Restricted Active Space State Interaction Research Articles

A Multiconfigurational Wave Function Theoretical Study on Electronic Structure and Magnetic Susceptibility of Dilanthanide Single Molecule Magnet.

Single molecule magnets (SMMs) have been a promising material for next-generation high-density information storage and molecular spintronics. N23--bridged dilanthanide complexes, {[(Me3Si)2N]2Ln(THF)(μ-η2:η2-N2)(THF)Ln[(Me3Si)2N]2}1-, exhibit high blocking temperatures and have been one of the promising candidates for future application. Rational understanding should be established between the magnetic properties and electronic structure. However, the theoretical study is still challenging due to the complexities in their electronic structures. Here, we theoretically studied the magnetic susceptibility of dilanthanide SMMs based on the state-of-the-art multistate-complete active space self-consistent field and perturbation theory at the second order and restricted active space state interaction with spin-orbit coupling calculations. Temperature dependence of the magnetic susceptibility (χmT-T curve) was quantitatively reproduced by the theoretical calculations. The complexities in the electronic states of these dilanthanide complexes originate from significantly strong static electron correlations in the lanthanide 4f and N2 π* orbitals and the SOC effect. The temperature dependence of the magnetic susceptibility results from the energy levels and magnetic properties of the low-lying excited state. The χmT values below 50 K are dominated by the ground state, while thermal distribution in the low-lying excited state affects the χmT values over 50 K. Saturation magnetization at low temperatures was also evaluated, and the result agrees with the experimental observation.

Electron Trap Depths in Cubic Lutetium Oxide Doped with Pr and Ti, Zr or Hf─From Ab Initio Multiconfigurational Calculations.

We propose a universal approach to model intervalence charge transfer (IVCT) and metal-to-metal charge transfer (MMCT) transitions between ions in solids. The approach relies on already well-known and reliable ab initio RASSCF/CASPT2/RASSI-SO calculations for a series of emission center coordination geometries (restricted active space self-consistent field, complete active space second-order perturbation theory, and restricted active space state interaction with spin-orbit coupling). Embedding with ab initio model potentials (AIMPs) is used to represent the crystal lattice. We propose a way to construct the geometries via interpolation of the coordinates obtained using solid-state density functional theory (DFT) calculations for the structures where the activator metal is at specific oxidation (charge) states of interest. The approach thus takes the best of two worlds: the precision of the embedded cluster calculations (including localized excited states) and the geometries from DFT, where the effects of ionic radii mismatch (and eventual nearby defects) can be modeled explicitly. The method is applied to the Pr activator and Ti, Zr, Hf codopants in cubic Lu2O3, in which the said ions are used to obtain energy storage and thermoluminescence properties. Electron trap charging and discharging mechanisms (not involving a conduction band) are discussed in the context of the IVCT and MMCT role in them. Trap depths and trap quenching pathways are analyzed.

Theoretical interpretations of photoelectron spectra of platinum atom, its cation and anion

Results of theoretical research on the ground and excited states of the platinum atom, its Pt− anion, and Pt+ cation are presented. Calculations were carried out using the four-component multi-configuration Dirac-Hartree-Fock method with the spin-free relativistic eight-order Douglas-Kroll-Hess method, and the infinite order two-component method at high correlated level. The spin-orbit (SO) coupling is introduced via the restricted active space state interaction method with the use of the atomic mean field SO integrals. The results are interpreted in comparison with the experimental data. The theoretical analysis suggests different assignments and interpretations of some atomic and ionic states, and existence of three anionic bound states. The obtained electron affinity to Pt−5d96s22D5/2 ground state is 2.104 eV (experimental value is 2.125 eV) which can be considered as very accurate result. The photodetachment Pt−1 to Pt0 spectra is provided. A comparative analysis of the accuracy of two-component methods is also presented.

Air-Stable Dy(III)-Macrocycle Enantiomers: From Chiral to Polar Space Group

Air-Stable Dy(III)-Macrocycle Enantiomers: From Chiral to Polar Space Group

Spin-Orbit Natural Transition Orbitals and Spin-Forbidden Transitions.

