Vibronic-structure tracking: a shortcut for vibrationally resolved UV/Vis-spectra calculations

Assessing the accuracy of TD-DFT excited-state geometries through optimal tuning with GW energy levels

We study the accuracy of excited state (ES) geometries using optimally tuned LC-PBE functionals with tuning based on GW quasiparticle energies. We compare the results obtained with the PBE, PBE0, non-tuned, and tuned LC-PBE functionals with available high-level CC reference values as well as experimental data. First, we compare ES geometrical parameters obtained for three different types of systems: molecules composed of a few atoms, 4-(dimethylamino)benzonitrile (DMABN), and conjugated dyes. To this end, we used wave-function results as benchmarks. Next, we evaluate the accuracy of the theoretically simulated spectra as compared to the experimental ones for five large dyes. Our results show that, besides small compact molecules for which tuning LC-PBE does not allow obtaining geometries more accurate than those computed with standard functionals, tuned range-separated functionals are clearly to be favored, not only for ES geometries but also for 0-0 energies, band shapes, and intensities for absorption and emission spectra. In particular, the results indicate that GW-tuned LC-PBE functionals provide improved matching with experimental spectra as compared to conventionally tuned functionals. It is an open question whether TD-DFT with GW-tuned functionals can qualitatively mimic the actual many-body Bethe-Salpeter (BSE/GW) formalism for which analytic ionic gradients remain to be developed.

Tailored anharmonic-harmonic vibrational profiles for fluorescent biomarkers

We propose a hybrid anharmonic-harmonic scheme for vibrational broadenings, which embeds a reduced-space vibrational configuration interaction (VCI) anharmonic wave function treatment in the independent-mode displaced harmonic oscillator (IMDHO) model. The resulting systematically-improvable VCI-in-IMDHO model allows including the vibronic effects of all vibrational degrees of freedom, while focusing the effort on the important degrees of freedom with minimal extra computational effort compared to a reduced-space VCI treatment. We show for oligothiophene examples that the VCI-in-IMDHO approach can yield accurate vibrational profiles employing smaller vibrational spaces in the VCI part than the reduced-space VCI approach. By this, the VCI-in-IMDHO model enables accurate calculation of vibrational profiles of common fluorescent dyes with more than 100 vibrational degrees of freedom. We illustrate this for three examples of fluorescent biomarkers of current interest. These are the oligothiophene-based fluorescent dye called HS84, 1,4-diphenylbutadiene, and an anthracene diimide. For all examples, we assess the impact of the anharmonic treatment on the vibrational broadening, which we find to be more pronounced for the intensities than for the peak positions.

The Static-Dynamic-Static Family of Methods for Strongly Correlated Electrons: Methodology and Benchmarking

A series of methods (SDSCI, SDSPT2, iCI, iCIPT2, iCISCF(2), iVI, and iCAS) is introduced to accurately describe strongly correlated systems of electrons. Born from the (restricted) static-dynamic-static (SDS) framework for designing many-electron wave functions, SDSCI is a minimal multireference (MR) configuration interaction (CI) approach that constructs and diagonalizes a [Formula: see text] matrix for [Formula: see text] states, regardless of the numbers of orbitals and electrons to be correlated. If the full molecular Hamiltonian H in the QHQ block (which describes couplings between functions of the first-order interaction space Q) of the SDSCI CI matrix is replaced with a zeroth-order Hamiltonian [Formula: see text] before the diagonalization is taken, we obtain SDSPT2, a CI-like second-order perturbation theory (PT2). Unlike most variants of MRPT2, SDSPT2 treats single and multiple states in the same way and is particularly advantageous in the presence of near degeneracy. On the other hand, if the SDSCI procedure is repeated until convergence, we will have iterative CI (iCI), which can converge quickly from the above to the exact solutions (full CI) even when starting with a poor guess. When further combined with the selection of important configurations followed by a PT2 treatment of dynamic correlation, iCI becomes iCIPT2, which is a near-exact theory for medium-sized systems. The microiterations of iCI for relaxing the coefficients of contracted many-electron functions can be generalized to an iterative vector interaction (iVI) approach for finding exterior or interior roots of a given matrix, in which the dimension of the search subspace is fixed by either the number of target roots or the user-specified energy window. Naturally, iCIPT2 can be employed as the active space solver of the complete active space (CAS) self-consistent field, leading to iCISCF(2), which can further be combined with iCAS for automated selection of active orbitals and assurance of the same CAS for all states and all geometries. The methods are calibrated by taking the Thiel set of benchmark systems as examples. Results for the corresponding cations, a new set of benchmark systems, are also reported.

