Modern aspects of the Jahn-Teller effect theory and applications to molecular problems

Support effects on conical intersections of Jahn-Teller fluxional metal clusters on the sub-nanoscale

The concept of fluxionality has been invoked to explain the enhanced catalytic properties of atomically precise metal clusters of subnanometer size. Cu3 isolated in the gas phase is a classical case of a fluxional metal cluster where a conical intersection leads to a Jahn-Teller (JT) distortion resulting in a potential energy landscape with close-lying multiminima and, ultimately, fluxional behavior. In spite of the role of conical intersections in the (photo)stability and (photo)catalytic properties of surface-supported atomic metal clusters, they have been largely unexplored. In this work, by applying a high-level multi-reference ab initio method aided with dispersion corrections, we analyze support effects on the conical intersection of Cu3 considering benzene as a model support molecule of carbon-based surfaces. We verify that the region around the conical intersection and the associated Jahn-Teller (JT) distortion is very slightly perturbed by the support when the Cu3 cluster approaches it in a parallel orientation: Two electronic states remain degenerate for a structure with C3 symmetry consistent with the D3h symmetry of unsupported Cu3 at the conical intersection. It extends over a one-dimensional seam that characterizes a physisorption minimum of the Cu3-benzene complex. The fluxionality of the Cu3 cluster, reflected in large fluctuations of relaxed Cu-Cu distances as a function of the active JT mode, is kept unperturbed upon complexation with benzene as well. In stark contrast, for the energetically favored perpendicular orientation of the Cu3 plane to the benzene ring plane, the conical intersection (CI) is located 12 100 cm-1 (∼1.5 eV) above the chemisorption minimum, with the fluxionality being kept at the CI's nearby and lost at the chemisorption well. The first excited state at the perpendicular orientation has a deep well (>4000 cm-1), being energetically closer to the CI. The transition dipole moment between ground and excited states has a significant magnitude, suggesting that the excited state can be observed through direct photo-excitation from the ground state. Besides demonstrating that the identity of an isolated Jahn-Teller metal cluster can be preserved against support effects at a physisorption state and lifted out at a chemisorption state, our results indicate that a correlation exists between conical intersection topography and fluxionality in the metal cluster's Cu-Cu motifs.

Jahn-Teller and pseudo-Jahn-Teller effects on the vibronic structure of the photoionized spectrum of cyanopropyne

Nonadiabatic quantum dynamics are carried out to illustrate the photoionized spectrum of the cyanopropyne (CH3-C≡C-C≡N) as reported in recent experimental measurements [Lamarre et al., J. Mol. Spectrosc. 315, 206 (2015)]. A detailed electronic structure calculation is performed to analyze the topographical details of the first five ionized states, of which three are degenerate states (X̃2E, B̃2E, and C̃2E) and two are non-degenerate states (Ã2A1 and D̃2A1). The degenerate E states of the C3V symmetry molecule are prone to Jahn-Teller (JT) instability, and in addition, symmetry allowed A1 - E vibronic coupling, i.e., pseudo-Jahn-Teller (PJT), effects are expected to have a significant impact in the detailed vibronic structure of these electronic states. The JT splittings of X̃2E and B̃2E degenerate states are small, whereas it is quite large at three high frequencies in the C̃2E electronic states. The large energy separation of X̃2E from the other states and the non-zero PJT coupling of the B̃2E state with the close-lying Ã2A1 state indicate the uncoupled nature of the X̃, Ã, and B̃ vibronic bands of C4H3N. The intersection minima of B̃ and C̃ states with the D̃ state nearly coincide with the energetic minimum of D̃ state. Therefore, the PJT couplings among these states will lead to a strong vibronic interaction to shape the respective band structure. To completely understand the JT and PJT interactions in the photoionized spectrum of C4H3N, the vibronic coupling model Hamiltonian was constructed to perform nuclear dynamics studies for these electronic states. The vibrational progressions in each vibronic band are identified and compared with the available experimental data in the literature. The impacts of JT and PJT effects in the first five ionized states of cyanopropyne are investigated and discussed in detail.

Ferroelectricity Induced by a Combination of Crystallographic Chirality and Axial Vector

Ferroelectric materials compatible with magnetism and/or conductive properties provide a platform for exploring unconventional phenomena, such as the magnetoelectric effect, nonreciprocal responses, and nontrivial superconductivity. Though recent studies on multiferroics have offered several approaches, the search for magnetic and/or conducting ferroelectric materials is still a challenging issue under the traditional "d0-ness" rule, refusing active d electrons. Here, we propose the emergence of ferroelectricity through a combination of crystallographic chirality and axial vector, accepting even non-d0 magnetic ions. This proposal is demonstrated in quasi-one-dimensional magnetic systems SrM2V2O8 (M = Ni, Mg, and Co). The ferroelectric phase transition is observed by measurements of neutron powder diffraction and dielectric properties in all compositions. Structural analyses and first-principles calculations indicate that these magnetic compounds are identified as proper-type ferroelectrics whose ferroelectric phase transition is achieved by spiral motions of crystallographic screw chains formed by edge-shared MO6 octahedra, considered as the combination of locally defined chirality and axial vector. Computationally predicted magnitude of spontaneous polarization of SrM2V2O8 reaches ∼100 μC/cm2, comparable to that of conventional ferroelectrics, despite the incorporation of non-d0 magnetic elements. The mechanism proposed in this study offers a unique approach to the exploration of new ferroelectrics beyond the traditional paradigms.

