Simulating Valence-to-Core X‑ray Emission Spectroscopy of Transition Metal Complexes with Time-Dependent Density Functional Theory

Valence-to-core (VtC) X-ray emission spectroscopy (XES) has emerged as a powerful technique for the structural characterization of complex organometallic compounds in realistic environments. Since the spectrum represents electronic transitions from the ligand molecular orbitals to the core holes of the metal centers, the approach is more chemically sensitive to the metal–ligand bonding character compared with conventional X-ray absorption techniques. In this paper we study how linear-response time-dependent density functional theory (LR-TDDFT) can be harnessed to simulate K-edge VtC X-ray emission spectra reliably. LR-TDDFT allows one to go beyond the single-particle picture that has been extensively used to simulate VtC-XES. We consider seven low- and high-spin model complexes involving chromium, manganese, and iron transition metal centers. Our results are in good agreement with experiment

Precursor Ion–Ion Aggregation in the Brust–Schiffrin Synthesis of Alkanethiol Nanoparticles

Tetraoctylammonium bromide is used in the Brust–Schiffrin nanoparticle synthesis to phase-transfer chloroaurate ions from the aqueous phase to the organic phase. While it is established that the quaternary ammonium complex self-associates in the organic phase, the actual self-assembled structure is poorly understood. We have confirmed the presence of ion–ion aggregates through quantitative ¹H nuclear magnetic resonance spectroscopy (NMR), pulsed field gradient, diffusion-ordered NMR (DOSY-NMR), and density functional theory (DFT) based NMR chemical shift calculations. Tetraoctylammonium complexes (TOA-X, where X = Br, Cl, AuCl_4–<i>x</i>Br_<i>x</i>, AuBr₄/Br, and AuBr₄/Cl/Br) were investigated to measure the extraction of water into deuterated chloroform. ¹H NMR- and DFT-based NMR shielding calculations indicated that deshielding of water is due to hydration of the anion and not the formation of the aqueous core of a reverse micelle. DOSY-NMR results were consistent with the formation of small aggregates at typical Brust–Schiffrin synthesis concentrations. The extent of aggregation correlated with the electronegativity of the anion and was analyzed with a modified, isodesmic, indefinite aggregation model. The substitution of bromoauric acid for chlororoauric acid at conditions emulating the Brust–Schiffrin synthesis in chloroform increased the aggregation of the quaternary ammonium complex. The increase in aggregation corresponded with an increase in the size of the produced nanoparticles from 4.3 to 4.6 nm. Understanding the self-assembly and supramolecular structure of precursors in the Brust–Schiffrin synthesis will enable further refinement of models describing the growth of noble metal nanoparticles

Charge-Transfer Versus Charge-Transfer-Like Excitations Revisited

Criteria to assess charge-transfer (CT) and CT-like character of electronic excitations are examined. Time-dependent density functional theory (TDDFT) calculations with non-hybrid, hybrid, and tuned long-range corrected (LC) functionals are compared with coupled-cluster (CC) benchmarks. The test set comprises an organic CT complex, two push–pull donor–acceptor chromophores, a cyanine dye, and several polycyclic aromatic hydrocarbons. Proper CT is easily identified. Excitations with significant density changes upon excitation within regions of close spatial proximity can also be diagnosed. For such excitations, the use of LC functionals in TDDFT sometimes leads to dramatic improvements of the singlet energies, similar to proper CT. It is shown that such CT-like excitations do not have the characteristics of physical charge transfer, and improvements with LC functionals may not be obtained for the right reasons. The TDDFT triplet excitation energies are underestimated for all systems, often severely. For the CT-like candidates, the singlet–triplet (S/T) separation changes from negative with a non-hybrid functional to positive with a tuned LC functional. For the cyanine, the S/T separation is systematically too large with TDDFT, leading to better error compensation for the singlet energy with a non-hybrid functional

Cation–Cation Interactions in [(UO₂)₂(OH)_<i>n</i>]^4–<i>n</i> Complexes

The structures and bonding of gas-phase [(UO₂)₂(OH)_<i>n</i>]^4–<i>n</i> (<i>n</i> = 2–6) complexes have been studied using density functional theory (DFT), MP2, and CCSD­(T) methods with particular emphasis on ground state structures featuring cation–cation interactions (CCIs) between the uranyl groups. An interesting trend is observed in the stabilities of members of this series of complexes. The structures of [(UO₂)₂(OH)₂]²⁺, [(UO₂)₂(OH)₄], and [(UO₂)₂(OH)₆]^2– featuring CCIs are found at higher energies (by 3–27 kcal/mol) in comparison to their conventional μ₂-dihydroxo structures. In contrast, the CCI structures of [(UO₂)₂(OH)₃]⁺ and [(UO₂)₂(OH)₅]⁻ are respectively degenerate with and lower in energy than the structures with the μ₂-dihydroxo format. The origin of this trend lies in the symmetry-based need to balance the coordination numbers and effective atomic charges of each uranium center. The calculated IR vibrational frequencies provide signature probes that can be used in differentiating the low-energy structures and in experimentally confirming the existence of the structures featuring CCIs

Entangled Valence Electron–Hole Dynamics Revealed by Stimulated Attosecond X‑ray Raman Scattering

We show that broadband X-ray pulses can create wavepackets of valence electrons and holes localized in the vicinity of a selected atom (nitrogen, oxygen, or sulfur in cysteine) by stimulated resonant Raman scattering. The subsequent dynamics reveals highly correlated motions of entangled electron and hole quasiparticles. This information goes beyond the time-dependent total charge density derived from X-ray diffraction

