Theoretical investigations on geometrical and electronic structures of silver clusters

Geometrical structures and ground and excited states of silver clusters are theoretically investigated using long-range corrected (LC) density functional theory (DFT) calculations. The discrepancy between HOMO-LUMO gaps and the vertical ionization potential minus vertical electron affinity values, which should be the same values, is explored to reveal the significance of long-range exchange effects on the electronic states of metal clusters. The difference between HOMO-LUMO gaps and HOMO-LUMO excitation energies, which is called “exciton binding energy,” is also tested. As a result, it is found that the long-range exchange effects are requisite in DFT calculations to quantitatively investigate the ground and excited states of metal clusters. © 2018 Wiley Periodicals, Inc.     

Photoabsorption cross sections of sodium clusters: electronic and geometrical effects

We study the origin of the discrepancy between the photoabsorption cross sections of small jellium spheres calculated by the time dependent local density approximation (TDLDA) and experiments for small metallic clusters. We have specifically studied Na ₂₁ ⁺ . We conclude that both non-local exchange-correlation effects beyond the LDA and geometrical effects beyond the jellium approximation should be taken in the same calculation. We also present local and non-local calculations for Na _n ^? (n=19, 91 and 197) within the framework of the jellium model. The large anions show a fragmentation of the plasmon due to its interference with the ionization threshold. This feature is absent in the TDLDA results.     

Singly and doubly excited states of butadiene, acrolein, and glyoxal: Geometries and electronic spectra

Excited-state geometries and electronic spectra of butadiene, acrolein, and glyoxal have been investigated by the symmetry adapted cluster configuration interaction (SAC-CI) method in their s-trans conformation. Valence and Rydberg states below the ionization threshold have been precisely calculated with sufficiently flexible basis sets. Vertical and adiabatic excitation energies were well reproduced and the detailed assignments were given taking account of the second moments. The deviations of the vertical excitation energies from the experiment were less than 0.3 eV for all cases. The SAC-CI geometry optimization has been applied to some valence and Rydberg excited states of these molecules in the planar structure. The optimized ground- and excited-state geometries agree well with the available experimental values; deviations lie within 0.03 A and 0.7 degrees for the bond lengths and angles, respectively. The force acting on the nuclei caused by the excitations has been discussed in detail by calculating the SAC-CI electron density difference between the ground and excited states; the geometry relaxation was well interpreted with the electrostatic force theory. In Rydberg excitations, geometry changes were also noticed. Doubly excited states (so-called 2 (1)A(g) states) were investigated by the SAC-CI general-R method considering up to quadruple excitations. The characteristic geometrical changes and large energetic relaxations were predicted for these states.     

The effect of silicon doping on the geometrical structures,stability, and electronic and spectral properties of magnesium clusters: DFT study of SiMgn (n = 1-12) clusters

Using the density functional theory (DFT) method at the B3LYP /6−311G (D) level, we studied how silicon doping affects the geometrical structure, stability, and electronic and spectral properties of magnesium clusters. The stable isomers of SiMg _n (n = 1-12) clusters were calculated by searching numerous initial configurations using the CALYPSO program. The geometrical structure optimization shows that most stable SiMg _n (n = 3-12) clusters are three-dimensional. In addition, geometrical structure growth patterns show that some structures of SiMg _n clusters can be directly formed by replacing one Mg atom in the corresponding Mg _{n + 1} cluster with one silicon atom, such as SiMg₈ and Mg₉ clusters. The stability of SiMg _n clusters is analyzed by calculating the average binding energy, fragmentation energy, and second-order energy difference. The results show that SiMg _n clusters with n = 5 and 8 are more stable than others. MO contents analysis show that the Si 3p-orbitals and Mg 3s-orbital are mainly responsible for the stability of these two clusters. The results of the natural charge population (NCP) and natural electronic configure (NEC) analysis of the electronic properties reveal that the charges in SiMg_n (n = 1-12) clusters transfer from magnesium atoms to silicon frame, and electronic charge distributions are primarily governed by s- and p-orbital interactions. In addition, the Vertical ionization potential (VIP), vertical electron affinity (VEA), and chemical hardness of ground sates of SiMg _n (n = 1-12) clusters were studied in detail and compared with the experimental results. The conclusions show that the chemical hardness of most SiMg _n clusters are lower than that of pure Mg _{n + 1} (n = 1-12) clusters, except for n = 1 and 8. This indicates that the doping of silicon atom can always reduce the chemical hardness of pure magnesium clusters. Finally, the infrared and Raman spectral properties of SiMg₅ and SiMg₈ clusters were calculated and discussed in detail.     

