Jahn–Teller and spin–orbit coupling effects in transition-metal trifluorides

Structure and Excitation Spectra of Third-Row Transition Metal Hexafluorides Based on Multi-Reference Exact Two-Component Theory

The structures and some vertical excitation energies of third-row transition metal hexafluorides (MF6, M = Re, Os, Ir, Pt, Au, Hg) were calculated using the generalized-active-space configuration interaction (GASCI) theory based on the exact two-component (X2C) Hamiltonian. The spin-orbit coupling (SOC) was included at the Hartree-Fock level, enabling us to analyze the SOC at the orbital level (spinor-representation). The excitation spectra were assigned based on the double group, a relativistic group theory applicable to states with the SOC. This study provides a fundamental understanding of the ligand field splitting, including the SOC, that is useful for the photochemistry and spin chemistry involving heavy elements.

Structural Phase Transition and Disproportionation of MnF3 Under High Pressure and High Temperature

Materials that once suffered under high-pressure and high-temperature conditions often display unusual phenomena that challenge traditional understanding. MnF3, an intermediate valence state Mn-F compound, exhibits a distorted octahedral crystal structure influenced by the Jahn-Teller effect. Here we report the structural phase transition and self-disproportionation of MnF3 under high pressure and high temperature. The initial octahedra phase I2/a-MnF3 transforms into the hendecahedra Pnma phase under high pressure. Subsequently, we found that molten Pnma-MnF3 self-disproportionate into MnF2 and MnF4 with the aid of laser heating at a pressure above 57.1 GPa. Raman spectra and UV-vis absorption experiments confirmed these changes that were ultimately confirmed by synchrotron radiation XRD. The equation of states for the volume with the pressure of these Mn-F compounds was also given. This work expands the study of Mn-F systems and provides guidance for the behavior of transition metal fluorides under high pressures and high temperatures.

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.

Spin–vibronic coupling in the quantum dynamics of a Fe(III) trigonal-bipyramidal complex

The presence of a high density of excited electronic states in the immediate vicinity of the optically bright state of a molecule paves the way for numerous photo-relaxation channels. In transition-metal complexes, the presence of heavy atoms results in a stronger spin–orbit coupling, which enables spin forbidden spin-crossover processes to compete with the spin-allowed internal conversion processes. However, no matter how effectively the states cross around the Franck–Condon region, the degree of vibronic coupling, of both relativistic and non-relativistic nature, drives the population distribution among these states. One such case is demonstrated in this work for the intermediate-spin Fe(III) trigonal-bipyramidal complex. A quantum dynamical investigation of the photo-deactivation mechanism in the Fe(III) system is presented using the multi-configurational time-dependent Hartree approach based on the vibronic Hamiltonian whose coupling terms are derived from the state-averaged complete active space self-consistent field/complete active space with second-order perturbation theory (CASPT2) calculations and spin–orbit coupling of the scalar-relativistic CASPT2 states. The results of this study show that the presence of a strong (non-relativistic) vibronic coupling between the optically bright intermediate-spin state and other low-lying states of the same spin-multiplicity overpowers the spin–orbit coupling between the intermediate-spin and high-spin states, thereby lowering the chances of spin-crossover while exhibiting ultrafast relaxation among the intermediate-spin states. In a special case, where the population transfer pathway via the non-relativistic vibronic coupling is blocked, the probability of the spin-crossover is found to increase. This suggests that a careful modification of the complex by incorporation of heavier atoms with stronger relativistic effects can enhance the spin-crossover potential of Fe(III) intermediate-spin complexes.

Vibration-Assisted Intersystem Crossing in the Ultrafast Excited-State Relaxation Dynamics of Halocoumarins

Due to its numerous applications, triplet formation and resulting phosphorescence remain a frontier area of research for over eight decades. Facile intersystem crossing (ISC) is the primary requirement for triplet formation and observation of phosphorescence. The incorporation of a heavy atom in molecules is one of the common approaches employed to facilitate ISC. A detailed study of the excited state dynamics that governs ISC is necessary to understand the mechanism of heavy atom effect (HAE). Incorporation of iodine at the 3 position of coumarin-1 reduces fluorescence quantum yield (ϕ_f) drastically as expected, whereas bromine substitution at the same position increased the ϕ_f. Such a contrasting effect of the two heavy atoms suggests that there are other features yet to be discovered to fully understand the HAE. Detailed steady state and femtosecond transient absorption studies along with theoretical calculations suggest that the C3-X (X = Br, I) bond vibration plays an important role in the ISC process. The study reveals that while in the case of the iodo-derivative there is no energy barrier in the singlet triplet crossing path, there is a barrier in the case of the bromo-derivative, which slows the ISC process. Such an unexpected phenomenon is not limited to halocoumarins as this rationalizes the photobehavior of 1-bromo-/iodo-substituted naphthalenes as well.

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.

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.

