X-ray Absorption in Insulators with Non-Hermitian Real-Time Time-Dependent Density Functional Theory

A DFT/MRCI Hamiltonian parameterized using only ab initio data. II. Core-excited states

A newly parameterized combined density functional theory and multi-reference configuration interaction (DFT/MRCI) Hamiltonian, termed core-valence separation (CVS)-QE12, is defined for the computation of K-shell core-excitation and core-ionization energies. This CVS counterpart to the recently reported QE8 Hamiltonian [Costain et al., J. Chem. Phys, 160, 224106 (2024)] is parameterized by fitting to benchmark quality ab initio data. The definition of the CVS-QE12 and QE8 Hamiltonians differ from previous CVS-DFT/MRCI parameterizations in three primary ways: (i) the replacement of the BHLYP exchange-correlation functional with QTP17 to yield a balanced description of both core and valence excitation energies, (ii) the adoption of a new, three-parameter damping function, and (iii) the introduction of separate scaling of the core-valence and valence-valence Coulombic interactions. Crucially, the parameters of the CVS-QE12 Hamiltonian are obtained via fitting exclusively to highly accurate ab initio vertical core-excitation and ionization energies computed at the CVS-EOM-CCSDT level of theory. The CVS-QE12 Hamiltonian is validated against further benchmark computations and is found to furnish K-edge core vertical excitation and ionization energies exhibiting absolute errors ≤0.5 eV at low computational cost.

Modeling Intermolecular Coulombic Decay with Non-Hermitian Real-Time Time-Dependent Density Functional Theory

In this work, we investigate the capability of using real-time time-dependent density functional theory (RT-TDDFT) in conjunction with a complex absorbing potential (CAP) to simulate the intermolecular Coulombic decay (ICD) processes following the ionization of an inner-valence electron. We examine the ICD dynamics in a series of noncovalent bonded dimer systems, including hydrogen-bonded and purely van der Waals (VdW)-bonded systems. In comparison to previous work, we show that RT-TDDFT simulations with a CAP correctly capture the ICD phenomenon in systems exhibiting a stronger binding energy. The calculated time scales for ICD of the studied systems are in the range of 5-50 fs, in agreement with previous studies. However, there is a breakdown in the accuracy of the methodology for the pure VdW-bonded systems. Overall, the presented RT-TDDFT/CAP methodology provides a powerful tool for differentiating between competing electronic relaxation pathways following inner-valence or core ionization without necessitating any a priori assumptions.

Simulating ultrafast transient absorption spectra from first principles using a time-dependent configuration interaction probe

Transient absorption spectroscopy (TAS) is among the most common ultrafast photochemical experiments, but its interpretation remains challenging. In this work, we present an efficient and robust method for simulating TAS signals from first principles. Excited-state absorption and stimulated emission (SE) signals are computed using time-dependent complete active space configuration interaction (TD-CASCI) simulations, leveraging the robustness of time-domain simulation to minimize electronic structure failure. We demonstrate our approach by simulating the TAS signal of 1'-hydroxy-2'-acetonapthone (HAN) from ab initio multiple spawning nonadiabatic molecular dynamics simulations. Our results are compared to gas-phase TAS data recorded from both jet-cooled (T ∼ 40 K) and hot (∼403 K) molecules via cavity-enhanced TAS (CE-TAS). Decomposition of the computed spectrum allows us to assign a rise in the SE signal to excited-state proton transfer and the ultimate decay of the signal to relaxation through a twisted conical intersection. The total cost of computing the observable signal (∼1700 graphics processing unit hours for ∼4 ns of electron dynamics) was markedly less than that of performing the ab initio multiple spawning calculations used to compute the underlying nonadiabatic dynamics.

Efficient exact exchange using Wannier functions and other related developments in planewave-pseudopotential implementation of RT-TDDFT

The plane-wave pseudopotential (PW-PP) formalism is widely used for the first-principles electronic structure calculation of extended periodic systems. The PW-PP approach has also been adapted for real-time time-dependent density functional theory (RT-TDDFT) to investigate time-dependent electronic dynamical phenomena. In this work, we detail recent advances in the PW-PP formalism for RT-TDDFT, particularly how maximally localized Wannier functions (MLWFs) are used to accelerate simulations using the exact exchange. We also discuss several related developments, including an anti-Hermitian correction for the time-dependent MLWFs (TD-MLWFs) when a time-dependent electric field is applied, the refinement procedure for TD-MLWFs, comparison of the velocity and length gauge approaches for applying an electric field, and elimination of long-range electrostatic interaction, as well as usage of a complex absorbing potential for modeling isolated systems when using the PW-PP formalism.