Natural transition orbitals (NTOs) are in widespread use for visualizing and analyzing electronic transitions. The present work introduces the analysis of formally spin-forbidden transitions with the help of complex-valued spin-orbit (SO) NTOs. The analysis specifically focuses on the components in such transitions that cause their intensity to be nonzero because of SO coupling. Transition properties such as transition dipole moments are partitioned into SO-NTO hole-particle pairs, such that contributions to the intensity from specific occupied and unoccupied orbitals are obtained. The method has been implemented within the restricted active space (RAS) self-consistent field wave function theory framework, with SO coupling treated by RAS state interaction. SO-NTOs have a broad range of potential applications, which is illustrated by the T2-S1 state mixing in pyrazine, spin-forbidden versus spin-allowed 4f-5d transitions in the Tb3+ ion, and the phosphorescence of tris(2-phenylpyridine) iridium [Ir(ppy)3].

Tuning Magnetic Relaxation in Square-Pyramidal Dysprosium Single-Molecule Magnets Using Apical Alkoxide Ligands

Tuning Magnetic Relaxation in Square-Pyramidal Dysprosium Single-Molecule Magnets Using Apical Alkoxide Ligands

Intramolecular Magnetic Interaction in a Photogenerated Dual Angular Momentum System in a Terbium-Phthalocyaninato 1:1 Complex.

Intramolecular magnetic interaction between a localized open-shell 4f-electronic system and a photoexcited macrocyclic π-conjugate system in terbium-phthalocyaninnato (Tb-Pc) 1:1 complex was investigated using variable-temperature variable-field magnetic circular dichroism (VTVH MCD) spectroscopy. The 1:1 complex [Tb(Pc)(cyclen)]Cl (Pc2- = phthalocyaninato dianion, cyclen = 1,4,7,10-tetraazacyclododecane) with the capping ligand providing an exact fourfold symmetry showed a significant temperature dependence and a nonlinear field dependence in the MCD intensity of the Pc-centered highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) π-π* transition, while a diamagnetic congener [Y(Pc)(cyclen)]Cl showed a temperature-independent MCD with a linear-field dependence. This indicates that the (4f)8 system of the Tb ion with a total angular momentum J and the photoexcited π-system of the Pc macrocycle with an orbital angular momentum L are magnetically coupled. By numerical simulation using a model where ground doublet state |Jz⟩ = |±6⟩ and excited quartet state |Jz, Lz⟩ = |±6, ±|Lz|⟩ are included, the J-L interaction magnitude ΔJL and the Pc-centered orbital angular momentum |Lz|ℏ were determined to be 1.1 cm-1 and 2.0 ℏ, respectively. From ab initio restricted active space self-consistent field (RASSCF)-restricted active space state interaction (RASSI) calculations on the π-π* excited states of the Tb complex, the magnitude of the J-L interaction was estimated. The comparison between the calculations on the Y and Tb complexes revealed that the ferromagnetic-type coupling occurs between the orbital component in the J of Tb and the L on Pc, supporting the model that we employed for the analysis of the experimental data.

Electron-Nucleus Hyperfine Coupling Calculated from Restricted Active Space Wavefunctions and an Exact Two-Component Hamiltonian.

Exact two-component (X2C) relativistic nuclear hyperfine magnetic field operators were incorporated in X2C ab initio wavefunction calculations at the multireference restricted active space (RAS) level for calculations of nuclear hyperfine magnetic properties. Spin-orbit coupling was treated via RAS state interaction (SO-RASSI). The method was tested by calculations of electron-nucleus hyperfine coupling constants. The approach, implemented in the OpenMolcas program, overcomes a major limitation of a previous SO-RASSI implementation for hyperfine coupling that relied on nonrelativistic hyperfine operators [J. Chem. Theor. Comput. 2015, 11, 538-549] and therefore had limited applicability. Results from calculations on systems with light and heavy main group elements, transition metals, lanthanides, and one actinide complex demonstrate reasonably good agreement with experimental data, where available, as long as the active space can generate sufficient spin polarization.

AuSi molecule revisited: IOTC/CASSCF/CASPT2 calculations

AbstractThe results of theoretical calculations for the ground and low‐lying excited states of the AuSi molecule are presented. Calculations were carried out using the spin‐free relativistic infinite‐order two‐component (IOTC) Hamiltonian in conjunction with the multistate CASPT2 method. For comparison, the ground state was also calculated using the IOTC‐CCSD(T) method. The spin‐orbit coupling is introduced via the restricted active space state interaction method with the use of the atomic mean‐field SO integrals. The results are compared with the available experimental and theoretical results. The spectroscopic parameters derived from the potential energy curves are presented. The results obtained suggest that the experimental data should be reconsidered.

