Subspace system identification framework for the analysis of multimoded propagation of THz-transient signals

We provide a system identification framework for the analysis of THz-transient data. The subspace identification algorithm for both deterministic and stochastic systems is used to model the time-domain responses of structures under broadband excitation. Structures with additional time delays can be modelled within the state-space framework using additional state variables. We compare the numerical stability of the commonly used least-squares ARX models to that of the subspace N4SID algorithm by using examples of fourth-order and eighth-order systems under pulse and chirp excitation conditions. These models correspond to structures having two and four modes simultaneously propagating respectively. We show that chirp excitation combined with the subspace identification algorithm can provide a better identification of the underlying mode dynamics than the ARX model does as the complexity of the system increases. The use of an identified state-space model for mode demixing, upon transformation to a decoupled realization form is illustrated. Applications of state-space models and the N4SID algorithm to THz transient spectroscopy as well as to optical systems are highlighted.

Electronic transitions and bonding properties in a series of five-coordinate “16-electron” complexes [Mn(CO)3(L2)]− (L2=chelating redox-active π-donor ligand)

In this article we present for the first time accurate density functional theory (DFT) and time-dependent (TD) DFT data for a series of electronically unsaturated five-coordinate complexes [Mn(CO)(3)(L-2)](-), where L-2 stands for a chelating strong pi-donor ligand represented by catecholate, dithiolate, amidothiolate, reduced alpha-diimine (1,4-dialkyl-1,4-diazabutadiene (R-DAB), 2,2'-bipyridine) and reduced 2,2'-biphosphinine types. The single-crystal X-ray structure of the unusual compound [Na(BPY)][Mn(CO)(3)(BPY)]center dot Et2O and the electronic absorption spectrum of the anion [Mn(CO)(3)(BPY)](-) are new in the literature. The nature of the bidentate ligand determines the bonding in the complexes, which varies between two limiting forms: from completely pi-delocalized diamagnetic {(CO)(3)Mn-L-2}(-) for L-2 = alpha-diimine or biphosphinine, to largely valence-trapped {(CO)(3)Mn-1-L-2(2-)}(-) for L-2(2-) = catecholate, where the formal oxidation states of Mn and L-2 can be assigned. The variable degree of the pi-delocalization in the Mn(L-2) chelate ring is indicated by experimental resonance Raman spectra of [Mn(CO)(3)(L-2)](-) (L-2=3,5-di-tBu-catecholate and iPr-DAB), where accurate assignments of the diagnostically important Raman bands have been aided by vibrational analysis. The L-2 = catecholate type of complexes is known to react with Lewis bases (CO substitution, formation of six-coordinate adducts) while the strongly pi-delocalized complexes are inert. The five-coordinate complexes adopt usually a distorted square pyramidal geometry in the solid state, even though transitions to a trigonal bipyramid are also not rare. The experimental structural data and the corresponding DFT-computed values of bond lengths and angles are in a very good agreement. TD-DFT calculations of electronic absorption spectra of the studied Mn complexes and the strongly pi-delocalized reference compound [Fe(CO)(3)(Me-DAB)] have reproduced qualitatively well the experimental spectra. Analyses of the computed electronic transitions in the visible spectroscopic region show that the lowest-energy absorption band always contains a dominant (in some cases almost exclusive) contribution from a pi(HOMO) -> pi*(LUMO) transition within the MnL2 metallacycle. The character of this optical excitation depends strongly on the composition of the frontier orbitals, varying from a partial L-2 -> Mn charge transfer (LMCT) through a fully delocalized pi(MnL2) -> pi*(MnL2) situation to a mixed (CO)Mn -> L-2 charge transfer (LLCT/MLCT). The latter character is most apparent in the case of the reference complex [Fe(CO)(3)(Me-DAB)]. The higher-lying, usually strongly mixed electronic transitions in the visible absorption region originate in the three lower-lying occupied orbitals, HOMO - 1 to HOMO - 3, with significant metal-d contributions. Assignment of these optical excitations to electronic transitions of a specific type is difficult. A partial LLCT/MLCT character is encountered most frequently. The electronic absorption spectra become more complex when the chelating ligand L-2, such as 2,2'-bipyridine, features two or more closely spaced low-lying empty pi* orbitals.

