Core Excitation Energies Research Articles

Long-range Corrected Density Functional Theory Including a Two-Gaussian Hartree-Fock Operator for High Accuracy Core-excitation Energy Calculations of Both the Second- and Third-Row Atoms (LC2gau-core-BOP).

In the previous work, LCgau-core-BOP, which includes the short-range interelectronic Gaussian attenuating Hartree-Fock (HF) exchange to the long-range HF exchange, showed high accuracy core-excitation energies from 1s orbitals of the second-row atoms (1s → π*, 1s → σ*, 1s → n*, and 1s → Rydberg), but underestimates the core-excitation energies from 1s orbitals of the third-row atoms. To improve this, we added one more Gaussian attenuating HF exchange to LCgau-core-BOP. We named it LC2gau-core-BOP, which achieves a mean absolute error (MAE) of 0.6 and 0.3 eV for core excitation energies of the second- and third-row atoms of the tested small molecules, respectively. We found that the inclusion of the short-range interelectronic HF exchange at a distance ranging from 0.2 to 0.6 a.u. contributes to the increase of performances on 1s orbital energy calculations of the second-row atoms, while the inclusion of more short-range interelectronic HF exchange at a distance ranging from 0 to 0.2 a.u. does to the increase of performance on 1s orbital energy calculations of the third-row atoms. It is notable that all of these improvements were accomplished using flexible Gaussian attenuating HF exchange inclusion. LC2gau-core-BOP shows deviations of less than 0.8 eV from experimental values for all of the core-excitation energies of the tested medium-size molecules consisting of thymine, oxazole, glycine, and dibenzothiophene sulfone. Moreover, by optimizing one parameter of the OP correlation functional, LC2gau-core-BOP provides atomization energies over the G3 test set with an accuracy comparable to that of B3LYP.

A DFT/MRCI Hamiltonian parameterized using only ab initio data: I. valence excited states

A new combined density functional theory and multi-reference configuration interaction (DFT/MRCI) Hamiltonian parameterized solely using the benchmark ab initio vertical excitation energies obtained from the QUEST databases is presented. This new formulation differs from all previous versions of the method in that the choice of the underlying exchange–correlation (XC) functional employed to construct the one-particle (orbital) basis is considered, and a new XC functional, QTP17, is chosen for its ability to generate a balanced description of core and valence vertical excitation energies. The ability of the new DFT/MRCI Hamiltonian, termed QE8, to furnish accurate excitation energies is confirmed using benchmark quantum chemistry computations, and a mean absolute error of 0.16 eV is determined for the wide range of electronic excitations included in the validation dataset. In particular, the QE8 Hamiltonian dramatically improves the performance of DFT/MRCI for doubly excited states. The performance of fast approximate DFT/MRCI methods, p-DFT/MRCI and DFT/MRCI(2), is also evaluated using the QE8 Hamiltonian, and they are found to yield excitation energies in quantitative agreement with the parent DFT/MRCI method, with the two methods exhibiting a mean difference of 0.01 eV with respect to DFT/MRCI over the entire benchmark set.

Core-Projected Hybrids Fix Systematic Errors in Time-Dependent Density Functional Theory Predicted Core-Electron Excitations.

Linear response time-dependent density functional theory (TDDFT) is widely applied to valence, Rydberg, and charge-transfer excitations but, in its current form, makes large errors for core-electron excitations. This work demonstrates that the admixture of nonlocal exact exchange in atomic core regions significantly improves TDDFT-predicted core excitations. Exact exchange admixture is accomplished using projected hybrid density functional theory [ J. Chem. Theory Comput. 2023, 19, 837-847]. Scalar relativistic TDDFT calculations using core-projected B3LYP accurately model core excitations of second-period elements C-F and third-period elements Si-Cl, without sacrificing performance for the relative shifts of core excitation energies. Predicted K-edge X-ray near absorption edge structure (XANES) of a series of sulfur standards highlight the value of this approach. Core-projected hybrids appear to be a practical solution to TDDFT's limitations for core excitations, in the way that long-range-corrected hybrids are a practical solution to TDDFT's limitations for Rydberg and charge-transfer excitations.

