Multireference Ab Initio Methods Research Articles

Multireference Ab Initio Calculations on Excited Electronic States of Carbazole-Based Organic Compounds for Thermally Activated Delayed Fluorescence.

The emerging technology of organic light-emitting diodes takes advantage of the thermally activated delayed fluorescence (TADF) mechanism for improved efficiency. Carbazole-based organic molecules are suitable for TADF emission because of charge transfer excitations between the electron-donor carbazole and an electron-acceptor unit. Computational design of new TADF molecules with the desired properties is challenging because charge-transfer excitations cannot be predicted accurately by time-dependent density functional theory. Four groups of carbazole-based donor-acceptor molecules have been studied using multireference ab initio methods to understand the nature of excited electronic states. The state-averaged complete active space self-consistent field (SA-CASSCF) and the N-electron valence state perturbation theory (NEVPT2) were used to calculate energies and oscillator strengths for multiple excited electronic states. The number of active electrons and orbitals and the number of excited states included in state-averaged CASSCF were selected such that the accuracy of ab initio predictions could be improved systematically. The procedure introduced here for the calculation of multiple excited electronic states of TADF candidates can be used to accelerate the computational search for efficient TADF materials.

Relativistic Douglas–Kroll–Hess calculations of hyperfine interactions within first-principles multireference methods

A relativistic magnetic hyperfine interaction Hamiltonian based on the Douglas–Kroll–Hess (DKH) theory up to the second order is implemented within the ab initio multireference methods, including spin–orbit coupling in the Molcas/OpenMolcas package. This implementation is applied to calculate relativistic hyperfine coupling (HFC) parameters for atomic systems and diatomic radicals with valence s or d orbitals by systematically varying active space size in the restricted active space self-consistent field formalism with restricted active space state interaction for spin–orbit coupling. The DKH relativistic treatment of the hyperfine interaction reduces the Fermi contact contribution to the HFC due to the presence of kinetic factors that regularize the singularity of the Dirac delta function in the nonrelativistic Fermi contact operator. This effect is more prominent for heavier nuclei. As the active space size increases, the relativistic correction of the Fermi contact contribution converges well to the experimental data for light and moderately heavy nuclei. The relativistic correction, however, does not significantly affect the spin-dipole contribution to the hyperfine interaction. In addition to the atomic and molecular systems, the implementation is applied to calculate the relativistic HFC parameters for large trivalent and divalent Tb-based single-molecule magnets (SMMs), such as Tb(III)Pc2 and Tb(II)(CpiPr5)2 without ligand truncation using well-converged basis sets. In particular, for the divalent SMM, which has an unpaired valence 6s/5d hybrid orbital, the relativistic treatment of HFC is crucial for a proper description of the Fermi contact contribution. Even with the relativistic hyperfine Hamiltonian, the divalent SMM is shown to exhibit strong tunability of HFC via an external electric field (i.e., strong hyperfine Stark effect).

Machine Learning-Enhanced Quantum Chemistry-Assisted Refinement of the Active Site Structure of Metalloproteins.

Understanding the fine structural details of inhibitor binding at the active site of metalloenzymes can have a profound impact on the rational drug design targeted to this broad class of biomolecules. Structural techniques such as NMR, cryo-EM, and X-ray crystallography can provide bond lengths and angles, but the uncertainties in these measurements can be as large as the range of values that have been observed for these quantities in all the published structures. This uncertainty is far too large to allow for reliable calculations at the quantum chemical (QC) levels for developing precise structure-activity relationships or for improving the energetic considerations in protein-inhibitor studies. Therefore, the need arises to rely upon computational methods to refine the active site structures well beyond the resolution obtained with routine application of structural methods. In a recent paper, we have shown that it is possible to refine the active site of cobalt(II)-substituted MMP12, a metalloprotein that is a relevant drug target, by matching to the experimental pseudocontact shifts (PCS) those calculated using multireference ab initio QC methods. The computational cost of this methodology becomes a significant bottleneck when the starting structure is not sufficiently close to the final one, which is often the case with biomolecular structures. To tackle this problem, we have developed an approach based on a neural network (NN) and a support vector regression (SVR) and applied it to the refinement of the active site structure of oxalate-inhibited human carbonic anhydrase 2 (hCAII), another prototypical metalloprotein target. The refined structure gives a remarkably good agreement between the QC-calculated and the experimental PCS. This study not only contributes to the knowledge of CAII but also demonstrates the utility of combining machine learning (ML) algorithms with QC calculations, offering a promising avenue for investigating other drug targets and complex biological systems in general.