Time-Dependent Density Functional Theory for X-ray Absorption Spectra: Comparing the Real-Time Approach to Linear Response

We simulate X-ray absorption spectra at elemental K-edges using time-dependent density functional theory (TDDFT) in both its conventional linear-response implementation and its explicitly time-dependent or "real-time" formulation. Real-time TDDFT simulations enable broadband spectra calculations without the need to invoke frozen occupied orbitals ("core/valence separation"), but we find that these spectra are often contaminated by transitions to the continuum that originate from lower-energy core and semicore orbitals. This problem becomes acute in triple-ζ basis sets, although it is sometimes sidestepped in double-ζ basis sets. Transitions to the continuum acquire surprisingly large dipole oscillator strengths, leading to spectra that are difficult to interpret. Meaningful spectra can be recovered by means of a filtering technique that decomposes the spectrum into contributions from individual occupied orbitals, and the same procedure can be used to separate L- and K-edge spectra arising from different elements within a given molecule. In contrast, conventional linear-response TDDFT requires core/valence separation but is free of these artifacts. It is also significantly more efficient than the real-time approach, even when hundreds of individual states are needed to reproduce near-edge absorption features and even when Padé approximants are used to reduce the real-time simulations to just 2-4 fs of time propagation. Despite the cost, the real-time approach may be useful to examine the validity of the core/valence separation approximation.

Irradiation of Plutonium Tributyl Phosphate Complexes by Ionizing Alpha Particles: A Computational Study

The PUREX solvent extraction process, widely used for recovering uranium and plutonium from spent nuclear fuel, utilizes an organic solvent composed of tributyl phosphate (TBP). The emission of ionizing particles such as alpha particles, resulting from the decay of plutonium, makes the organic solvent vulnerable to degradation. Here, we study the ultrashort time alpha irradiation of tributylphosphate (TBP) and Pu(NO3)4(TBP)2 complex formed in the PUREX process. Electron dynamics is propagated by Real-Time-Dependent Auxiliary Density Functional Theory (RT-TD-ADFT). We investigate the use of previously proposed absorption boundary conditions (ABC) in the molecular orbital space to treat secondary electron emission. Basis set and exchange correlation functional effects with ABC are reported as well as a detailed analysis of the ABC parametrization. Preliminary results on the water molecule and then on TBP show that the phenomenological nature of the ABC parameters necessitates selecting appropriate values for each system under study. Irradiation of free and complexed TBP shows an influence of the ligands on the variation of atomic charges on the femtosecond time scale. An accumulation of atomic charges in the alkyl chains of TBP is observed in the case where the nitrate groups are predominantly irradiated. In addition, we find that the Pu atom regains its electric charge very rapidly after being hit by the projectile, with the coordination sphere serving as an electron reservoir to preserve its formal redox state. This study paves the road toward a full understanding of the degradation of organic extracants employed in the nuclear industry.

Comparison of Length, Velocity, and Symmetric Gauges for the Calculation of Absorption and Electric Circular Dichroism Spectra with Real-Time Time-Dependent Density Functional Theory

A velocity and symmetric gauge implementation for real-time time-dependent density functional theory (RT-TDDFT) in the CP2K package using a Gaussian and plane wave approach is presented, including the explicit gauge-transformed contributions due to the nonlocal part of pseudopotentials. Absorption spectra of gas-phase α-pinene are calculated in length and velocity gauges in the long-wavelength approximation for the application of a δ pulse in linear and full order. The velocity gauge implementation is also applied to a solvated uracil molecule to showcase its use within periodic boundary conditions (PBC). For the calculation of the expectation value of the electric dipole moment in PBC, both the velocity representation and the modern theory of polarization give equivalent absorption spectra if a distributed reference point is used for the nonlocal term of the velocity operator. The discussion of linear response theory takes place in a unified framework in terms of linear response functions in propagator notation, distinguishing the parts of the linear response functions associated with perturbation and response. To further investigate gauge dependence, electric circular dichroism (ECD) spectra of α-pinene were calculated either as magnetic response to an electric field perturbation, in length or velocity gauge, or as electric response to a magnetic field perturbation in the symmetric gauge. Both approaches, electric and magnetic perturbations, have been found to yield equivalent ECD spectra.