Theoretical interpretation of photoelectron spectra of the iridium neutral atom and anion

The results of theoretical calculations for the ground and excited levels of the iridium neutral atom and its negative ion are presented, and the corresponding photodetachment energies. Calculations were carried out with the four-component multiconfiguration Dirac-Hartree-Fock method and with the spin-free relativistic second- and eight-order Douglas-Kroll-Hess method, and the infinite order two-component method, and high-level correlated methods. The spin-orbit coupling is introduced via the restricted active space state interaction method with the use of the atomic mean-field SO integrals. The results are compared and interpreted in comparison with the experimental results. The theoretical analysis suggest different assignment and interpretation of atomic and anionic levels, and existence of several anionic bound states. A comparative analysis of the accuracy of two-component methods is also presented.

Exact semi-classical light-matter interaction operator applied to two-photon processes with strong relativistic effects.

X-ray processes involve interactions with high-energy photons. For these short wavelengths, the perturbing field cannot be treated as constant, and there is a need to go beyond the electric-dipole approximation. The exact semi-classical light-matter interaction operator offers several advantages compared to the multipole expansion such as improved stability and ease of implementation. Here, the exact operator is used to model x-ray scattering in metal K pre-edges. This is a relativistic two-photon process where absorption is dominated by electric-dipole forbidden transitions. With the restricted active space state-interaction approach, spectra can be calculated even for the multiconfigurational wavefunctions including second-order perturbation. However, as the operator itself depends on the transition energy, the cost for evaluating integrals for hundreds of thousands unique transitions becomes a bottleneck. Here, this is solved by calculating the integrals in a molecular-orbital basis that only runs over the active space, combined with a grouping scheme where the operator is the same for close-lying transitions. This speeds up the calculations of single-photon processes and is critical for the modeling of two-photon scattering processes. The new scheme is used to model Kα resonant inelastic x-ray scattering of iron-porphyrin complexes with relevance to studies of heme enzymes, for which the total computational time is reduced by several orders of magnitude with an effect on transition intensities of 0.1% or less.

Relativistic calculations of AuSi+ and AuSi−

AbstractTheoretical calculations of the electronic structure of the ground state and a series of excited states of the AuSi+ and AuSi− molecules are presented. The calculations were carried out with the spin‐free relativistic infinite‐order two‐component (IOTC) method and high‐level complete active space self‐consistent field/complete active space perturbation theory correlated methods. The spin‐orbit (SO) coupling was introduced via the restricted active space state interaction method with the use of the atomic mean‐field SO integrals. The work presents the spectroscopic parameters of calculated states and full potential energy curves of the ionic AuSi+ and AuSi− structures for the first time. Electrostatic potential maps projected on the electron density surface illustrate the significant relativistic effects on going from nonrelativistic to scalar relativistic treatments.

A Density Functional Theory and ab Initio Investigation of the Oxidation Reaction of CO by IO Radicals.

To get an insight into the possible reactivity between iodine oxides and CO, a first step was to study the thermochemical properties and kinetic parameters of the reaction between IO and CO using theoretical chemistry tools. All stationary points involved were optimized using the Becke's three-parameter hybrid exchange functional coupled with the Lee-Yang-Parr nonlocal correlation functional (B3LYP) and the Møller-Plesset second-order perturbation theory (MP2). Single-point energy calculations were performed using the coupled cluster theory with the iterative inclusion of singles and doubles and the perturbative estimation for triple excitations (CCSD(T)) and the aug-cc-pVnZ (n = T, Q, and 5) basis sets on geometries previously optimized at the aug-cc-pVTZ level. The energetics was then recalculated using the one-component DK-CCSD(T) approach with the relativistic ANO basis sets. The spin-orbit coupling for the iodine containing species was calculated a posteriori using the restricted active space state interaction method in conjunction with the multiconfigurational perturbation theory (CASPT2/RASSI) employing the complete active space (CASSCF) wave function as the reference. The CCSD(T) energies were also corrected for BSSE for molecular complexes and refined with the extrapolation to CBS limit while the DK-CCSD(T) values were refined with the extrapolation to FCI. The exploration of the potential energy surface revealed a two-steps mechanism with a trans and a cis pathway. The rate constants for the direct and complex mechanism were computed as a function of temperature (250-2500 K) using the canonical transition state theory. The three-parameter Arrhenius expressions obtained for the direct and indirect mechanism at the DK-CCSD(T)-cf level of theory is 1.49 × 10(-17) × T(1.77) exp(-47.4 (kJ mol(-1))/RT).

