Calculating excited state properties using Kohn-Sham density functional theory

Fractional-Electron and Transition-Potential Methods for Core-to-Valence Excitation Energies Using Density Functional Theory

Methods for computing X-ray absorption spectra based on a constrained core hole (possibly containing a fractional electron) are examined. These methods are based on Slater's transition concept and its generalizations, wherein core-to-valence excitation energies are determined using Kohn-Sham orbital energies. Methods examined here avoid promoting electrons beyond the lowest unoccupied molecular orbital, facilitating robust convergence. Variants of these ideas are systematically tested, revealing a best-case accuracy of 0.3-0.4 eV (with respect to experiment) for K-edge transition energies. Absolute errors are much larger for higher-lying near-edge transitions but can be reduced below 1 eV by introducing an empirical shift based on a charge-neutral transition-potential method, in conjunction with functionals such as SCAN, SCAN0, or B3LYP. This procedure affords an entire excitation spectrum from a single fractional-electron calculation, at the cost of ground-state density functional theory and without the need for state-by-state calculations. This shifted transition-potential approach may be especially useful for simulating transient spectroscopies or in complex systems where excited-state Kohn-Sham calculations are challenging.

Atomic-scale observation of solvent reorganization influencing photoinduced structural dynamics in a copper complex photosensitizer

Photochemical reactions in solution are governed by a complex interplay between transient intramolecular electronic and nuclear structural changes and accompanying solvent rearrangements. State-of-the-art time-resolved X-ray solution scattering has emerged in the last decade as a powerful technique to observe solute and solvent motions in real time. However, disentangling solute and solvent dynamics and how they mutually influence each other remains challenging. Here, we simultaneously measure femtosecond X-ray emission and scattering to track both the intramolecular and solvation structural dynamics following photoexcitation of a solvated copper photosensitizer. Quantitative analysis assisted by molecular dynamics simulations reveals a two-step ligand flattening strongly coupled to the solvent reorganization, which conventional optical methods could not discern. First, a ballistic flattening triggers coherent motions of surrounding acetonitrile molecules. In turn, the approach of acetonitrile molecules to the copper atom mediates the decay of intramolecular coherent vibrations and induces a further ligand flattening. These direct structural insights reveal that photoinduced solute and solvent motions can be intimately intertwined, explaining how the key initial steps of light harvesting are affected by the solvent on the atomic time and length scale. Ultimately, this work takes a step forward in understanding the microscopic mechanisms of the bidirectional influence between transient solvent reorganization and photoinduced solute structural dynamics.

Synthesis, Structure, and Thermal Properties of Volatile Group 11 Triazenides as Potential Precursors for Vapor Deposition

Group 11 thin films are desirable as interconnects in microelectronics. Although many M-N-bonded Cu precursors have been explored for vapor deposition, there is currently a lack of suitable Ag and Au derivatives. Herein, we present monovalent Cu, Ag, and Au 1,3-di-tert-butyltriazenides that have potential for use in vapor deposition. Their thermal stability and volatility rival that of current state-of-the-art group 11 precursors with bidentate M-N-bonded ligands. Solution-state thermolysis of these triazenides yielded polycrystalline films of elemental Cu, Ag, and Au. The compounds are therefore highly promising as single-source precursors for vapor deposition of coinage metal films.

Novel chiral Schiff base Palladium(II), Nickel(II), Copper(II) and Iron(II) complexes: Synthesis, characterization, anticancer activity and molecular docking studies

In this study, two chiral Schiff base ligands (L1 and L2) were synthesized from the condensation reaction of (S)-2-amino-3-phenyl-1-propanol with 2-hydroxybenzaldehyde and 2-hydroxy-1-naphthaldehyde as metal precursors for the preparation of transition metal complexes with Pd(II), Fe(II), Ni(II) and Cu(II). The compounds were characterized by using X-ray (for L1-Pd(II)), NMR, FT-IR, UV-Vis, magnetic susceptibility, molar conductivity, and elemental analysis. The in vitro cytotoxic effects of ligands (L1 and L2) and their metal complexes on colon cancer cells (DLD-1), breast cancer cells (MDA-MB-231) and healthy lung human cell lines were investigated by using the 3-(4,5-dimethylthiazol-2-yl)-2,5‑diphenyl tetrazolium bromide (MTT) assay. Among the synthesized compounds, L1-Pd(II) was particularly found to be the most potent anticancer drug candidate in this series with IC50 values of 4.07, and 9.97 µM in DLD-1 and MDA-MB-231 cell lines, respectively. In addition, molecular docking results indicate that Glu122, Asn103, Ala104, Lys126, Phe114, Leu123, and Lys126 amino acids are the binding site of the colon cancer antigen protein, in which the most active complex, L1-Pd(II) can inhibit the current target.

