Spin-orbit Configuration Interaction Research Articles

A CASSCF/MRCI trajectory surface hopping simulation of the photochemical dynamics and the gas phase ultrafast electron diffraction patterns of cyclobutanone.

We present the simulation of the photochemical dynamics of cyclobutanone induced by the excitation of the 3s Rydberg state. For this purpose, we apply the complete active space self-consistent field method together with the spin-orbit multireference configuration interaction singles treatment, combined with the trajectory surface hopping for the inclusion of nonadiabatic effects. The simulations were performed in the spin-adiabatic representation, including nine electronic states derived from three singlet and two triplet spin-diabatic states. Our simulations reproduce the two previously observed primary dissociation channels: the C2 pathway yielding C2H4 + CH2CO and the C3 pathway producing c-C3H6 + CO. In addition, two secondary products, CH2 + CO from the C2 pathway and C3H6 from the C3 pathway, both of them previously reported, are also observed in our simulation. We determine the ratio of the C3:C2 products to be about 2.8. Our findings show that most of the trajectories reach their electronic ground state within 200fs, with dissociation events finished after 300fs. We also identify the minimum energy conical intersections that are responsible for the relaxation and provide an analysis of the photochemical reaction mechanism based on multidimensional scaling. Furthermore, we demonstrate a minimal impact of triplet states on the photodissociation mechanism within the observed timescale. In order to provide a direct link to experiments, we simulate the gas phase ultrafast electron diffraction patterns and connect their features to the underlying structural dynamics.

Tailoring light-induced charge transfer and intersystem crossing in FeCO using time-dependent spin-orbit configuration interaction.

Real-time (RT) electronic structure methods provide a natural framework for describing light-matter interactions in arbitrary time-dependent electromagnetic fields (EMF). Optically induced excited state transitions are of particular interest, which require tuned EMF to drive population transfer to and from the specific state(s) of interest. Intersystem crossing, or spin-flip, may be driven through shaped EMF or laser pulses. These transitions can result in long-lived "spin-trapped" excited states, which are especially useful for materials requiring charge separation or protracted excited state lifetimes. Time-dependent configuration interaction (TDCI) is unique among RT methods in that it may be implemented in a basis of eigenstates, allowing for rapid propagation of the time-dependent Schrödinger equation. The recent spin-orbit TDCI (TD-SOCI) enables a real-time description of spin-flip dynamics in an arbitrary EMF and, therefore, provides an ideal framework for rational pulse design. The present study explores the mechanism of multiple spin-flip pathways for a model transition metal complex, FeCO, using shaped pulses designed to drive controlled intersystem crossing and charge transfer. These results show that extremely tunable excited state dynamics can be achieved by considering the dipole transition matrix elements between the states of interest.

A spin–orbit configuration interaction study of the low-lying electronic states of the diatomic lithium antimonide cation

High-level ab initio calculations were performed to determine the structural features, electronic characteristics and transitional properties of LiSb+, which is a hitherto experimentally unknown diatomic cation. We acquired and evaluated the potential energy curves, spectroscopic constants and vibrational energy levels for low-lying Λ-S electronic states and their related Ω states. The spin–orbit coupling effect has a slight impact on these states. Transitional properties, such as transition dipole moments, Einstein coefficients, Franck–Condon factors and vibrational branching ratios, as well as the radiative lifetimes of transitions from excited Ω states to the ground state, have been identified and discussed. We anticipate that these prognostic results will act as guidelines for future research.

Environmental considerations in ab initio calculations of electronic states of PtCl4 -2 complexes.

Many quantum chemical methods used for large complexes are based on a limited treatment of electrons due to the computational demand dictated by the number of electrons that must be explicitly considered, especially when considering the chemical environment. Such treatments can fail to correlate accurately with electronic spectra. Ab initio electronic structure theory using the spin-orbit configuration interaction method is applied in a study of spectral transitions in PtCl4 2- including counter-ion environmental effects. In this method, electronic wave functions are eigenfunctions of the total angular momentum operator belonging to one of the symmetry types of the molecular double group. PtCl4 2- is investigated as a charged gas phase complex, a point-charge-neutralized complex, and a pseudopotential-neutralized complex. Results indicate that the use of a whole-atom relativistic effective core potential for the potassium cation provides a more accurate representation of the environment than a point charge and accurately represents electronic states without increasing the complexity of the calculation and, therefore, its computational demand.

Excited states of polonium(IV): electron correlation and spin-orbit coupling in the Po4+ free ion and in the bare and solvated [PoCl5]- and [PoCl6]2- complexes.