Ultrafast charge separation in a photoreactive rhenium-appended porphyrin assembly monitored by picosecond transient infrared spectroscopy

Rhenium(bipyridine)(tricarbonyl)(picoline) units have been linked covalently to tetraphenylmetalloporphyrins of magnesium and zinc via an amide bond between the bipyridine and one phenyl substituent of the porphyrin. The resulting complexes, abbreviated as [Re(CO)(3)(Pic)Bpy-MgTPP][OTf] and [Re(CO)(3)(Pic)Bpy-ZnTPP][OTf], exhibit no signs of electronic interaction between the Re(CO)(3)(bpy) units and the metalloporphyrin units in their ground states. However, emission spectroscopy reveals solvent-dependent quenching of porphyrin emission on irradiation into the long-wavelength absorption bands localized on the porphyrin. The characteristics of the excited states have been probed by picosecond time-resolved absorption (TRVIS) spectroscopy and time-resolved infrared (TRIR) spectroscopy in nitrile solvents. The presence of the charge-separated state involving electron transfer from MgTPP or ZnTPP to Re(bpy) is signaled in the TRIR spectra by a low-frequency shift in the nu(CO) bands of the Re(CO)(3) moiety similar to that observed by spectroelectrochemical reduction. Long-wavelength excitation of [Re(CO)(3)(Pic)Bpy-MTPP][OTf] results in characteristic TRVIS spectra of the S-1 state of the porphyrin that decay with a time constant of 17 ps (M = Mg) or 24 ps (M = Zn). The IR bands of the CS state appear on a time scale of less than 1 ps (Mg) or ca. 5 ps (Zn) and decay giving way to a vibrationally excited (i.e., hot) ground state via back electron transfer. The IR bands of the precursors recover with a time constant of 35 ps (Mg) or 55 ps (Zn). The short lifetimes of the charge-transfer states carry implications for the mechanism of reaction in the presence of triethylamine.

A new interpretation of the bonding properties and UV–vis spectra of [M3(CO)12] clusters (M = Ru, Os): a TD-DFT study

DFT and TD-DFT calculations (ADF program) were performed in order to analyze the electronic structure of the [M-3(CO)(12)] clusters (M = Ru, Os) and interpret their electronic spectra. The highest occupied molecular orbitals are M-M bonding (sigma) involving different M-M bonds, both for Ru and Os. They participate in low-energy excitation processes and their depopulation should weaken M-M bonds in general. While the LUMO is M-NI and M-CO anti-bonding (sigma*), the next, higher-lying empty orbitals have a main contribution from CO (pi*) and either a small (Ru) or an almost negligible one (Os) from the metal atoms. The main difference between the two clusters comes from the different nature of these low-energy unoccupied orbitals that have a larger metal contribution in the case of ruthenium. The photochemical reactivity of the two clusters is reexamined and compared to earlier interpretations.

Excited states of nitro-polypyridine metal complexes and their ultrafast decay. Time-resolved IR absorption, spectroelectrochemistry, and TD-DFT calculations of fac-[Re(Cl)(CO)3(5-Nitro-1,10-phenanthroline)]

The lowest absorption band of fac-[Re(Cl)(CO)(3)(5-NO2-phen)] encompasses two close-lying MLCT transitions. The lower one is directed to LUMO, which is heavily localized on the NO2 group. The UV-vis absorption spectrum is well accounted for by TD-DFT (G03/PBEPBE1/CPCM), provided that the solvent, MeCN, is included in the calculations. Near-UV excitation of fac-[Re(Cl)(CO)(3)(5-NO2-phen)] populates a triplet metal to ligand charge-transfer excited state, (MLCT)-M-3, that was characterized by picosecond time-resolved IR spectroscopy. Large positive shifts of the v(CO) bands upon excitation (+70 cm(-1) for the A'(1) band) signify a very large charge separation between the Re(Cl)(CO)3 unit and the 5-NO2-phen ligand. Details of the excited-state character are revealed by TD-DFT calculated changes of electron density distribution. Experimental excited-state v(CO) wavenumbers agree well with those calculated by DFT. The (MLCT)-M-3 state decays with a ca. 10 ps lifetime (in MeCN) into another transient species, that was identified by TRIR and TD-DFT calculations as an intraligand (3)n pi* excited state, whereby the electron density is excited from the NO2 oxygen lone pairs to the pi* system of 5-NO2-phen. This state is short-lived, decaying to the ground state with a similar to 30 ps lifetime. The presence of an n pi* state seems to be the main factor responsible for the lack of emission and the very short lifetimes of 3 MLCT states seen in all d(6)-metal complexes of nitro-polypyridyl ligands. Localization of the excited electron density in the lowest (MLCT)-M-3 states parallels localization of the extra electron in the reduced state that is characterized by a very small negative shift of the v(CO) IR bands (-6 cm(-1) for A'(1)) but a large downward shift of the v(s)(NO2) IR band. The Re-Cl bond is unusually stable toward reduction, whereas the Cl ligand is readily substituted upon oxidation.