Cyanobacterial Phycobilisome Allostery as Revealed by Quantitative Mass Spectrometry.

Phycobilisomes (PBSs) are the major photosynthetic light-harvesting complexes in cyanobacteria and red algae. PBS, a multisubunit protein complex, has two major interfaces that comprise intrinsically disordered regions (IDRs): rod-core and core-membrane. IDRs do not form regular, three-dimensional structures on their own. Their presence in the photosynthetic pigment-protein complexes portends their structural and functional importance. A recent model suggests that PB-loop, an IDR located on the PBS subunit ApcE and C-terminal extension (CTE) of the PBS subunit ApcG, forms a structural protrusion on the PBS core-membrane side, facing the thylakoid membrane. Here, the structural synergy between the rod-core region and the core-membrane region was investigated using quantitative mass spectrometry (MS). The AlphaFold-predicted CpcG-CTE structure was first modeled onto the PBS rod-core region, guided and justified by the isotopically encoded structural MS data. Quantitative cross-linking MS analysis revealed that the structural proximity of the PB-loop in ApcE and ApcG-CTE is significantly disturbed in the absence of six PBS rods, which are attached to PBS via CpcG-CTE, indicative of drastic conformational changes and decreased structural integrity. These results suggest that CpcG-rod attachment on the PBS rod-core side is essentially required for the PBS core-membrane structural assembly. The hypothesized long-range synergy between the rod-core interface (where the orange carotenoid protein also functions) and the terminal energy emitter of PBS must have important regulatory roles in PBS core assembly, light-harvesting, and excitation energy transmission. These data also lend strategies that genetic truncation of the light-harvesting antennas aimed for improved photosynthetic productivity must rely on an in-depth understanding of their global structural integrity.

Resonant double-core excitations with ultrafast, intense X-ray pulses

Intense few-to-sub-femtosecond soft X-ray pulses can produce neutral, two-site excited double-core-hole states by promoting two core electrons to the same unoccupied molecular orbital. We theoretically investigate double nitrogen K-edge excitations of nitrous oxide (N 2 O) with multiconfigurational electronic structure calculations. We show that the second core-excitation energy is reduced with respect to its ground state value. A site-selective double core-excitation mechanism using intense few-femtosecond x-rays is investigated using time-dependent Schrödinger equation (TDSE) simulations. The subsequent two-step Auger–Meitner and two-electrons-one-electron decay spectra of the double core-excited states are analysed using a Mulliken population analysis of the multiconfirational wavefunctions. The change in the electron emission lineshape between the absorption of 1 or 2 photons in the resonant core-excitation is predicted by combining this approach with the TDSE simulations. We examine the possibility of resolving the double core-excited states with X-ray pump-probe techniques by calculating the chemical shifts of the core-electron binding energy of the core-excited states and decay products.

Density functionals for core excitations.

The core excitation energies and related principal ionization energies are obtained for selected molecules using several density functionals and compared with benchmark equation-of-motion coupled cluster (EOM-CC) results. Both time-dependent and time-independent formulations of excitation spectra in the time-dependent density functional theory and the EOM-CC are employed to obtain excited states that are not always easily accessible with the time-independent method. Among those functionals, we find that the QTP(00) functional, which is only parameterized to reproduce the five IPs of water, provides excellent core IPs and core excitation energies, consistently yielding better excitation and ionization energies. We show that orbital eigenvalues of KS density functional theory play an important role in determining the accuracy of the excitation and photoelectron spectra.

Assessing the performance of ΔSCF and the diagonal second-order self-energy approximation for calculating vertical core excitation energies.

Vertical core excitation energies are obtained using a combination of the ΔSCF method and the diagonal second-order self-energy approximation. These methods are applied to a set of neutral molecules and their anionic forms. An assessment of the results with the inclusion of relativistic effects is presented. For core excitations involving delocalized symmetry orbitals, the applied composite method improves upon the overestimation of ΔSCF by providing approximate values close to experimental K-shell transition energies. The importance of both correlation and relaxation contributions to the vertical core-excited state energies, the concept of local and nonlocal core orbitals, and the consequences of breaking symmetry are discussed.

