Chasing unphysical TD-DFT excited states in transition metal complexes with a simple diagnostic tool

Coordination of Al(C6F5)3 vs. B(C6F5)3 on group 6 end-on dinitrogen complexes: chemical and structural divergences

The coordination of the Lewis superacid tris(pentafluorophenyl)alane (AlCF) to phosphine-supported, group 6 bis(dinitrogen) complexes [ML2(N2)2] is explored, with M = Cr, Mo or W and L = dppe (1,2-bis(diphenylphosphino)ethane), depe (1,2-bis(diethylphosphino)ethane), dmpe (1,2-bis(dimethylphosphino)ethane) or 2 × PMe2Ph. Akin to tris(pentafluorophenyl)borane (BCF), AlCF can form 1 : 1 adducts by coordination to one distal nitrogen of general formula trans-[ML2(N2){(μ-η1:η1-N2)Al(C6F5)3}]. The boron and aluminium adducts are structurally similar, showing a comparable level of N2 push-pull activation. A notable exception is a bent (BCF adducts) vs. linear (AlCF adducts) M-N-N-LA motif (LA = Lewis acid), explained computationally as the result of steric repulsion. A striking difference arose when the formation of two-fold adducts was conducted. While in the case of BCF the 2 : 1 Lewis pairs could be observed in equilibrium with the 1 : 1 adduct and free borane but resisted isolation, AlCF forms robust 2 : 1 adducts trans-[ML2{(μ-η1:η1-N2)Al(C6F5)3}2] that isomerise into a more stable cis configuration. These compounds could be isolated and structurally characterized, and represent the first examples of trinuclear heterometallic complexes formed by Lewis acid-base interaction exhibiting p and d elements. Calculations also demonstrate that from the bare complex to the two-fold aluminium adduct, substantial decrease of the HOMO-LUMO gap is observed, and, unlike the trans adducts (1 : 1 and 1 : 2) for which the HOMO was computed to be a pure d orbital, the one of the cis-trinuclear compounds mixes a d orbital with a π* one of each N2 ligands. This may translate into a more favourable electrophilic attack on the N2 ligands instead of the metal centre, while a stabilized N2-centered LUMO should ease electron transfer, suggesting Lewis acids could be co-activators for electro-catalysed N2 reduction. Experimental UV-vis spectra for the tungsten family of compounds were compared with TD-DFT calculations (CAM-B3LYP/def2-TZVP), allowing to assign the low extinction bands found in the visible spectrum to unusual low-lying MLCT involving N2-centered orbitals. As significant red-shifts are observed upon LA coordination, this could have important implications for the development of visible light-driven nitrogen fixation.

Monitoring Density Redistribution at the Excited State in a Dual Emitting Molecule: An Analysis Based on Real-Time Density Functional Theory and Density Descriptors

In this work, we computed and analyzed, by means of density-based descriptors, the real-time evolution of both the locally excited (LE) and charge-transfer (CT) excited states for the planar and twisted conformations of the DMABN (4-(N,N-dimethylamino)benzonitrile) molecule using real-time time-dependent density functional theory (DFT) and three different exchange-correlation energy functionals (EXC) belonging to the same family (the PBE one). Our results based on the analysis of density-based descriptors show that the underlying EXC modifies the evolution in time of the density. In particular, comparing the frequency of density reorganization computed with the three functionals (PBE, PBE0, and LC-PBE), we found that the frequency of electronic interconversion of the individual determinants involved during the dynamics increases from PBE to PBE0 and to LC-PBE. This allows us to show that there is a correlation between the delocalization of the electronic density and the frequency of reorganization. In particular, the greater the mean hole-electron distance during the dynamics, the lower is the frequency of density reorganization.

Photophysical Studies of Helicate and Mesocate Double-Stranded Dinuclear Ru(II) Complexes

The metal-ligand charge transfer (3MLCT) and phosphorescence-quenching metal-centered (3MC) states of the helicate and mesocate diastereoisomers of a double-stranded dinuclear polypyridylruthenium(II) complex have been investigated using ultrafast transient absorption spectroscopy. At 294 K, transient signals of the helicate decayed significantly slower than those of the mesocate, whereas at 77 K, no clear contrast in kinetics was observed. Contributions to excited-state decay from high-lying 3MLCT states were identified at both temperatures. Spectroscopic data (294 K) suggest that the 3MC state of the helicate lies above the 3MLCT and that the reverse is true for the mesocate; this was further validated by density functional theory calculations. The stabilization of the 3MC state relative to the 3MLCT state in the mesocate was explained by a reduction in ligand field strength due to distortion near the ligand bridge, which causes further deviation from octahedral geometry compared to the helicate. This work illustrates how minor structural differences can significantly influence excited state dynamics.

Visualizing and characterizing excited states from time-dependent density functional theory

Time-dependent density functional theory (TD-DFT) is the most widely-used electronic structure method for excited states, due to a favorable combination of low cost and semi-quantitative accuracy in many contexts, even if there are well recognized limitations. This Perspective describes various ways in which excited states from TD-DFT calculations can be visualized and analyzed, both qualitatively and quantitatively. This includes not just orbitals and densities but also well-defined statistical measures of electron-hole separation and of Frenkel-type exciton delocalization. Emphasis is placed on mathematical connections between methods that have often been discussed separately. Particular attention is paid to charge-transfer diagnostics, which provide indicators of when TD-DFT may not be trustworthy due to its categorical failure to describe long-range electron transfer. Measures of exciton size and charge separation that are directly connected to the underlying transition density are recommended over more ad hoc metrics for quantifying charge-transfer character.

