A new interpretation of the photoelectron spectrum of VSi 4 − cluster by density functional theory and multiconfigurational CASSCF/CASPT2 calculations

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.

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.

Electronic States of CoSin-/0/+ (n = 1-3) Clusters from Density Matrix Renormalization Group-CASPT2 Calculations

Density matrix renormalization group-CASPT2 (DMRG-CASPT2), CASPT2, and density functional theory are employed to describe the complicated geometrical and electronic structures of CoSi_n^-/0/+ (n = 1-3) clusters. The active spaces of DMRG-CASPT2 are extended to 23 orbitals. The DMRG-CASPT2 method with such large active spaces is reasonable to provide highly accurate relative energies of the electronic states. The pure BP86, PBE, and TPSS functionals appear to be suitable to compute the relative energies of the electronic states of cobalt-doped silicon clusters. The leading configurations, bond distances, vibrational frequencies, normal modes, and relative energies of the electronic states are reported. The electron detachment energies of the removals of one electron from the anionic and neutral clusters are estimated. All six bands in the photoelectron spectrum of CoSi₃^- are interpreted based on the computed electron detachment energies and Franck-Condon factor simulations.

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.

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.