Accurate Core-Excited States via Inclusion of Core Triple Excitations in Similarity-Transformed Equation-of-Motion Theory.

The phenomenon of orbital relaxation upon excitation of core electrons is a major problem in the linear-response treatment of core-hole spectroscopies. Rather than addressing relaxation through direct dynamical correlation of the excited state via equation-of-motion coupled cluster theory (EOMEE-CC), we extend the alternative similarity-transformed equation-of-motion coupled cluster theory (STEOMEE-CC) by including the core-valence separation (CVS) and correlation of triple excitations only within the calculation of core ionization energies. This new method, CVS-STEOMEE-CCSD+cT, significantly improves on CVS-EOMEE-CCSD and unmodified CVS-STEOMEE-CCSD when compared to full CVS-EOM-CCSDT for K-edge core-excitation energies of a set of small molecules. The improvement in both absolute and relative (shifted) peak positions is nearly as good as that for transition-potential coupled cluster (TP-CC), which includes an explicit treatment of orbital relaxation, and CVS-EOMEE-CCSD*, which includes a perturbative treatment of triple excitations.

Accurate core excitation and ionization energies from a state-specific coupled-cluster singles and doubles approach.

We investigate the use of orbital-optimized references in conjunction with single-reference coupled-cluster theory with single and double substitutions (CCSD) for the study of core excitations and ionizations of 18 small organic molecules, without the use of response theory or equation-of-motion (EOM) formalisms. Three schemes are employed to successfully address the convergence difficulties associated with the coupled-cluster equations, and the spin contamination resulting from the use of a spin symmetry-broken reference, in the case of excitations. In order to gauge the inherent potential of the methods studied, an effort is made to provide reasonable basis set limit estimates for the transition energies. Overall, we find that the two best-performing schemes studied here for ΔCCSD are capable of predicting excitation and ionization energies with errors comparable to experimental accuracies. The proposed ΔCCSD schemes reduces statistical errors against experimental excitation energies by more than a factor of two when compared to the frozen-core core-valence separated (FC-CVS) EOM-CCSD approach - a successful variant of EOM-CCSD tailored towards core excitations.

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 (2DCM), 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 (2DCGM) are significantly more accurate than X2C calculations for which screened two-electron spin-orbit interactions are included via atomic mean-field integrals.

Core-Level Excitation Energies of Nucleic Acid Bases Expressed as Orbital Energies of the Kohn-Sham Density Functional Theory with Long-Range Corrected Functionals.

The core electron binding energies (CEBEs) and core-level excitation energies of thymine, adenine, cytosine, and uracil are studied by the Kohn-Sham (KS) method with long-range corrected (LC) functionals. The CEBEs are estimated according to the Koopmans-type theorem for density functional theory. The excitation energies from the core to the valence π* and Rydberg states are calculated as the orbital energy differences between core-level orbitals of a neutral parent/cation and unoccupied π* or Rydberg orbitals of its cation. The model is intuitive, and the spectra can easily be assigned. Core excitation energies from oxygen 1s, nitrogen 1s, and carbon 1s to π* and Rydberg states, and the chemical shifts, agree well with previously reported theoretical and experimental data. The straightforward use of KS orbitals in this scheme carries the advantage that it can be applied efficiently to large systems such as biomolecules and nanomaterials.

Simulation of attosecond transient soft x-ray absorption in solids using generalized Kohn–Sham real-time time-dependent density functional theory

Time-dependent density functional theory (TDDFT) simulations of transient core-level spectroscopies require a balanced treatment of both valence- and core-electron excitations. To this end, tuned range-separated hybrid exchange–correlation functionals within the generalized Kohn–Sham scheme offer a computationally efficient means of simultaneously improving the accuracy of valence and core excitation energies in TDDFT by mitigating delocalization errors across multiple length-scales. In this work range-separated hybrid functionals are employed in conjunction with the velocity-gauge formulation of real-time TDDFT to simulate static as well as transient soft x-ray near-edge absorption spectra in a prototypical solid-state system, monolayer hexagonal boron nitride, where excitonic effects are important. In the static case, computed soft x-ray absorption edge energies and line shapes are seen to be in good agreement with experiment. Following laser excitation by a pump pulse, soft x-ray probe spectra are shown to exhibit characteristic features of population induced bleaching and transient energy shifts of exciton peaks. The methods outlined in this work therefore illustrate a practical means for simulating attosecond time-resolved core-level spectra in solids within a TDDFT framework.

