The simulation of X-ray absorption spectra from ground and excited electronic states using core-valence separated DFT/MRCI

Unraveling the variational breakdown of core valence separation calculations: Diagnostic and cure to the over relaxation error of double core hole states

The core valence separation (CVS) approximation is the most employed strategy to prevent the variational collapse of standard wave function optimization when attempting to compute electronic states bearing one or more electronic vacancies in core orbitals. Here, we explore the spurious consequences of this approximation on the properties of the computed core hole states. We especially focus on the less studied case of double core hole (DCH) states, whose spectroscopic interest has recently been rapidly growing. We show that the CVS error leads to a systematic underestimation of DCH energies, a property in stark contrast with the case of single core hole states. We highlight that the CVS error can then be interpreted as an over relaxation effect and design a new correction strategy adapted to these specificities.

Robust relativistic many-body Green's function based approaches for assessing core ionized and excited states

A two-component contour deformation (CD) based GW method that employs frequency sampling to drastically reduce the computational effort when assessing quasiparticle states far away from the Fermi level is outlined. Compared to the canonical CD-GW method, computational scaling is reduced by an order of magnitude without sacrificing accuracy. This allows for an efficient calculation of core ionization energies. The improved computational efficiency is used to provide benchmarks for core ionized states, comparing the performance of 15 density functional approximations as Kohn-Sham starting points for GW calculations on a set of 65 core ionization energies of 32 small molecules. Contrary to valence states, GW calculations on core states prefer functionals with only a moderate amount of Hartree-Fock exchange. Moreover, modern ab initio local hybrid functionals are also shown to provide excellent generalized Kohn-Sham references for core GW calculations. Furthermore, the core-valence separated Bethe-Salpeter equation (CVS-BSE) is outlined. CVS-BSE is a convenient tool to probe core excited states. The latter is tested on a set of 40 core excitations of eight small inorganic molecules. Results from the CVS-BSE method for excitation energies and the corresponding absorption cross sections are found to be in excellent agreement with those of reference damped response BSE calculations.

Tuning UV Pump X-ray Probe Spectroscopy on the Nitrogen K Edge Reveals the Radiationless Relaxation of Pyrazine: Ab Initio Simulations Using the Quasiclassical Doorway-Window Approximation

Transient absorption UV pump X-ray probe spectroscopy has been established as a versatile technique for the exploration of ultrafast photoinduced dynamics in valence-excited states. In this work, an ab initio theoretical framework for the simulation of time-resolved UV pump X-ray probe spectra is presented. The method is based on the description of the radiation-matter interaction in the classical doorway-window approximation and a surface-hopping algorithm for the nonadiabatic nuclear excited-state dynamics. Using the second-order algebraic-diagrammatic construction scheme for excited states, UV pump X-ray probe signals were simulated for the carbon and nitrogen K edges of pyrazine, assuming a duration of 5 fs of the UV pump and X-ray probe pulses. It is predicted that spectra measured at the nitrogen K edge carry much richer information about the ultrafast nonadiabatic dynamics in the valence-excited states of pyrazine than those measured at the carbon K edge.

Double-Hybrid Density Functional Theory for Core Excitations: Theory and Benchmark Calculations

The double-hybrid (DH) time-dependent density functional theory is extended to core excitations. Two different DH formalisms are presented utilizing the core-valence separation (CVS) approximation. First, a CVS-DH variant is introduced relying on the genuine perturbative second-order correction, while an iterative analogue is also presented using our second-order algebraic-diagrammatic construction [ADC(2)]-based DH ansatz. The performance of the new approaches is tested for the most popular DH functionals using the recently proposed XABOOM [J. Chem. Theory Comput.2021, 17, 1618] benchmark set. In order to make a careful comparison, the accuracy and precision of the methods are also inspected. Our results show that the genuine approaches are highly competitive with the more advanced CVS-ADC(2)-based methods if only excitation energies are required. In contrast, as expected, significant differences are observed in oscillator strengths; however, the precision is acceptable for the genuine functionals as well. Concerning the performance of the CVS-DH approaches, the PBE0-2/CVS-ADC(2) functional is superior, while its spin-opposite-scaled variant is also recommended as a cost-effective alternative. For these approaches, significant improvements are realized in the error measures compared with the popular CVS-ADC(2) method.

Electron-Affinity Time-Dependent Density Functional Theory: Formalism and Applications to Core-Excited States

The lack of particle-hole attraction and orbital relaxation within time-dependent density functional theory (TDDFT) lead to extreme errors in the prediction of K-edge X-ray absorption spectra (XAS). We derive a linear-response formalism that uses optimized orbitals of the n - 1-electron system as the reference, building orbital relaxation and a proper hole into the initial density. Our approach is an exact generalization of the static-exchange approximation that ameliorates the particle-hole interaction error associated with the adiabatic approximation and reduces errors in TDDFT XAS by orders of magnitude. With a statistical performance of just 0.5 eV root-mean-square error and the same computational scaling as TDDFT under the core-valence separation approximation, we anticipate that this approach will be of great utility in XAS calculations of large systems.

