GUGA-based MRCI approach with core-valence separation approximation (CVS) for the calculation of the core-excited states of molecules

We develop and demonstrate how to use the Graphical Unitary Group Approach (GUGA)-based MRCISD with Core-Valence Separation (CVS) approximation to compute the core-excited states. First, perform a normal Self-Consistent-Field (SCF) or valence MCSCF calculation to optimize the molecular orbitals. Second, rotate the optimized target core orbitals and append to the active space, form an extended CVS active space, and perform a CVS-MCSCF calculation for core-excited states. Finally, construct the CVS-MRCISD expansion space and perform a CVS-MRCISD calculation to optimize the CI coefficients based on the variational method. The CVS approximation with GUGA-based methods can be implemented by flexible truncation of the Distinct Row Table. Eliminating the valence-excited configurations from the CVS-MRCISD expansion space can prevent variational collapse in the Davidson iteration diagonalization. The accuracy of the CVS-MRCISD scheme was investigated for excitation energies and compared with that of the CVS-MCSCF and CVS-CASPT2 methods using the same active space. The results show that CVS-MRCISD is capable of reproducing well-matched vertical core excitation energies that are consistent with experiments by combining large basis sets and a rational reference space. The calculation results also highlight the fact that the dynamic correlation between electrons makes an undeniable contribution in core-excited states.

Mapping the electronic transitions of protonation sites in peptides using soft X-ray action spectroscopy

Near-edge X-ray absorption mass spectrometry (NEXAMS) around the nitrogen and oxygen K-edges was employed on gas-phase peptides to probe the electronic transitions related to their protonation sites, namely at basic side chains, the N-terminus and the amide oxygen. The experimental results are supported by replica exchange molecular dynamics and density-functional theory and restricted open-shell configuration with single calculations to attribute the transitions responsible for the experimentally observed resonances. We studied five tailor-made glycine-based pentapeptides, where we identified the signature of the protonation site of N-terminal proline, histidine, lysine and arginine, at 406 eV, corresponding to N 1s → σ*(NHx+) (x = 2 or 3) transitions, depending on the peptides. We compared the spectra of pentaglycine and triglycine to evaluate the sensitivity of NEXAMS to protomers. Separate resonances have been identified to distinguish two protomers in triglycine, the protonation site at the N-terminus at 406 eV and the protonation site at the amide oxygen characterized by a transition at 403.1 eV.

Benchmark relativistic delta-coupled-cluster calculations of K-edge core-ionization energies of third-row elements

A benchmark computational study of K-edge core-ionization energies of third-row elements using relativistic delta-coupled-cluster (ΔCC) methods and a revised core-valence separation (CVS) scheme is reported. High-level relativistic (HLR) corrections beyond the spin-free exact two-component theory in its one-electron variant (SFX2C-1e), including the contributions from two-electron picture-change effects, spin-orbit coupling, the Breit term, and quantum electrodynamics effects, have been taken into account and demonstrated to play an important role. Relativistic ΔCC calculations are shown to provide accurate results for core-ionization energies of third-row elements. The SFX2C-1e-CVS-ΔCC results augmented with HLR corrections show a maximum deviation of less than 0.5 eV with respect to experimental values.

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.

Frontier orbital stability of nitroxyl organic radicals probed by means of inner shell resonantly enhanced valence band photoelectron spectroscopy

We have investigated the frontier orbitals of persistent organic radicals known as nitroxyls by resonant photoelectron spectroscopy (ResPES) under inner shell excitation. By means of this site-specific technique, we were able to disentangle the different atomic contributions to the outer valence molecular orbitals and examine several core-hole relaxation pathways involving the singly occupied molecular orbital (SOMO) localized on the nitroxyl group. To interpret the ResPES intensity trends, especially the strong enhancement of the SOMO ionized state at the N K-edge, we computed the Dyson spin orbitals (DSOs) pertaining to the transitions between the core-excited initial states and several of the singly ionized valence final states. We found that the computed vertical valence ionization potentials and norms of the DSOs are reasonably reliable when based on the long-range corrected CAM-B3LYP density functional. Thanks to their unpaired electrons, nitroxyls have recently found application in technological fields implying a spin control, such as spintronics and quantum computing. The present findings on the electronic structure of nitroxyl persistent radicals furnish important hints for their implementation in technological devices and, more in general, for the synthesis of new and stable organic radicals with tailored properties.