Polonium (Po, Z = 84) is a main-block element with poorly known physico-chemical properties. Not much information has been firmly acquired since its discovery by Marie and Pierre Curie in 1898, especially regarding its speciation in aqueous solution and spectroscopy. In this work, we revisit the absorption properties of two complexes, [PoCl5]- and [PoCl6]2-, using quantum mechanical calculations. These complexes have the potential to exhibit a maximum absorption at 418 nm in HCl medium (for concentrations of 0.5 mol L-1 and above). Initially, we examine the electronic spectra of the Po4+ free ion and of its isoelectronic analogue, Bi3+, in the spin-orbit configuration interaction (SOCI) framework. Our findings demonstrate that the SOCI matrix should be dressed with correlated electronic energies and that the quality of the spectra is largely improved by decontracting the reference states at the complete active space plus singles (CAS + S) level. Subsequently, we investigate the absorption properties of the [PoCl5]- and [PoCl6]2- complexes in two stages. Firstly, we perform methodological tests at the MP2/def2-TZVP gas phase geometries, indicating that the decontraction of the reference states can be skipped without compromising the accuracy significantly. Secondly, we study the solution absorption properties by means of single-point calculations performed at the solvated geometries, obtained by an implicit solvation treatment or a combination of implicit and explicit solvation. Our results highlight the importance of saturating the first coordination sphere of the PoIV ion to obtain a qualitatively correct picture. Finally, we conclude that the known-for-decades 418 nm peak could be attributed to a mixture of both the [PoCl5(H2O)]- and [PoCl6]2- complexes. This finding not only aligns with the behaviour of the analogous BiIII ion under similar conditions but also potentially provides an explanation for previous discrepancies in the literature.

Theoretical dissociation, ionization, and spin-orbit energetics of the diatomic platinum hydrides PtH, PtH+, and PtH.

Spin-orbit configuration interaction (SO-CI) and coupled-cluster [CCSDT(Q)] theoretical methods are combined to evaluate zero-temperature thermochemical properties of PtH, PtH+, and PtH-. We obtain vibrational zero-point energies and spin-orbit stabilization energies, which lead to predictions for observable quantities: ionization energy IE(PtH) = (9.44 ± 0.07) eV; electron affinity EA(PtH) = (1.65 ± 0.04) eV; and dissociation energies D0(Pt-H) = (329.6 ± 3.9) kJ mol-1, D0(Pt+-H) = (279.3 ± 5.7) kJ mol-1, and D0(Pt--H) = (285.0 ± 2.4) kJ mol-1 (uncertainty coverage factor = 2). Compared with available experiments, our value of D0(Pt+-H) is higher by (8 ± 8) kJ mol-1, EA(PtH) is higher by 0.15eV, and D0(Pt-H) is lower than the upper bound by (2 ± 4) kJ mol-1.

Spin–orbit configuration interaction study of spectral properties of PbO

Relativistic calculations of the structural and spectral properties of the PbO molecule can provide fundamental information about the importance of a proper treatment of angular momentum coupling among electrons in order to achieve accurate computational results for spectral properties. Specifically, the nature of these couplings in PbO is expected to be intermediate between the LS- and jj-coupling limits because of its light/heavy element composition. This article reports potential energy curves, transition energies, electric dipole transition moments, permanent dipole moments and spectroscopic constants of PbO calculated using a multireference single plus double excitations spin–orbit configuration interaction approach in the context of relativistic effective core potentials and their concomitant spin–orbit coupling operators. The calculated results are in general agreement with both available experimental results as well as earlier calculations. New values for properties of excited states are also reported. It is noteworthy that certain properties show larger deviations from previous calculations. These deviations are attributed to direct and indirect relativistic effects resulting from diatomic electron–electron angular momentum coupling effects, which are included consistently in the calculations reported herein.

Cover Feature: Development and Application of a Complete Active Space Spin‐Orbit Configuration Interaction Program Designed for Single Molecule Magnets (ChemPhysChem 1/2022)

The Cover Feature illustrates how magnetic data of powder samples of oligonuclear transition metal complexes can be simulated and analysed from ab initio energy levels and wave functions obtained by spin orbit configuration interaction. More information can be found in the Article by Bodenstein, Heimermann, Fink, and van Wüllen.

Development and Application of a Complete Active Space Spin-Orbit Configuration Interaction Program Designed for Single Molecule Magnets.