The electronic structure of small lithium clusters

Ab initio molecular orbital calculations using the STO-6G and STO6-21G basis sets have been performed for the cluster series Li _n ⁺ , Li _n , and Li _n ^– (wheren=2–7). Thirty-two optimized structures are discussed and reported, many of which (especially for the anionic structures) have not yet been considered. The calculations suggest that for all three species the optimum geometries are planar. Of the two levels of theories that were investigated, STO-6G//STO-6G and STO6-21G//STO-6G, the latter hybrid theory was found to be less reliable. In particular, for the anionic structures these calculations should provide a platform from which more sophisticated, i.e., configuration interaction, geometry optimization can be performed.     

Gas-phase structures of neutral silicon clusters

Vibrational spectra of neutral silicon clusters Si(n), in the size range of n = 6-10 and for n = 15, have been measured in the gas phase by two fundamentally different IR spectroscopic methods. Silicon clusters composed of 8, 9, and 15 atoms have been studied by IR multiple photon dissociation spectroscopy of a cluster-xenon complex, while clusters containing 6, 7, 9, and 10 atoms have been studied by a tunable IR-UV two-color ionization scheme. Comparison of both methods is possible for the Si(9) cluster. By using density functional theory, an identification of the experimentally observed neutral cluster structures is possible, and the effect of charge on the structure of neutrals and cations, which have been previously studied via IR multiple photon dissociation, can be investigated. Whereas the structures of small clusters are based on bipyramidal motifs, a trigonal prism as central unit is found in larger clusters. Bond weakening due to the loss of an electron leads to a major structural change between neutral and cationic Si(8).     

Theoretical modeling of ionization energies of argon clusters: nuclear delocalization effects

Temperature dependence of vertical ionization energies is modeled for small argon clusters (N ≤ 13) using classical parallel-tempering Monte Carlo methods and extended interaction models based on the diatomics-in-molecules approach. Quantum effects at the zero temperature are also discussed in terms of zero-point nuclear vibrations, either at the harmonic approximation level or at the fully anharmonic level using the diffusion Monte Carlo calculations. Both approaches lead to a considerable improvement of the theoretical predictions of argon clusters ionization energies and represent a realistic way of modeling of ionization energies for weakly bound and floppy complexes in general. A thorough comparison with a recent electron-impact experiment [O. Echt et al., J. Chem. Phys. 123, 084313 (2005)] is presented and a novel interpretation of the experimental data is proposed.     

Electron-impact ionization of helium clusters close to the threshold: appearance energies

We have investigated the ionization threshold behavior of small helium cluster ions (cluster size n=2-10) formed via electron-impact ionization of neutral helium droplets and derive appearance energies for mass-selected cluster ions using a nonlinear least-square-fitting procedure. Moreover, we report magic numbers in the mass spectrum observed at the electron energy of 70 eV. The apparatus used for the present measurements is a hemispherical electron monochromator combined with a quadrupole mass spectrometer. Our experiment demonstrates that helium clusters are not only exclusively formed via direct ionization above the atomic ionization potential but also indirectly via autoionizing Rydberg states. The present results are compared with previous electron-impact and photoionization results.     

Photodissociation investigation of doubly charged ethanol clusters induced by inner-shell electron ionization

Fragmentation of doubly charged ethanol clusters [(C(2)H(5)OH)(n)] following the O 1s ionization has been investigated by means of the photoelectron-photoion-photoion coincidence (PEPIPICO) method. The dominant fission channel of (C(2)H(5)OH)(n)(2+) was the formation of protonated cluster ion pairs [H(C(2)H(5)OH)(l)(+)/H(C(2)H(5)OH)(m)(+)]. The fragmentation mechanisms of these ion pairs were discussed based on the analysis of the PEPIPICO contour shape. It was clarified that the prominent fragmentation channel was a secondary decay mechanism, where neutral evaporation occurs after charge separation. On the other hand, the formation of small fragment ions was suppressed, excluding the formation of certain specific fragments (H(3)O(+), C(2)H(5)(+)/COH(+), and C(2)H(4)OH(+)). The formation of small fragment ions was suppressed due to the cooling effect caused by the neutral evaporation and the decrease in the electrostatic repulsive force caused by charge separation.     