Relativistic local hybrid functionals and their impact on 1s core orbital energies.

In this work, we report the first relativistic density functional theory calculations using relativistic local hybrid functionals. Besides outlining the construction of relativistic local hybrid exchange within a two-component-relativistic framework based on the picture-change transformation of the density matrix and a recently developed relativistic iso-orbital indicator, we investigate the influence of two-electron-relativistic effects, using relativistic functional ingredients in local hybrid functionals, and the choice of the exchange-correlation functional on atomic 1s core orbital energies of light and heavier elements. Finally, we discuss the applicability of relativistic 1s core orbital shifts for the relativistic correction of non-relativistic 1s core excitation energies.

EOM-CC methods with approximate triple excitations applied to core excitation and ionisation energies

A number of iterative and perturbative approximations to the full equation-of-motion coupled cluster method with single, double, and triple excitations (EOM-CCSDT) are evaluated in the context of calculating the K-edge core-excitation and core-ionisation energies of several small molecules. Several of these methods are found to accurately reproduce the full EOM-CCSDT energies well, in particular the EOM-CCSD* method which, when using the core-valence separation (CVS) ansatz, scales rigorously with the sixth power of molecular size. These results highlight that very accurate core excitation and ionisation energies for molecules with first-row atoms can be computed at a cost not much larger than that for EOM-CCSD.

New and Efficient Equation-of-Motion Coupled-Cluster Framework for Core-Excited and Core-Ionized States.

We present a fully analytical implementation of the core-valence separation (CVS) scheme for the equation-of-motion (EOM) coupled-cluster singles and doubles (CCSD) method for calculations of core-level states. Inspired by the CVS idea as originally formulated by Cederbaum, Domcke, and Schirmer, pure valence excitations are excluded from the EOM target space and the frozen-core approximation is imposed on the reference-state amplitudes and multipliers. This yields an efficient, robust, practical, and numerically balanced EOM-CCSD framework for calculations of excitation and ionization energies as well as state and transition properties (e.g., spectral intensities, natural transition, and Dyson orbitals) from both the ground and excited states. The errors in absolute excitation/ionization energies relative to the experimental reference data are on the order of 0.2-3.0 eV, depending on the K-edge considered and on the basis set used, and the shifts are systematic for each edge. Compared to a previously proposed CVS scheme where CVS was applied as a posteriori projection only during the solution of the EOM eigenvalue equations, the new scheme is computationally cheaper. It also achieves better cancellation of errors, yielding similar spectral profiles but with absolute core excitation and ionization energies that are systematically closer to the corresponding experimental data. Among the presented results are calculations of transient-state X-ray absorption spectra, relevant for interpretation of UV-pump/X-ray probe experiments.

Assessment of basis sets for density functional theory-based calculations of core-electron spectroscopies

The performance of Gaussian basis sets for density functional theory-based calculations of core-electron spectroscopies is assessed. The convergence of core-electron binding energies and core-excitation energies using a range of basis sets including split-valence, correlation-consistent, polarisation-consistent and individual gauge for localised orbitals basis sets is studied. For varDelta self-consistent field calculations of core-electron binding energies and core-excitation energies of first-row elements, relatively small basis sets can accurately reproduce the values of much larger basis sets, with the IGLO basis sets performing particularly well. Calculations for the K-edge of second-row elements are more challenging, and of the smaller basis sets, pcSseg-2 has the best performance. For the correlation-consistent basis sets, inclusion of core-valence correlation functions is important, with the cc-pCVTZ basis set giving accurate results. Time-dependent density functional theory-based calculations of core-excitation energies show less sensitivity to the basis set with relatively small basis sets, such as pcSseg-1 or pcSseg-2, reproducing the values for much larger basis sets accurately. In contrast, time-dependent density functional theory calculations of X-ray emission energies are highly dependent on the basis set, but the IGLO-II, IGLO-III and pcSseg-2 basis sets provide a good level of accuracy.

