Vibronic structure of the permanganate absorption spectrum from time-dependent density functional calculations

Time dependent vibrational electronic coupled cluster (VECC) theory for non-adiabatic nuclear dynamics

A time-dependent vibrational electronic coupled-cluster (VECC) approach is proposed to simulate photo-electron/UV-VIS absorption spectra as well as time-dependent properties for non-adiabatic vibronic models, going beyond the Born-Oppenheimer approximation. A detailed derivation of the equations of motion and a motivation for the ansatz are presented. The VECC method employs second-quantized bosonic construction operators and a mixed linear and exponential ansatz to form a compact representation of the time-dependent wave-function. Importantly, the method does not require a basis set, has only a few user-defined inputs, and has a classical (polynomial) scaling with respect to the number of degrees of freedom (of the vibronic model), resulting in a favorable computational cost. In benchmark applications to small models and molecules, the VECC method provides accurate results compared to multi-configurational time-dependent Hartree calculations when predicting short-time dynamical properties (i.e., photo-electron/UV-VIS absorption spectra) for non-adiabatic vibronic models. To illustrate the capabilities, the VECC method is also successfully applied to a large vibronic model for hexahelicene with 14 electronic states and 63 normal modes, developed in the group by Aranda and Santoro [J. Chem. Theory Comput. 17, 1691, (2021)].

Kinetics of Direct Reaction of Vanadate, Chromate, and Permanganate with Graphene Nanoplatelets for Use in Water Purification

Oxometalates of vanadium(V), chromium(VI), and manganese(VII) have negative impacts on water resources due to their toxicity. To remove them, the kinetics of 0.04 mM oxometalates in natural and synthetic water were studied using graphene nanoplatelets (GNP). The GNP were dispersible in water and formed aggregates >15 µm that could be easily separated. Within 30 min, the GNP were covered with ~0.4 mg/g vanadium and ~1.0 mg/g chromium as Cr(OH)3. The reaction of 0.04 mM permanganate with 50 mg of GNP resulted in a coverage of 10 mg/g in 5 min, while the maximum value was 300 mg/g manganese as Mn2O3/MnO. TEM showed a random metal distribution on the surfaces; no clusters or nanoparticles were detected. The rate of disappearance in aerated water followed a pseudo second-order adsorption kinetics (PSO) for V(V), a pseudo second-order reaction for Cr(VI), and a pseudo first-order reaction for Mn(VII). For Cr(VI) and Mn(VII), the rate constants were found to depend on the GNP mass. Oxygen sorption occurred with PSO kinetics as a parallel slow process upon contact of GNP with air-saturated water. For thermally regenerated GNP, the rate constant decreased for V(V) but increased for Cr(VI), while no effect was observed for Mn(VII). GNP capacity was enhanced through regeneration for V(V) and Cr(VI); no effect was observed for Mn(VII). The reactions are well-suited for use in water purification processes and the reaction products, GNP, decorated with single metal atoms, are of great interest for the construction of sensors, electronic devices, and for application in single-atom catalysis (SAC).

On the Origins of Some Spectroscopic Properties of "Purple Iron" (the Tetraoxoferrate(VI) Ion) and Its Pourbaix Safe-Space

In this work, the authors attempt to interpret the visible, infrared and Raman spectra of ferrate(VI) by means of theoretical physical-inorganic chemistry and historical highlights in this field of interest. In addition, the sacrificial decomposition of ferrate(VI) during water treatment will also be discussed together with a brief mention of how Rayleigh scattering caused by the decomposition of Fe^VIO₄²⁻ may render absorbance readings erroneous. This work is not a compendium of all the instrumental methods of analysis which have been deployed to identify ferrate(VI) or to study its plethora of reactions, but mention will be made of the relevant techniques (e.g., Mössbauer Spectroscopy amongst others) which support and advance this overall discourse at appropriate junctures, without undue elaboration on the foundational physics of these techniques.

Electronic Structure and Spectroscopic Properties of Group-7 Tri-Oxo-Halides MO3X (M = Mn-Bh, X = F-Ts)

The 24 trioxide halide molecules MO₃X of the manganese group (M = Mn-Bh; X = F-Ts), which are iso-valence-electronic with the famous MnO_4^- ion, have been quantum-chemically investigated by quasi-relativistic density-functional and ab initio correlated approaches. Geometric and electronic structures, valence and oxidation numbers, vibrational and electronic spectral properties, energetic stabilities of the monomers in the gas phase, and the decay mode of MnO₃F have been investigated. The light Mn-3d species are most strongly electron-correlated, indicating that the concept of a closed-shell Lewis-type single-configurational structure [Mn⁺⁷(d⁰) O^-2(p⁶)₃ F^-(p⁶)] reaches its limits. The concept of real-valued spin orbitals φ(r)·α and φ(r)·β breaks down for the heavy Bh-6d, At-6p and Ts-7p elements because of the dominating spin-orbit coupling. The vigorous decomposition of MnO₃F at ambient conditions starts by the autocatalyzed release of n O₂ and the formation of Mn_mO_3m-2nF_m clusters, triggered by the electron-depleted "oxylic" character of the oxide ligands in MnO₃X.