On the rearrangement and dissociation mechanism of SiH4+ in its triply-degenerate ground state

An ab initio molecular orbital study has been performed to explore the structural rearrangement and dissociation of SiH4+ radical cation at the X̃2T2 ground electronic state. All stationary points located on the lowest adiabatic sheet of Jahn-Teller (JT) split X̃2T2 state are fully optimized and characterized by performing harmonic vibrational frequency calculations. The structural rearrangement is predicted to start with JT distortions involving the doubly-degenerate (e) and triply-degenerate (t2) modes. The e mode reduces the initial Td symmetry of the SiH4+ ground state to a D2d saddle point, which eventually dissociates into the SiH3+(2A1) + H products via C3v local minimum. In turn, an e-type bending of αH-Si-H yields the SiH2+(2A1) + H2 products through the first C3v local minimum and then the Cs(2A') global minimum. In the alternative pathway, the t2 mode distorts the initial Td symmetry into a loosely bound C3v local minimum, which further dissociates into the SiH3+(2A1) + H asymptote via totally symmetric Si-H stretching mode, and SiH2+(2A1) + H2 products via H-Si-H bending (e) mode through the Cs(2A') global minimum. It is further predicted that the Cs global minimum interconverts equivalent structures via a C2v transition structure. In addition, the two dissociation products are found to be connected by a second C2v transition structure.

Synthesis of 2D layered transition metal (Ni, Co) hydroxides via edge-on condensation

Layered transition metal hydroxides (LTMHs) with transition metal centers sandwiched between layers of coordinating hydroxide anions have attracted considerable interest for their potential in developing clean energy sources and storage technologies. However, two-dimensional (2D) LTMHs remain largely understudied in terms of physical properties and applications in electronic devices. Here, for the first time we report > 20 μm α-Ni(OH)2 2D crystals, synthesized from hydrothermal reaction. And an edge-on condensation mechanism assisted with the crystal field geometry is proposed to understand the 2D intra-planar growth of the crystals, which is also testified through series of systematic comparative studies. We also report the successful synthesis of 2D Co(OH)2 crystals (> 40 μm) with more irregular shape due to the slightly distorted octahedral geometry of the crystal field. Moreover, the detailed structural characterization of synthesized α-Ni(OH)2 are performed. The optical band gap energy is extrapolated as 2.54 eV from optical absorption measurements and the electronic bandgap is measured as 2.52 eV from reflected electrons energy loss spectroscopy (REELS). We further demonstrate its potential as a wide bandgap (WBG) semiconductor for high voltage operation in 2D electronics with a high breakdown strength, 4.77 MV/cm with 4.9 nm thickness. The successful realization of the 2D LTMHs opens the door for future exploration of more fundamental physical properties and device applications.

Formation Mechanisms of Electronically Excited Nitrogen Molecules from N + N2 and N + N + N Collisions Revealed by Full-Dimensional Potential Energy Surfaces

This work reports six new full-dimensional adiabatic potential energy surfaces (PESs) of the N3 system (four 4A″ states and two 2A″ states) at the MRCI + Q/AVQZ level of theory that correlated to N2(X1Σg+) + N(4S), N2(X1Σg+) + N(2D), N2(A3Σu+) + N(4S), N2(B3Πg) + N(4S), N2(W3Δu) + N(4S), and N(4S) + N(4S) + N(4S) channels. The neural networks with a proper account of the nuclear permutation invariant symmetry of N3 were employed to fit the PESs based on about 4000 ab initio points. The accuracy of the PESs was validated by excellent agreement on the equilibrium bond length, vertical excitation energy, and dissociation energy with experimental values. Two possible mechanisms of the formation of N2(A) were found. One is that the collision occurs between N2(X) and N(4S) in the 14A″ state, followed by a nonadiabatic transition through the conical intersection with the 24A″ PES, resulting in the formation of the N2(A) + N(4S) product. The other takes place in the collision among three N(4S) atoms in the adiabatic 24A″ state, and then, N2(A) + N(4S) is formed. This is the first systematical research of the N3 system focusing on the formation of the excited states of N2 via both adiabatic and nonadiabatic pathways.

The Unified Hamiltonian Formalism of Spin-Orbit Jahn-Teller and Pseudo-Jahn-Teller Problems in All Axial Symmetries

Spatial degeneracy of electronic states closely connects spin-orbit coupling and vibronic coupling, which together determine properties of materials, especially heavy element compounds. Accurate description of those materials entails accurate mathematical formulas for spin-orbit vibronic Hamiltonians. For the first time ever, we in this work derive the Hamiltonian formalism to describe all spin-orbit Jahn-Teller and pseudo-Jahn-Teller vibronic problems in all axial symmetries. The conventional one-electron approximation of spin-orbit coupling, which was the foundation of all previous studies in this field, is not involved in the present work. Actually, the present formalism is applicable to all time-reversal symmetric hermitian Hamiltonian that has a Rank-1 dependence on the spin operator, without any restriction on the type and the number of term symbols and vibrational modes.