Thermal rate constants and kinetic isotope effects of the H + H2O2 reactions: barrier height and reaction energy from single- and multireference methods.

One of the more significant sub-mechanisms of H2/O2 combustion involves the reaction of hydrogen peroxide with hydrogen atoms (H + H2O2), resulting in the production of OH + H2O (R1) and H2 + HO2 (R2) paths. Previous experimental and ab initio calculations reveal some variations in the barrier height for (R1). To improve the energetics of both (R1) and (R2), single reference and multireference ab initio methods are employed, and the rate constants and H/D kinetic isotope effects (KIEs) are calculated as a function of temperature. For (R1), the best results for the barrier height and reaction energies computed with the CASPT2(15,11)/aug-cc-pV6Z are 5.2 and - 70.3kcal.mol-1, respectively. CCSD(T)/aug-cc-pV5Z + CV (core-valence) calculations for (R2) give 9.7 and - 15.6kcal.mol-1 to those parameters. The CVT/SCT rate constants of both paths agree well with the fitted rate constants from uncertainty-weighted statistical analysis of the 14-mechanism of H2/O2. The kinetic isotopic effect (kH/kD) for the reaction D + H2O2 → DH + HO2 was found to be 0.47, which is in excellent agreement with the experimental value of 0.43. The structures of reactants, transition state, and products of (R1) and (R2) are calculated with the aug-cc-pVTZ basis set and M062X DFT, CCSD(T), and CASSCF methods. The barrier heights and reaction energies of (R1) and (R2) are computed using the M06-2X, CCSD(T), MRCI, and CASPT2 methods and various basis sets. The rate constants are calculated with the variational transition state theory including multidimensional tunneling corrections (VTST-MT), with potential energy surfaces built by the M06-2X/aug-cc-pVTZ approach.

Spin-Vibronic Dynamics in Open-Shell Systems beyond the Spin Hamiltonian Formalism.

Vibronic coupling has a dramatic influence over a large number of molecular processes, ranging from photochemistry to spin relaxation and electronic transport. The simulation of vibronic coupling with multireference wave function methods has been largely applied to organic compounds, and only early efforts are available for open-shell systems such as transition metal and lanthanide complexes. In this work, we derive a numerical strategy to differentiate the molecular electronic Hamiltonian in the context of multireference ab initio methods and inclusive of spin-orbit coupling effects. We then provide a formulation of open quantum system dynamics able to predict the time evolution of the electron density matrix under the influence of a Markovian phonon bath up to fourth-order perturbation theory. We apply our method to Co(II) and Dy(III) molecular complexes exhibiting long spin relaxation times and successfully validate our strategy against the use of an effective spin Hamiltonian. Our study sheds light on the nature of vibronic coupling, the importance of electronic excited states in spin relaxation, and the need for high-level computational chemistry to quantify it.

Exchange Interactions and Magnetic Properties of a Molecular Mn18-Ring Complex.

[Mn3O(OAc)7(HOAc)]6·xAcOH (x = 6-9) represents a rare example of a compound containing molecular Mn18-rings. These are formed by Mn3(µ3-O) subunits in which the high-spin Mn(III) centers are bridged by three pairs of acetate anions (AcO-). An AcOH molecule coordinates to one of the Mn atoms leading to [Mn3(µ3-O)(µ2-OAc)6(AcOH)]-units, designated in short as Mn3-units, that are interconnected by acetate anions via the other two Mn atoms to form Mn18-rings. Magnetic measurements show weak ferromagnetic interactions between them that are suppressed in strong magnetic field. Quantum-chemical calculations on Mn3 model complexes using independently DFT and ab-initio multi reference methods (CASSCF/NEVPT2) show a correlation between the orientation of the pseudo-Jahn-Teller axes of pairs of Mn(III) magnetic centers and corresponding exchange coupling energies. Weak coupling between Mn3-units within the Mn18-ring allowed to simulate the magnetic susceptibility vs temperature dependence in terms of basically uncoupled magnetic moments of each Mn3-unit within the ring.