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.

The elusive dynamics of aqueous permanganate photochemistry

Despite decades of investigation, mechanistic details of aqueous permanganate photo-decomposition remain unclear. Here we follow photoinduced dynamics of aqueous permanganate with femtosecond spectroscopy. Photoexcitation of KMnO₄(aq) in the visible unleashes a sub-picosecond cascade of non-radiative transitions, leading to a distinct species which relaxes to S₀ with a lifetime of 16 ps. Tuning excitation to the UV shows increasing formation of a metastable intermediate, which outlives our ∼1 ns window of detection. Guided by electronic structure calculations and observations from three pulse excitation experiments, we assign the 16 ps species as the lowest Jahn-Teller component of the ³T₁ triplet state and suggest a plausible sequence of radiationless transitions, which rapidly populate it. In conjunction with photodecomposition quantum yields obtained from the literature, these results demonstrate that aqueous permanganate photo-decomposition proceeds through a long-lived intermediate which is formed in parallel to the triplet in less than one ps upon UV absorption. The possibility that this is the postulated highly oxidative peroxo species, a fraction of which leads to the stable (MnO₂^- + O₂) fragments, is discussed. Finally, periodic modulations detected in the pump-probe signal are assigned to ground-state vibrational coherences excited by impulsive Raman. Their wavelength-dependent absolute phases outline the borders between adjacent electronic transitions in the linear spectrum of permanganate.

An unknown component of a selective and mild oxidant: structure and oxidative ability of a double salt-type complex having κ1O-coordinated permanganate anions and three- and four-fold coordinated silver cations

Compounds containing redox active permanganate anions and complexed silver cations with reducing pyridine ligands are used not only as selective and mild oxidants in organic chemistry but as precursors for nanocatalyst synthesis in low-temperature solid-phase quasi-intramolecular redox reactions. Here we show a novel compound (4Agpy₂MnO₄·Agpy₄MnO₄) that has unique structural features including (1) four coordinated and one non-coordinated permanganate anion, (2) κ¹O-permanganate coordinated Ag, (3) chain-like [Ag(py)₂]⁺ units, (4) non-coordinated ionic permanganate ions and an [Ag(py)₄]⁺ tetrahedra as well as (5) unsymmetrical hydrogen bonds between pyridine α-CHs and a permanganate oxygen. As a result of the oxidizing permanganate anion and reducing pyridine ligand, a highly exothermic reaction occurs at 85 °C. If the decomposition heat is absorbed by alumina or oxidation-resistant organic solvents (the solvent absorbs the heat to evaporate), the decomposition reaction proceeds smoothly and safely. During heating of the solid material, pyridine is partly oxidized into carbon dioxide and water; the solid phase decomposition end product contains mainly metallic Ag, Mn₃O₄ and some encapsulated carbon dioxide. Surprisingly, the enigmatic carbon-dioxide is an intercalated gas instead of the expected chemisorbed carbonate form. The title compound is proved to be a mild and efficient oxidant toward benzyl alcohols with an almost quantitative yield of benzaldehydes.

Franck-Condon Models for Simulating the Band Shape of Electronic Absorption Spectra

Band shape is an essential ingredient in the simulation of electronic absorption spectra. The excitation of multiple series of vibrational levels during an electronic excitation is a main contributor to band shapes. Here we present two simple models based on the Franck-Condon displaced-harmonic-oscillator model. The models are both derived from the time-dependent formulation of electronic spectroscopy. They assume that the transition dipoles do not depend on geometry and that the potential energy surfaces are locally quadratic; one model is second order in time and is called LQ2, and the other is third order in time and is called LQ3. These models are suitable for simulating the unresolved vibronic band shapes of electronic spectra that involve many vibrational modes. The models are straightforward and can be easily applied to simulate absorption spectra that are composed of many electronic transitions. As compared to carrying out molecular dynamics simulations, they require relatively few electronic structure calculations, and the additional cost for constructing the spectra is negligible. Therefore, the models are suitable for simulating the spectra of complex systems such as transition-metal complexes.