Static Electron Correlation in Anharmonic Molecular Vibrations: A Hybrid TAO-DFT Study

Hybrid thermally-assisted-occupation density functional theory is used to examine the effects of static electron correlation on the prediction of a benchmark set of experimentally observed molecular vibrational frequencies. The B3LYP and B97-1 thermally-assisted-occupation measure of static electron correlation is important for describing the vibrations of many of the molecules that make up several popular test sets of experimental data. Shifts are seen for known multireference systems and for many molecules containing atoms from the second row of the periodic table of elements. Several molecules only show significant shifts in select vibrational modes, and significant improvements are seen for the prediction of hydrogen stretching frequencies throughout the test set.

Comparison of Linear Response Theory, Projected Initial Maximum Overlap Method, and Molecular Dynamics-Based Vibronic Spectra: The Case of Methylene Blue

The simulation of optical spectra is essential to molecular characterization and, in many cases, critical for interpreting experimental spectra. The most common method for simulating vibronic absorption spectra relies on the geometry optimization and computation of normal modes for ground and excited electronic states. In this report, we show that the utilization of such a procedure within an adiabatic linear response (LR) theory framework may lead to state mixings and a breakdown of the Born-Oppenheimer approximation, resulting in a poor description of absorption spectra. In contrast, computing excited states via a self-consistent field method in conjunction with a maximum overlap model produces states that are not subject to such mixings. We show that this latter method produces vibronic spectra much more aligned with vertical gradient and molecular dynamics (MD) trajectory-based approaches. For the methylene blue chromophore, we compare vibronic absorption spectra computed with the following: an adiabatic Hessian approach with LR theory-optimized structures and normal modes, a vertical gradient procedure, the Hessian and normal modes of maximum overlap method-optimized structures, and excitation energy time-correlation functions generated from an MD trajectory. Because of mixing between the bright S₁ and dark S₂ surfaces near the S₁ minimum, computing the adiabatic Hessian with LR theory and time-dependent density functional theory with the B3LYP density functional predicts a large vibronic shoulder for the absorption spectrum that is not present for any of the other methods. Spectral densities are analyzed and we compare the behavior of the key normal mode that in LR theory strongly couples to the optical excitation while showing S₁/S₂ state mixings. Overall, our study provides a note of caution in computing vibronic spectra using the excited-state adiabatic Hessian of LR theory-optimized structures and also showcases three alternatives that are less sensitive to adiabatic state mixing effects.

The ΔSCF method for non-adiabatic dynamics of systems in the liquid phase

Computational studies of ultrafast photoinduced processes give valuable insights into the photochemical mechanisms of a broad range of compounds. In order to accurately reproduce, interpret, and predict experimental results, which are typically obtained in a condensed phase, it is indispensable to include the condensed phase environment in the computational model. However, most studies are still performed in vacuum due to the high computational cost of state-of-the-art non-adiabatic molecular dynamics (NAMD) simulations. The quantum mechanical/molecular mechanical (QM/MM) solvation method has been a popular model to perform photodynamics in the liquid phase. Nevertheless, the currently used QM/MM embedding techniques cannot sufficiently capture all solute-solvent interactions. In this Perspective, we will discuss the efficient ΔSCF electronic structure method and its applications with respect to the NAMD of solvated compounds, with a particular focus on explicit quantum mechanical solvation. As more research is required for this method to reach its full potential, some challenges and possible directions for future research are presented as well.