We present a spin‐orbit configuration interaction program which has been tailored for the description of the magnetic properties of polynuclear metal complexes with partially filled d‐ and f‐shells. The spin‐orbit operators are directly included in the configuration interaction program based on Slater‐determinants. The lowest states are obtained by a Block‐Davidson‐type diagonalisation. The usage of localised active orbitals enables the construction of start vectors from tensor products of single‐center wave functions that already include spin‐orbit interaction. This allows for an analysis of the role and the interplay of the different metal centres. Furthermore, in case of weak coupling of the metal centres these tensor products are already close to the final wave functions ensuring fast convergence. In combination with a two‐layer hybrid parallelisation, this makes the program highly efficient. Based on the spin‐orbit coupled wave functions, magnetic D‐tensors, g‐tensors and temperature‐dependent susceptibilities can be calculated. The applicability and performance of the program is shown exemplarily on a trinuclear transition metal (CoIIVIICoII) complex.

On the Accuracy of Mean-Field Spin-Orbit Operators for 3d Transition-Metal Systems.

We present an extensive study of the performance of mean-field approximations to the spin-orbit operators on realistic molecular systems, as widely used in applications like single-molecule magnets, molecular quantum bits, and molecular spintronic devices. The test systems feature a 3d transition-metal center ion (V, Cr, Mn, Fe, Co, and Ni) in various coordinations and a multitude of energetically close-lying open-shell configurations that can couple via the spin-orbit operator. We performed complete active space spin-orbit configuration interaction calculations and compared the full two-electron Breit-Pauli spin-orbit operator to different approximations: the one-center approximation, the spin-orbit mean-field approach with electron densities from different state-averaging procedures, and the atomic mean-field integral approximation. We show that the mean-field approaches can lead to significant errors in the spin-orbital coupling matrix elements, which becomes particularly visible for the computed zero-field splittings. The one-center approximation, keeping all relevant two-electron terms, seems to be a significantly more accurate choice for the examples from our test set.

Polarizability of atomic Pt, Pt+, and Pt.

Electrostatic properties are important for understanding and modeling many phenomena, such as the adsorption of a catalytic metal upon an oxide support. The charge transfer between the metal and the support can lead to positive or negative charges on the metal. Here, the static dipole polarizability is computed for atomic platinum in charge states 0, +1, and -1 in several low-lying electronic terms and levels. Core pseudopotentials are used along with coupled-cluster theory. The best results are estimates for the coupled-cluster CCSDTQ/q-aug-cc-pwCV∞Z-PP values for atomic terms, combined with compositional data from spin-orbit configuration interaction. The polarizability of the anion Pt- is especially challenging for the theory with wildly varying results from different coupled-cluster perturbative approximations such as CCSD(T). For atomic mercury (Hg), selected as a nearby experimental value, our polarizability volume is larger than experiment by 0.8 bohrs3 (or 0.12 × 10-30 m3). For the ground level of neutral platinum, Pt(3D3), we find α0 = (41.2 ± 1.1) bohrs3 or (6.10 ± 0.16) × 10-30 m3. A handful of density functional theory methods are tested and found generally within 10% of our best values.

Quantum chemical topology at the spin-orbit configuration interaction level: Application to astatine compounds.

We report a methodology that allows the investigation of the consequences of the spin-orbit coupling by means of the QTAIM and ELF topological analyses performed on top of relativistic and multiconfigurational wave functions. In practice, it relies on the "state-specific" natural orbitals (NOs; expressed in a Cartesian Gaussian-type orbital basis) and their occupation numbers (ONs) for the quantum state of interest, arising from a spin-orbit configuration interaction calculation. The ground states of astatine diatomic molecules (AtX with X = AtF) and trihalide anions (IAtI- , BrAtBr- , and IAtBr- ) are studied, at exact two-component relativistic coupled cluster geometries, revealing unusual topological properties as well as a significant role of the spin-orbit coupling on these. In essence, the presented methodology can also be applied to the ground and/or excited states of any compound, with controlled validity up to including elements with active 5d, 6p, and/or 5f shells, and potential limitations starting with active 6d, 7p, and/or 6f shells bearing strong spin-orbit couplings.

Analytic non-adiabatic derivative coupling terms for spin-orbit MRCI wavefunctions. II. Derivative coupling terms and coupling angle for KHeA2Π1/2⇔KHeB2Σ1/2.

A method for calculating the analytic nonadiabatic derivative coupling terms (DCTs) for spin-orbit multi-reference configuration interaction wavefunctions is reviewed. The results of a sample calculation using a Stuttgart basis for KHe are presented. Additionally, the DCTs are compared with a simple calculation based on the Nikitin's 3 × 3 description of the coupling between the Σ and Π surfaces, as well as a method based on Werner's analysis of configuration interaction coefficients. The nonadiabatic coupling angle calculated by integrating the radial analytic DCTs using these different techniques matches extremely well. The resultant nonadiabatic energy surfaces for KHe are presented.