Modeling the absorption spectrum of the permanganate ion in vacuum and in aqueous solution

The absorption spectrum of MnO₄⁻ in vacuum and aqueous solution is modeled using the range-separated complete active space short-range density functional theory method (CAS-srDFT) combined with either implicit (PCM) or explicit (PE) solvent models. The experimental vacuum-to-water solvent shift of the lowest intense transition is reproduced by PE-CAS-srDFT.

Combined spectroscopic and computational analysis of the vibrational properties of vitamin B12 in its Co3+, Co2+, and Co1+ oxidation states

While the geometric and electronic structures of vitamin B12 (cyanocobalamin, CNCbl) and its reduced derivatives Co(2+)cobalamin (Co(2+)Cbl) and Co(1+)cobalamin (Co(1+)Cbl(-)) are now reasonably well established, their vibrational properties, in particular their resonance Raman (rR) spectra, have remained quite poorly understood. The goal of this study was to establish definitive assignments of the corrin-based vibrational modes that dominate the rR spectra of vitamin B12 in its Co(3+), Co(2+), and Co(1+) oxidation states. rR spectra were collected for all three species with laser excitation in resonance with the most intense corrin-based π → π* transitions. These experimental data were used to validate the computed vibrational frequencies, eigenvector compositions, and relative rR intensities of the normal modes of interest as obtained by density functional theory (DFT) calculations. Importantly, the computational methodology employed in this study successfully reproduces the experimental observation that the frequencies and rR excitation profiles of the corrin-based vibrational modes vary significantly as a function of the cobalt oxidation state. Our DFT results suggest that this variation reflects large differences in the degree of mixing between the occupied Co 3d orbitals and empty corrin π* orbitals in CNCbl, Co(2+)Cbl, and Co(1+)Cbl(-). As a result, vibrations mainly involving stretching of conjugated C-C and C-N bonds oriented along one axis of the corrin ring may, in fact, couple to a perpendicularly polarized electronic transition. This unusual coupling between electronic transitions and vibrational motions of corrinoids greatly complicates an assignment of the corrin-based normal modes of vibrations on the basis of their rR excitation profiles.

Analysis and prediction of absorption band shapes, fluorescence band shapes, resonance Raman intensities, and excitation profiles using the time-dependent theory of electronic spectroscopy

A general method for the simulation of absorption (ABS) and fluorescence band shapes, resonance-Raman (rR) spectra, and excitation profiles based on the time-dependent theory of Heller is discussed. The following improvements to Heller's theory have been made: (a) derivation of new recurrence relations for the time-dependent wave packet overlap in the case of frequency changes between the ground and electronically excited states, (b) a new series expansion that gives insight into the nature of Savin's preresonance approximation, (c) incorporation of inhomogeneous broadening effects into the formalism at no additional computational cost, and (d) derivation of a new and simple short-time dynamics based equation for the Stokes shift that remains valid in the case of partially resolved vibrational structure. Our implementation of the time-dependent theory for the fitting of experimental spectra and the simulation of model spectra as well as the quantum mechanical calculation of the model parameters is discussed. The implementation covers all electronic structure approaches which are able to deliver ground- and excited-state energies and transition dipole moments. The technique becomes highly efficient if analytic gradients for the excited-state surface are available. In this case, the computational cost for the simultaneous prediction of ABS, fluorescence, and rR spectra is equal to that of a single excited-state geometry optimization step while the limitations of the short-time dynamics approximation are completely avoided. As a test case we discuss the well-known case of the strongly allowed 1 (1)A(g) --> 1 (1)B(u) transition in 1,3,5 trans-hexatriene in detail using method ranging from simple single-reference treatments to elaborate multireference electronic structure approaches. At the highest computational level, the computed spectra show the best agreement that has so far been obtained with quantum chemical methods for this problem.

Nonadiabatic couplings from time-dependent density functional theory: Formulation in the Casida formalism and practical scheme within modified linear response

We present an efficient method to compute nonadiabatic couplings (NACs) between the electronically ground and excited states of molecules, within the framework of time-dependent density functional theory (TDDFT) in frequency domain. Based on the comparison of dynamic polarizability formulated both in the many-body wave function form and the Casida formalism, a rigorous expression is established for NACs, which is similar to the calculation of oscillator strength in the Casida formalism. The adiabatic local density approximation (ALDA) gives results in reasonable accuracy as long as the conical intersection (ci) is not approached too closely, while its performance quickly degrades near the ci point. This behavior is consistent with the real-time TDDFT calculation. Through the use of modified linear response theory together with the ground-state-component separation scheme, the performance of ALDA can be greatly improved, not only in the vicinity of ci but also for Rydberg transitions and charge-transfer excitations. Several calculation examples, including the quantization of NACs from the Jahn-Teller effect in the H3 system, have been given to show that TDDFT can efficiently give NACs with an accuracy comparable to that of wave-function-based methods.