Synthesis, Characterization, and Thermal Study of Divalent Germanium, Tin, and Lead Triazenides as Potential Vapor Deposition Precursors

Only a few M-N bonded divalent group 14 precursors are available for vapor deposition, in particular for Ge and Pb. A majority of the reported precursors are dicoordinated with the Sn(II) amidinates, the only tetracoordinated examples. No Ge(II) and Pb(II) amidinates suitable for vapor deposition have been demonstrated. Herein, we present tetracoordinated Ge(II), Sn(II), and Pb(II) complexes bearing two sets of chelating 1,3-di-tert-butyltriazenide ligands. These compounds are thermally stable, sublime quantitatively between 60 and 75 °C (at 0.5 mbar), and show ideal single-step volatilization by thermogravimetric analysis.

Reduced Two-Electron Interactions in Anharmonic Molecular Vibrational Calculations Involving Localized Normal Coordinates

Spatially localized vibrational normal mode coordinates are shown to reduce the importance of calculating the full set of two-electron terms in the molecular electronic Schrödinger equation. Electron correlation and dispersion interactions become less significant in (E,E)-1,3,5,7-octatetraene vibrational self-consistent field calculations when displacing remote atoms along multiple coordinates. Electron correlation interactions between spatially remote modes are also found to be less important compared to their corresponding uncorrelated interaction terms. Attenuation of the Coulomb operator indicates that the two-electron terms between remote electrons become less important for accurately describing the strongly contributing mode-coupling terms between sets of localized vibrational modes.

Synthesis and Thermal Study of Hexacoordinated Aluminum(III) Triazenides for Use in Atomic Layer Deposition

Amidinate and guanidinate ligands have been used extensively to produce volatile and thermally stable precursors for atomic layer deposition. The triazenide ligand is relatively unexplored as an alternative ligand system. Herein, we present six new Al(III) complexes bearing three sets of a 1,3-dialkyltriazenide ligand. These complexes volatilize quantitatively in a single step with onset volatilization temperatures of ∼150 °C and 1 Torr vapor pressures of ∼134 °C. Differential scanning calorimetry revealed that these Al(III) complexes exhibited exothermic events that overlapped with the temperatures of their mass loss events in thermogravimetric analysis. Using quantum chemical density functional theory computations, we found a decomposition pathway that transforms the relatively large hexacoordinated Al(III) precursor into a smaller dicoordinated complex. The pathway relies on previously unexplored interligand proton migrations. These new Al(III) triazenides provide a series of alternative precursors with unique thermal properties that could be highly advantageous for vapor deposition processes of Al containing materials.

Six aluminum(III) 1,3-dialkyltriazenides were synthesized and their thermal properties explored. The compounds were purified by recrystallization and could be easily sublimed. Thermogravimetric analysis of compounds showed that all, except one, gave a single step evaporation with onset volatilization temperatures of ∼150 °C. DFT calculations revealed a unique decomposition pathway that leads to a small and more reactive Al species that would be highly advantageous for the surface reactions of atomic layer deposition.

Simulation of vibrationally resolved absorption spectra of neutral and cationic polyaromatic hydrocarbons

The identification of the carriers of the absorption features associated with the diffuse interstellar bands (DIBs) is a long-standing problem in astronomical spectroscopy. Computational simulations can contribute to the assignment of the carriers of DIBs since variations in molecular structure and charge state can be studied more readily than through experimental measurements. Polyaromatic hydrocarbons have been proposed as potential carriers of these bands, and it is shown that simulations based upon density functional theory and time-dependent density functional theory calculations can describe the vibrational structure observed in experiment for neutral and cationic naphthalene and pyrene. The vibrational structure arises from a small number of vibrational modes involving in-plane atomic motions, and the Franck–Condon–Herzberg–Teller approximation improves the predicted spectra in comparison with the Franck–Condon approximation. The study also highlights the challenges for the calculations to enable the assignment in the absence of experimental data, namely prediction of the energy separation between the different electronic states to a sufficient level of accuracy and performing vibrational analysis for higher-lying electronic states.