Direct observation of geometric-phase interference in dynamics around a conical intersection

Conical intersections are ubiquitous in chemistry and physics, often governing processes such as light harvesting, vision, photocatalysis and chemical reactivity. They act as funnels between electronic states of molecules, allowing rapid and efficient relaxation during chemical dynamics. In addition, when a reaction path encircles a conical intersection, the molecular wavefunction experiences a geometric phase, which can affect the outcome of the reaction through quantum-mechanical interference. Past experiments have measured indirect signatures of geometric phases in scattering patterns and spectroscopic observables, but there has been no direct observation of the underlying wavepacket interference. Here we experimentally observe geometric-phase interference in the dynamics of a wavepacket travelling around an engineered conical intersection in a programmable trapped-ion quantum simulator. To achieve this, we develop a technique to reconstruct the two-dimensional wavepacket densities of a trapped ion. Experiments agree with the theoretical model, demonstrating the ability of analogue quantum simulators-such as those realized using trapped ions-to accurately describe nuclear quantum effects.

Synthesis and Magnetic Properties of the Multiferroic [C(NH2)3]Cr(HCOO)3 Metal-Organic Framework: The Role of Spin-Orbit Coupling and Jahn-Teller Distortions

We report for the first time the synthesis of [C(NH2)3]Cr(HCOO)3 stabilizing Cr2+ in formate perovskite, which adopts a polar structure and orders magnetically below 8 K. We discuss in detail the magnetic properties and their coupling to the crystal structure based on first-principles calculations, symmetry, and model Hamiltonian analysis. We establish a general model for the orbital magnetic moment of [C(NH2)3]M(HCOO)3 (M = Cr, Cu) based on perturbation theory, revealing the key role of the Jahn-Teller distortions. We also analyze their spin and orbital textures in k-space, which show unique characteristics.

Heteroatom-Based Diradical(oid)s

Heteroatom-centered diradical(oid)s have been in the focus of molecular main group chemistry for nearly 30 years. During this time, the diradical concept has evolved and the focus has shifted to the rational design of diradical(oid)s for specific applications. This review article begins with some important theoretical considerations of the diradical and tetraradical concept. Based on these theoretical considerations, the design of diradical(oid)s in terms of ligand choice, steric, symmetry, electronic situation, element choice, and reactivity is highlighted with examples. In particular, heteroatom-centered diradical reactions are discussed and compared with closed-shell reactions such as pericyclic additions. The comparison between closed-shell reactivity, which proceeds in a concerted manner, and open-shell reactivity, which proceeds in a stepwise fashion, along with considerations of diradical(oid) design, provides a rational understanding of this interesting and unusual class of compounds. The application of diradical(oid)s, for example in small molecule activation or as molecular switches, is also highlighted. The final part of this review begins with application-related details of the spectroscopy of diradical(oid)s, followed by an update of the heteroatom-centered diradical(oid)s and tetraradical(oid)s published in the last 10 years since 2013.

Femtosecond symmetry breaking and coherent relaxation of methane cations via x-ray spectroscopy

Understanding the relaxation pathways of photoexcited molecules is essential to gain atomistic level insight into photochemistry. Herein, we performed a time-resolved study of ultrafast molecular symmetry breaking via geometric relaxation (Jahn-Teller distortion) on the methane cation. Attosecond transient absorption spectroscopy with soft X-rays at the carbon K-edge revealed that the distortion occurred within 10 ± 2 femtoseconds after few-femtosecond strong-field ionization of methane. The distortion activated coherent oscillations in the asymmetric scissoring vibrational mode of the symmetry broken cation, which were detected in the X-ray signal. These oscillations were damped within 58 ± 13 femtoseconds, as vibrational coherence was lost with the energy redistributing into lower-frequency vibrational modes. This study completely reconstructs the molecular relaxation dynamics of this prototypical example and opens new avenues for exploring complex systems.

Reversible Single Electron Redox Steps Convert Polycycles with a C3 P3 Core to a Planar Triphosphinine

Reaction of the imidazolium-stabilized diphosphete-diide IDP with trityl phosphaalkyne affords a mixture which contains the molecules 1 a and 1 b with a central C₃ P₃ core, which formally carries a two-fold negative charge. In order to avoid the formation of an antiaromatic 8π electron system within a conjugated dianionic six-membered [C₃ P₃ ]^2- ring, 1 a adopts a bicyclic [3.1.0] and 1 b a tricyclic [2.2.0.0] structure which are in a dynamic equilibrium. 1 a, b can be reversibly oxidized to a triphosphinine dication [5]²⁺ with a central flat aromatic six-membered C₃ P₃ ring. This two-electron redox reaction occurs in two single-electron transfer steps via the 7π-radical cation [4]⋅⁺ , which could also be isolated and fully characterized. The profound reversible structural change observed for the two-electron redox couple [5]²⁺ /1 a, b is in sharp contrast to the C₆ H₆ /[C₆ H₆ ]^2- couple, which undergoes only a modest structural deformation.

How Does Pseudo-Jahn-Teller Effect Induce the Photoprotective Potential of Curcumin?

In this paper, the molecular and electronic structure of curcumin is studied. High-symmetric gas-phase tautomers and their deprotonated forms in various symmetry groups are identified. The stability of lower-symmetry structures was explained by using the Pseudo-Jahn-Teller (PJT) effect. This effect leads to stable structures of different symmetries for the neutral enol and keto forms. The presented analysis demonstrated the potential significance of the PJT effect, which may modulate the setting of electronic and vibrational (vibronic) energy levels upon photodynamic processes. The PJT effect may rationalize the photoprotection action and activity of naturally occurring symmetric dyes.