Effects from spin-orbit coupling on electron-nucleus hyperfine coupling calculated at the restricted active space level for Kramers doublets.

Calculations of electron-nucleus hyperfine coupling were implemented at the restricted active space state interaction (RASSI) level to treat spin-orbit (SO) coupling, based on scalar relativistic restricted active space wave functions. The current implementation is suitable for light atomic systems, for light ligand atoms in heavy metal complexes, and for spin-orbit coupling-induced hyperfine coupling of heavy atoms if the unpaired electrons are described by orbitals with high angular momentum. Spin polarization is reasonably well treated by allowing one hole and one electron in a window of active orbitals ('ras1', 'ras3') surrounding the principal active space ('ras2'). A benchmark set of Kramers doublet states of molecules with light and heavy atoms is used to evaluate the approach and verify the implementation. For NpF6, the impact of SO coupling on the Np and F hyperfine coupling tensors is investigated in detail. It is demonstrated that the Np hyperfine coupling is strongly dominated by SO effects, that there is a large SO effect on the F hyperfine tensor components, and that SO coupling causes the fluorine dipolar term to acquire an isotropic component.

Two C3 -symmetric Dy3III complexes with triple di-μ-methoxo-μ-phenoxo bridges, magnetic ground state, and single-molecule magnetic behavior.

Two series of isostructural C(3)-symmetric Ln(3) complexes Ln(3)⋅[BPh(4)] and Ln(3)⋅0.33[Ln(NO(3))(6)] (in which Ln(III) =Gd and Dy) have been prepared from an amino-bis(phenol) ligand. X-ray studies reveal that Ln(III) ions are connected by one μ(2)-phenoxo and two μ(3)-methoxo bridges, thus leading to a hexagonal bipyramidal Ln(3)O(5) bridging core in which Ln(III) ions exhibit a biaugmented trigonal-prismatic geometry. Magnetic susceptibility studies and ab initio complete active space self-consistent field (CASSCF) calculations indicate that the magnetic coupling between the Dy(III) ions, which possess a high axial anisotropy in the ground state, is very weakly antiferromagnetic and mainly dipolar in nature. To reduce the electronic repulsion from the coordinating oxygen atom with the shortest Dy-O distance, the local magnetic moments are oriented almost perpendicular to the Dy(3) plane, thus leading to a paramagnetic ground state. CASSCF plus restricted active space state interaction (RASSI) calculations also show that the ground and first excited state of the Dy(III) ions are separated by approximately 150 and 177 cm(-1), for Dy(3)⋅[BPh(4)] and Dy(3)⋅0.33[Dy(NO(3))(6)], respectively. As expected for these large energy gaps, Dy(3)⋅[BPh(4)] and Dy(3)⋅0.33[Dy(NO(3)(6)] exhibit, under zero direct-current (dc) field, thermally activated slow relaxation of the magnetization, which overlap with a quantum tunneling relaxation process. Under an applied Hdc field of 1000 Oe, Dy(3)⋅[BPh(4)] exhibits two thermally activated processes with U(eff) values of 34.7 and 19.5 cm(-1), whereas Dy(3)⋅0.33[Dy(NO(3))(6)] shows only one activated process with Ueff =19.5 cm(-1).

Calculation of X-ray photoelectron spectra with the use of the normalized elimination of the small component method

A method for the calculation of X-ray photoelectron spectra (XPS) based on the use of the normalized elimination of the small component (NESC) formalism combined with the restricted active space state interaction (RASSI) approach with atomic mean field integrals (AMFI) is developed. Benchmark calculations carried out for the 4f XPS of U5+show that the NESC/RASSI/AMFI method is capable of reproducing the results of the full 4-component relativistic calculations with excellent accuracy. The NESC/RASSI/AMFI method is applied to study the 4p and 5p XPS of ytterbium phosphide YbP. The results of the calculations suggest an alternative interpretation of the satellite peaks in the 4p XPS of YbP.

