)WN(4) of 152.4°, is the most stable geometry.
Guided by pyramid-like C3v WN6 isomer, Cs WN7 is yielded. Specifically, W atom interacts with one N atom and three N2 units directly. W-N(3) and N(3)-N(6) bond lengths, together with total energies, are associated with the electron spin states, W-N(3) and N(3)-N(6) bond lengths as well the total energies increase steadily, along with the pronounced drops of stability, as spin S goes from S = 1/2 to S = 5/2, indicating that doublet Cs WN7 isomer is the most stable geometry.
The initial planar circle Cs WN7(B) is considered and calculated. Cs WN7(B) isomer with quintet spin state is a transition state, however, doublet and quintet Cs WN7(B) isomers are energetically stable structures. Specifically, this geometry can be described as W interacting with three N atom simultaneously with W-N(1) and W-N(7) bond lengths of 1.861 and 1.952 Å, W-N(1), W-N(2) and W-N(7) bonds form the π chemical bonding. Similar to C2v WN7 above, N-N units interact with σ chemical bonding.
Based upon the relative energies of low-lying WN7 isomers, it obviously indicates that doublet Cs WN7 isomer is the lowest in total energy, therefore, it is selected as the ground state, the corresponding electron state is 2A’. It is important to note that W in the most stable WN7 isomer is interested in interacting with more N2 units with chemisorption nitrogen forms. One can rule out the possibility that tungsten atom or tungsten clusters do react with molecular nitrogen more favorable than with atomic nitrogen, in the other word, molecular chemisorption of N2 is energetically more favorable than atomic one (dissociative chemisorption).
WN8
The WN8 isomers with C2v and Cs symmetries are considered. C2v WN8 isomer is yielded after one N is capped on the top of C2v WN7 isomer, W interacts with one N2 unit and two N3 units simultaneously. W-N(1) and N-N bond lengths, together with the total energies, are correlated to the spin states. An elongation of R0(W-N(4)), R1 and R3 bond lengths is found, on the contrary, total energy decreases monotonously when spin S varies from S = 0 to 2, reflecting the higher stability of C2v WN8 isomer with spin singlet state as compared with the C2v WN8 isomer with triplet and quintet spin states. Compared with C2v WN7 isomer, W-N(4) in C2v WN8 is shorter than that in C2v WN7 isomer after an addition of N(8) in C2v WN8 isomer. Unfortunately, quintet C2v WN8 isomer is a transition state, therefore, triplet C2v WN8, which is lower in total energy than that with singlet spin state, is selected as the ground state.
Guided by geometry of Cs WN7 isomer above, new geometry is yielded by capped one N atom on Cs WN7 isomer. W atom in C2v WN8(B) isomer interacts with four N2 units simultaneously with nonequivalent W-N and N-N bond lengths. C2v WN8(B) isomer with spin of this species considered is optimized. Unfortunately, quintet C2v WN8(B) isomer is a transition state. Based upon the calculated total energies, it is surprised to know that C2v WN8(B) isomer is lower in total energy than triplet C2v WN8 isomer, furthermore, the singlet C2v WN8(B) is more stable than quartet C2v WN8. Therefore, singlet C2v WN8(B) is selected as the ground state, the corresponding electron state is 1A1. According to the finding above, one can find that W atom in WN8 isomers prefers to interact with four N2 units with chemisorption forms, in the other word, the WN8 prefers to interact with the N2 units rather than N3 units.
WN9
WN9 with C2v symmetry, which is yielded by capped one N atom on the C2v WN8 isomer, is undertaken, W in C2v WN9 isomer interacts directly with three N3 units. W-N bond lengths in C2v WN9 isomer are longer than those of the corresponding C2v WN8 isomer above. In addition, N-N bond distance in C2v WN9 is about 0.02Å longer than that in free N2 molecule. Frequency analysis on C2v WN9 isomer shows that the sextet spin configuration is a transition state, however, C2v WN9 with doublet and quartet spin configurations turn out to be the stable structures. Total energy of C2v WN9 makes it certain that C2v WN9 with triplet spin configuration is the most stable structure.
Cs WN9 isomer, which is yielded after one N atom capped on C2v WN8(B) isomer, is optimized considering of spin species. Theoretical results reveal that the total energy, W-N(3) as well as N(8)-N(9) bond length is associated with spin of this species, furthermore, theoretical result shows that doublet Cs WN9 isomer is lower in total energy than the quartet and sextet states, thus, doublet Cs WN9 isomer is the most stable structure.
Based upon theoretical results on Cs and C2v isomers, one notices that Cs isomer is 7.095 eV lower in total energy than that of C2v isomer. Therefore, doublet Cs WN9 isomer has an enhanced stability and is the most stable structure. W prefers to interact with three N2 units rather than N3 units, which is show previously [5], in the other word, W is in favorable of chemisorption nitrogen rather than dissociative nitrogen.
Relative stability
The relative stability of the most stable WNn(n = 1–9) clusters is calculated according to the formula
Where the total energy of nitrogen atom is calculated at the (U)B3LYP/6–31G(d) level, theoretical results of total energies for N with doublet, quartet, and sextet spin states are –54.4789986, –54.5844894, and –53.4687708 Hartree, respectively. According to the calculated results of N atom, it reveals that N atom with quartet spin state is the most stable structure. The calculated E(n,n-1) values for WNn (n = 1–9) isomers are 3.140, 6.711, 4.520, 3.194, 7.261, 16.356, 4.940, and 2.976 eV, respectively, which is show in Fig. 2. The most remarkable results of E(3,2), E(6,5), and E(7,6) are found, indicating that the WN3, WN6, and WN7 clusters emerge as the most abundant in mass spectroscopy. It should be mentioned that WN7 is the most stable isomers.
Summary
WNn (n = 1–9) clusters are investigated theoretically by using density functional theory methods. Geometry optimizations are carried out under the constraint of well-defined symmetries at the (U)B3LYP level employing a pseudopotential method in conjunction with double-zeta basis sets for W atom and 6–31G(d) basis sets for N atoms. In this article, total energies, relative stabilities as well as chemical bonding and equilibrium geometries of WNn (n = 1–9) clusters are systematically discussed theoretically. The calculated results reveal that the lowest-energy WNn (n = 1–9) isomers prefer to interact with N2 units rather than N3 and N units, furthermore, the circle-like low-lying WNn structures are taken into account, which turn out to be less stable than the other isomers with N2 acting as building blocks, in the other words, W is in favorable of chemisorption nitrogen rather than dissociative nitrogen, which is in good agreement with experimental observation. Based up the findings above, we can conclude that transition metal W in the lowest-energy WNn clusters is in favorable of interacting with N2 units for small TM-N clusters, and we can not say for certain if TM prefers to bind N3 units in the large TM-N clusters [33]. Relative stability of the WNn isomers emerges that the most remarkable WN3, WN6, and WN7 isomers are larger, which correspond to the abundant in mass spectroscopy. In addition, natural population analyses, and natural electron configurations are calculated in order to elucidate the charge distributions in the clusters. Theoretical results reveal that W transfers the charges to N atoms near W atom, which plays an important role in chemical bonding.
Footnotes
Acknowledgments
This work is supported by Yong teacher training Program of Shanghai Education committee and the Robert A. Welch Foundation (USA) as well as Physical electronics disciplines (NO: 12XKJC01). This paper has been performed partly on the Supercomputing Center of NSRL of University of Science and Technology of China.