Modeling Spin-Crossover Dynamics

In this article, we review nonadiabatic molecular dynamics (NAMD) methods for modeling spin-crossover transitions. First, we discuss different representations of electronic states employed in the grid-based and direct NAMD simulations. The nature of interstate couplings in different representations is highlighted, with the main focus on nonadiabatic and spin-orbit couplings. Second, we describe three NAMD methods that have been used to simulate spin-crossover dynamics, including trajectory surface hopping, ab initio multiple spawning, and multiconfiguration time-dependent Hartree. Some aspects of employing different electronic structure methods to obtain information about potential energy surfaces and interstate couplings for NAMD simulations are also discussed. Third, representative applications of NAMD to spin crossovers in molecular systems of different sizes and complexities are highlighted. Finally, we pose several fundamental questions related to spin-dependent processes. These questions should be possible to address with future methodological developments in NAMD.

Quenchable amorphous glass-like material from VF3

The quite simple but relatively stable VF3-type compounds are known to be of major interest due to their building blocks - octahedra that are extremely important in perovskites as well. Here, we show that the VF6 octahedron in VF3 varies over a fairly wide pressure range (0-50 GPa), maintaining undisturbed rhombohedral crystal symmetry. Half of this pressure, VF6 rotates easily while the other undergoes strong uniaxial deformation in a "super-dense" condition. The congested sphere packing ultimately does not endure and drives the material to amorphize. We observed that the amorphous state could be quenched and acquire a transparent glass-like appearance when unloaded to ambient conditions. Dramatic, pressure-induced changes are clarified by phonon dispersion curves with the imaginary phonon mode, the so-called phonon soft mode, which indicates the structural instability. The distortion of the VF6 octahedra is attributed to the distinctive amorphization that could be further searched for throughout the whole almost identical VF3-type series providing metal trifluorides of various amorphous species.

Spin-state energetics of metallocenes: How do best wave function and density functional theory results compare with the experimental data?

We benchmark the accuracy of quantum-chemical methods, including wave function theory methods [coupled cluster theory at the CCSD(T) level, multiconfigurational perturbation-theory (CASPT2, NEVPT2) and internally contracted multireference configuration interaction (MRCI)] and 30 density functional theory (DFT) approximations, in reproducing the spin-state splittings of metallocenes. The reference values of the electronic energy differences are derived from the experimental spin-crossover enthalpy for manganocene and the spectral data of singlet-triplet transitions for ruthenocene, ferrocene, and cobaltocenium. For ferrocene and cobaltocenium we revise the previous experimental interpretations regarding the lowest triplet energy; our argument is based on the comparison with the lowest singlet excitation energy and herein reported, carefully determined absorption spectrum of ferrocene. When deriving vertical energies from the experimental band maxima, we go beyond the routine vertical energy approximation by introducing vibronic corrections based on simulated vibrational envelopes. The benchmarking result confirms the high accuracy of the CCSD(T) method (in particular, for UCCSD(T) based on Hartree-Fock orbitals we find for our dataset: maximum error 0.12 eV, weighted mean absolute error 0.07 eV, weighted mean signed error 0.01 eV). The high accuracy of the single-reference method is corroborated by the analysis of a multiconfigurational character of the complete active space wave function for the triplet state of ferrocene. On the DFT side, our results confirm the non-universality problem with approximate functionals. The present study is an important step toward establishing an extensive and representative benchmark set of experiment-derived spin-state energetics for transition metal complexes.

Density Functional Theory Calculations of Structural, Electronic, and Magnetic Properties of the 3d Metal Trifluorides MF3 (M = Ti-Ni) in the Solid State

We employ density functional theory with Hubbard U correction or hybrid functionals to study the series of magnetic 3d metal trifluorides MF₃ (M = Ti-Ni). Experimental lattice parameters are reproduced with an error margin of 0.5%-4.3%. Cooperative Jahn-Teller distortions are reproduced for MnF₃ , but also found in TiF₃ and CoF₃ at smaller levels compared to MnF₃ . Trends in electronic structure with respect to positions of the d bands are linked to the magnetic properties where M = Ti-Cr are weak magnetic Mott-Hubbard insulators, M = Fe-Ni are strong magnetic charge-transfer insulators and MnF₃ falls in between. Our work contributes to the characterization of the relatively unknown NiF₃ , since FeF₃ and CoF₃ have similar electronic and magnetic properties. However, NiF₃ does not show a Jahn-Teller distortion as present in CoF₃ . © 2019 Wiley Periodicals, Inc.

Vibronic interaction in CO3− photo-detachment: Jahn–Teller effects beyond structural distortion and general formalisms for vibronic Hamiltonians in trigonal symmetries

Expansion formalisms for trigonal Jahn–Teller and pseudo-Jahn–Teller vibronic Hamiltonians are developed and used to study and correctly interpret the photoelectron spectrum of CO₃⁻.

Hamiltonian formalism of spin–orbit Jahn–Teller and pseudo-Jahn–Teller problems in trigonal and tetragonal symmetries

A formalism for expansions of all bimodal spin–orbit Jahn–Teller and pseudo-Jahn–Teller Hamiltonian operators in trigonal and tetragonal symmetries is presented.