Electronic Absorption Spectroscopy of H2X (X = O, Te, Po): Theoretical Treatment of Spin-Orbit Effects

The electronic spectroscopy of H2X (X = O, Te, Po) was investigated by means of spin-orbit configuration interaction (EPCISO) and restricted active space state interaction (SO-RASSI). The transition energies to the low-lying singlet and triplet states of H2O, in which the SO interaction is zero, compare rather well with the experimental data as well as to other theoretical values. The theoretical electronic absorption spectrum is characterized by three allowed transitions A1B1 (2px(O)*g/3s(O)), B1A1(g*g/3s(O)) and A1B2(g*u) calculated at 7.68, 9.94, and 11.72 eV, respectively. The theoretical absorption spectra of H2X (X = Te, Po) are shifted to the red with the A1B1 (npx(X)*g) states calculated at 5.06 eV (H2Te) and 4.40 eV (H2Po) and the A1B2 (g*u) states calculated at 7.89 eV (H2Te) and 7.77 eV (H2Po). The largest SO splitting amounts to 0.34 eV and is found for the lowest a3A1 of H2Po. In H2Te the SO effects are still negligible with a maximum splitting of 0.04 eV for the lowest a3B2. The two methods lead to comparable results but the EPCISO approach depends strongly on the reference wavefunction.

Role of electronic curve crossing of benzene S1 state in the photodissociation of aryl halides, effect of fluorination: RASSI‐SO MS‐CASPT2 study

AbstractAn ab initio study of the role of electronic curve crossing of benzene S1 state in the photo dissociation dynamics of the iodobenzene and effect of fluorination is presented. Two dissociative life times observed in iodobenzene is attributed to the coupled repulsive potential energy curves of the low‐lying n−σ*, π−σ*, π−π* states. The direct channel is attributed to the alkyl like transition and the indirect channel is attributed to the mixing of the alkyl like transitions with the low lying benzene π−π* transitions. Fluorination of iodobenzene results in a substantial increase in the direct channel product. To analyze the possible role of electronic curve crossing of these transitions, potential energy curves of low‐lying n−σ*, π−σ*, π−π* states were studied including spin‐orbit and relativistic effects using the Restricted Active Space state interaction multistate complete active space perturbation theory (RASSI‐MS‐CASPT2) method. Crossing behavior of spin‐free and spin‐orbit potential energy curves was analyzed for the role of the benzene S1 state. Our results indicate the curve crossing region to be around 2.00–2.35 Å for both C6H5I and C6F5I. Analysis of effect of fluorination on the energies of states corresponding to benzene π−π* and n−σ* transitions suggests an increase in the energy of benzene π−π* states and a decrease in the energy of the states corresponding to n−σ* transitions. Increased spin‐orbit gap, increased separation of the benzene S1(π−π*) state and n−σ* states in the region of curve crossing, lesser mixing of the π−π* and n−σ* states, an order of magnitude decrease in the transition strength to the benzene singlet transition all contributed to the observed substantial increase in the quantum yield of the direct channel product on fluorination of aryl halides. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Theoretical study of PbO and the PbO anion

PbO and PbO − were studied utilizing CCSD(T), CASSCF/CASPT2, and the Fock Space FSCCSD methods. Relativistic effects were treated by the spin-free, two-component infinite-order Douglas–Kroll–Hess, Dirac–Coulomb and the restricted active space state interaction RASSI–SO methods. Our adiabatic electron affinity (EA), 0.696 eV, agrees favorably with experiment (0.714 eV). Theoretical dissociation energies D e of PbO and PbO − (3.91 and 3.20 eV) differ from experiment by 0.04 and 0.07 eV, respectively. The electron correlation, relativistic scalar and spin–orbit effects are crucial for obtaining good agreement of theoretical and experimental data for EA and D e. Equilibrium bond distance and vibrational frequency are less sensitive to SO effects.

Relativistic and correlated calculations on the ground and excited states of ThO

We report on the performance of the third-order Douglas–Kroll ab initio model potential (DK3-AIMP) method-based electron-correlated spin–orbit calculations. Our treatment assumes that the problem can be separated into a spin–free correlation treatment and a spin–orbit calculation. The correlation effects were calculated using the multistate complete active space second-order perturbation method, and the spin–orbit effects were treated by means of the restricted active space state interaction spin–orbit method, where the spin–orbit effects were approximated by the Douglas–Kroll type of atomic mean-field spin–orbit method. We used our method for illustrative calculations on the ground and low-lying electronic states of thorium monoxide. For a proper description of the inner core region in the spin–orbit calculations, an auxiliary spin–orbit basis set was introduced. The DK3-AIMP-based electron-correlated spin–orbit calculations on ThO yield good agreement with corresponding all-electron results and with the available experimental data. This confirms that the DK3-AIMP method can be easily combined with highly accurate correlation treatments and relativistic effects, both of which are vital for studying the actinides. To our knowledge, the literature contains no references to AIMP calculations on the low-lying states of ThO.