Elucidation of LMCT Excited States for Lanthanoid Complexes: A Theoretical and Solid-State Experimental Framework

Photophysical and magnetic properties arising from both ground and excited states of lanthanoid ions are relevant for numerous applications. These properties can be substantially affected, both adversely and beneficially, by ligand-to-metal charge-transfer (LMCT) states. However, probing LMCT states remains a significant challenge in f-block chemistry, particularly in the solid state. Intriguingly, the europium compounds [Eu^III(18-c-6)(X₄Cat)(NO₃)]·MeCN (18-c-6 = 18-crown-6; X = Cl (tetrachlorocatecholate, 1-Eu) or Br (tetrabromocatecholate, 2-Eu) are distinctly darkly-colored, in marked contrast to the analogues with other lanthanoid ions in the 1-Ln and 2-Ln series (Ln = La, Ce, Nd, Gd, Tb, and Dy). Herein, we report a multi-technique investigation of these compounds that has allowed elucidation of the LMCT character of the relevant absorption bands using magnetometry, absorption and emission spectroscopies, and solid-state electrochemistry. To support experimental observations, we present a semi-quantitative multireference ab initio model that (i) captures the anomalously low-lying LMCT excited state observed in the visible spectrum of 1-Eu (and its absence in the other 1-Ln analogues); (ii) elucidates the contribution of the LMCT excitation to the crystal field split ⁷F_J ground-state wave functions; and (iii) identifies the crucial role played by radial dynamical correlation of the Eu^III 4f electrons in the description of the LMCT excited state, modeled by the inclusion of 4f → 5f excitations in the optimized wave function. By providing a set of experimental and theoretical tools, this work establishes a framework for the elucidation of LMCT excited states in lanthanoid compounds in the solid state.

Following the density evolution using real time density functional theory and density based indexes: Application to model push-pull molecules

Considering as test case a family of organic rod like push-pull molecules, we derived and applied density based index enabling the description and diagnostic of the electronic density evolution in real time-time dependent density functional theory (RT-TDDFT) simulations. In particular, both the charge transfer (CT) distance and a diagnostic index, the D_CT and M_AC ^RT respectively, were computed on the fly from the density distribution obtained at a given time and the reference ground state density and their mean values were compared with what obtained at Linear Response-TDDFT level. Besides giving a way of analyzing the density redistribution occurring in time, these tools allowed to show how RT-TDDFT, which is definitely a powerful method to model the evolution of the density in CT or charge separation processes, can be affected by the same artifacts known for LR-TDDFT approaches and, particularly, to those related to the use of approximate exchange correlation functionals. The analysis here performed allowed to identify and discard on fly the electronic configurations corresponding to spurious situations.

Modeling the spectral properties of poly(x-phenylenediamine) conducting polymers using a combined TD-DFT and electrostatic embedding approach

The absorption spectra of polymers derived from ortho, meta and para phenylenediamines (o-PDA, m-PDA and p-PDA) have been simulated combining periodic density functional theory (DFT) calculations with time-dependent DFT simulations. These latter have been carried out on finite clusters embedded in a set of point charges devised to exactly reproduce the electrostatic potential of the periodic chains. The results are compared with those obtained for solvated o-PDA, m-PDA and p-PDA oligomers of increasing sizes extracted from the periodic structures. The electronic transitions involved have been investigated by a qualitative analysis based on isodensity maps completed by a quantitative analysis based on the density-based index (D_CT ). For poly-(o)- and poly-(p)- phenylenediamines the agreement with the experimental data is achieved already by modeling solvated dimers whereas the inclusion of long-range electrostatic effects is mandatory for poly-(m)-phenylenediamine highlighting the importance of an accurate treatment of the electrostatic environment when a finite cluster approach is considered.

Shallow and deep trap states of solvated electrons in methanol and their formation, electronic excitation, and relaxation dynamics

We present condensed-phase first-principles molecular dynamics simulations to elucidate the presence of different electron trapping sites in liquid methanol and their roles in the formation, electronic transitions, and relaxation of solvated electrons (e_met⁻) in methanol. Excess electrons injected into liquid methanol are most likely trapped by methyl groups, but rapidly diffuse to more stable trapping sites with dangling OH bonds. After localization at the sites with one free OH bond (1OH trapping sites), reorientation of other methanol molecules increases the OH coordination number and the trap depth, and ultimately four OH bonds become coordinated with the excess electrons under thermal conditions. The simulation identified four distinct trapping states with different OH coordination numbers. The simulation results also revealed that electronic transitions of e_met⁻ are primarily due to charge transfer between electron trapping sites (cavities) formed by OH and methyl groups, and that these transitions differ from hydrogenic electronic transitions involving aqueous solvated electrons (e_aq⁻). Such charge transfer also explains the alkyl-chain-length dependence of the photoabsorption peak wavelength and the excited-state lifetime of solvated electrons in primary alcohols.

Condensed-phase first-principles molecular dynamics simulations elucidate the presence of different electron trapping sites in liquid methanol and their roles in the formation, electronic transitions, and relaxation of solvated electrons.