Enhanced Electronic g-Factors in Magic Number Main Group Bimetallic Nanoclusters

We report the observation of large electronic g-factors in magic number main group bimetallic nanoclusters by performing Stern-Gerlach deflection experiments at 10 K. The clusters AlPb12 and InPb12 exhibit values of g = 3.5-4.0, whereas GaPb12 clusters surprisingly reveal a value of g < 2.0. Multireference ab initio methods are applied to unmask the origin of the g-factors and to gain insight into the electronic structure. The interplay of the pyritohedral molecular symmetry, a particularly strong spin-orbit coupling involved in the ground state, and the presence of low-lying degenerate excited states causes large positive g-factors in AlPb12 and InPb12. Contrarily, the spin-orbit coupling in the GaPb12 ground state is completely quenched. This is due to the d-block contraction lowering the nonbonding Ga 5s orbital and consequently forming an icosahedral ground state. Thus, endohedral p-doped tetrel clusters, composed of purely main group elements, state a novel and unique class of magnetic compounds and their study contributes to a more profound understanding of the metal-metal interaction in polynuclear clusters as well as magnetism at the molecular level.

Computational Insights into Electronic Excitations, Spin-Orbit Coupling Effects, and Spin Decoherence in Cr(IV)-Based Molecular Qubits.

The great success of point defects and dopants in semiconductors for quantum information processing has invigorated a search for molecules with analogous properties. Flexibility and tunability of desired properties in a large chemical space have great advantages over solid-state systems. The properties analogous to point defects were demonstrated in the Cr(IV)-based molecular family, Cr(IV)(aryl)4, where the electronic spin states were optically initialized, read out, and controlled. Despite this kick-start, there is still a large room for enhancing properties crucial for molecular qubits. Here, we provide computational insights into key properties of the Cr(IV)-based molecules aimed at assisting the chemical design of efficient molecular qubits. Using the multireference ab initio methods, we investigate the electronic states of Cr(IV)(aryl)4 molecules with slightly different ligands, showing that the zero-phonon line energies agree with the experiment and that the excited spin-triplet and spin-singlet states are highly sensitive to small chemical perturbations. By adding spin-orbit interaction, we find that the sign of the uniaxial zero-field splitting (ZFS) parameter is negative for all considered molecules and discuss optically induced spin initialization via non-radiative intersystem crossing. We quantify (super)hyperfine coupling to the 53Cr nuclear spin and to the 13C and 1H nuclear spins, and we discuss electron spin decoherence. We show that the splitting or broadening of the electronic spin sub-levels due to superhyperfine interaction with 1H nuclear spins decreases by an order of magnitude when the molecules have a substantial transverse ZFS parameter.

Theoretical investigation of CH-bond activation by photocatalytic excited SO2 and the effects of C-, N-, S-, and Se-doped TiO2.

The photocatalytic sulfoxidation on TiO2 discovered by Parrino et al. represents a new, interesting and lower energy route for the synthesis of sulfonic acids. Sulfonic acids are important precursors for dyes, detergents and drugs. In the commonly known industrial process, SO2 and a specific hydrocarbon are converted into sulfonic acids using high-energy UV light. In this reaction, SO2 is excited into a metastable triplet state (3SO2), which has the potential to activate a CH-bond of hydrocarbons and start a radical reaction cycle. By introducing TiO2 as a photocatalyst, it has been shown that visible light can be used for the synthesis. This offers the potential to be a cost-effective reaction approach for industrial use. However, experimental studies indicate that the initial excitation mechanism of SO2 on TiO2 is significantly different from the catalyst-free mechanism. Parrino et al. were able to reveal first evidence for the existence of a charge-transfer process from SO2 to the TiO2 surface by means of electrochemical experiments. First theoretical investigations from first principles were able to further substantiate the existence of a charge-transfer. However, to fully understand this mechanism, more accurate methods such as Time Dependent Density Functional Theory (TD-DFT) or ab initio multireference methods such as the Complete Active Space Self Consistent Field (CASSCF) method are required. Furthermore, after understanding the charge-transfer mechanism, the introduction of dopants into TiO2 can be investigated in order to possibly redshift the excitation energy. This might open the route to using lower energy light for the sulfoxidation of hydrocarbons on TiO2 as a new potential industrial reaction for the synthesis of sulfonic acids. In this work, we will study the initial step of the photocatalytic sulfoxidation of hydrocarbons using the TD-DFT and CASSCF methods by using a combined approach consisting of calculations with periodic boundary conditions and a newly constructed embedded cluster model. Furthermore, we will explore the effects of doping by introducing four heteroatoms (C, N, S, and Se) into the TiO2 surfaces anatase[101] and rutile[110] to find a possible enhancement of the photocatalytic reactivity by lowering the electronic excitation energy.