Photochromic dithienylethene derivatives containing Ru(II) or Os(II) metal units. Sensitized photocyclization from a triplet state

Efficient photocyclization from a low-lying triplet state is reported for a photochromic dithienylperfluorocyclopentene with Ru(bpy)(3) units attached via a phenylene linker to the thiophene rings. The ring-closure reaction in the nanosecond domain is sensitized by the metal complexes. Upon photoexcitation into the lowest Ru-to-bpy (MLCT)-M-1 state followed by intersystem crossing to emitting (MLCT)-M-3 states, photoreactive (IL)-I-3 states are populated by an efficient energy-transfer process. The involvement of these (IL)-I-3 states explains the quantum yield of the photocyclization, which is independent of the excitation wavelength but decreases strongly in the presence of dioxygen. This behavior differs substantially from the photocyclization of the nonemissive dithienylperfluorocyclopentene free ligand, which occurs from the lowest (IL)-I-1 state on a picosecond time scale and is insensitive to oxygen quenching. Cyclic voltammetric studies have also been performed to gain further insight into the energetics of the system. The very high photocyclization quantum yields, far above 0.5 in both cases, are ascribed to the strong steric repulsion between the bulky substituents on the dithienylperfluorocyclopentene bridge bearing the chelating bipyridine sites or the Ru(bpy)(3) moieties, forcing the system to adopt nearly exclusively the reactive antiparallel conformation. In contrast, replacement of both Ru(II) centers by Os(II) completely prevents the photocyclization reaction upon light excitation into the low-lying Os-to-bpy (MLCT)-M-1 state. The photoreaction can only be triggered by optical population of the higher lying (IL)-I-1 excited state of the central photochromic unit, but its yield is low due to efficient energy transfer to the luminescent lowest (MLCT)-M-3 state.

Rhenium-to-benzoylpyridine and rhenium-to-bipyridine MLCT excited states offac-[Re(Cl)(4-benzoylpyridine)2(CO)3] andfac-[Re(4-benzoylpyridine)(CO)3(bpy)]+: a time-resolved spectroscopic and spectroelectrochemical study

The lowest allowed electronic transition of fac-[Re(Cl)(CO)(3)(bopy)(2)] (bopy = 4-benzoylpyridine) has a Re --> bopy MLCT character, as revealed by UV-vis and stationary resonance Raman spectroscopy. Accordingly, the lowest-lying, long-lived, excited state is Re --> bopy (MLCT)-M-3. Electronic depopulation of the Re(CO)(3) unit and population of a bopy pi* orbital upon excitation are evident by the upward shift of v(Cequivalent toO) vibrations and a downward shift of the ketone v(C=O) vibration, respectively, seen in picosecond time-resolved IR spectra. Moreover, reduction of a single bopy ligand in the (MLCT)-M-3 excited state is indicated by time-resolved visible and resonance Raman (TR3) spectra that show features typical of bopy(.-). In contrast, the lowest allowed electronic transition and lowest-lying excited state of a new complex fac-[Re(bopy)(CO)(3)(bpy)](+) (bpy = 2,2'-bipyridine) have been identified as Re --> bpy MLCT with no involvement of the bopy ligand, despite the fact that the first reduction of this complex is bopy-localized, as was proven spectroelectrochemically. This is a rare case in which the localizations of the lowest MLCT excitation and the first reduction are different. (MLCT)-M-3 excited states of both fac-[Re(Cl)(CO)(3)(bopy)(2)] and fac-[Re(bopy)(CO)(3)(bpy)](+) are initially formed vibrationally hot. Their relaxation is manifested by picosecond dynamic shifts of v(Cequivalent toO) IR bands. The X-ray structure of fac-[Re(bopy)(CO)(3)(bpy)](PF6CH3CN)-C-. has been determined.