A Nonheme Mononuclear {FeNO}7 Complex that Produces N2 O in the Absence of an Exogenous Reductant

A new nonheme iron(II) complex, Fe^II (Me₃ TACN)((OSi^Ph2 )₂ O) (1), is reported. Reaction of 1 with NO_(g) gives a stable mononitrosyl complex Fe(NO)(Me₃ TACN)((OSi^Ph2 )₂ O) (2), which was characterized by Mössbauer (δ=0.52 mm s^-1 , |ΔE_Q |=0.80 mm s^-1 ), EPR (S=3/2), resonance Raman (RR) and Fe K-edge X-ray absorption spectroscopies. The data show that 2 is an {FeNO}⁷ complex with an S=3/2 spin ground state. The RR spectrum (λ_exc =458 nm) of 2 combined with isotopic labeling (¹⁵ N, ¹⁸ O) reveals ν(N-O)=1680 cm^-1 , which is highly activated, and is a nearly identical match to that seen for the reactive mononitrosyl intermediate in the nonheme iron enzyme FDPnor (ν(NO)=1681 cm^-1 ). Complex 2 reacts rapidly with H₂ O in THF to produce the N-N coupled product N₂ O, providing the first example of a mononuclear nonheme iron complex that is capable of converting NO to N₂ O in the absence of an exogenous reductant.

On the origin of the shift between vertical excitation and band maximum in molecular photoabsorption

The analysis of the photoabsorption spectra of molecules shows that the band maximum is usually redshifted in comparison to the vertical excitation. We conducted a throughout analysis of this shift based on low-dimensional analytical and numerical model systems, showing that its origin is rooted in the frequency change between the ground and the excited states in multidimensional systems. Moreover, we deliver a benchmark of ab initio results for the shift based on a comparison of vertical excitations and band maxima calculated with the nuclear ensemble approach for the 28 organic molecules in the Mülheim molecular dataset. The mean value of the shift calculated over 60 transitions is 0.11 ± 0.08 eV. The mean value of the band width is 0.32 ± 0.14 eV.

Graphical abstract

Vibrationally resolved emission spectra of luminescent conjugated oligothiophenes from anharmonic calculations

We report on accurate and efficient calculations of vibrationally resolved emission spectra for oligothiophenes from anharmonic vibrational configuration interaction wave-function calculations in reduced vibrational spaces. These reduced spaces are chosen based on the independent mode displaced harmonic oscillator model. Good agreement with experiment is obtained for all-trans oligothiophenes with two to five rings also when employing only a few active modes. Vibrational modes incorporating inter-ring carbon-carbon stretches and a ring breathing mode are found to be the main players in the vibrational progression for the emission from the first excited electronic state for all investigated oligothiophene derivatives. The presented framework is here illustrated for oligothiophenes, but we have made no underlying system-dependent assumptions and believe it to become a valuable tool for the rational design of fluorescence biomarkers.

Structures, Spectroscopic Properties, and Dioxygen Reactivity of 5- and 6-Coordinate Nonheme Iron(II) Complexes: A Combined Enzyme/Model Study of Thiol Dioxygenases

The synthesis of four new FeII(N4S(thiolate)) complexes as models of the thiol dioxygenases are described. They are composed of derivatives of the neutral, tridentate ligand triazacyclononane (R3TACN; R = Me, iPr) and 2-aminobenzenethiolate (abtx; X = H, CF3), a non-native substrate for thiol dioxygenases. The coordination number of these complexes depends on the identity of the TACN derivative, giving 6-coordinate (6-coord) complexes for FeII(Me3TACN)(abtx)(OTf) (1: X = H; 2: X = CF3) and 5-coordinate (5-coord) complexes for [FeII(iPr3TACN)(abtx)](OTf) (3: X = H; 4: X = CF3). Complexes 1-4 were examined by UV-vis, 1H/19F NMR, and Mössbauer spectroscopies, and density functional theory (DFT) calculations were employed to support the data. Mössbauer spectroscopy reveals that the 6-coord 1-2 and 5-coord 3- 4 exhibit distinct spectra, and these data are compared with that for cysteine-bound CDO, helping to clarify the coordination environment of the cys-bound FeII active site. Reaction of 1 or 2 with O2 at -95 °C leads to S-oxygenation of the abt ligand, and in the case of 2, a rare di(sulfinato)-bridged complex, [Fe2III(μ-O)((2-NH2) p-CF3C6H3SO2)2](OTf)2 ( 5), was obtained. Parallel enzymatic studies on the CDO variant C93G were carried out with the abt substrate and show that reaction with O2 leads to disulfide formation, as opposed to S-oxygenation. The combined model and enzyme studies show that the thiol dioxygenases can operate via a 6-coord FeII center, in contrast to the accepted mechanism for nonheme iron dioxygenases, and that proper substrate chelation to Fe appears to be critical for S-oxygenation.