A theoretical study of the chiroptical properties of molecules with isotopically engendered chirality

There has been a considerable interest in the chiroptical properties of molecules whose chirality is exclusively due to an isotopic substitution and numerous examples for the electronic circular dichroism (CD) spectra of isotopically chiral systems have been reported in literature. Four different explanations have been proposed for the mechanism as to how the isotopic substitution induces a chiral perturbation of the otherwise achiral electronic wave function; however, up to now no conclusive answer has been given about the dominating effect responsible for the experimental observations. In this study we will present, for the first time, fully quantum-mechanical calculations of the CD spectra of three different molecular systems with isotopically engendered chirality. As examples, we consider the spectra of organic molecules with ketone and alpha-diketone carbonyl and diene chromophores. The effect of vibronic couplings for the reorientation of the electric and magnetic transition dipole moments is taken into account within the Herzberg-Teller approximation. The ground and excited state geometries and vibrational normal modes are obtained with (time-dependent) density functional theory [(TD)DFT], while the vibronic coupling effects are calculated at the TDDFT and density functional theory/multireference configuration interaction (DFT/MRCI) levels of theory. Generally, the band shapes of the experimental CD spectra are reproduced very well, and also the absolute CD intensities from the simulations are of the right order of magnitude. The sign and the intensity of the CD band are determined by a delicate balance of the contributions of a large number of individual vibronic transitions, and it is found that the vibrational normal modes with a large displacement are dominant. The separation of the calculated CD spectrum into the different contributions due to the overlap of the in-plane and out-of-plane components (regarding the symmetry plane of the unsubstituted molecule) of the electric and magnetic transition dipole moments yields information about the influence of the vibronic coupling effects for the reorientation of the corresponding transition dipole moments. In conclusion, the calculations clearly show that vibronic effects are responsible or at least dominant for the chiroptical properties of isotopically chiral organic molecules.

Vibronic coupling in the excited cationic states of ethylene: simulation of the photoelectron spectrum between 12 and 18 eV

The effect of vibronic coupling on structure and spectroscopy is investigated in the excited cationic states of ethylene. It is found from equation of motion coupled cluster singles and doubles method for ionization potential electronic structure calculations in a triple-zeta plus double polarization basis set that ethylene in its third (B (2)A(g)) and fourth (C (2)B(2u)) ionized states does not have a stable minimum-energy geometry. The potential-energy surfaces of these states are energetically distinct and well separated at the ground-state geometry of ethylene, but in a geometry optimization as the structure of the ion relaxes, these surfaces end up in conical intersections and finally in the stable equilibrium geometry of the second ionized state (A (2)B(3g)). The topology of the potential-energy surfaces can be clearly understood using a vibronic model Hamiltonian. Furthermore, by diagonalizing this model Hamiltonian, the photoelectron spectrum of ethylene corresponding to the second, third, and fourth ionized states (12-18 eV) is simulated. Spectra from vibronic simulations including up to quartic coupling constants and using various normal-mode basis sets are compared to those from vertical Franck-Condon simulations to understand the importance of vibronic coupling and nonadiabatic effects and to examine the influence of individual normal modes on the spectrum.

Nonadiabatic effects in the photoelectron spectrum of the pyrazolide-d3 anion: Three-state interactions in the pyrazolyl-d3 radical

The 351.1 nm photoelectron spectrum of the 1-pyrazolide-d(3) anion has been measured. The photoelectron angular distributions indicate the presence of nearly degenerate electronic states of the 1-pyrazolyl-d(3) radical. Equation-of-motion ionization potential coupled-cluster singles and doubles (EOMIP-CCSD) calculations have been performed to study the low-lying electronic states. The calculations strongly suggest that three electronic states, energetically close to each other, are accessed in the photodetachment process. Strong interactions of the pseudo-Jahn-Teller type in each pair of the three states are evident in the calculations for the radical at the anion geometry. Model diabatic potentials of the three states have been constructed around the anion geometry in terms of the anion reduced normal coordinates up to the second order. An analytic method to parametrize the quadratic vibronic coupling (QVC) model potentials has been introduced. Parameters of the QVC model potentials have been determined from the EOMIP-CCSD and CCSD(T) calculations. Simulations of the 1-pyrazolide-d(3) spectrum have been performed with the model Hamiltonian, treating all vibronic interactions amongst the three states simultaneously. The simulation reproduces the fine structure of the observed spectrum very well, revealing complicated nonadiabatic effects in the low-lying states of the radical. The ground state of the 1-pyrazolyl-d(3) radical is (2)A(2) and the electron affinity is 2.935+/-0.006 eV. The first excited state is (2)B(1) with a term energy of 32+/-1 meV. While the high-symmetry (C(2v)) stationary points of the X (2)A(2) and A (2)B(1) states are minima, that of the state is a saddle point as a result of the pseudo-Jahn-Teller interactions with the other two states. The topology of the adiabatic potential energy surfaces is discussed.