UV-Vis Absorption Spectroscopy of Polonium(IV) Chloride Complexes: An Electronic Structure Theory Study.

More than a hundred years after its discovery, the chemistry of the polonium radioelement is still largely unknown. However, it is quite clear that the properties of this heavy element ( Z = 84) may be affected by relativistic effects, in particular scalar relativistic effects and the so-called spin-orbit coupling (SOC). In this Article, we revisit the interpretation of UV-vis absorption spectra of polonium(IV) complexes in HCl medium, reported decades ago. From the data, two complexes were hypothesized, complex I with a maximum of absorption at 344 nm (at low HCl concentration) and complex II with a maximum at 418 nm (the only visible peak for HCl concentrations above 0.5 M). By monitoring the absorbance at 344 and 418 nm as a function of both the HCl concentration and the pH, complex I was formulated as [Po(OH)Cl x]3- x while complex II was formulated as [PoCl2+ x]2- x. In this work, we study the ground-state geometries of the [Po(OH)Cl x]3- x and [PoCl2+ x]2- x complexes for x = 4-2, i.e. for the most probable complexes, with density functional theory (DFT), demonstrating that solvation can remarkably change the geometries of such systems. The electronic excitation energies are then computed with time-dependent DFT (TD-DFT), second-order N-electron valence state perturbation theory (NEVPT2), and contracted spin-orbit configuration interaction (c-SOCI), showing (i) that the SOC must be at play to obtain excitation energies in the right energy domain and (ii) that the quantum chemical calculations point toward x = 4, i.e., toward the [Po(OH)Cl4]- and [PoCl6]2- complexes.

Quantum Chemical Study of the Redox Potential of the Co(OH2)62+/3+ Couple and the Singlet-Quintet Gibbs Energy Difference of the Co(OH2)63+ Ion.

The geometry and vibrational frequencies of Co(OH2)62+ in the quartet state and Co(OH2)63+ in the singlet and quintet states were computed with quantum mechanics/molecular mechanics (QM/MM), whereby the LC-BOP-LRD functional was used for the QM part involving the Co(OH2)6n+ ( n = 2, 3) ions. The surrounding 124 MM water molecules were treated with the MMFF94 force field. The hydration energy differences between low-spin Co(OH2)63+ and Co(OH2)62+ or Co(OH2)63+ in the quintet state were also calculated using this method. The electronic energy of the Co(OH2)6n+ ( n = 2, 3) ions was calculated with wave function theory, multistate extended general multiconfiguration quasi-degenerate second-order perturbation theory and spin-orbit configuration interaction. The redox potential of the Co(OH2)62+/3+ couple, and the singlet-quintet (adiabatic) Gibbs energy difference of Co(OH2)63+, computed based on these data, agree with the experiment.

Time-resolved inner-shell photoelectron spectroscopy: From a bound molecule to an isolated atom

Due to its element- and site-specificity, inner-shell photoelectron spectroscopy is a widely used technique to probe the chemical structure of matter. Here we show that time-resolved inner-shell photoelectron spectroscopy can be employed to observe ultrafast chemical reactions and the electronic response to the nuclear motion with high sensitivity. The ultraviolet dissociation of iodomethane (CH$_3$I) is investigated by ionization above the iodine 4d edge, using time-resolved inner-shell photoelectron and photoion spectroscopy. The dynamics observed in the photoelectron spectra appear earlier and are faster than those seen in the iodine fragments. The experimental results are interpreted using crystal field and spin-orbit configuration interaction calculations, and demonstrate that time-resolved inner-shell photoelectron spectroscopy is a powerful tool to directly track ultrafast structural and electronic transformations in gas-phase molecules.

Quantum Chemical Study of the Water Exchange Mechanism of the Neptunyl(VI) and -(V) Aqua Ions.

The water exchange reaction of the neptunyl(VI) and -(V) aqua ions was investigated with quantum chemical methods. Associative ( a) and dissociative ( d) exchange mechanisms were studied. The geometries and vibrational frequencies were computed with density functional theory (DFT) and multiconfiguration self-consistent field (MCSCF) methods. The Gibbs activation energies (Δ G‡) for a and d pathways were calculated with DFT and wave function theory (WFT), extended general multiconfiguration quasi-degenerate second-order perturbation theory (XGMC-QDPT2) including spin-orbit (SO) coupling at the SO configuration interaction (CI) level. The DFT-WFT agreement for Δ G‡ was poor for the investigated functionals except for LC-BOP-LRD. Due to ligand-field effects, Δ G‡ for the associatively activated exchange reaction of NpO2(OH2)52+ with a fδ1 electron configuration is higher than for the actinyl(VI) aqua ions of U, Pu, and Am exhibiting f0, fδ2, and fδ2fϕ1 electron configurations.

