Computational Investigation of the Geometrical and Electronic Structures of VGen-/0 (n = 1-4) Clusters by Density Functional Theory and Multiconfigurational CASSCF/CASPT2 Method

Mn2 Dimers Encapsulated in Silicon Cages: A Complex Challenge to MC-SCF Theory

MC-SCF wavefunctions for three endohedral Mn/Si clusters, Mn2Si10, Mn2Si12, and [Mn2Si13]+, show evidence for strong static correlation, both in the Mn-Si bonds (’in–out correlation’) and between the two Mn centers (’up–down correlation’). We use both Restricted and Generalized Active Spaces (RAS and GAS) to place constraints on the configurations included in the trial wavefunction, showing that, particularly in the high-symmetry cases, the GAS approach captures more of the static correlation. The important correlating pairs are similar across the series, indicating that the electronic structure of the endohedral Mn2 unit is, to a first approximation, independent of the size of the silicon cage in which it is embedded.

First-row transition metal doped germanium clusters Ge16M: some remarkable superhalogens

A theoretical study of geometric and electronic structures, stability and magnetic properties of both neutral and anionic Ge16M0/- clusters with M being a first-row 3d transition metal atom, is performed using quantum chemical approaches. Both the isoelectronic Ge16Sc- anion and neutral Ge16Ti that have a perfect Frank-Kasper tetrahedral T d shape and an electron shell filled with 68 valence electrons, emerge as magic clusters with an enhanced thermodynamic stability. The latter can be rationalized by the simple Jellium model. Geometric distortions from the Frank-Kasper tetrahedron of Ge16M having more or less than 68 valence electrons can be understood by a Jahn-Teller effect. Remarkably, DFT calculations reveal that both neutral Ge16Sc and Ge16Cu can be considered as superhalogens as their electron affinities (≥3.6 eV) exceed the value of the halogen atoms and even that of icosahedral Al13. A detailed view of the magnetic behavior of Ge16M0/- clusters shows that the magnetic moments of the atomic metals remain large even when they are quenched upon doping. When M goes from Sc to Zn, the total spin magnetic moment of Ge16M0/- increases steadily and reaches the maximum value of 3 μ B with M = Mn before decreasing towards the end of the first-row 3d block metals. Furthermore, the IR spectra of some tetrahedral Ge16M are also predicted.

Evolution of Vibrational Spectra in the Manganese-Silicon Clusters Mn2Sin, n = 10, 12, and 13, and Cationic [Mn2Si13]. J Phys Chem A 2022;126:1617-1626. [PMID: 35238570 PMCID: PMC9084549 DOI: 10.1021/acs.jpca.1c10027]

A comparison of DFT-computed and measured infrared spectra reveals the ground state structures of a series of gas-phase silicon clusters containing a common Mn₂ unit. Mn₂Si₁₂ and [Mn₂Si₁₃]⁺ are both axially symmetric, allowing for a clean separation of the vibrational modes into parallel (a₁) and perpendicular (e₁) components. Information about the Mn–Mn and Mn–Si bonding can be extracted by tracing the evolution of these modes as the cluster increases in size. In [Mn₂Si₁₃]⁺, where the antiprismatic core is capped on both hexagonal faces, a relatively simple spectrum emerges that reflects a pseudo-D_6d geometry. In cases where the cluster is more polar, either because there is no capping atom in the lower face (Mn₂Si₁₂) or the capping atom is present but displaced off the principal axis (Mn₂Si₁₃), the spectra include additional features derived from vibrational modes that are forbidden in the parent antiprism.

Open Shells in Endohedral Clusters: Structure and Bonding in the [Fe2@Ge16]4- Anion and Comparison to Isostructural [Co2@Ge16]4

The anionic cluster [Fe₂@Ge₁₆]^4- has been characterized and shown to be isostructural to the known D_2h-symmetric α isomer of the cobalt analogue [Co₂@Ge₁₆]^4-. Together with the known pair of compounds [Co@Ge₁₀]^3- and [Fe@Ge₁₀]^3-, the title compound completes a set of four closely related germanium clusters that allow us to explore how the metal-metal and metal-cage interactions evolve as a function of size and of the identity of the metal. The results of spin-unrestricted density functional theory (DFT) and multiconfigurational self-consistent field (MC-SCF) calculations present a consistent picture of the electronic structure where transfer of electron density from the metal to the cage is significant, particularly in the Fe clusters where the exchange stabilization of unpaired spin density is an important driving force.

