We discuss our implementation and application of time-dependent density functional theory (TDDFT) to core-level near-edge absorption spectroscopy, using both linear-response (LR) and real-time (RT) approaches. We briefly describe our restricted excitation window TDDFT (REW-TDDFT) approach for core excitations, which has also been reported by other groups. This is followed by a detailed discussion of real-time TDDFT techniques tailored to core excitations, including obtaining spectral information through delta-function excitation, postprocessing time-dependent signals, and resonant excitation through quasi-monochromatic excitation. We present results for the oxygen K-edge of water and carbon monoxide; the carbon K-edge of carbon monoxide; the ruthenium L3-edge for the hexaamminerutheium(III) ion, including scalar relativistic corrections via the zeroth order regular approximation (ZORA); and the carbon and fluorine K-edges for a series of fluorobenzenes. In all cases, the calculated spectra are found to be in reasonable agreement with experimental results, requiring only a uniform shift ranging from -4 eV to +19 eV, i.e., on the order of a few percent of the excitation energy. Real-time TDDFT visualization of excited state charge densities is used to visually examine the nature of each excitation, which gives insight into the effects of atoms bound to the absorbing center.

In this paper we present a time-domain time-dependent density functional theory (TDDFT) approach to calculate frequency-dependent polarizability and hyperpolarizabilities. In this approach, the electronic degrees of freedom are propagated within the density matrix based TDDFT framework using the efficient modified midpoint and unitary transformation algorithm. We use monochromatic waves as external perturbations and apply the finite field method to extract various orders of the time-dependent dipole moment. By fitting each order of time-dependent dipole to sinusoidal waves with harmonic frequencies, one can obtain the corresponding (hyper)polarizability tensors. This approach avoids explicit Fourier transform and therefore does not require long simulation time. The method is illustrated with application to the optically active organic molecule para-nitroaniline, of which the frequency-dependent polarizability α(-ω; ω), second-harmonic generation β(-2ω; ω, ω), optical rectification β(0; -ω, ω), third-harmonic generation γ(-3ω; ω, ω, ω), and degenerate four-wave mixing γ(-ω; ω, ω, -ω) are calculated.

This study uses transient X-ray absorption (XA) spectroscopy and time-dependent density functional theory (TD-DFT) to directly visualize the charge density around the metal atom and the surrounding ligands following an ultrafast metal-to-ligand charge-transfer (MLCT) process in the widely used Ru(II) solar cell dye, Ru(dcbpy)2(NCS)2 (termed N3). We measure the Ru L-edge XA spectra of the singlet ground ((1)A1) and the transient triplet ((3)MLCT) excited state of N3(4-) and perform TD-DFT calculations of 2p core-level excitations, which identify a unique spectral signature of the electron density on the NCS ligands. We find that the Ru 2p, Ru eg, and NCS π* orbitals are stabilized by 2.0, 1.0, and 0.6 eV, respectively, in the transient (3)MLCT state of the dye. These results highlight the role of the NCS ligands in governing the oxidation state of the Ru center.

Ruthenium L3-edge X-ray absorption (XA) spectroscopy probes unoccupied 4d orbitals of the metal atom and is increasingly being used to investigate the local electronic structure in ground and excited electronic states of Ru complexes. The simultaneous development of computational tools for simulating Ru L3-edge spectra is crucial for interpreting the spectral features at a molecular level. This study demonstrates that time-dependent density functional theory (TDDFT) is a viable and predictive tool for simulating ruthenium L3-edge XA spectroscopy. We systematically investigate the effects of exchange correlation functional and implicit and explicit solvent interactions on a series of Ru(II) and Ru(III) complexes in their ground and electronic excited states. The TDDFT simulations reproduce all of the experimentally observed features in Ru L3-edge XA spectra within the experimental resolution (0.4 eV). Our simulations identify ligand-specific charge transfer features in complicated Ru L3-edge spectra of [Ru(CN)6](4-) and Ru(II) polypyridyl complexes illustrating the advantage of using TDDFT in complex systems. We conclude that the B3LYP functional most accurately predicts the transition energies of charge transfer features in these systems. We use our TDDFT approach to simulate experimental Ru L3-edge XA spectra of transition metal mixed-valence dimers of the form [(NC)5M(II)-CN-Ru(III)(NH3)5](-) (where M = Fe or Ru) dissolved in water. Our study determines the spectral signatures of electron delocalization in Ru L3-edge XA spectra. We find that the inclusion of explicit solvent molecules is necessary for reproducing the spectral features and the experimentally determined valencies in these mixed-valence complexes. This study validates the use of TDDFT for simulating Ru 2p excitations using popular quantum chemistry codes and providing a powerful interpretive tool for equilibrium and ultrafast Ru L3-edge XA spectroscopy.