Curvature and Frontier Orbital Energies in Density Functional Theory

Perdew et al. discovered two different properties of exact Kohn–Sham density functional theory (DFT): (i) The exact total energy versus particle number is a series of linear segments between integer electron points. (ii) Across an integer number of electrons, the exchange-correlation potential “jumps” by a constant, known as the derivative discontinuity (DD). Here we show analytically that in both the original and the generalized Kohn–Sham formulation of DFT the two properties are two sides of the same coin. The absence of a DD dictates deviation from piecewise linearity, but the latter, appearing as curvature, can be used to correct for the former, thereby restoring the physical meaning of orbital energies. A simple correction scheme for any semilocal and hybrid functional, even Hartree–Fock theory, is shown to be effective on a set of small molecules, suggesting a practical correction for the infamous DFT gap problem. We show that optimally tuned range-separated hybrid functionals can inherently minimize <i>both</i> DD and curvature, thus requiring no correction, and that this can be used as a sound theoretical basis for novel tuning strategies

Modeling Optical Spectra of Large Organic Systems Using Real-Time Propagation of Semiempirical Effective Hamiltonians

We present an implementation of a time-dependent semiempirical method (INDO/S) in NWChem using real-time (RT) propagation to address, in principle, the entire spectrum of valence electronic excitations. Adopting this model, we study the UV/vis spectra of medium-sized systems such as P3B2 and <i>f</i>-coronene, and in addition much larger systems such as ubiquitin in the gas phase and the betanin chromophore in the presence of two explicit solvents (water and methanol). RT-INDO/S provides qualitatively and often quantitatively accurate results when compared with RT- TDDFT or experimental spectra. Even though we only consider the INDO/S Hamiltonian in this work, our implementation provides a framework for performing electron dynamics in large systems using semiempirical Hartree–Fock Hamiltonians in general

Simulating One-Photon Absorption and Resonance Raman Scattering Spectra Using Analytical Excited State Energy Gradients within Time-Dependent Density Functional Theory

A parallel implementation of analytical time-dependent density functional theory gradients is presented for the quantum chemistry program NWChem. The implementation is based on the Lagrangian approach developed by Furche and Ahlrichs. To validate our implementation, we first calculate the Stokes shifts for a range of organic dye molecules using a diverse set of exchange-correlation functionals (traditional density functionals, global hybrids, and range-separated hybrids) followed by simulations of the one-photon absorption and resonance Raman scattering spectrum of the phenoxyl radical, the well-studied dye molecule rhodamine 6G, and a molecular host–guest complex (TTF⊂CBPQT⁴⁺). The study of organic dye molecules illustrates that B3LYP and CAM-B3LYP generally give the best agreement with experimentally determined Stokes shifts unless the excited state is a charge transfer state. Absorption, resonance Raman, and fluorescence simulations for the phenoxyl radical indicate that explicit solvation may be required for accurate characterization. For the host–guest complex and rhodamine 6G, it is demonstrated that absorption spectra can be simulated in good agreement with experimental data for most exchange-correlation functionals. However, because one-photon absorption spectra generally lack well-resolved vibrational features, resonance Raman simulations are necessary to evaluate the accuracy of the exchange-correlation functional for describing a potential energy surface

Nonequilibrium Chemical Effects in Single-Molecule SERS Revealed by Ab Initio Molecular Dynamics Simulations

Recent developments in nanophotonics have paved the way for achieving significant advances in the realm of single-molecule chemical detection, imaging, and dynamics. In particular, surface-enhanced Raman scattering (SERS) is a powerful analytical technique that is now routinely used to identify the chemical identity of single molecules. Understanding how nanoscale physical and chemical processes affect single-molecule SERS spectra and selection rules is a challenging task and is still actively debated. Herein, we explore underappreciated chemical phenomena in ultrasensitive SERS. We observe a fluctuating excited electronic state manifold, governed by the conformational dynamics of a molecule (4,4′-dimercaptostilbene, DMS) interacting with a metallic cluster (Ag₂₀). This affects our simulated single-molecule SERS spectra; the time trajectories of a molecule interacting with its unique local environment dictates the relative intensities of the observable Raman-active vibrational states. Ab initio molecular dynamics of a model Ag₂₀–DMS system are used to illustrate both concepts in light of recent experimental results

Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT

We present a special symmetric Lanczos algorithm and a kernel polynomial method (KPM) for approximating the absorption spectrum of molecules within the linear response time-dependent density functional theory (TDDFT) framework in the product form. In contrast to existing algorithms, the new algorithms are based on reformulating the original non-Hermitian eigenvalue problem as a product eigenvalue problem and the observation that the product eigenvalue problem is self-adjoint with respect to an appropriately chosen inner product. This allows a simple symmetric Lanczos algorithm to be used to compute the desired absorption spectrum. The use of a symmetric Lanczos algorithm only requires half of the memory compared with the nonsymmetric variant of the Lanczos algorithm. The symmetric Lanczos algorithm is also numerically more stable than the nonsymmetric version. The KPM algorithm is also presented as a low-memory alternative to the Lanczos approach, but the algorithm may require more matrix-vector multiplications in practice. We discuss the pros and cons of these methods in terms of their accuracy as well as their computational and storage cost. Applications to a set of small and medium-sized molecules are also presented