Inner-shell excitation of PF3, PCl3, PCl2CF3, OPF3 and SPF3

Highly Accurate and Robust Constraint-Based Orbital-Optimized Core Excitations

We adapt our recently developed constraint-based orbital-optimized excited-state method (COOX) for the computation of core excitations. COOX is a constrained density functional theory (cDFT) approach based on excitation amplitudes from linear-response time-dependent DFT (LR-TDDFT), and has been shown to provide accurate excitation energies and excited-state properties for valence excitations within a spin-restricted formalism. To extend COOX to core-excited states, we introduce a spin-unrestricted variant which allows us to obtain orbital-optimized core excitations with a single constraint. Using a triplet purification scheme in combination with the constrained unrestricted Hartree-Fock formalism, scalar-relativistic zero-order regular approximation corrections, and a semiempirical treatment of spin-orbit coupling, COOX is shown to produce highly accurate results for K- and L-edge excitations of second- and third-period atoms with subelectronvolt errors despite being based on LR-TDDFT, for which core excitations pose a well-known challenge. L- and M-edge excitations of heavier atoms up to uranium are also computationally feasible and numerically stable, but may require more advanced treatment of relativistic effects. Furthermore, COOX is shown to perform on par with or better than the popular ΔSCF approach while exhibiting more robust convergence, highlighting it as a promising tool for inexpensive and accurate simulations of X-ray absorption spectra.

Direct Observation of Charge, Energy, and Hydrogen Transfer between the Backbone and Nucleobases in Isolated DNA Oligonucleotides

Understanding how charge and energy, as well as protons and hydrogen atoms, are transferred in molecular systems as a result of an electronic excitation is fundamental for understanding the interaction between ionizing radiation and biological matter on the molecular level. To localize the excitation at the atomic scale, it was chosen to target phosphorus atoms in the backbone of gas-phase oligonucleotide anions and cations, by means of resonant photoabsorption at the L- and K-edges. The ionic photoproducts of the excitation process were studied by a combination of mass spectrometry and X-ray spectroscopy. The combination of absorption site selectivity and photoproduct sensitivity allowed the identification of X-ray spectral signatures of specific processes. Moreover, charge and/or energy as well as H transfer from the backbone to nucleobases has been directly observed. Although the probability of one versus two H transfer following valence ionization depends on the nucleobase, ionization of sugar or phosphate groups at the carbon K-edge or the phosphorus L-edge mainly leads to single H transfer to protonated adenine. Moreover, our results indicate a surprising proton-transfer process to specifically form protonated guanine after excitation or ionization of P 2p electrons.

First-principles correction scheme for linear-response time-dependent density functional theory calculations of core electronic states

Linear-response time-dependent density functional theory (LR-TDDFT) for core level spectroscopy using standard local functionals suffers from self-interaction error and a lack of orbital relaxation upon creation of the core hole. As a result, LR-TDDFT calculated x-ray absorption near edge structure spectra needed to be shifted along the energy axis to match experimental data. We propose a correction scheme based on many-body perturbation theory to calculate the shift from first-principles. The ionization potential of the core donor state is first computed and then substituted for the corresponding Kohn-Sham orbital energy, thus emulating Koopmans's condition. Both self-interaction error and orbital relaxation are taken into account. The method exploits the localized nature of core states for efficiency and integrates seamlessly in our previous implementation of core level LR-TDDFT, yielding corrected spectra in a single calculation. We benchmark the correction scheme on molecules at the K- and L-edges as well as for core binding energies and report accuracies comparable to higher order methods. We also demonstrate applicability in large and extended systems and discuss efficient approximations.

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.