All-electron relativistic computations on the low-lying electronic states, bond length, and vibrational frequency of CeF diatomic molecule with spin-orbit coupling effects.

Ab initio all-electron computations have been carried out for Ce+ and CeF, including the electron correlation, scalar relativistic, and spin-orbit coupling effects in a quantitative manner. First, the n-electron valence state second-order multireference perturbation theory (NEVPT2) and spin-orbit configuration interaction (SOCI) based on the state-averaged restricted active space multiconfigurational self-consistent field (SA-RASSCF) and state-averaged complete active space multiconfigurational self-consistent field (SA-CASSCF) wavefunctions have been applied to evaluations of the low-lying energy levels of Ce+ with [Xe]4f1 5d1 6s1 and [Xe]4f1 5d2 configurations, to test the accuracy of several all-electron relativistic basis sets. It is shown that the mixing of quartet and doublet states is essential to reproduce the excitation energies. Then, SA-RASSCF(CASSCF)/NEVPT2 + SOCI computations with the Sapporo(-DKH3)-2012-QZP basis set were carried out to determine the energy levels of the low-lying electronic states of CeF. The calculated excitation energies, bond length, and vibrational frequency are shown to be in good agreement with the available experimental data. © 2018 Wiley Periodicals, Inc.

Excited interatomic potential energy surfaces of Rb + He that correlate with Rb terms 52S through 72S.

The excited state interatomic potential energy surfaces for Rb + He are computed at the spin-orbit multi-reference configuration interaction level of theory using all-electron basis sets of triple and quadruple-zeta quality that have been contracted for Douglas-Kroll-Hess (DKH) Hamiltonian and includes core-valence correlation. Davidson-Silver corrections (MRCI+Q) are employed to ameliorate size consistency error. An extrapolation of CASSCF energies is performed using the procedure of Karton and Martin whereas extrapolation of correlation energy is performed using an expression involving the inverse powers of (lmax + 1/2), the highest angular momentum value present in the basis set. The spin-orbit energies in the limit of complete basis set are obtained by replacing the energy eigenvalues in the spin-orbit matrix by the relativistic-corrected MRCI+Q energies extrapolated to the complete basis set limit. MRCI diabatic potential energy surfaces for a few selected 2Σ states are calculated to study the general topology and avoided crossings and repulsive form of the 6s 2Σ+ state. Important features of the potential energy surfaces are discussed with implications for alkali laser spectroscopy.

Electronic Structure and Energy Transfer in Europium(III)-Ciprofloxacin Complexes: A Theoretical Study.

The structure and ligand-localized excited states of [Eu(cfqH) (cfq)(H2O)4]Cl2 (cfqH is ciprofloxacin) are studied by XMCQDPT2/CASSCF with full geometry optimization. The complex includes one anionic and one zwitterionic ligand. Two low-lying triplet states, both localized on the anionic ligand, are found. One of them has sufficient energy to transfer to the (5)D1 sublevel of Eu(3+), because its T-S0 vertical transition energy is equal (or very close) to the (7)F0-(5)D1 Eu(3+) excitation energy. The other triplet state has a very small S0-T1 gap, which favors fast nonradiative relaxation. Two other triplet states are localized on the zwitterionic ligand. One low-lying excited singlet state (S1) is localized on the anionic ligand; the other excited singlet is localized on the zwitterionic one. Spin-orbit coupling constants were calculated for the relaxed geometry of each state (ground state, two low-lying triplets, and one low-lying excited singlet) by spin-orbit configuration interaction (CI) with Pauli-Breit Hamiltonian. Large spin-orbit coupling constants between S1 and both triplets together with small energy gaps are indicative of fast intersystem crossing (ISC) from the excited singlet state to the triplet manifold. This ISC process is followed by energy transfer from the ligand-localized triplet states to the (5)D1 sublevel of Eu(3+). However, relatively large spin-orbit coupling constants between S0 and one of the triplet states together with the small T-S0 energy gap shows that this state can decay without transferring its energy to Eu(3+). This mechanism is expected to be common for other Ln(3+)-fluoroquinolone complexes.