Calculation of excitation energies of open-shell molecules with spatially degenerate ground states. II. Transformed reference via intermediate configuration Kohn-Sham time dependent density functional theory oscillator strengths and magnetic circular dichroism C terms

An extension of the transformed reference via an intermediate configuration Kohn-Sham time dependent density functional theory (TRICKS-TDDFT) method for calculating the transition energies of molecules with spatially degenerate ground states is proposed that enables oscillator strengths to also be evaluated. The oscillator strengths are calculated starting from a description of the degenerate ground state and the excited states of interest in terms of linear combinations of Slater determinants based upon the F-vectors obtained in the TRICKS-TDDFT calculation. This approach for calculating oscillator strengths can also be applied to several other properties that involve excited states. An example of such a property, the C term of magnetic circular dichroism (MCD), is presented. The new method is illustrated through example calculations of the absorbance and MCD spectra of several octahedral and C(4v) d(5) transition metal complexes. The calculated transition energies and oscillator strengths are somewhat too low and too high, respectively, but these errors are within the range that would normally be expected for TDDFT calculations of this type. The calculations help to resolve some previously unexplained problems with the MCD spectra of the C(4v) complexes.

Calculation of excitation energies of open-shell molecules with spatially degenerate ground states. I. Transformed reference via an intermediate configuration Kohn-Sham density-functional theory and applications to d1 and d2 systems with octahedral and tetrahedral symmetries

A method for calculating the UV-vis spectra of molecules with spatially degenerate ground states using time-dependent density-functional theory (TDDFT) is proposed. The new transformed reference via an intermediate configuration Kohn-Sham TDDFT (TRICKS-TDDFT) method avoids the difficulties caused by the multireference nature of spatially degenerate states by rather than utilizing the ground state instead taking a nondegenerate excited state with desirable properties as the reference for the TDDFT calculation. The scope and practical application of the method are discussed. Like all open-shell TDDFT calculations this method at times suffers from the inability to produce transitions to states that are eigenfunctions of the total spin operator. A technique for alleviating this difficulty to some extent is proposed. The applicability and accuracy of the TRICKS-TDDFT method is demonstrated through example calculations of several d(1) and d(2) transition metal complexes with tetrahedral and octahedral symmetries. For the most part, the results of these calculations are similar in quality to to those obtained from standard TDDFT calculations.

Importance of vibronic effects on the circular dichroism spectrum of dimethyloxirane

We present a theoretical study on the vibrational structure of a circular dichroism (CD) spectrum using time-dependent density-functional theory in combination with a Franck-Condon-type approach. This method is applied to analyze the complex CD spectrum of dimethyloxirane, which involves delicate cancellations of positive and negative CD bands. Our approach reveals that these cancellations are strongly affected by the shapes of the CD bands, and that it is vital for an accurate simulation of the spectrum to take the different envelopes of these bands into account. One crucial point in some former theoretical studies on this compound, which were restricted to vertical excitations, was the appearance of a strong negative CD band in the energy range of 7.0-7.5 eV, which is not present in the experimental spectrum. We can explain the disappearance of this 2B band by a strong vibrational progression along normal modes with C-O stretching character, so that the band extends over an energy range of almost 1.1 eV. Thus, it overlaps with many other (mostly positive) CD bands, leading to a cancellation of its intensity. The dominant vibrational features in the experimental spectrum can be assigned to the 1B, 3B, and 5B bands, which show several clear vibrational peaks and a total bandwidth of only 0.3-0.5 eV. In order to obtain close agreement between the simulated and the experimental spectrum we have to apply small shifts to the vertical excitation energies that enter the calculation. These shifts account both for possible errors in the time-dependent density-functional theory calculations and for the neglect of differential zero-point energy between ground and excited states in our gradient-based vertical Franck-Condon approach.