Simulating X-ray photoelectron spectra with strong electron correlation using multireference algebraic diagrammatic construction theory

A new theoretical approach for the simulations of X-ray photoelectron spectra of strongly correlated molecular systems that combines multireference algebraic diagrammatic construction theory (MR-ADC) with a core–valence separation (CVS) technique.

Resolving competing conical intersection pathways: time-resolved X-ray absorption spectroscopy of trans-1,3-butadiene

Time-resolved X-ray absorption spectroscopy is emerging as a uniquely powerful tool to probe coupled electronic-nuclear dynamics in photo-excited molecules. Theoretical studies to date have established that time-resolved X-ray absorption spectroscopy is an atom-specific probe of excited-state wave packet passage through a seam of conical intersections (CIs). However, in many molecular systems, there are competing dynamical pathways involving CIs of different electronic and nuclear character. Discerning these pathways remains an important challenge. Here, we demonstrate that time-resolved X-ray absorption spectroscopy (TRXAS) has the potential to resolve competing channels in excited-state non-adiabatic dynamics. Using the example of 1,3-butadiene, we show how TRXAS discerns the different electronic structures associated with passage through multiple conical intersections. trans-1,3-Butadiene exhibits a branching between polarized and radicaloid pathways associated with ethylenic "twisted-pyramidalized" and excited-state cis-trans isomerization dynamics, respectively. The differing electronic structures along these pathways give rise to different XAS signals, indicating the possibility of resolving them. Furthermore, this indicates that XAS, and other core-level spectroscopic techniques, offer the appealing prospect of directly probing the effects of selective chemical substitution and its ability to affect chemical control over excited-state molecular dynamics.

Removing the Deadwood from DFT/MRCI Wave Functions: The p-DFT/MRCI Method

The combined density functional theory and multireference configuration interaction (DFT/MRCI) method is a powerful tool for the calculation of excited electronic states of large molecules. There exists, however, a large amount of superfluous configurations in a typical DFT/MRCI wave function. We show that this deadwood may be effectively removed using a simple configuration pruning algorithm based on second-order Epstein-Nesbet perturbation theory. The resulting method, which we denote p-DFT/MRCI, is shown to result in orders of magnitude saving in computational timings, while retaining the accuracy of the original DFT/MRCI method.

Relativistic EOM-CCSD for Core-Excited and Core-Ionized State Energies Based on the Four-Component Dirac-Coulomb(-Gaunt) Hamiltonian

We report an implementation of the core-valence separation approach to the four-component relativistic Hamiltonian-based equation-of-motion coupled-cluster with singles and doubles theory (CVS-EOM-CCSD) for the calculation of relativistic core-ionization potentials and core-excitation energies. With this implementation, which is capable of exploiting double group symmetry, we investigate the effects of the different CVS-EOM-CCSD variants and the use of different Hamiltonians based on the exact two-component (X2C) framework on the energies of different core-ionized and -excited states in halogen- (CH₃I, HX, and X^-, X = Cl-At) and xenon-containing (Xe, XeF₂) species. Our results show that the X2C molecular mean-field approach [Sikkema, J.; J. Chem. Phys. 2009, 131, 124116], based on four-component Dirac-Coulomb mean-field calculations (²DC^M), is capable of providing core excitations and ionization energies that are nearly indistinguishable from the reference four-component energies for up to and including fifth-row elements. We observe that two-electron integrals over the small-component basis sets lead to non-negligible contributions to core binding energies for the K and L edges for atoms such as iodine or astatine and that the approach based on Dirac-Coulomb-Gaunt mean-field calculations (²DCG^M) are significantly more accurate than X2C calculations for which screened two-electron spin-orbit interactions are included via atomic mean-field integrals.

XABOOM: An X-ray Absorption Benchmark of Organic Molecules Based on Carbon, Nitrogen, and Oxygen 1s → π* Transitions

The performance of several standard and popular approaches for calculating X-ray absorption spectra at the carbon, nitrogen, and oxygen K-edges of 40 primarily organic molecules up to the size of guanine has been evaluated, focusing on the low-energy and intense 1s → π* transitions. Using results obtained with CVS-ADC(2)-x and fc-CVS-EOM-CCSD as benchmark references, we investigate the performance of CC2, ADC(2), ADC(3/2), and commonly adopted density functional theory (DFT)-based approaches. Here, focus is on precision rather than on accuracy of transition energies and intensities-in other words, we target relative energies and intensities and the spread thereof, rather than absolute values. The use of exchange-correlation functionals tailored for time-dependent DFT calculations of core excitations leads to error spreads similar to those seen for more standard functionals, despite yielding superior absolute energies. Long-range corrected functionals are shown to perform particularly well compared to our reference data, showing error spreads in energy and intensity of 0.2-0.3 eV and ∼10%, respectively, as compared to 0.3-0.6 eV and ∼20% for a typical pure hybrid. In comparing intensities, state mixing can complicate matters, and techniques to avoid this issue are discussed. Furthermore, the influence of basis sets in high-level ab initio calculations is investigated, showing that reasonably accurate results are obtained with the use of 6-311++G**. We name this benchmark suite as XABOOM (X-ray absorption benchmark of organic molecules) and provide molecular structures and ground-state self-consistent field energies and spectroscopic data. We believe that it provides a good assessment of electronic structure theory methods for calculating X-ray absorption spectra and will become useful for future developments in this field.