Time-Step Targeting Time-Dependent and Dynamical Density Matrix Renormalization Group Algorithms with ab Initio Hamiltonians.

We study the dynamical density matrix renormalization group (DDMRG) and time-dependent density matrix renormalization group (td-DMRG) algorithms in the ab initio context to compute dynamical correlation functions of correlated systems. We analyze the strengths and weaknesses of the two methods in small model problems and propose two simple improved formulations, DDMRG++ and td-DMRG++, that give increased accuracy at the same bond dimension at a nominal increase in cost. We apply DDMRG++ to obtain the oxygen core-excitation energy in the water molecule in a quadruple-zeta quality basis, which allows us to estimate the remaining correlation error in existing coupled cluster results. Further, we use DDMRG++ to compute the local density of states and gaps and td-DMRG++ to compute the complex polarization function, in linear hydrogen chains with up to 50 H atoms, to study metallicity and delocalization as a function of bond length.

Correlated natural transition orbitals for core excitation energies in multilevel coupled cluster models.

In this article, we present a black-box approach for the selection of orbital spaces when computing core excitation energies in the multilevel coupled cluster (MLCC) framework. Information available from the lower level of theory is used to generate correlated natural transition orbitals (CNTOs) for the high-level calculation by including both singles and doubles information in the construction of the transition orbitals. The inclusion of the doubles excitation information is essential to obtain a set of orbitals that all contain physical information, in contrast to the natural transition orbitals where only a small subset of the virtual orbitals contains physical information. The CNTOs may be included in an active space based on a cutoff threshold for the eigenvalues corresponding to the orbitals. We present MLCC results for core excitation energies calculated using coupled cluster singles and doubles (CCSD) in the inactive space and CCSD with perturbative triples (CC3) in the active space. The use of CNTOs results in small errors compared to full CC3.

Short- and long-range corrected hybrid density functionals with the D3 dispersion corrections.

We propose a short- and long-range corrected (SLC) hybrid scheme employing 100% Hartree-Fock exchange at both zero and infinite interelectronic distances, wherein three SLC hybrid density functionals with the D3 dispersion corrections (SLC-LDA-D3, SLC-PBE-D3, and SLC-B97-D3) are developed. SLC-PBE-D3 and SLC-B97-D3 are shown to be accurate for a very diverse range of applications, such as core ionization and excitation energies, thermochemistry, kinetics, noncovalent interactions, dissociation of symmetric radical cations, vertical ionization potentials, vertical electron affinities, fundamental gaps, and valence, Rydberg, and long-range charge-transfer excitation energies. Relative to ωB97X-D, SLC-B97-D3 provides significant improvement for core ionization and excitation energies and noticeable improvement for the self-interaction, asymptote, energy-gap, and charge-transfer problems, while performing similarly for thermochemistry, kinetics, and noncovalent interactions.

Increasing the applicability of density functional theory. V. X-ray absorption spectra with ionization potential corrected exchange and correlation potentials.

Core excitation energies are computed with time-dependent density functional theory (TD-DFT) using the ionization energy corrected exchange and correlation potential QTP(0,0). QTP(0,0) provides C, N, and O K-edge spectra to about an electron volt. A mean absolute error (MAE) of 0.77 and a maximum error of 2.6 eV is observed for QTP(0,0) for many small molecules. TD-DFT based on QTP (0,0) is then used to describe the core-excitation spectra of the 22 amino acids. TD-DFT with conventional functionals greatly underestimates core excitation energies, largely due to the significant error in the Kohn-Sham occupied eigenvalues. To the contrary, the ionization energy corrected potential, QTP(0,0), provides excellent approximations (MAE of 0.53 eV) for core ionization energies as eigenvalues of the Kohn-Sham equations. As a consequence, core excitation energies are accurately described with QTP(0,0), as are the core ionization energies important in X-ray photoionization spectra or electron spectroscopy for chemical analysis.