Self-Adaptive Real-Time Time-Dependent Density Functional Theory for X-ray Absorptions

Real-time time-dependent density functional theory (RT-TDDFT) can in principle access the whole absorption spectrum of a many-electron system exposed to a narrow pulse. However, this requires an accurate and efficient propagator for the numerical integration of the time-dependent Kohn-Sham equation. While a low-order time propagator is already sufficient for the low-lying valence absorption spectra, it is no longer the case for the X-ray absorption spectra (XAS) of systems composed even only of light elements, for which the use of a high-order propagator is indispensable. It is then crucial to choose a largest possible time step and a shortest possible simulation time, so as to minimize the computational cost. To this end, we propose here a robust AutoPST approach to determine automatically (Auto) the propagator (P), step (S), and time (T) for relativistic RT-TDDFT simulations of XAS.

Intruder Peak-Free Transient Inner-Shell Spectra Using Real-Time Simulations

Real-time methods are convenient for simulating core-level absorption spectra but suffer from nonphysical intruder peaks when using atom-centered basis sets. In transient absorption spectra, these peaks exhibit highly nonphysical time-dependent modulations in their energies and oscillator strengths. In this paper, we address the origins of these intruder peaks and propose a straightforward and effective solution based on a filtered dipole operator. In combination with real-time time-dependent density functional theory (RT-TDDFT), we demonstrate how to compute intruder-free attosecond transient X-ray absorption spectra for the aminophenol (C₆H₇NO) oxygen and nitrogen K-edges and the α-quartz (SiO₂) silicon L-edge. Without filtering, the computed spectra are qualitatively wrong. This procedure is suitable for both static and transient inner-shell spectroscopy studies and can easily be implemented in a range of real-time methodologies.

Theoretical Calculation of Core-Excited States along Dissociative Pathways beyond Second-Order Perturbation Theory

We extend the multireference driven similarity renormalization (MR-DSRG) method to compute core-excited states by combining it with a GASSCF treatment of orbital relaxation and static electron correlation effects. We consider MR-DSRG treatments of dynamical correlation truncated at the level of perturbation theory (DSRG-MRPT2/3) and iterative linearized approximations with one- and two-body operators [MR-LDSRG(2)] in combination with a spin-free exact-two-component (X2C) one-electron treatment of scalar relativistic effects. This approach is calibrated and tested on a series of 16 core-excited states of five closed- and open-shell diatomic molecules containing first-row elements (C, N, and O). All GASSCF-MR-DSRG theories show excellent agreement with experimental adiabatic transitions energies, with mean absolute errors ranging between 0.17 and 0.35 eV, even for the challenging partially doubly excited states of the N₂⁺ molecule. The vibrational structure of all these transitions, obtained from using a full potential energy scan, shows a mean absolute error as low as 25 meV for DSRG-MRPT2 and 12/13 meV for DSRG-MRPT3 and MR-LDSRG(2). We generally find that a treatment of dynamical correlation that goes beyond the second-order level in perturbation theory improves the accuracy of the potential energy surface, especially in the bond-dissociation region.

Simulated field-modulated x-ray absorption in titania

In this paper, we present a method to compute the x-ray absorption near-edge structure (XANES) spectra of solid-state transition metal oxides using real-time time-dependent density functional theory, including spin-orbit coupling effects. This was performed on bulk-mimicking anatase titania (TiO₂) clusters, which allows for the use of hybrid functionals and atom-centered all electron basis sets. Furthermore, this method was employed to calculate the shifts in the XANES spectra of the Ti L-edge in the presence of applied electric fields to understand how external fields can modify the electronic structure, and how this can be probed using x-ray absorption spectroscopy. Specifically, the onset of t_2g peaks in the Ti L-edge was observed to red shift and the e_g peaks were observed to blue shift with increasing fields, attributed to changes in the hybridization of the conduction band (3d) orbitals.

First-Principles Simulations of X-ray Transient Absorption for Probing Attosecond Electron Dynamics