Potential energy surfaces of a stacked dimer of benzene and its radical cation: what remains and what appears

A stepwise qualitative consideration of the reduction in symmetry for the highly symmetrical "right sandwich" and "twisted sandwich" structures of the stacked benzene dimer caused by the pseudo-Jahn-Teller effect made it possible to construct a scheme of the potential energy surface (PES) of this dimer. Thirty-six equivalent structures of minimum energy are ordered on this extremely flat surface, transforming into each other in an almost barrier-free manner. There are two kinds of these transformations, both of which are pseudorotation. The transformation pathways inherent in this neutral dimer are also characteristic of its radical cation (RC). Structural transformations of the RC are inextricably linked with changes in its electronic state since its stationary structures relate to different electronic states. (C₆H₆)₂⁺˙ exists in the form of two orbital isomers, each of which "pseudorotates" on its own area of the PES. During the pseudorotation, the SOMO distribution on the fragments of (C₆H₆)₂⁺˙ changes, which is identical to what occurs during the pseudorotation of the Jahn-Teller benzene RC. These areas are connected by pairwise interconversions of their minimum energy structures. The interconversion of the orbital isomers is a bypassing of conical intersections between corresponding electronic states, which occurs through a synchronized pseudorotation of the fragments. The conclusions of the qualitative consideration and the results of quantum chemical calculations of various levels performed for (C₆H₆)₂⁺˙ are in full agreement with each other. The revealed features of the structure of the PES of the two reference systems in studying the intermolecular and ion-molecule interactions are the basis for considering their more complex analogs, primarily their less symmetrical ones.

Structure, optical and luminescence properties of anhydrous samarium iodate Sm3(IO3)9(HIO3)4

A new non-centrosymmetric iodate crystal Sm₃(IO₃)₉(HIO₃)₄ has been successfully synthesized by a hydrothermal method. The crystal structure is a three-dimensional network with samarium polyhedra linked by iodate groups. It shows a moderate second harmonic generation response of 1.1 × KH₂PO₄ (KDP). The strongest emission in its luminescence spectrum is located at 600 nm under 403 nm excitation. Hence, Sm₃(IO₃)₉(HIO₃)₄ is a potential orange laser material.

From six to eight Π-electron bare rings of group-XIV elements and beyond: can planarity be deciphered from the "quasi-molecules" they embed?

Ab initio molecular orbital theory is used to study the structures of six and eight π-electron bare rings of group-XIV elements, and even larger [n]annulenes up to C₁₈H₁₈, including some of their mono-, di-, tri-, and tetra-anions. While some of the above rings are planar, others are nonplanar. A much spotlighted case is cyclo-octatetraene (C₈H₈), which is predicted to be nonplanar together with its heavier group-XIV analogues Si₈H₈ and Ge₈H₈, with the solely planar members of its family having the stoichiometric formulas C₄Si₄H₈ and C₄Ge₄H₈. A similar situation arises with the six π-electron bare rings, where benzene and substituted ones up to C₃Si₃H₆ or so are planar, while others are not. However, the explanations encountered in the literature find support in ab initio calculations for such species, often rationalized from distinct calculated features. Using second-order Møller-Plesset perturbation theory and, when affordable (particularly tetratomics, which may allow even higher levels), the coupled-cluster method including single, double, and perturbative triple excitations, a common rationale is suggested based on a novel concept of quasi-molecules or the (3+4)-atom partition scheme. Any criticism of tautology is therefore avoided. The same analysis has also been successfully applied to even larger [n]annulenes, to their mixed family members involving silicon and germanium atoms, and to the C₁₈ carbon ring. Furthermore, it has been extended to annulene anions to check the criteria of the popular Hückel rule for planarity and aromaticity. Exploratory work on cycloarenes is also reported. Besides a partial study of the involved potential energy surfaces, equilibrium geometries and harmonic vibrational frequencies have been calculated anew, for both the parent and the actual prototypes of the quasi-molecules.

Unified one-electron Hamiltonian formalism of spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in tetrahedral and octahedral symmetries

Heavy element compounds with high symmetries often feature both spin-orbit coupling and vibronic coupling. This is especially true for systems with tetrahedral and octahedral symmetries, whose electronic states may be three-fold degenerate and experience complicated Jahn-Teller and pseudo-Jahn-Teller interactions. To accurately describe these interactions, high quality spin-orbit vibronic Hamiltonian operators are needed. In this study, we present a unified one-electron Hamiltonian formalism for spin-orbit vibronic interactions for systems in all tetrahedral and octahedral symmetries. The formalism covers all spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in the symmetries with arbitrary types and arbitrary numbers of vibrational modes, and generates Hamiltonian expansion formulas of arbitrarily high order.