A Combined Study of Tc Redox Speciation in Complex Aqueous Systems: Wet-Chemistry, Tc K-/L3-Edge X-ray Absorption Fine Structure, and Ab Initio Calculations

The combination of wet-chemistry experiments (measurements of pH, Eh, and [Tc]) and advanced spectroscopic techniques (K- and L3-edge X-ray absorption fine structure spectroscopy) confirms the formation of a very stable Tc(V)-gluconate complex under anoxic conditions. In the presence of gluconate and an excess of Sn(II) (at pe + pH ≈ 2), technetium forms a very stable Tc(IV)-gluconate complex significantly enhancing the solubility defined by TcO2(s) in hyperalkaline gluconate-free systems. A new setup for "tender" X-ray spectroscopy (spectral range, ∼2-5 keV) in transmission or total fluorescence yield detection mode based on a He flow cell has been developed at the INE Beamline for radionuclide science (KIT light source). This setup allows handling of radioactive specimens with total activities up to one million times the exemption limit. For the first time, Tc L3-edge measurements (∼2.677 keV) of Tc species in liquid (aqueous) media are reported, clearly outperforming conventional K-edge spectroscopy as a tool to differentiate Tc oxidation states and coordination environments. The coupling of L3-edge X-ray absorption near-edge spectroscopy measurements and relativistic multireference ab initio methods opens new perspectives in the definition of chemical and thermodynamic models for systems of relevance in the context of nuclear waste disposal, environmental, and pharmaceutical applications.

Ground and excited electronic structure analysis of XM4 (X = N, P and M = Li, Na) and their anions.

High-level coupled-cluster, electron propagator, and multi-reference ab initio methods are employed to study the ground and excited electronic states of the XM4 (X = N, P and M = Li, Na) series. All XM4 species bear lower ionization potentials and can be classified as superalkalis. In the ground state each possesses a diffuse electron in the periphery. This expanded electron cloud of tetrahedral NLi4, NNa4, and PNa4 molecules is spherical (similar to an s-orbital) and evenly distributed around the XM4+ core. The outer electron is promoted to higher-angular momentum p-, d-, 2s-type orbitals in excited states. Singly occupied molecular orbitals of excited PLi4 are deformed due to its lower C1 symmetry. The aug-cc-pVQZ basis set was found to describe the excited states of XM4 accurately and efficiently. The bound singlet and triplet electronic states of XM4- that possess two peripheral electrons are also analyzed.

Advanced Magnetic Resonance Studies of Tetraphenylporphyrinatoiron(III) Halides

High-Frequency and -Field EPR (HFEPR) studies of Fe(TPP)X (X = F, Cl, Br; I, TPP2−= meso-tetraphenylporphyrinate dianion) and far-IR magnetic spectroscopic (FIRMS) studies of Fe(TPP)Br and Fe(TPP)I have been conducted to probe magnetic intra- and inter-Kramers doublet transitions in these S = 5/2 metalloporphyrin complexes, yielding zero-field splitting (ZFS) and g parameters for the complexes: Fe(TPP)F, D = +4.67(1) cm−1, E = 0.00(1) cm−1, g⊥ = 1.97(1), g|| = 2.000(5) by HFEPR; Fe(TPP)Cl, D = +6.458(2) cm−1, E = +0.015(5) cm−1, E/D = 0.002, g⊥ = 2.004(3), g|| = 2.02(1) by HFEPR; Fe(TPP)Br, D = +9.03(5) cm−1, E = +0.047(5) cm−1, E/D = 0.005, giso = 1.99(1) by HFEPR and D = +9.05 cm−1, giso = 2.0 by FIRMS; Fe(TPP)I, D = +13.84 cm−1, E = +0.07 cm−1, E/D = 0.005, giso = 2.0 by HFEPR and D = +13.95 cm−1, giso = 2.0 by FIRMS (the sign of E was in each case arbitrarily assigned as that of D). These results demonstrate the complementary nature of field- and frequency-domain magnetic resonance experiments in extracting with high accuracy and precision spin Hamiltonian parameters of metal complexes with S > 1/2. The spin Hamiltonian parameters obtained from these experiments have been compared with those obtained from other physical methods such as magnetic susceptibility, magnetic Mossbauer spectroscopy, inelastic neutron scattering (INS), and variable-temperature and -field magnetic circular dichroism (VT-VH MCD) experiments. INS, Mossbauer and MCD give good agreement with the results of HFEPR/FIRMS; the others not as much. The electronic structure of Fe(TPP)X (X = F, Cl, Br, I) was studied earlier by multi-reference ab initio methods to explore the origin of the large and positive D-values, reproducing the trends of D from the experiments. In the current work, a simpler model based on Ligand Field Theory (LFT) is used to explain qualitatively the trend of increasing ZFS from X = F to Cl to Br and to I as the axial ligand. Tetragonally elongated high-spin d5 systems such as Fe(TPP)X exhibit D > 0, but X plays a key role. Spin delocalization onto X means that there is a spin–orbit coupling (SOC) contribution to D from X•, as opposed to none from closed-shell X−. Over the range X = F, Cl, Br, I, X• character increases as does the intrinsic SOC of X• so that D increases correspondingly over this range.