Evolution of the geometrical and electronic structures of Gan(n=2-26) clusters: a density-functional theory study

Density-functional theory with generalized gradient approximation for the exchange-correlation potential has been used to calculate the lowest-energy geometries and electronic structure of neutral gallium clusters containing up to 26 atoms. Harmonic vibrational frequency analysis is undertaken to assure that the lowest-energy geometries are real local minima. With increasing cluster size, we find that the gallium clusters tend to adopt compact structures. The structures comprise triangular units that connect each other with different dihedral angles. The lowest-energy structure can be obtained by capping an atom on the structure of smaller one. The capping site occurs at a site where interactions with more atoms are available. The binding energy evolves monotonically with size, but Ga(8), Ga(14), and Ga(20) exhibit particularly higher stability. Except Ga(2) and Ga(4), all even-numbered gallium clusters we studied are closed-shell singlet states with a substantial highest occupied and lowest unoccupied molecular orbitals gap. The odd-numbered clusters are open shell with a small gap. The size dependence of cluster's ionization potentials and electron affinities is discussed and compared with available experiment.     

Theoretical investigation of electronic structures and excitation energies of doubly N-confused porphyrin and its group 11 transition metal (III) complexes

Density functional theory is carried out to study cis-doubly N-confused porphyrin and its metal (Cu3+, Ag3+, and Au3+) complexes. The electronic structures and bonding situations of these molecules have been investigated by using the natural bond orbital analysis and the topological analysis of the electron localization function. We have studied the electronic spectra of cis-doubly N-confused porphyrin and its metal complexes with time-dependent density functional theory. The introduction of group 11 transition metals leads to blueshifts of their electronic spectra with respect to that of cis-doubly N-confused porphyrin. In particular, the absorption spectra of the copper complex show some weak Q bands that mainly arise from a combination of ligand-to-metal charge transfer and ligand-to-ligand charge transfer transitions. The relativistic time-dependent density functional theory with spin-orbit coupling calculations indicates that the effects of spin-orbit coupling on the excitation energies of the copper and silver complexes are so small that it is safe enough to neglect spin-orbit interactions for these two complexes. However, it has a significant effect on the absorption spectra of the gold complex.     

Electronically excited states of water clusters of 7-azaindole: structures, relative energies, and electronic nature of the excited states

The geometries of 1H-7-azaindole and the 1H-7-azaindole(H(2)O)(1-2) complexes and the respective 7H tautomers in their ground and two lowest electronically excited pi-pi(*) singlet states have been optimized by using the second-order approximated coupled cluster model within the resolution-of-the-identity approximation. Based on these optimized structures, adiabatic excitation spectra were computed by using the combined density functional theory/multireference configuration interaction method. Special attention was paid to comparison of the orientation of transition dipole moments and excited state permanent dipole moments, which can be determined accurately with rotationally resolved electronic Stark spectroscopy. The electronic nature of the lowest excited state is shown to change from L(b) to L(a) upon water complexation.     

Binding energies of small lithium clusters (Li(n)) and hydrogenated lithium clusters (Li(n)H)

Large coupled cluster computations utilizing the Dunning weighted correlation-consistent polarized core-valence (cc-pwCVXZ) hierarchy of basis sets have been conducted, resulting in a panoply of internally consistent geometries and atomization energies for small Li(n) and Li(n)H (n=1-4) clusters. In contrast to previous ab initio results, we predict a monotonic increase in atomization energies per atom with increasing cluster size for lithium clusters, in accordance with the historical Knudsen-effusion measurements of Wu. For hydrogenated lithium clusters, our results support previous theoretical work concerning the relatively low atomization energy per atom for Li(2)H compared to LiH and Li(3)H. The CCSD(T)/cc-pwCVQZ atomization energies for LiH, Li(2)H, Li(3)H, and the most stable isomer of Li(4)H, including zero-point energy corrections, are 55.7, 79.6, 113.0, and 130.6 kcal/mol, respectively. The latter results are not consistent with the most recent experiments of Wu.     