Interpretation of photoelectron spectra of CoGen- (n = 4, 5) clusters by multiconfigurational RASPT2 calculations

The low-lying electronic states CoGe_n^-/0 (n = 4, 5) have been investigated with density functional theory and the state-of-the-art RASSCF/RASPT2 method to give assignments for the anion photoelectron spectra. The BP86 functional was employed to optimize the geometrical structures of the electronic states, while the RASSCF/RASPT2 was applied to calculate the single-point energies. With the RASSCF/RASPT2 approach, the active spaces are extended to a size of 21 orbitals for CoGe₄^-/0 and 24 orbitals for CoGe₅^-/0. The ground states of CoGe₄^-/0 are determined to be ³A″ and ²A″ of a trigonal bipyramidal structure in which the Co atom is situated at the equatorial corner of the bipyramid. The vertical detachment energies of the transitions from the anionic ground state to the neutral ²A″, 1⁴A″, ²A', 2⁴A″, 3⁴A″, 1⁴A', 2⁴A', and 6⁴A″ states are evaluated to be 2.29, 2.39, 2.60, 2.83, 3.17, 3.24, 3.47, and 4.00 eV. For the CoGe₅^-/0 clusters, the ground states are computed to be ¹A₁ and 1²A₂ of an octahedral structure. The vertical detachment energies of the removal of one electron from the anionic ground state to result in the 1²A₂, 1²A₁, 2²A₁, 1²B₁, 1²B₂, 4²B₁, 4²B₂, and 6²A₂ states are estimated to be 2.16, 2.79, 2.84, 3.06, 3.06, 3.59, 3.59, and 4.22 eV. All features in the photoelectron spectra of CoGe₄^- and CoGe₅^- are interpreted based on the computed electron detachment energies of the anionic ground states.

DFT-based investigation of different properties for transition metal-doped germanium TMGen (TM = Ru, Rh; n = 1-20) clusters

The geometries and energetic, electronic, and magnetic features of transition metal-doped germanium (TMGe_n with TM = Ru, Rh; n = 1-20) clusters are systematically studied by means of first principle computations on the basis of the density functional theory (DFT) approach. The doping TM atom largely participates to strengthen the Ge_n cluster stability by increasing the binding energies. A good stability is obtained for RuGe₁₂, RhGe₁₂, and RhGe₁₄ clusters. The various explored isomers of TMGe_n clusters possess a total spin magnetic moment going from 0 to 2μ_B, except for RhGe₂ with 3μ_B. These results open nice perspectives of these good candidate clusters for applications in nanoelectronics and nanotechnologies.

Structure, stability, and electronic properties of niobium-germanium and tantalum-germanium clusters

The structural, electronic and magnetic properties of niobium- and tantalum-doped germanium clusters MGe_n (M = Nb, Ta and n = 1-19) were investigated by first principles calculations within the density functional theory (DFT) approach. Growth pattern behaviors, stabilities, and electronic properties are presented and discussed. Endohedral cage-like structures in which the metal atom is encapsulated are favored for n ≥ 10. The doping metal atom contributes largely to strengthening the stability of the germanium cage-like structures, with binding energy ordered as follows BE(Ge_n + 1) < BE (VGe_n) < BE(NbGe_n) < BE(TaGe_n). Our results highlight the relative high stability of NbGe₁₅, TaGe₁₅ and VGe₁₄. Graphical abstract Structure, stability, and electronic properties of niobium-germanium and tantalum-germanium clusters.

Spin State Energetics of VGe n -/0 (n = 5-7) Clusters and New Assignments of the Anion Photoelectron Spectra

The geometrical structures, electron leading configurations, and relative energies of the low-lying states of VGe _n ^-/0 (n = 5-7) clusters have been investigated with density functional theory and CASSCF/CASPT2 method. The pure GGA BP86 functional gave almost the same relative energy order for the low-lying states as the CASPT2 method. At the BP86 and CASPT2 levels, the ground states of VGe _n ^-/0 (n = 5-7) clusters were proposed to be the ¹ A₁ and ² A₁ of A-VGe₅ ^-/0 , ³ A″ and ² A″, ² A' (² E₂ ) of A-VGe₆ ^-/0 , and ¹ A' and ² A' of A-VGe₇ ^-/0 isomers. The adiabatic and vertical detachment energies (ADEs and VDEs) of the detachments of one electron from several orbitals of the anionic ground states were reported at the CASPT2 level. The calculated ADEs and VDEs corresponded well with the experimental values as observed in the 266 nm anion photoelectron spectra. © 2018 Wiley Periodicals, Inc.

The Electronic Structures of CoGe n-/0 ( n = 1-3) Clusters from Multiconfigurational CASSCF/CASPT2 and RASSCF/RASPT2 Calculations

Density functional theory and multiconfigurational CASPT2 and RASPT2 methods are employed to investigate the low-lying states of CoGe _n^-/0 ( n = 1-3) clusters. With the RASPT2 approach, the active space is extended to 14 orbitals for CoGe^-/0, 17 orbitals for CoGe₂^-/0, and 20 orbitals for CoGe₃^-/0. These active spaces include the 3d, 4s, and 4d of Co and 4p of Ge. The 4d of Co is incorporated into these active spaces in order to account for the important double-shell effect of Co. The structural parameters, vibrational frequencies, and relative energies of the low-lying states of CoGe _n^-/0 ( n = 1-3) are reported. The ground states of CoGe _n^- ( n = 1-3) are computed to be ³Φ of linear CoGe^-, ³B₁ of cyclic CoGe₂^-, and ³B₁ of cyclic CoGe₃^- isomer. The ground states of the neutral clusters are calculated to be ²Δ of linear CoGe, ⁴B₁ of cyclic CoGe₂, and ⁴A″ of tetrahedral CoGe₃ isomer. The calculated adiabatic and vertical detachment energies of the anionic ground states are in agreement with the experimental values as observed in the 266 nm anion photoelectron spectra.