Multireference Ground and Excited State Electronic Structures of Free- versus Iron Porphyrin-Carbenes.

Iron porphyrin carbenes (IPCs) are important reaction intermediates in engineered carbene transferase enzymes and homogeneous catalysis. However, discrepancies between theory and experiment complicate the understanding of IPC electronic structure. In the literature, this has been framed as whether the ground state is an open- vs closed-shell singlet (OSS vs CSS). Here we investigate the structurally dependent ground and excited spin-state energetics of a free carbene and its IPC analogs with variable trans axial ligands. In particular, for IPCs, multireference ab initio wave function methods are more consistent with experiment and predict a mixed singlet ground state that is dominated by the CSS (Fe(II) ← {:C(X)Y}0) configuration (i.e., electrophilic carbene) but that also has a small, non-negligible contribution from an Fe(III)-{C(X)Y}-• configuration (hole in d(xz), i.e., radical carbene). In the multireference approach, the "OSS-like" excited states are metal-to-ligand charge transfer (MLCT) in nature and are energetically well above the CSS-dominated ground state. The first, lowest energy of these "OSS-like" excited states is predicted to be heavily weighted toward the Fe(III)-{C(X)Y}-• (hole in d(yz)) configuration. As expected from exchange considerations, this state falls energetically above a triplet of the same configuration. Furthermore, potential energy surfaces (PESs) along the IPC Fe-C(carbene) bond elongation exhibit increasingly strong mixings between CSS/OSS characters, with the Fe(III)-{C(X)Y}-• configuration (hole in d(xz)) growing in weight in the ground state during bond elongation. The relative degree of electrophilic/radical carbene character along this structurally relevant PES can potentially play a role in reactivity and selectivity patterns in catalysis. Future studies on IPC reaction coordinates should evaluate contributions from ground and excited state multireference character.

Ab initio analysis of the optical spectra and EPR parameters of Ni2+ ions in CaF2 and CdF2 crystals

Crystals with fluorite type structure doped with transition metals (TM) in different oxidation states provide the possibility of investigating optical spectra, magnetic properties and ligand field (LF) parameters of TM in cubic eightfold coordination. If the doped ion in the host crystal matrix has a degenerate ground state then, due to the strong T⊗τ Jahn-Teller (JT) effect, the cubic coordination geometry of the impurity ion will be distorted to octahedral, with the change in its properties. In this paper we present the results of the ab initio investigation of absorption optical spectra, JT stabilization energy in the ground state, spin-Hamiltonian and ligand field parameters of divalent nickel ion doped in cubic CaF2 and CdF2 crystals. The analysis of new cluster [NiF6]4- with trigonal symmetry (D3d) at the Ni2+site was made based on the ab initio multireference methods (MR). All calculations are applied to the [NiF6]4- cluster embedded in an extended point charge field of host matrix ions built according to the Gellé-Lepetit procedure. After density functional theory (DFT) optimization of the doped crystals, the ab initio energy calculation of the electronic states and corresponding wave functions of Ni2+ ions is performed from the complete active space self-consistent field (CASSCF). The improved energy states obtained by using different approaches such as N-electron valence second order perturbation theory (NEVPT2), second order dynamic correlation dressed complete active space (DCD-CAS2), difference dedicate configuration interaction with three degrees of freedom (MRDDCI3) and spectroscopy-oriented configuration interactions (SORCI), were analyzed. In addition, the ab initio ligand field theory (AILFT) procedure allows extracting all LF parameters and spin-orbit coupling constant. The obtained results are discussed and the comparison with the available in the literature corresponding experimental values literature yields a reasonably agreement between theory and experiment, which justifies this new route of investigation.The structural mechanism around Ni2+ center through JT effect, combined with the above mentioned methodology, allows for more consistent and reliable calculations of optical spectra and spin-Hamiltonian parameters of any impurity ions doped in eightfold cubic coordination.