Jahn-Teller Effect in Orthorhombic Manganites: Ab Initio Hamiltonian and Roto-vibrational Spectrum

For the first time, using three different electronic structure methodologies, namely, CASSCF, RS2c, and MRCI(SD), we construct ab initio adiabatic potential energy surfaces (APESs) and nonadiabatic coupling term (NACT) of two electronic states (⁵E_g) of MnO₆^9- unit, where eight such units share one La atom in LaMnO₃ crystal. While fitting those APESs with analytic functions of normal modes (Q_x, Q_y), an empirical scaling factor is introduced considering the mass ratio of eight MnO₆^9- units with and without one La atom to explore the environmental (mass) effect on MnO₆^9- unit. When the roto-vibrational levels of MnO₆^9- Hamiltonian are calculated, peak positions computed from ab initio constructed excited APESs are found to be enough close with the experimental satellite transitions [ J. Exp. Theor. Phys. 2016, 122, 890-901] endorsing our earlier model results [ J. Chem. Phys. 2019, 150, 064703]. In order to explore the electron-nuclear coupling in an alternate way, theoretically "exact" and numerically "accurate" beyond Born-Oppenheimer (BBO) theory based diabatic potential energy surfaces (PESs) of MnO₆^9- are constructed to generate the photoelectron (PE) spectra. The PE spectral band also exhibits good peak by peak correspondence with the higher satellite transitions in the dielectric function spectra of the LaMnO₃ complex.

The inversion of tetrahedral p-block element compounds: general trends and the relation to the second-order Jahn-Teller effect

The tetrahedron is the primary structural motif among the p-block elements and determines the architecture of our bio- and geosphere. However, a broad understanding of the configurational inversion of tetrahedral compounds is missing. Here, we report over 250 energies (DLPNO-CCSD(T)) for square planar inversion of third- and fourth-period element species of groups 13, 14, and 15. Surprisingly low inversion barriers are identified for compounds of industrial relevance (e.g., ≈100 kJ mol-1 for Al(OH)4 -). More fundamentally, the second-order Jahn-Teller theorem is disclosed as suitable to rationalize substituent and central element effects. Bond analysis tools give further insights into the preference of eight valence electron systems with four substituents to be tetrahedral. Hence, this study develops a model to understand, memorize, and predict the angular flexibility of tetrahedral species. Perceiving the tetrahedron not as forcingly rigid but as a dynamic structural entity might leverage new approaches and visions for adaptive matter.

The copper sulfate hydration cycle. Crystal structures of CuSO4 (Chalcocyanite), CuSO4·H2O (Poitevinite), CuSO4·3H2O (Bonattite) and CuSO4·5H2O (Chalcanthite) at low temperature using non-spherical atomic scattering factors

Sky blue CuSO4·3H2O is the midpoint of the copper sulfate hydration cycle. The progression from colourless CuSO4 to bright blue CuSO4·5H2O is intimately linked to the relative number of sulfato versus aqua ligands coordinated to copper.

The Jahn-Teller and pseudo-Jahn-Teller effects in propyne radical cation

The Jahn-Teller (JT) and pseudo-Jahn-Teller (PJT) effects in the X 2E, A 2E and B 2A1 electronic states of propyne radical cation are investigated with the aid of ab initio...

Unified one-electron Hamiltonian formalism of spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in axial symmetries

Spin-orbit coupling and vibronic coupling are both closely related to orbital degeneracy of electronic states. Both types of coupling play significant roles in determining properties of heavy element compounds and shall be treated on the same footing. In this work, we derive a unified one-electron Hamiltonian formalism for spin-orbit and vibronic interactions for systems in all axial symmetries. The one-electron formalism is usually adequate as the spin-orbit interaction can often be approximated as a one-electron interaction. For the first time, the formalism covers spin-orbit and vibronic couplings in all axial symmetries from C₁ to D_∞h, arbitrary types of vibrational modes in those symmetries, and an arbitrary number of those modes and gives Hamiltonian expansions up to an arbitrary order.

High-fidelity first principles nonadiabaticity: diabatization, analytic representation of global diabatic potential energy matrices, and quantum dynamics

Nonadiabatic dynamics, which goes beyond the Born-Oppenheimer approximation, has increasingly been shown to play an important role in chemical processes, particularly those involving electronically excited states. Understanding multistate dynamics requires rigorous quantum characterization of both electronic and nuclear motion. However, such first principles treatments of multi-dimensional systems have so far been rather limited due to the lack of accurate coupled potential energy surfaces and difficulties associated with quantum dynamics. In this Perspective, we review recent advances in developing high-fidelity analytical diabatic potential energy matrices for quantum dynamical investigations of polyatomic uni- and bi-molecular nonadiabatic processes, by machine learning of high-level ab initio data. Special attention is paid to methods of diabatization, high fidelity construction of multi-state coupled potential energy surfaces and property surfaces, as well as quantum mechanical characterization of nonadiabatic nuclear dynamics. To illustrate the tremendous progress made by these new developments, several examples are discussed, in which direct comparison with quantum state resolved measurements led to either confirmation of the observation or sometimes reinterpretation of the experimental data. The insights gained in these prototypical systems greatly advance our understanding of nonadiabatic dynamics in chemical systems.

Ca3(TeO3)2(MO4) (M = Mo, W): Mid-Infrared Nonlinear Optical Tellurates with Ultrawide Transparency Ranges and Superhigh Laser-Induced mage ThreDasholds

