Van Tan Tran

Multiconfigurational Second-Order Perturbation Theory Restricted Active Space (RASPT2) Studies on Mononuclear First-Row Transition-Metal Systems.

A series of model transition-metal complexes, CrF6, ferrocene, Cr(CO)6, ferrous porphin, cobalt corrole, and FeO/FeO(-), have been studied using second-order perturbation theory based on a restricted active space self-consistent field reference wave function (RASPT2). Several important properties (structures, relative energies of different structural minima, binding energies, spin state energetics, and electronic excitation energies) were investigated. A systematic investigation was performed on the effect of: (a) the size and composition of the global RAS space, (b) different (RAS1/RAS2/RAS3) subpartitions of the global RAS space, and (c) different excitation levels (out of RAS1/into RAS3) within the RAS space. Calculations with active spaces, including up to 35 orbitals, are presented. The results obtained with smaller active spaces (up to 16 orbitals) were compared to previous and current results obtained with a complete active space self-consistent field reference wave function (CASPT2). Higly accurate RASPT2 results were obtained for the heterolytic binding energy of ferrocene and for the electronic spectrum of Cr(CO)6, with errors within chemical accuracy. For ferrous porphyrin the intermediate spin (3)A2g ground state is (for the first time with a wave function-based method) correctly predicted, while its high magnetic moment (4.4 μB) is attributed to spin-orbit coupling with very close-lying (5)A1g and (3)Eg states. The toughest case met in this work is cobalt corrole, for which we studied the relative energy of several low-lying Co(II)-corrole π radical states with respect to the Co(III) ground state. Very large RAS spaces (25-33 orbitals) are required for this system, making compromises on the size of RAS2 and/or the excitation level unavoidable, thus increasing the uncertainty of the RASPT2 results by 0.1-0.2 eV. Still, also for this system, the RASPT2 method is shown to provide distinct improvements over CASPT2, by overcoming the strict limitations in the size of the active space inherent to the latter method.

Description of the geometric and electronic structures responsible for the photoelectron spectrum of FeO4(

The relative stabilities of all low-lying conformations of FeO(4)(0/-) stoichiometry were investigated at the quantum mechanical BPW91, CASPT2, and RCCSD(T) levels of theory. For both the anionic and neutral clusters, the determination of the most stable structure appears to be a demanding task. The density functional theory and wave function second-order perturbation theory computational techniques place the doublet state of the tetrahedron-like O(4)Fe(-) conformation substantially lower, up to 0.81 eV, than the doublet state of η(2)-(O(2))FeO(2)(-). The coupled-cluster method reduces the energy difference to less than 0.01 eV. This equal stability of the ground states of O(4)Fe(-) and η(2)-(O(2))FeO(2)(-) leads to the assignment of the experimental photoelectron spectrum of FeO(4)(-). The lowest binding energy band (X band) is ascribed to the (2)A(1) → (1)A(1) ionization of η(2)-(O(2))FeO(2)(-), while the higher energy band (A band) mainly corresponds to the (2)E → (1)A(1) transition between the O(4)Fe(0/-) conformations. For a specific conformation, CASPT2 calculates the best electron detachment energies. The highest energy peak in this band with the weakest intensity could be ascribed to the (2)A(2) → (3)A(2) transition between the η(2)-(O(2))FeO(2) conformations. The two progressions are the result of ionizations from the anti-bonding orbitals of predominant iron 3d. For a specific conformation, CASPT2 calculates the best electron detachment energies. A BPW91 Franck-Condon simulation of the observed vibrational progressions further confirms the proposed assignments.

Assignment of the photoelectron spectra of FeS3(-) by density functional theory, CASPT2, and RCCSD(T) calculations.