Simplified Treatment of Electronic Structures of the Lowest Singlet and Triplet States of Didehydropyrazines.

Experiments on the lowest lying singlet and triplet states of didehydropyrazine isomers (that focus on energy gaps, geometries, and vibrational frequencies) have been carried out computationally by implementing the improved virtual orbital-based multireference (MR) ab initio methods. Pyrazines possess a reasonable MR nature making their description challenging with the conventional quantum chemical approaches. Although wave functions of the diradicals usually have two dominant configurations, a larger reference space is warranted to consistently and accurately describe pyrazine diradicals indicating the complex nature of the systems. Present calculations predict a singlet ground state for ortho- and para-pyrazines, while a triplet ground state is suggested for the meta isomer. The adiabatic singlet-triplet energy gap for the para form is found to be notably higher (by 28.4 kcal/mol) compared to ortho (2.0 kcal/mol) and meta isomers (-5.1 kcal/mol). Accurate and reliable computations are imperative for forecasting the state-ordering in such diradicals. The structural properties obtained from the present calculations lend strong support toward future experimental explorations on these systems.

High-level theoretical study of the hydrogen abstraction reaction H2S + O2 = SH + HO2 and prediction of the rate constants

Hydrogen abstraction reaction of hydrogen sulfide (H2S) by molecule oxygen (O2) forming hydroperoxyl radical (HO2) and hydrosulfide radical (SH) is very important for both atmospheric and combustion chemistry. This work reports a systematic theoretical study on this reaction using a combination of high-level quantum chemistry methods and chemical kinetic theory. Geometry optimizations for all species are performed at QCISD/cc-pVQZ level of theory. The energies for minima and transition state are computed using both single- and multi-reference ab initio methods. It is found that the transition state of this reaction exhibits significant multi-reference nature based on 〈S2〉 and T1 diagnostic during CCSD(T) calculations. The predicted reaction barrier from high-level multi-reference CASPT2(20e,13o)/aug-cc-pVTZ method is higher than those from CCSD(T) and W1BD methods by 6–7 kcal mol−1. Reaction energy barriers from a series of DFT methods also show large deviations compared with both single- and multi-reference methods. Thermal rate constants are calculated over a temperature range from 300 to 2500 K by employing canonical transition state theory with Eckart tunneling correction and the treatment of torsional mode. This work provides accurate rate constants for this reaction and fundamental benchmark results for H/O/S reaction systems, which is valuable for theoretical chemistry and kinetic modeling of sulfur chemistry.

Spectroscopy of the electronic excited states of thioxophosphane, HPS, and of its deuterated species.

The stable low energy states of the HPS and DPS molecules have been studied through multi-reference ab initio methods in conjunction with large atomic basis sets. Stable states for these species have been examined up to 7 eV above the ground state minimum. We found six stable electronic states that are mostly mono-configurational. These states may be involved in the photodynamics and photodissociation of this molecule. In particular, the 2 1A' state presents two minima on the potential energy surface, one of them close to linear configuration. This state may be populated after the absorption of a visible photon from the ground state and gives rise to large amplitude motions that may eventually induce isomerization to electronically excited HSP. Moreover, we characterized these states spectroscopically to facilitate the assignment of the vibronic spectra of the HPS and DPS species. For these low-energy states, we thus computed vertical and adiabatic excitation energies, and for the stable ones, a full set of spectroscopic constants including harmonic frequencies and anharmonic vibrational, rotational, and centrifugal distortion constants. The calculated potential energy surfaces for these states have been used in a variational procedure to deduce the pattern of vibrational levels up to 4000 cm-1 above the corresponding vibrationless level. Our data may serve for the assignment of the IR and Vis spectra of HPS and DPS.