Intense interests in mid-infrared (MIR) nonlinear optical (NLO) crystals have erupted in recent years due to the development of optoelectronic applications ranging from remote monitoring to molecular spectroscopy. Here, two polar crystals Ca₃(TeO₃)₂(MO₄) (M = Mo, W) were grown from TeO₂-MO₃ flux by high-temperature solution methods. Ca₃(TeO₃)₂(MoO₄) and Ca₃(TeO₃)₂(WO₄) are isostructural, which feature novel structures consisting of asymmetric MO₄ tetrahedra and TeO₃ trigonal pyramids. Optical characterizations show that both crystals display ultrawide transparency ranges (279 nm to 5.78 μm and 290 nm to 5.62 μm), especially high optical transmittance over 80% in the important atmospheric transparent window of 3-5 μm, and superhigh laser damage thresholds (1.63 GW/cm² and 1.50 GW/cm²), 54.3 and 50 times larger than that of state-of-the-art MIR NLO AgGaS₂, respectively. Notably, they exhibit the widest band gaps and the loftiest laser-induced threshold damages among the reported tellurates so far. Moreover, Ca₃(TeO₃)₂(MO₄) exhibit type I phase matching at two working wavelengths owing to their large birefringence and strong second-harmonic generation responses from the distorted anions, as further elucidated by the first-principles calculations. The above characteristics indicate that Ca₃(TeO₃)₂(MO₄) crystals are high-performance MIR NLO materials, especially applying in high-power MIR laser operations.

The superatomic state beyond conventional magic numbers: Ligated metal chalcogenide superatoms

The field of cluster science is drawing increasing attention due to the strong size and composition-dependent properties of clusters and the exciting prospect of clusters serving as the building blocks for materials with tailored properties. However, identifying a unifying central paradigm that provides a framework for classifying and understanding the diverse behaviors is an outstanding challenge. One such central paradigm is the superatom concept that was developed for metallic and ligand-protected metallic clusters. The periodic electronic and geometric closed shells in clusters result in their properties being based on the stability they gain when they achieve closed shells. This stabilization results in the clusters having a well-defined valence, allowing them to be classified as superatoms-thus extending the Periodic Table to a third dimension. This Perspective focuses on extending the superatomic concept to ligated metal-chalcogen clusters that have recently been synthesized in solutions and form assemblies with counterions that have wide-ranging applications. Here, we illustrate that the periodic patterns emerge in the electronic structure of ligated metal-chalcogenide clusters. The stabilization gained by the closing of their electronic shells allows for the prediction of their redox properties. Further investigations reveal how the selection of ligands may control the redox properties of the superatoms. These ligated clusters may serve as chemical dopants for two-dimensional semiconductors to control their transport characteristics. Superatomic molecules of multiple metal-chalcogen superatoms allow for the formation of nano-p-n junctions ideal for directed transport and photon harvesting. This Perspective outlines future developments, including the synthesis of magnetic superatoms.

Influence of Cation Size on the Local Atomic Structure and Electronic Properties of Ta Perovskite Oxynitrides

Partial anion substitution in transition metal oxides provides rich opportunities to control and tune physical and chemical properties, for example, combining the merits of oxides and nitrides. In addition, the possibility of resulting anion sublattice order provides a means to target polar and chiral structures based on a wide array of accessible structural archetypes by design. Here, we investigate the local structures of a family of perovskite tantalum oxynitrides-ATaO₂N (A = Ba, Sr, and Ca)-using a combination of experimental and theoretical approaches including neutron total scattering, density functional theory (DFT), and ab initio molecular dynamics (AIMD) simulations. We present the first experimental study of chemical short-range order (CSRO) in CaTaO₂N, confirming local cis N ordering of the anion sub-lattice. Our systematic exploration of a local structure across the A cation size series (from the larger Ba to the smaller Ca) reveals a perovskite motif increasingly distorted with respect to long-range average structures. DFT and AIMD simulations support the observed trends. Overall, structures with cis ordering of the nitrogen anions in each TaO₄N₂ octahedron are favored over those with trans ordering. With diminishing A cation size, local cis ordering and Ta off-centering play decreasing roles in overall lattice stability, overshadowed by the stabilizing effects of octahedral tilting. The influence of these factors on local dipole formation and frustrated dipole ordering are discussed.

Designing new ferromagnetic double perovskites: the coexistence of polar distortion and half-metallicity

Advancing technology and growing interdisciplinary fields raise the need for new materials that simultaneously possess several significant physics quantities to meet human demands. In this research, using density functional theory, we aim to design A₂MnVO₆ (A = Ca, Ba) as new double perovskites and investigate their structural, electronic, and magnetic properties. Structural calculations based on the total energies show the optimized monoclinic and orthorhombic crystal structures for the Ca₂MnVO₆ (CMVO) and Ba₂MVO₆ (BMVO) compounds, respectively. Through performing calculations, we reveal that the Jahn-Teller effect plays an important role in polar distortions of VO₆ and elongation of MnO₆ octahedra, resulting from the V⁵⁺(3d⁰) and Mn³⁺(3d⁴:t32ge1g) electron configurations. The spin-polarized calculations predict the half-metallic ferromagnetic ground state for CMVO and BMVO with a total magnetic moment of 4.00 μ_B f.u.^-1 Our findings introduce CMVO and BMVO double perovskites as promising candidates for designing ferromagnetic polar half-metals and spintronic applications.

Exploring vibronic coupling in the benzene radical cation and anion with different levels of the GW approximation

The linear vibronic coupling constants of the benzene radical cation and anion have been obtained with different levels of the GW approximation, including G₀W₀, eigenvalue self-consistent GW, and quasiparticle self-consistent GW, as well as DFT with the following exchange-correlation functionals: BLYP, B3LYP, CAM-B3LYP, tuned CAM-B3LYP, and an IP-tuned CAM-B3LYP functional. The vibronic coupling constants were calculated numerically using the gradients of the eigenvalues of the degenerate HOMOs and LUMOs of the neutral benzene molecule for DFT, while the numerical gradients of the quasiparticle energies were used in the case of GW. The results were evaluated against those of high level wave function methods in the literature, and the approximate self-consistent GW methods and G₀W₀ with long-range corrected functionals were found to yield the best results on the whole.