Impact of different potentials on the structures and energies of clusters

Cluster studies have attracted much interest in the past decades because of their extraordinary properties. To describe the interaction between atoms or molecules and predict the energies and structures, potential functions are developed. However, different potentials generally produce different structures and energies for a cluster. To study the effect of potentials on the structure of a cluster, He clusters in the size range of 13-140 are investigated by Lennard-Jones (LJ), Pirani, and Hartree-Fock-dispersion individual damping (HFD-ID) potential with dynamic lattice searching (DLS) method. Potential function curves, cluster structures, bonds, and energies of the global minima are compared. The results show that cluster energies decrease with the values of the potential functions, the differences between structures depend upon the disagreements of the potentials, and the preferable motif of a cluster changes from icosahedron to decahedron with the increase of the derivative of the short-range part of the potentials.     

Geometries and electronic structures of negatively charged carbon clusters

Self-consistent field molecular orbital calculations have been performed on neutral and negatively charged clusters of carbon atoms using an extended basis set designed to obtain correct electron affinity. Correlation effects have been included perturbatively up to second order. The optimized geometries of theC _n ^? (n ≤ 7) anions are all linear chains as observed in experiments. The calculated electron affinities are comparable with experimental data. Studies of the stabilities of doubly charged anions show that clusters uptoC ₇ ^?? are unstable.     

Structural and electronic properties of boron-doped lithium clusters: ab initio and DFT studies

The lowest-energy structures and electronic properties of the BLi(n) (n = 1-7) clusters are reported using the B3LYP, MP2, and CCSD(T) methods with the aug-cc-pVDZ basis set. Though the results at the B3LYP level agree well with those at the CCSD(T) level, the MP2 method is rather unsatisfactory. The first three-dimensional ground state in the BLi(n) clusters occurs for BLi(4), and the impurity B atom is seen to be trapped in a Li cage from the BLi(6) cluster onwards. The evolution of the binding energies, vertical ionization potentials, and polarizability with size of cluster shows the BLi(5) cluster to be most stable among the BLi(n) clusters. Besides, the BLi(5) cluster is also found to have the largest reaction enthalpy (49.8 kcal/mol) upon losing a Li atom, which is different from the previous prediction. The unique stability of the 8-valence electron BLi(5) can be understood from the cluster electronic shell model (CSM). However, in contradiction to the prediction of the CSM, the 2s level is filled prior to the 1d level in the BLi(n) clusters.     

Geometries and electronic structures of W4 and W clusters

Geometries and electronic structures of W₄ and W clusters were studied by use of density functional methods B3LYP, B3P86, B3PW91, BHLYP, BLYP, and MPW1PW91. The calculated results indicate that the three‐dimensional structure of singlet state with either D_2d symmetry (B3LYP, B3P86, B3PW91, BLYP, and MPW1PW91) or C_2v symmetry (BHLYP) is the ground state for the W₄ cluster. For the W cluster, the doublet state is preferred, and the most stable structure is also 3D with either D_2d symmetry (B3LYP, B3PW91, BHLYP, BLYP) or C_2v symmetry (B3P86 and MPW1PW91). The calculated electron affinity at B3P86 gives the best performance compared with experiment. For the dissociation channel, W + W₃ is suggested to be the possible route for the W₄ cluster. For the W cluster, W + W is the most likely route for dissociation, in agreement with experiment. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Benchmark structures and binding energies of small water clusters with anharmonicity corrections

For (H(2)O)(n) where n = 1-10, we used a scheme combining molecular dynamics sampling with high level ab initio calculations to locate the global and many low lying local minima for each cluster. For each isomer, we extrapolated the RI-MP2 energies to their complete basis set limit, included a CCSD(T) correction using a smaller basis set and added finite temperature corrections within the rigid-rotor-harmonic-oscillator (RRHO) model using scaled and unscaled harmonic vibrational frequencies. The vibrational scaling factors were determined specifically for water clusters by comparing harmonic frequencies with VPT2 fundamental frequencies. We find the CCSD(T) correction to the RI-MP2 binding energy to be small (<1%) but still important in determining accurate conformational energies. Anharmonic corrections are found to be non-negligble; they do not alter the energetic ordering of isomers, but they do lower the free energies of formation of the water clusters by as much as 4 kcal/mol at 298.15 K.