Molecular dynamics and metadynamics simulations of [2 + 2] photocycloaddition

AbstractTriplet state mechanism of [2 + 2] photocycloaddition forming a cyclobutane ring from two ethylenes is investigated in the context of photocatalysis. High‐level ab initio calculations are combined with ab initio adiabatic molecular dynamics and ab initio metadynamics for rare events modeling. In a photocatalytic scheme, a reactant reaches the triplet state either via intersystem crossing (ISC) or triplet sensitization. The model system adopts a biradical structure, which represents energy intersection with the ground state. The system either completes cyclization or undergoes fragmentation into two olefinic units. The potential and free energy surfaces of the cyclobutane/ethylenes system are mapped with multireference approaches describing possible reaction pathways. To obtain a full picture of a double bond photoreactivity, ab initio adiabatic dynamical calculations were used to estimate reaction yields and to model the effects of excess energy. The potential use of density functional theory based approaches for [2 + 2] photocycloaddition was investigated for future simulations and design of realistic photocatalytic systems. Dynamical aspects of [2 + 2] photocycloaddition via a triplet state manifold are investigated by combining ab initio multireference methods and ab initio molecular dynamics and metadynamics. The reaction pathways are studied for a model system of two ethylenes forming a cyclobutane ring to provide a basis for further studies on design of photocatalytic systems.

Identification of α-Fe in High-Silica Zeolites on the Basis of ab Initio Electronic Structure Calculations.

α-Fe is the precursor of the reactive FeIV═O core responsible for methane oxidation in Fe-containing zeolites. To get more insight into the nature and stability of α-Fe in different zeolites, the binding of Fe(II) at six-membered-ring cation exchange sites (6MR) in ZSM-5, zeolite beta, and ferrierite was investigated using DFT and multireference ab initio methods (CASSCF/CASPT2). CASPT2 ligand field (LF) excitation energies of all sites were compared with the experimental DR-UV-vis spectra reported by Snyder et al. From this comparison it is concluded that the 16000 cm-1 band of α-Fe, observed in all three zeolites, can uniquely be assigned to a high-spin square-planar (SP) Fe(II) located at a 6MR with an Al-Si-Si-Al sequence, where the Al atoms are positioned opposite in the ring and as close to each other as possible. The stability of such conformations is also confirmed by the binding energies obtained from DFT. The bands at 10000 cm-1 in the experimental spectra, assigned to spectator Fe(II), are attributed to six-coordinated trigonal-prismatic Fe(II) species, as calculated for the γ-site in ZSM-5. The entatic effect of the zeolite lattice on the stability of the SP sites was investigated by making use of the unconstrained Fe(II) model complex FeL2 (with L = [Al(OH)4]-). The SP conformer is approximately 2 kcal/mol more stable than the tetrahedral form, indicating that the SP coordination environment of α-Fe is not imposed by the zeolite lattice but rather electronically preferred by Fe(II) in the environment of four O ligands. A significant contribution to the stability of the SP conformer is provided by mixing of the doubly occupied 3dz2 orbital with the higher lying 4s.

Theoretical Study on the Photoelectron Spectra of Ln(COT)2–: Lanthanide Dependence of the Metal–Ligand Interaction

We have performed a theoretical analysis of the recently reported photoelectron (PE) spectra of the series of sandwich complex anions Ln(COT)2- (Ln = La-Lu, COT = 1,3,5,7-cyclooctatetraene), focusing on the Ln dependence of the vertical detachment energies. For most Ln, the π molecular orbitals, largely localized on the COT ligands, have the energy order of e1g < e1u < e2g < e2u as in the actinide analogues, reflecting the substantial orbital interaction with the Ln 5d and 5p orbitals. Thus, it would be expected that the lanthanide contraction would increase the orbital interaction so that the overlaps between the COT π and Ln atomic orbitals tend to increase across the series. However, the PE spectra and theoretical calculations were not consistent with this expectation, and the details have been clarified in this study. Furthermore, the energy level splitting patterns of the anion and neutral complexes have been studied by multireference ab initio methods, and the X peak splittings observed in the PE spectra only for the middle-range Ln complexes were found to be due to the specific interaction between the Ln 4f and ligand π orbitals of the neutral complexes in e2u symmetry. Because the magnitude of this 4f-ligand interaction depends critically on the final state 4f electron configuration and the spin state, a significant Ln dependence in the PE spectra is explained.