An assessment of different electronic structure approaches for modeling time-resolved x-ray absorption spectroscopy

We assess the performance of different protocols for simulating excited-state x-ray absorption spectra. We consider three different protocols based on equation-of-motion coupled-cluster singles and doubles, two of them combined with the maximum overlap method. The three protocols differ in the choice of a reference configuration used to compute target states. Maximum-overlap-method time-dependent density functional theory is also considered. The performance of the different approaches is illustrated using uracil, thymine, and acetylacetone as benchmark systems. The results provide guidance for selecting an electronic structure method for modeling time-resolved x-ray absorption spectroscopy.

Quantifying the error of the core-valence separation approximation

For the calculation of core-excited states probed through X-ray absorption spectroscopy, the core-valence separation (CVS) scheme has become a vital tool. This approach allows us to target such states with high specificity, albeit introducing an error. We report the implementation of a post-processing step for CVS excitations obtained within the algebraic-diagrammatic construction scheme for the polarization propagator, which removes this error. Based on this, we provide a detailed analysis of the CVS scheme, identifying its accuracy to be dominated by an error balance between two neglected couplings, one between core and valence single excitations and the other between single and double core excitations. The selection of the basis set is shown to be vital for a proper description of both couplings, with tight polarizing functions being necessary for a good balance of errors. The CVS error is confirmed to be stable across multiple systems, with an element-specific spread for K-edge spectrum calculations of only about ±0.02 eV. A systematic lowering of the CVS error by 0.02 eV-0.03 eV is noted when considering excitations to extremely diffuse states, emulating ionization.

Probing competing relaxation pathways in malonaldehyde with transient X-ray absorption spectroscopy

Excited-state intramolecular hydrogen transfer (ESIHT) is a fundamental reaction relevant to chemistry and biology. Malonaldehyde is the simplest example of ESIHT, yet only little is known experimentally about its excited-state dynamics. Several competing relaxation pathways have been proposed, including internal conversion mediated by ESIHT and C[double bond, length as m-dash]C torsional motion as well as intersystem crossing. We perform an in silico transient X-ray absorption spectroscopy (TRXAS) experiment at the oxygen K-edge to investigate its potential to monitor the proposed ultrafast decay pathways in malonaldehyde upon photoexcitation to its bright S₂(ππ*) state. We employ both restricted active space perturbation theory and algebraic-diagrammatic construction for the polarization propagator along interpolated reaction coordinates as well as representative trajectories from ab initio multiple spawning simulations to compute the TRXAS signals from the lowest valence states. Our study suggests that oxygen K-edge TRXAS can distinctly fingerprint the passage through the H-transfer intersection and the concomitant population transfer to the S₁(nπ*) state. Potential intersystem crossing to T₁(ππ*) is detectable from reappearance of the double pre-edge signature and reversed intensities. Moreover, the torsional deactivation pathway induces transient charge redistribution from the enol side towards the central C-atom and manifests itself as substantial shifts of the pre-edge features. Given the continuous advances in X-ray light sources, our study proposes an experimental route to disentangle ultrafast excited-state decay channels in this prototypical ESIHT system and provides a pathway-specific mapping of the TRXAS signal to facilitate the interpretation of future experiments.

Highly Accurate Prediction of Core Spectra of Molecules at Density Functional Theory Cost: Attaining Sub-electronvolt Error from a Restricted Open-Shell Kohn-Sham Approach

We present the use of the recently developed square gradient minimization (SGM) algorithm for excited-state orbital optimization to obtain spin-pure restricted open-shell Kohn-Sham (ROKS) energies for core excited states of molecules. The SGM algorithm is robust against variational collapse and offers a reliable route to converging orbitals for target excited states at only 2-3 times the cost of ground-state orbital optimization (per iteration). ROKS/SGM with the modern SCAN/ωB97X-V functionals is found to predict the K-edge of C, N, O, and F to a root mean squared error of ∼0.3 eV. ROKS/SGM is equally effective at predicting L-edge spectra of third period elements, provided a perturbative spin-orbit correction is employed. This high accuracy can be contrasted with traditional time-dependent density functional theory (TDDFT), which typically has greater than 10 eV error and requires translation of computed spectra to align with experiment. ROKS is computationally affordable (having the same scaling as ground-state DFT and a slightly larger prefactor) and can be applied to geometry optimizations/ab initio molecular dynamics of core excited states, as well as condensed phase simulations. ROKS can also model doubly excited/ionized states with one broken electron pair, which are beyond the ability of linear response based methods.