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Theoretical Chemistry

Density functional theory study of small nickel clusters

Profile image of Satyender GoelSatyender GoelProfile image of Artëm E MasunovArtëm E Masunov

2012, Journal of Molecular Modeling

https://doi.org/10.1007/S00894-011-1100-X
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Abstract

The stable geometries and atomization energies for the clusters Ni n (n=2-5) are predicted with all-electron density functional theory (DFT), using the BMK hybrid functional and a Gaussian basis set. Possible isomers and several spin states of these nickel clusters are considered systematically. The ground spin state and the lowest energy isomers are identified for each cluster size. The results are compared to available experimental and other theoretical data. The molecular orbitals of the largest cluster are plotted for all spin states. The relative stabilities of these states are interpreted in terms of superatom orbitals and no-pair bonding.

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Results and discussion the experimental value of 2.1 eV. Several DFT studies have been performed in the past using pure DFT (LDA and GGA) functionals [9, 13, 16, 19, 20, 23, 24], which are reported to produce better geometries but not energies. Similarly, our BMK predictions for triplet and singlet dissociation energies are better than ab initio CASPT2 [21] ones (1.93 eV and 1.95 eV, respectively), while the CASPT2 predictions for the bond lengths (2.24A and 2.25 A) [21] are superior to our BMK predictions. It is worth noting the increase in bond length and decrease in binding energy with increasing multiplicity, which disfavors higher spin states due to easy bond breaking.
Results and discussion the experimental value of 2.1 eV. Several DFT studies have been performed in the past using pure DFT (LDA and GGA) functionals [9, 13, 16, 19, 20, 23, 24], which are reported to produce better geometries but not energies. Similarly, our BMK predictions for triplet and singlet dissociation energies are better than ab initio CASPT2 [21] ones (1.93 eV and 1.95 eV, respectively), while the CASPT2 predictions for the bond lengths (2.24A and 2.25 A) [21] are superior to our BMK predictions. It is worth noting the increase in bond length and decrease in binding energy with increasing multiplicity, which disfavors higher spin states due to easy bond breaking.
energies (eV), as displayed by each structure. Binding energies in parentheses are the last SCF energies after several steps for unconverged geometries Table 1 Geometries of Niz2, Ni3, Nis and four isomers of Ni, with several spin states (singlet, triplet, quintet, septet, nonet, undectet, duodectet and tridectet), along with their bond lengths (A) and binding than 90°, which is in agreement with our findings. An LDA and GGA study with various basis sets [9] reported only the energies of the lowest spin state (triplet). The best binding energy reported by Arvizu et. al. [9] with TZVP-GGA (3.32 eV) is more than our BMK predictions. The higher energy in this case is likely to be due to overestimation on the part of the GGA method, consistent with the Ni dimer results (2.64 eV from [9] vs. our BMK predictions of 1.99 eV, as compared to the experimental value of 2.1 eV [18]). (square planar, two tetrahedral, and rhombic) for Ni in several spin states (singlet, triplet, quintet, septet, nonet, undectet and tridectet). We represent these structures with a letter in parentheses: Ni,(s) is square planar, Ni,(tl) is tetrahedral, Ni,(t2) is distorted tetrahedral, and Ni,(r) is rhombic. We determined that the rhombic (planar) structure was favored in the case of Ni, in all but one nonet state, where Ni,(tl) and Ni4(t2) were equally stable. We also found that many of our other initial geometries [square planar 3 Ni,(s) and distorted tetrahedral >°Nia(t2)] converged to the stable rhombic (planar) type structure Nig(r). This led us to draw the conclusion that the quintet is the most stable spin state for Niy. Our results differ from those reported by Arvizu et al. [9] and Petkov et al. [23]. They reported tha quintet Ni,(tl) is the ground state structure, while we predict that quintet Ni,(r) is the ground-state geometry. The binding energy of °Ni4(tl), 4.02 eV (GGA/TZVP level of and GGA study with various basis sets [9] reported only the
energies (eV), as displayed by each structure. Binding energies in parentheses are the last SCF energies after several steps for unconverged geometries Table 1 Geometries of Niz2, Ni3, Nis and four isomers of Ni, with several spin states (singlet, triplet, quintet, septet, nonet, undectet, duodectet and tridectet), along with their bond lengths (A) and binding than 90°, which is in agreement with our findings. An LDA and GGA study with various basis sets [9] reported only the energies of the lowest spin state (triplet). The best binding energy reported by Arvizu et. al. [9] with TZVP-GGA (3.32 eV) is more than our BMK predictions. The higher energy in this case is likely to be due to overestimation on the part of the GGA method, consistent with the Ni dimer results (2.64 eV from [9] vs. our BMK predictions of 1.99 eV, as compared to the experimental value of 2.1 eV [18]). (square planar, two tetrahedral, and rhombic) for Ni in several spin states (singlet, triplet, quintet, septet, nonet, undectet and tridectet). We represent these structures with a letter in parentheses: Ni,(s) is square planar, Ni,(tl) is tetrahedral, Ni,(t2) is distorted tetrahedral, and Ni,(r) is rhombic. We determined that the rhombic (planar) structure was favored in the case of Ni, in all but one nonet state, where Ni,(tl) and Ni4(t2) were equally stable. We also found that many of our other initial geometries [square planar 3 Ni,(s) and distorted tetrahedral >°Nia(t2)] converged to the stable rhombic (planar) type structure Nig(r). This led us to draw the conclusion that the quintet is the most stable spin state for Niy. Our results differ from those reported by Arvizu et al. [9] and Petkov et al. [23]. They reported tha quintet Ni,(tl) is the ground state structure, while we predict that quintet Ni,(r) is the ground-state geometry. The binding energy of °Ni4(tl), 4.02 eV (GGA/TZVP level of and GGA study with various basis sets [9] reported only the
theory), as reported by Arvizu et. al. [9], was less than that predicted in this study (4.57 eV) for the same spin state and geometry, which differed from the observations made in the case of Ni3 above. In another study by Reuse et al. [20], the authors pointed out the importance of Jahn-Teller distortion in predicting the correct structure. They stated that for the atomic Ni configuration d’s', d electrons can be ignored; only the contribution from the s electrons need be considered. According to the Jahn-Teller theorem, an electronic system with degenerate energy levels is unstable, and structural distortion will occur in order to remove this degeneracy [34]. This is why we observed that the square- planar tetramer with four valent electrons underwent structural distortion into the planar rhombus structure.
theory), as reported by Arvizu et. al. [9], was less than that predicted in this study (4.57 eV) for the same spin state and geometry, which differed from the observations made in the case of Ni3 above. In another study by Reuse et al. [20], the authors pointed out the importance of Jahn-Teller distortion in predicting the correct structure. They stated that for the atomic Ni configuration d’s', d electrons can be ignored; only the contribution from the s electrons need be considered. According to the Jahn-Teller theorem, an electronic system with degenerate energy levels is unstable, and structural distortion will occur in order to remove this degeneracy [34]. This is why we observed that the square- planar tetramer with four valent electrons underwent structural distortion into the planar rhombus structure.

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