We have built a laboratory spectrometer for X-ray emission spectroscopy. The instrument is employed in catalysis research. The key component is a von Hamos full cylinder optic with Highly Annealed Pyrolytic Graphite (HAPG) as a dispersive element. With this very efficient optic, the spectrometer subtends an effective solid angle of detection of around 1 msr, allowing for the analysis of dilute samples. The resolving power of the spectrometer is approximately E/∆E = 4000, with an energy range of ∼2.3 keV-10 keV. The instrument and its characteristics are described herein. Further, a comparison with a prototype spectrometer, based on the same principle, shows the substantial improvement in the spectral resolution and energy range for the present setup. The paper concludes with a discussion of sample handling. A compilation of HAPG fundamentals and related publications are given in a brief Appendix.

Time-resolved nitrogen-1s spectroscopy in the X-ray water window is presented as a novel probe of metal-ligand interactions and transient states in nitrogen-containing organic compounds. New information on iron(II) polypyridyl complexes via nitrogen core-level transitions yields insight into the charge density of the photoinduced high-spin state by comparing experimental results with time-dependent density functional theory. In the transient high-spin state, the 3d electrons of the metal center are more delocalized over the nearest-neighbor nitrogen atoms despite increased bond lengths. Our findings point to a strong coupling of electronic states with charge-transfer character, facilitating the ultrafast intersystem crossing cascade in these systems. The study also highlights the importance of local charge density measures to complement chemical interaction concepts of charge donation and back-bonding with molecular orbital descriptions of states.

We study photoinduced metal-nitrosyl linkage isomerism in sodium nitroprusside (Na(2)[Fe(II)(CN)(5)NO]·2H(2)O, SNP) dissolved in methanol using picosecond transient infrared (IR) spectroscopy. The high sensitivity of this technique allows the simultaneous observation of two known metastable (MS) iron-nitrosyl linkage isomers of SNP, [Fe(II)(CN)(5)(η(1)-ON)](2-) (MS1) and [Fe(II)(CN)(5)(η(2)-NO)](2-) (MS2), at room temperature. The transient population of free nitrosyl radicals (NO·) is also measured in the sample solution. These three transient species are detected using their distinct nitrosyl stretching frequencies at 1794 cm(-1) (MS1), 1652 cm(-1) (MS2), and 1851 cm(-1) (NO·). The metastable isomers and NO· are formed on a subpicosecond time scale and have lifetimes greater than 100 ns. A UV (400 nm)-pump power dependence study reveals that MS1 can be formed with one photon, while MS2 requires two photons to be populated at room temperature in solution. Other photodissociation products including cyanide ion, Prussian blue, and [Fe(III)(CN)(5)(CH(3)OH)](2-) are observed. We develop a photochemical kinetic scheme to model our data, and the analysis reveals that photoisomerization and photodissociation of the metal-NO moiety are competing photochemical pathways in SNP dissolved in methanol at room temperature. Based on the analysis, the solvent-associated Fe(III) species and Prussian blue form on a 130 and 320 ps time scale, respectively. The simultaneous detection and characterization of photoinduced linkage isomerism (MS1 and MS2) and photodissociation of the metal-NO bond in SNP highlights the importance of understanding the role played by metastable metal-nitrosyl linkage isomers in the photochemistry of metal-nitrosyl compounds in chemistry and biology.

Spectroscopic probes of the electronic structure of transition metal-containing materials are invaluable to the design of new molecular catalysts and magnetic systems. Herein, we show that 2p3d resonant inelastic X-ray scattering (RIXS) can be used to observe both spin-allowed and (in the V case) spin-forbidden d-d excitation energies in molecular vanadium complexes. The spin-allowed d-d excitation energies determined by 2p3d RIXS are in good agreement with available optical data. In V(acac), a previously undetected spin-forbidden singlet state has been observed. The presence of this feature provides a ligand-field independent signature of V. It is also shown that d-d excitations may be obtained for porphyrin complexes. This is generally prohibitive using optical approaches due to intense porphyrin π-to-π* transitions. In addition, the intensities of charge-transfer features in 2p3d RIXS spectroscopy are shown to be a clear indication of metal-ligand covalency. The utility of 2p3d RIXS for future studies of complex inorganic systems is highlighted.