Neutral excitation density-functional theory: an efficient and variational first-principles method for simulating neutral excitations in molecules

We introduce neutral excitation density-functional theory (XDFT), a computationally light, generally applicable, first-principles technique for calculating neutral electronic excitations. The concept is to generalise constrained density functional theory to free it from any assumptions about the spatial confinement of electrons and holes, but to maintain all the advantages of a variational method. The task of calculating the lowest excited state of a given symmetry is thereby simplified to one of performing a simple, low-cost sequence of coupled DFT calculations. We demonstrate the efficacy of the method by calculating the lowest single-particle singlet and triplet excitation energies in the well-known Thiel molecular test set, with results which are in good agreement with linear-response time-dependent density functional theory (LR-TDDFT). Furthermore, we show that XDFT can successfully capture two-electron excitations, in principle, offering a flexible approach to target specific effects beyond state-of-the-art adiabatic-kernel LR-TDDFT. Overall the method makes optical gaps and electron-hole binding energies readily accessible at a computational cost and scaling comparable to that of standard density functional theory. Owing to its multiple qualities beneficial to high-throughput studies where the optical gap is of particular interest; namely broad applicability, low computational demand, and ease of implementation and automation, XDFT presents as a viable candidate for research within materials discovery and informatics frameworks.

Ultrafast nonadiabatic dynamics probed by nitrogen K-edge absorption spectroscopy

Quantum dynamics simulations are used to simulate the ultrafast X-ray Absorption Near-Edge Structure (XANES) spectra of photoexcited pyrazine including two strongly coupled electronically excited states and four normal mode degrees of freedom.

Probing ultrafast C-Br bond fission in the UV photochemistry of bromoform with core-to-valence transient absorption spectroscopy

UV pump-extreme UV (XUV) probe femtosecond transient absorption spectroscopy is used to study the 268 nm induced photodissociation dynamics of bromoform (CHBr₃). Core-to-valence transitions at the Br(3d) absorption edge (∼70 eV) provide an atomic scale perspective of the reaction, sensitive to changes in the local valence electronic structure, with ultrafast time resolution. The XUV spectra track how the singly occupied molecular orbitals of transient electronic states develop throughout the C-Br bond fission, eventually forming radical Br and CHBr₂ products. Complementary ab initio calculations of XUV spectral fingerprints are performed for transient atomic arrangements obtained from sampling excited-state molecular dynamics simulations. C-Br fission along an approximately C S symmetrical reaction pathway leads to a continuous change of electronic orbital characters and atomic arrangements. Two timescales dominate changes in the transient absorption spectra, reflecting the different characteristic motions of the light C and H atoms and the heavy Br atoms. Within the first 40 fs, distortion from C 3 v symmetry to form a quasiplanar CHBr₂ by the displacement of the (light) CH moiety causes significant changes to the valence electronic structure. Displacement of the (heavy) Br atoms is delayed and requires up to ∼300 fs to form separate Br + CHBr₂ products. We demonstrate that transitions between the valence-excited (initial) and valence + core-excited (final) state electronic configurations produced by XUV absorption are sensitive to the localization of valence orbitals during bond fission. The change in valence electron-core hole interaction provides a physical explanation for spectral shifts during the process of bond cleavage.

Excited-State Potential Energy Surfaces, Conical Intersections, and Analytical Gradients from Ground-State Density Functional Theory

Kohn-Sham density functional theory (KS-DFT) has been a well-established theoretical foundation for ground-state electronic structure and has achieved great success in practical calculations. Recently, utilizing the eigenvalues from KS or generalized KS (GKS) calculations as an approximation to the quasiparticle energies, our group demonstrated a method to calculate the excitation energies from (G)KS calculation on the ground-state ( N - 1)-electron system. This method is now called QE-DFT (quasiparticle energies from DFT). In this work, we extend this QE-DFT method to describe excited-state potential energy surfaces (PESs), conical intersections, and the analytical gradients of excited-state PESs. The analytical gradients were applied to perform geometry optimization for excited states. In conjunction with several commonly used density functional approximations, QE-DFT can yield PESs in the vicinity of the equilibrium structure with accuracy similar to that from time-dependent DFT (TD-DFT). Furthermore, it describes conical intersection well, in contrast to TD-DFT. Good results for geometry optimization, especially bond length, of low-lying excitations for 14 small molecules are presented. The capability of describing excited-state PESs, conical intersections, and analytical gradients from QE-DFT and its efficiency based on just ground-state DFT calculations should be of great interest for describing photochemical and photophysical processes in complex systems.