The geometric structures of FeS(3) and FeS(3)(-) with spin multiplicities ranging from singlet to octet were optimized at the B3LYP level, allowing two low-lying conformations for these clusters to be identified. The planar D(3h) conformation contains three S(2-) atomic ligands (S(3)Fe(0/-)), whereas the C(2v) structure contains, in addition to an atomic S(2-) ligand, also a S(2)(2-) ligand that is side-on-bound to the iron cation: an η(2)-S(2)FeS conformation. Subsequently, energy differences between the various states of these conformations were estimated by carrying out geometry optimizations at the multireference CASPT2 level. Several competing structures for the ground state of the anionic cluster were recognized at this level. Relative stabilities were also estimated by performing single-point RCSSD(T) calculations on the B3LYP geometries. The ground state of the neutral complex was unambiguously found to be (5)B(2). The ground state of the anion is considerably less certain. The 1(4)B(2), 2(4)B(2), (4)B(1), and (6)A(1) states were all found as low-lying η(2)-S(2)FeS(-) states. Also, (4)B(2) of S(3)Fe(-) has a comparable CASPT2 energy. In contrast, B3LYP and RCCSD(T) mutually agree that the S(3)Fe(-) state is at a much higher energy. Energetically, the bands of the photoelectron spectra of FeS(3)(-) are reproduced at the CASPT2 level as ionizations from either the (4)B(2) or (6)A(1) state of η(2)-S(2)FeS. However, the Franck-Condon factors obtained from a harmonic vibrational analysis at the B3LYP level show that only the (4)B(2)-to-(5)B(2) ionization, which preserves the η(2)-S(2)Fe-S conformation, provides the best vibrational progression match with the X band of the experimental photoelectron spectra.

On the Electronic and Geometric Structures of FeO2–/0 and the Assignment of the Anion Photoelectron Spectrum

The photoelectron spectrum of FeO2(-) has been assigned by performing geometry optimizations at the CASPT2 and RCCSD(T) levels of computation. All relevant states are found to possess floppy C2v geometrical structures as the Renner-Teller splittings of the linear states are extremely small and the corresponding energy barriers for the OFeO bond angle inversions are calculated in the range of a few hundred wavenumbers. In this sense, the description of the electronic structure in terms of the D∞h point group is acceptable, and the experimentally proposed linear structure for FeO2(-) is theoretically confirmed. High accuracy single-point multireference RASPT2 and single-reference RCCSD(T) calculations support a (2)Δg as the ground state of the anion, even though the energy differences between the (4)Πg and (6)Σg(+) states are smaller than 0.2 eV. After this identification of the doublet ground state, the photoelectron spectra of FeO2(-) could be assigned in all aspects. The (2)Δg→(3)Δg ionization appears to be at the origin of the X band at 2.36 eV, while the A band at 3.31 eV should be ascribed to the (2)Δg→(3)Σg(+) ionization. This assignment is substantiated by Franck-Condon factors for which BP86 optimized geometries and harmonic vibrational frequencies were employed. Indeed, no pronounced vibrational progression should be observed since both bands involve electron detachments out of nonbonding mainly 3d iron molecular orbitals.

Molecular structures for FeS4(-/0) as determined from an ab initio study of the anion photoelectron spectra.

For the purpose of assigning the photoelectron spectra of the FeS4(-) molecular entity, geometric and electronic structures of low-lying FeS4(-/0) isomers were investigated at the B3LYP, CASPT2, and RCCSD(T) computational quantum chemical levels. The anionic ground state is predicted to be the (4)B1g state of the D2h (η(2)-(S2))2Fe(-) isomer with two S2(2-) molecular ligands side-on bond in a D2h fashion to iron, which has an oxidation state of +3. The experimental photoelectron spectra of FeS4(-) were successfully assigned as originating from this isomer. The composed lowest energy X band is the result of ionizations to the (3)B3g, (5)B1u, and (5)B1g states. Analyses of the CASSCF orbitals indicated an almost degeneracy of the nonbonding 3d orbitals of iron and the π* orbitals of S2(2-). All the experimental observed higher ionization energy bands could also be theoretically assigned as originating from the proposed anion ground state by detachment of an electron from either of these iron or ligand orbitals.