Understanding Terminal versus Bridging End-on N2 Coordination in Transition Metal Complexes

Terminal and bridging end-on coordination of N₂ to transition metal complexes offer possibilities for distinct pathways in ammonia synthesis and N₂ functionalization. Here we elucidate the fundamental factors controlling the two binding modes and determining which is favored for a given metal-ligand system, using both quantitative density functional theory (DFT) and qualitative molecular orbital (MO) analyses. The Gibbs free energy for converting two terminal MN₂ complexes into a bridging MNNM complex and a free N₂ molecule (2ΔG_eq^°) is examined through systematic variations of the metal and ligands; values of ΔG_eq^° range between +9.1 and -24.0 kcal/mol per M-N₂ bond. We propose a model that accounts for these broad variations by assigning a fixed π-bond order (BO^π) to the triatomic terminal MNN moiety that is equal to that of the free N₂ molecule, and a variable BO^π to the bridging complexes based on the character (bonding or antibonding) and occupancy of the π-MOs in the tetratomic MNNM core. When the conversion from terminal to bridging coordination and free N₂ is associated with an increase in the number of π-bonds (ΔBO_eq^π > 0), the bridging mode is greatly favored; this condition is satisfied when each metal provides 1, 2, or 3 electrons to the π-MOs of the MNNM core. When each metal in the bridging complex provides 4 electrons to the MNNM π-MOs, ΔBO_eq^π = 0; the equilibrium in this case is approximately ergoneutral and the direction can be shifted by dispersion interactions.

Unified Hamiltonian Formalism of Jahn-Teller and Pseudo-Jahn-Teller Problems in Axial Symmetries

A formalism for expansions of all Jahn-Teller and pseudo-Jahn-Teller Hamiltonian operators in all axial symmetries is presented. The formalism provides Hamiltonian expansions up to arbitrarily high order and including an arbitrary number of vibrational modes, which are of arbitrary types. It consists of three equations and two tables. The formalism is user-friendly since it can be used without understanding its derivation. An example of E₃^″⊗e₁^' Jahn-Teller interaction is used to demonstrate the correctness of the formalism. A Python program is developed to automate the generation of Hamiltonian expansions for all axial Jahn-Teller and pseodo-Jahn-Teller problems and interface the expansions to the MCTDH quantum dynamics simulation program. This is the first unified Hamiltonian formalism for axial Jahn-Teller and pseudo-Jahn-Teller problems. Also it is the only one.

How important are the residual nonadiabatic couplings for an accurate simulation of nonadiabatic quantum dynamics in a quasidiabatic representation?

Diabatization of the molecular Hamiltonian is a standard approach to remove the singularities of nonadiabatic couplings at conical intersections of adiabatic potential energy surfaces. In general, it is impossible to eliminate the nonadiabatic couplings entirely-the resulting "quasidiabatic" states are still coupled by smaller but nonvanishing residual nonadiabatic couplings, which are typically neglected. Here, we propose a general method for assessing the validity of this potentially drastic approximation by comparing quantum dynamics simulated either with or without the residual couplings. To make the numerical errors negligible to the errors due to neglecting the residual couplings, we use the highly accurate and general eighth-order composition of the implicit midpoint method. The usefulness of the proposed method is demonstrated on nonadiabatic simulations in the cubic Jahn-Teller model of nitrogen trioxide and in the induced Renner-Teller model of hydrogen cyanide. We find that, depending on the system, initial state, and employed quasidiabatization scheme, neglecting the residual couplings can result in wrong dynamics. In contrast, simulations with the exact quasidiabatic Hamiltonian, which contains the residual couplings, always yield accurate results.

New Syntheses, Analytic Spin Hamiltonians, Structural and Computational Characterization for a Series of Tri-, Hexa- and Hepta-Nuclear Copper (II) Complexes with Prototypic Patterns

We present a series of pyrazolato-bridged copper complexes with interesting structures that can be considered prototypic patterns for tri-, hexa- and hepta- nuclear systems. The trinuclear shows an almost regular triangle with a μ3-OH central group. The hexanuclear has identical monomer units, the Cu6 system forming a regular hexagon. The heptanuclear can be described as two trinuclear moieties sandwiching a central copper ion via carboxylate bridges. In the heptanuclear system, the pyrazolate bridges are consolidating the triangular faces, which are sketching an elongated trigonal antiprism. The magnetic properties of these systems, dominated by the strong antiferromagnetism along the pyrazolate bridges, were described transparently, outlining the energy levels formulas in terms of Heisenberg exchange parameters J, within the specific topologies. We succeeded in finding a simple Kambe-type resolution of the Heisenberg spin Hamiltonian for the rather complex case of the heptanuclear. In a similar manner, the weak intermolecular coupling of two trimer units (aside from the strong exchange inside triangles) was resolved by closed energy formulas. The hexanuclear can be legitimately proposed as a case of coordination-based aromaticity, since the phenomenology of the six-spins problem resembles the bonding in benzene. The Broken-Symmetry Density Functional Theory (BS-DFT) calculations are non-trivial results, being intrinsically difficult at high nuclearities.