Quantum chemical calculations of tryptophan → heme electron and excitation energy transfer rates in myoglobin

The development of optical multidimensional spectroscopic techniques has opened up new possibilities for the study of biological processes. Recently, ultrafast two-dimensional ultraviolet spectroscopy experiments have determined the rates of tryptophan → heme electron transfer and excitation energy transfer for the two tryptophan residues in myoglobin (Consani et al., Science, 2013, 339, 1586). Here, we show that accurate prediction of these rates can be achieved using Marcus theory in conjunction with time-dependent density functional theory. Key intermediate residues between the donor and acceptor are identified, and in particular the residues Val68 and Ile75 play a critical role in calculations of the electron coupling matrix elements. Our calculations demonstrate how small changes in structure can have a large effect on the rates, and show that the different rates of electron transfer are dictated by the distance between the heme and tryptophan residues, while for excitation energy transfer the orientation of the tryptophan residues relative to the heme is important. © 2017 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Femtosecond x-ray spectroscopy of an electrocyclic ring-opening reaction

The ultrafast light-activated electrocyclic ring-opening reaction of 1,3-cyclohexadiene is a fundamental prototype of photochemical pericyclic reactions. Generally, these reactions are thought to proceed through an intermediate excited-state minimum (the so-called pericyclic minimum), which leads to isomerization via nonadiabatic relaxation to the ground state of the photoproduct. Here, we used femtosecond (fs) soft x-ray spectroscopy near the carbon K-edge (~284 electron volts) on a tabletop apparatus to directly reveal the valence electronic structure of this transient intermediate state. The core-to-valence spectroscopic signature of the pericyclic minimum observed in the experiment was characterized, in combination with time-dependent density functional theory calculations, to reveal overlap and mixing of the frontier valence orbital energy levels. We show that this transient valence electronic structure arises within 60 ± 20 fs after ultraviolet photoexcitation and decays with a time constant of 110 ± 60 fs.

Intermediate vibrational coordinate localization with harmonic coupling constraints

Optimized normal coordinates can significantly improve the speed and accuracy of vibrational frequency calculations. However, over-localization can occur when using unconstrained spatial localization techniques. The unintuitive mixtures of stretching and bending coordinates that result can make interpreting spectra more difficult and also cause artificial increases in mode-coupling during anharmonic calculations. Combining spatial localization with a constraint on the coupling between modes can be used to generate coordinates with properties in-between the normal and fully localized schemes. These modes preserve the diagonal nature of the mass-weighted Hessian matrix to within a specified tolerance and are found to prevent contamination between the stretching and bending vibrations of the molecules studied without a priori classification of the different types of vibration present. Relaxing the constraint can also be used to identify which normal modes form specific groups of localized modes. The new coordinates are found to center on more spatially delocalized functional groups than their fully localized counterparts and can be used to tune the degree of vibrational correlation energy during anharmonic calculations.

Examining the impact of harmonic correlation on vibrational frequencies calculated in localized coordinates

Carefully choosing a set of optimized coordinates for performing vibrational frequency calculations can significantly reduce the anharmonic correlation energy from the self-consistent field treatment of molecular vibrations. However, moving away from normal coordinates also introduces an additional source of correlation energy arising from mode-coupling at the harmonic level. The impact of this new component of the vibrational energy is examined for a range of molecules, and a method is proposed for correcting the resulting self-consistent field frequencies by adding the full coupling energy from connected pairs of harmonic and pseudoharmonic modes, termed vibrational self-consistent field (harmonic correlation). This approach is found to lift the vibrational degeneracies arising from coordinate optimization and provides better agreement with experimental and benchmark frequencies than uncorrected vibrational self-consistent field theory without relying on traditional correlated methods.

Experimental and theoretical XPS and NEXAFS studies of N-methylacetamide and N-methyltrifluoroacetamide

Experimental and theoretical spectra of N-methylacetamide and N-methyltrifluoroacetamide at the K-edges are reported.

Modelling excited states of weakly bound complexes with density functional theory

Different dispersion correction parameters are required to describe the interaction when the molecule is in an excited Rydberg state.