Vibronic Structure of the Permanganate Absorption Spectrum from Time-Dependent Density Functional Calculations

Abstract

The UV absorption spectrum of the permanganate anion is a prototype transition-metal complex spectrum. Despite this being a simple d 0 T d system, for which a beautiful spectrum with detailed vibrational structure has been available since 1967, the assignment of the second and third bands is still very controversial. The issue can be resolved only by an elucidation of the intricate vibronic structure of the spectrum. We investigate the vibronic coupling by means of linear-response time-dependent density functional calculations. By means of a diabatizing scheme that employs the transition densities obtained in the TDDFT calculations in many geometries around R e , we construct a Taylor series expansion in the normal coordinates of a diabatic potential energy matrix, coupling 24 excited states. The simulated vibronic structure is in good agreement with the experimental absorption spectrum after the adjustment of some of the calculated vertical excitation energies. The peculiar blurred vibronic structure of the second band, which is a very distinctive feature of the experimental spectrum, is fully reproduced in the calculations. It is caused by the double-well shape of the adiabatic energy surface along the Jahn-Teller active e mode of the allowed 1 E state arising from the second 1 T 2 state, which exhibits a Jahn-Teller splitting into 1 B 2 and 1 E states. We trace the double-well shape to an avoided crossing between two diabatic states with different orbital-excitation character. The crossing can be explained at the molecular orbital level from the Jahn-Teller splitting of the set of 7t 2 {3d xy , 3d xz , 3d yz } orbitals (the LUMO + 1), to which the excitations characterizing the diabatic states take place. In contrast to its character in the two well regions, at R e the 2 1 T 2 state is not predominantly an excitation to the LUMO + 1, but has more HOMO -1 f LUMO (2e ) {3d x 2 -y 2 , 3d z 2 }) character. The changing character of the 2 1 T 2 -1 E state along the e mode implies that the assignment of the experimental bands to single orbital transitions is too simplistic intrinsically. This spectrum, and notably the blurring of the vibronic structure in the second band, can be understood only from the extensive configurational mixing and vibronic coupling between the excited states. This solves the long-standing assignment problem of these bands.

Covalency in Metal–Oxygen Multiple Bonds Evaluated Using Oxygen K-edge Spectroscopy and Electronic Structure Theory

“…This approach has been applied successfully to simulate spectra for several other transition metal systems 26,27,[34][35][36] and to simulate the absorption spectrum of permanganate. 37 Each calculated spectrum has been shifted by approximately +13 eV to account for omission of electronic relaxation and other effects (see Methods). 38,39 Absolute energies and peak splittings for the first two features in the O K-edge spectra measured using NIXS and obtained by XAS (STXM and FY) all agree with the TDDFT simulated values (Table 1).…”

“…This approach has been applied successfully to simulate spectra for several other transition metal systems 26,27,[34][35][36] and to simulate the absorption spectrum of permanganate. 37 Each calculated spectrum has been shifted by approximately +13…”

An Explicit Quantum Chemical Method for Modeling Large Solvation Shells Applied to Aminocoumarin C151

“…This also holds true when comparing the solvent shift to a shift between experimental gas-phase and solution spectra because gas-phase dynamics may also change the average excitation energy by 0.1-0.2 eV compared to vertical excitation energies, as is known from other CPMD 10 or vibronic coupling simulations. 27 We performed similar calculations for the snapshots obtained with water as a solvent. Considering the pure structural effect, we obtained an average excitation energy of 3.085 eV, which is comparable to n-hexane.…”

“…A direct comparison of the simulations in acetonitrile and water, however, indicates a shift of 0.11 eV between these two solvents, compared with an experimental shift of <0.01 eV. 18 Moreover, it is known from CPMD simulations 10 or studies of the vibrational broadening of absorption bands [25][26][27] that vertical excitation energies and band maxima for gas-phase molecules often differ by 0.1-0.2 eV; so, this aspect should be taken into account in the calculation of shifts in excitation energies. Hence, in the present study, we want to assess the quality of the frozen-density embedding scheme in combination with a classical MD simulation for the calculation of solvatochromic shifts.…”

Subsystem density-functional theory as an effective tool for modeling ground and excited states, their dynamics and many-body interactions

“…Additional properties for which subsystem LR-TDDFT can be applied include polarizabilities and optical rotation parameters which can be used for the calculation of oscillator and rotatory strengths [169], induced circular dichroism, [163,166] vibronic spectroscopy. [163,170,171] and resonance Raman spectra. [172] We refer the readers to Ref.…”