Theoretical investigation of tetrahedral distortion of four-coordinate iron(II) centres in FePd(CN)4

The tetrahedral distortion of iron(ii) centres in the cyanide-bridged framework FePd(CN)4 was recently demonstrated experimentally. Here, we theoretically confirmed the electronically driven tetrahedral distortion of iron(ii) by comparing the density of states and total energies of FePd(CN)4 (d6) and ZnPd(CN)4 (d10). The calculation results suggested that a Jahn-Teller-like effect is caused on the tetrahedral geometry by the electronic effect of unequally occupied non-bonding 3d orbitals in the corresponding structure.

Lithium Niobate Single Crystals and Powders Reviewed—Part I

A review of lithium niobate single crystals and polycrystals in the form of powders has been prepared. Both the classical and recent literature on this topic are revisited. It is composed of two parts with sections. The current part discusses the earliest developments in this field. It treats in detail the basic concepts, the crystal structure, some of the established indirect methods to determine the chemical composition, and the main mechanisms that lead to the manifestation of ferroelectricity. Emphasis has been put on the powdered version of this material: methods of synthesis, the accurate determination of its chemical composition, and its role in new and potential applications are discussed. Historical remarks can be found scattered throughout this contribution. Particularly, an old conception of the crystal structure thought as a derivative structure from one of higher symmetry by generalized distortion is here revived.

Table-Top X-ray Spectroscopy of Benzene Radical Cation

Ultrafast table-top X-ray spectroscopy at the carbon K-edge is used to measure the X-ray spectral features of benzene radical cations (Bz⁺). The ground state of the cation is prepared selectively by two-photon ionization of neutral benzene, and the X-ray spectra are probed at early times after the ionization by transient absorption using X-rays produced by high harmonic generation (HHG). Bz⁺ is well-known to undergo Jahn-Teller distortion, leading to a lower symmetry and splitting of the π orbitals. Comparison of the X-ray absorption spectra of the neutral and the cation reveals a splitting of the two degenerate π* orbitals as well as an appearance of a new peak due to excitation to the partially occupied π-subshell. The π* orbital splitting of the cation, elucidated on the basis of high-level calculations in a companion theoretical paper [Vidal et al. J. Phys. Chem. A. http://dx.doi.org/10.1021/acs.jpca.0c08732], is discovered to be due to both the symmetry distortion and even more dominant spin coupling of the unpaired electron in the partially vacant π orbital (from ionization) with the unpaired electrons resulting from the transition from the 1s_C core orbital to the fully vacant π* orbitals.

Interplay of Open-Shell Spin-Coupling and Jahn-Teller Distortion in Benzene Radical Cation Probed by X-ray Spectroscopy

We report a theoretical investigation and elucidation of the X-ray absorption spectra of neutral benzene and of the benzene cation. The generation of the cation by multiphoton ultraviolet (UV) ionization and the measurement of the carbon K-edge spectra of both species using a table-top high-harmonic generation source are described in the companion experimental paper [Epshtein, M.; et al. J. Phys. Chem. A http://dx.doi.org/10.1021/acs.jpca.0c08736]. We show that the 1s_C → π transition serves as a sensitive signature of the transient cation formation, as it occurs outside of the spectral window of the parent neutral species. Moreover, the presence of the unpaired (spectator) electron in the π-subshell of the cation and the high symmetry of the system result in significant differences relative to neutral benzene in the spectral features associated with the 1s_C → π* transitions. High-level calculations using equation-of-motion coupled-cluster theory provide the interpretation of the experimental spectra and insight into the electronic structure of benzene and its cation. The prominent split structure of the 1s_C → π* band of the cation is attributed to the interplay between the coupling of the core → π* excitation with the unpaired electron in the π-subshell and the Jahn-Teller distortion. The calculations attribute most of the splitting (∼1-1.2 eV) to the spin coupling, which is visible already at the Franck-Condon structure, and we estimate the additional splitting due to structural relaxation to be around ∼0.1-0.2 eV. These results suggest that X-ray absorption with increased resolution might be able to disentangle electronic and structural aspects of the Jahn-Teller effect in the benzene cation.

A systematic model study quantifying how conical intersection topography modulates photochemical reactions

Despite their important role in photochemistry and expected presence in most polyatomic molecules, conical intersections have been thoroughly characterized in a comparatively small number of systems. Conical intersections can confer molecular photoreactivity or photostability, often with remarkable efficacy, due to their unique structure: at a conical intersection, the adiabatic potential energy surfaces of two or more electronic states are degenerate, enabling ultrafast decay from an excited state without radiative emission, known as nonadiabatic transfer. Furthermore, the precise conical intersection topography determines fundamental properties of photochemical processes, including excited-state decay rate, efficacy, and molecular products that are formed. However, these relationships have yet to be defined comprehensively. In this article, we use an adaptable computational model to investigate a variety of conical intersection topographies, simulate resulting nonadiabatic dynamics, and calculate key photochemical observables. We varied the vibrational mode frequencies to modify conical intersection topography systematically in four primary classes of conical intersections and quantified the resulting rate, total yield, and product yield of nonadiabatic decay. The results reveal that higher vibrational mode frequencies reduce nonadiabatic transfer, but increase the transfer rate and resulting photoproduct formation. These trends can inform progress toward experimental control of photochemical reactions or tuning of molecules' photochemical properties based on conical intersections and their topography.