X-ray transient absorption spectroscopy (XTAS) is a promising technique for measuring electron dynamics in molecules and solids with attosecond time resolutions. In XTAS, the elemental specificity and spatial locality of core-to-valence X-ray absorption is exploited to relate modulations in the time-resolved absorption spectra to local electron density variations around particular atoms. However, interpreting these absorption modulations and frequency shifts as a function of the time delay in terms of dynamics can be challenging. In this paper, we present a first-principles study of attosecond XTAS in a selection of simple molecules based on real-time time-dependent density functional theory (RT-TDDFT) with constrained DFT to emulate the state of the system following the interaction with a ultraviolet pump laser. In general, there is a decrease in the optical density and a blue shift in the frequency with increasing electron density around the absorbing atom. In carbon monoxide (CO), modulations in the O K-edge occur at the frequency of the valence electron dynamics, while for dioxygen (O₂) they occur at twice the frequency, due to the indistinguishability of the oxygen atoms. In 4-aminophenol (H₂NC₆H₄OH), likewise, there is a decrease in the optical density and a blue shift in the frequency for the oxygen and nitrogen K-edges with increasing charge density on the O and N, respectively. Similar effects are observed in the nitrogen K-edge for a long-range charge-transfer excitation in a benzene (C₆H₆)-tetracyanoethylene (C₆N₄; TCNE) dimer but with weaker modulations due to the delocalization of the charge across the entire TCNE molecule. Additionally, in all cases, there are pre-edge features corresponding to core transitions to depopulated orbitals. These potentially offer a background-free signal that only appears in pumped molecules.

Momentum-resolved TDDFT algorithm in atomic basis for real time tracking of electronic excitation

Ultrafast electronic dynamics in solids lies at the core of modern condensed matter and materials physics. To build up a practical ab initio method for studying solids under photoexcitation, we develop a momentum-resolved real-time time dependent density functional theory (rt-TDDFT) algorithm using numerical atomic basis, together with the implementation of both the length and vector gauge of the electromagnetic field. When applied to simulate elementary excitations in two-dimensional materials such as graphene, different excitation modes, only distinguishable in momentum space, are observed. The momentum-resolved rt-TDDFT is important and computationally efficient for the study of ultrafast dynamics in extended systems.

Births in the United States, 2017

This report presents selected highlights from 2017 final birth data on key demographic, health care utilization, and infant health indicators. General fertility rates (the number of births per 1,000 females aged 15-44 years) and teen birth rates are presented by race and Hispanic origin. The use of Medicaid as the source of payment for the delivery and preterm birth rates are presented by the age of the mother. Data for 2017 are compared with 2016 for each indicator.

Attosecond Charge Migration with TDDFT: Accurate Dynamics from a Well-Defined Initial State

We investigate the ability of time-dependent density functional theory (TDDFT) to capture attosecond valence electron dynamics resulting from sudden X-ray ionization of a core electron. In this special case the initial state can be constructed unambiguously, allowing for a simple test of the accuracy of the dynamics. The response following nitrogen K-edge ionization in nitrosobenzene shows excellent agreement with fourth-order algebraic diagrammatic construction (ADC(4)) results, suggesting that a properly chosen initial state allows TDDFT to adequately capture attosecond charge migration. Visualizing hole motion using an electron localization picture (ELF), we provide an intuitive chemical interpretation of the charge migration as a superposition of Lewis dot resonance structures.

Optimized Finite Difference Method for the Full-Potential XANES Simulations: Application to Molecular Adsorption Geometries in MOFs and Metal-Ligand Intersystem Crossing Transients

Accurate modeling of the X-ray absorption near-edge spectra (XANES) is required to unravel the local structure of metal sites in complex systems and their structural changes upon chemical or light stimuli. Two relevant examples are reported here concerning the following: (i) the effect of molecular adsorption on 3d metals hosted inside metal-organic frameworks and (ii) light induced dynamics of spin crossover in metal-organic complexes. In both cases, the amount of structural models for simulation can reach a hundred, depending on the number of structural parameters. Thus, the choice of an accurate but computationally demanding finite difference method for the ab initio X-ray absorption simulations severely restricts the range of molecular systems that can be analyzed by personal computers. Employing the FDMNES code [Phys. Rev. B, 2001, 63, 125120] we show that this problem can be handled if a proper diagonalization scheme is applied. Due to the use of dedicated solvers for sparse matrices, the calculation time was reduced by more than 1 order of magnitude compared to the standard Gaussian method, while the amount of required RAM was halved. Ni K-edge XANES simulations performed by the accelerated version of the code allowed analyzing the coordination geometry of CO and NO on the Ni active sites in CPO-27-Ni MOF. The Ni-CO configuration was found to be linear, while Ni-NO was bent by almost 90°. Modeling of the Fe K-edge XANES of photoexcited aqueous [Fe(bpy)3](2+) with a 100 ps delay we identified the Fe-N distance elongation and bipyridine rotation upon transition from the initial low-spin to the final high-spin state. Subsequently, the X-ray absorption spectrum for the intermediate triplet state with expected 100 fs lifetime was theoretically predicted.