General formalism for vibronic Hamiltonians in tetragonal symmetry and beyond

We derive general expansion formulas in vibrational coordinates for all bimodal Jahn–Teller and pseudo-Jahn–Teller Hamiltonians in tetragonal symmetry.

2T2g ← 1A1g photo-electron spectrum of octahedral tungsten hexacarbonyl

The ²T_2g ← ¹A_1g photo-electron spectrum of octahedral tungsten hexacarbonyl W(CO)₆ is investigated quantum dynamically. The photo-electron spectrum is calculated by construction of a model Hamiltonian in which the T_2g ⊗ (2a_1g ⊕ 2e_g ⊕ 2t_2g) Jahn-Teller (JT) problem up to second-order vibronic coupling (including all possible bilinear terms) together with the spin-orbit (SO) coupling up to the zeroth-order SO splitting is treated. A computational method was suggested to generate all vibronic coupling parameters of the Hamiltonian model and potential energy surfaces (PESs) based on fitting of the minimum eigenvalue of the Hamiltonian model to the adiabatic energies of the energetically lowest branch of the ²T_2g electronic state of W(CO)₆⁺˙. This calculation was performed using density functional theory (DFT), and the photo-electron spectrum produced in this way was found to be in good agreement with the experimental results.

A combined quantum-chemical and matrix-isolation study on molecular manganese fluorides

Molecular manganese fluorides were studied in solid neon, argon and fluorine using IR spectroscopy and quantum-chemical calculations at DFT and CCSD(T) levels.

Spin-vibronic quantum dynamics for ultrafast excited-state processes

Ultrafast intersystem crossing (ISC) processes coupled to nuclear relaxation and solvation dynamics play a central role in the photophysics and photochemistry of a wide range of transition metal complexes. These phenomena occurring within a few hundred femtoseconds are investigated experimentally by ultrafast picosecond and femtosecond transient absorption or luminescence spectroscopies, and optical laser pump-X-ray probe techniques using picosecond and femtosecond X-ray pulses. The interpretation of ultrafast structural changes, time-resolved spectra, quantum yields, and time scales of elementary processes or transient lifetimes needs robust theoretical tools combining state-of-the-art quantum chemistry and developments in quantum dynamics for solving the electronic and nuclear problems. Multimode molecular dynamics beyond the Born-Oppenheimer approximation has been successfully applied to many small polyatomic systems. Its application to large molecules containing a transition metal atom is still a challenge because of the nuclear dimensionality of the problem, the high density of electronic excited states, and the spin-orbit coupling effects. Rhenium(I) α-diimine carbonyl complexes, [Re(L)(CO)3(N,N)](n+) are thermally and photochemically robust and highly flexible synthetically. Structural variations of the N,N and L ligands affect the spectroscopy, the photophysics, and the photochemistry of these chromophores easily incorporated into a complex environment. Visible light absorption opens the route to a wide range of applications such as sensors, probes, or emissive labels for imaging biomolecules. Halide complexes [Re(X)(CO)3(bpy)] (X = Cl, Br, or I; bpy = 2,2'-bipyridine) exhibit complex electronic structure and large spin-orbit effects that do not correlate with the heavy atom effects. Indeed, the (1)MLCT → (3)MLCT intersystem crossing (ISC) kinetics is slower than in [Ru(bpy)3](2+) or [Fe(bpy)3](2+) despite the presence of a third-row transition metal. Counterintuitively, singlet excited-state lifetime increases on going from Cl (85 fs) to Br (128 fs) and to I (152 fs). Moreover, correlation between the Re-X stretching mode and the rate of ISC is observed. In this Account, we emphasize on the role of spin-vibronic coupling on the mechanism of ultrafast ISC put in evidence in [Re(Br)(CO)3(bpy)]. For this purpose, we have developed a model Hamiltonian for solving an 11 electronic excited states multimode problem including vibronic and SO coupling within the linear vibronic coupling (LVC) approximation and the assumption of harmonic potentials. The presence of a central metal atom coupled to rigid ligands, such as α-diimine, ensures nuclear motion of small amplitudes and a priori justifies the use of the LVC model. The simulation of the ultrafast dynamics by wavepacket propagations using the multiconfiguration time-dependent Hartree (MCTDH) method is based on density functional theory (DFT), and its time-dependent extension to excited states (TD-DFT) electronic structure data. We believe that the interplay between time-resolved experiments and these pioneering simulations covering the first picoseconds and including spin-vibronic coupling will promote a number of quantum dynamical studies that will contribute to a better understanding of ultrafast processes in a wide range of organic and inorganic chromophores easily incorporated in biosystems or supramolecular devices for specific functions.

Jahn-Teller effect in VCl4

A theoretical study is made of the Jahn-Teller and other properties of vanadium tetrachloride. Relativistic effective core potentials and corresponding valence spin-orbit operators are used with Gaussian atomic orbitals to compute self-consistent-field and spin-orbit configuration-interaction wave functions. Energy-surface parameters, electronic excitation energies, vibronic energy levels, and g factors are computed. Electron correlation is shown to have a substantial effect on the Jahn-Teller properties. As have others, we find the Jahn-Teller effect in VCl4 to be of the dynamic form.