A new interpretation of the photoelectron spectra of CrC2

In this work, the computational quantum chemical DFT, CASPT2, and RCCSD(T) methods have been utilized to investigate the geometric and electronic structures of cyclic and linear CrC2(-/0) clusters. The neutral ground state is firmly identified as the cyclic (5)A1 state. For the anionic cluster, two nearly degenerate isomers were recognized, namely a cyclic (6)A1 state and a linear (6)Σ(+) state. Therefore, assignments of the observed bands in the photoelectron spectra of CrC2(-) have been made based on both of these isomers. With the exception of the B band all other experimental observed bands could be ascribed to the cyclic isomer. The computed detachment energies show that the former band must be exclusively assigned to the ionization of (6)Σ(+) of the linear structure, which can possibly also contribute to some higher energy bands. Additional support for the proposed assignments is provided by multidimensional Franck-Condon factor simulations for the (6)A1→(5)A1 and (6)A1→(5)B1 transitions that show a nearly perfect match with the observed vibrational progressions of the X and A bands in the 532 nm spectra.

Quantum chemical study of the geometrical and electronic structures of ScSi3−/0 clusters and assignment of the anion photoelectron spectra

The geometrical and electronic structures of ScSi3 (-/0) clusters have been studied with the B3LYP, CCSD(T), and CASPT2 methods. The ground state of the anionic cluster was evaluated to be the (1)A1 of rhombic η(2)-(Si3)Sc(-) isomer, whereas that of the neutral cluster was computed to be the (2)A1 of the same isomer. All features in the 266 and 193 nm photoelectron spectra of ScSi3 (-) cluster were interpreted by the one- and two-electron detachments from the (1)A1 of rhombic η(2)-(Si3)Sc(-) isomer. The Franck-Condon factor simulation results show that the first broad band starting at 1.78 eV in the spectra comprises several vibrational progression peaks of two totally symmetric modes with the corresponding frequencies of 296 and 354 cm(-1).

Geometric and Electronic Structures for MnS2(-/0) Clusters by Interpreting the Anion Photoelectron Spectrum with Quantum Chemical Calculations.

Geometric and electronic structures of linear SMnS, cyclic η(2)-MnS2, and linear η(1)-MnS2 isomers of MnS2(-) clusters have been investigated with B3LYP, CCSD(T), and NEVPT2 methods. The ground state of the anionic cluster is determined as (5)Πg of the linear SMnS(-) isomer, while the ground state of the neutral cluster may be either the (4)Σg(-) of the same isomer or the (6)A1 of the η(2)-MnS2 cluster. The experimental photoelectron spectrum of the MnS2(-) cluster is interpreted by contributions of these two isomers. The high-intensity band at a binding energy of 2.94 eV is attributed to the (5)Πg → (4)Σg(-) transition between the linear SMnS(-/0) clusters. The lower energy feature in the spectrum at binding energies between 1.9 and 2.8 eV and exhibiting a low intensity, is ascribed to electron detachments within the less stable η(2)-MnS2(-/0) clusters. Ionizations from the lowest energy (7)A1 state of this isomer to the neutral (6)A1, (6)A2, (8)A2, and (6)B2 states are responsible for this part of the spectrum. The extreme low intensity part between 1.3 and 1.9 eV can be due to excited states of either SMnS(-) or η(2)-MnS2(-).

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

Density functional theory and the multiconfigurational CASSCF/CASPT2 method have been employed to study the low-lying states of VGen-/0 (n = 1-4) clusters. For VGe-/0 and VGe2-/0 clusters, the relative energies and geometrical structures of the low-lying states are reported at the CASSCF/CASPT2 level. For the VGe3-/0 and VGe4-/0 clusters, the computational results show that due to the large contribution of the Hartree-Fock exact exchange, the hybrid B3LYP, B3PW91, and PBE0 functionals overestimate the energies of the high-spin states as compared to the pure GGA BP86 and PBE functionals and the CASPT2 method. On the basis of the pure GGA BP86 and PBE functionals and the CASSCF/CASPT2 results, the ground states of anionic and neutral clusters are defined, the relative energies of the excited states are computed, and the electron detachment energies of the anionic clusters are evaluated. The computational results are employed to give new assignments for all features in the photoelectron spectra of VGe3- and VGe4- clusters.

The Electronic Structures of CoGen−/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.