Core-shell excitation of isoxazole at the C, N, and O K-edges – an experimental NEXAFS and theoretical TD-DFT study

The near-edge X-ray absorption fine structure (NEXAFS) spectra of the gas-phase isoxazole molecule have been measured by collecting total ion yields at the C, N, and O K-edges. The spectral...

Efficient implementation of the single-reference algebraic diagrammatic construction theory for charged excitations: Applications to the TEMPO radical and DNA base pairs

We present an efficient implementation of the second- and third-order single-reference algebraic diagrammatic construction (ADC) theory for electron attachment and ionization energies and spectra [EA/IP-ADC(n), n = 2, 3]. Our new EA/IP-ADC program features spin adaptation for closed-shell systems, density fitting for efficient handling of the two-electron integral tensors, and vectorized and parallel implementation of tensor contractions. We demonstrate capabilities of our efficient implementation by applying the EA/IP-ADC(n) (n = 2, 3) methods to compute the photoelectron spectrum of the (2,2,6,6-tetramethylpiperidin-1-yl)oxyl (TEMPO) radical, as well as the vertical and adiabatic electron affinities of TEMPO and two DNA base pairs (guanine-cytosine and adenine-thymine). The spectra and electron affinities computed using large diffuse basis sets with up to 1028 molecular orbitals are found to be in good agreement with the best available results from the experiment and theoretical simulations.

Vibrationally resolved valence and core photoionization and photoexcitation spectra of an electron-deficient trivalent boron compound: the case of catecholborane

Compounds containing trivalent boron (TB) as the electron-deficient site(s) find numerous practical uses ranging from Lewis bases in organic synthesis to high-tech industry, with a number of novel applications anticipated. We present an experimental and theoretical study of the gas-phase valence photoionization (VUV-PES), core photoionization (XPS) and photoexcitation (NEXAFS) spectra of a representative TB compound catecholborane (CB). For modelling and assigning the spectra we used the ΔDFT and restricted single excitation space TD-DFT methods for the XPS and NEXAFS, and OVGF and EOM-CCSD for the VUV-PES. The vibrationally resolved structure was computed in the Franck-Condon (FC) and Herzberg-Teller (FCHT) approximations generally resulting in a good agreement with the observed spectral features. For the prediction of core-electron binding energies (CEBEs) several density functionals were tested. The best performance overall was furnished by ωB97X-D suggesting that including the dispersion correction is beneficial. The FCHT vibronic intensities are in clear discrepancy with the B 1s NEXAFS spectrum if the harmonic approximation is used for the B-H wagging mode both in the ground and in the first core-excited state. Instead, a much better agreement is obtained if the excited state potential is approximated to a symmetric double-well. The observed vibronic pattern could be a general fingerprint of the presence of TB centre(s), specifically, the transfer of the (core) density to the vacant boron p-orbital in the excited state.

Density Functional Theory Based Methods for the Calculation of X-ray Spectroscopy

The availability of new light sources combined with the realization of the unique capabilities of spectroscopy in the X-ray region has driven tremendous advances in the field of X-ray spectroscopy. Currently, these techniques are emerging as powerful analytical tools for the study of a wide range of problems encompassing liquids, materials, and biological systems. Time-resolved measurements add a further dimension to X-ray spectroscopy, opening up the potential to resolve ultrafast chemical processes at an atomic level. X-ray spectroscopy encompasses a range of techniques which provide complementary information, and these include X-ray photoelectron spectroscopy (XPS), X-ray absorption spectroscopy (XAS), X-ray emission spectroscopy (XES), and resonant inelastic X-ray scattering (RIXS). In many studies, the interpretation of the experimental data relies upon calculations to enable the nature of the underlying molecular structure, electronic structure, and bonding to be revealed. Density functional theory (DFT) based methods are some of the most widely used methods for the simulation of X-ray spectra. In this Account, we focus on our recent contributions to the simulation of a range of X-ray spectroscopic techniques using DFT and linear-response time-dependent density functional theory (TDDFT) and show how these methods can provide a computational toolkit for the simulation of X-ray spectroscopy. The importance of the exchange-correlation functional for the calculation of XAS is discussed, and the introduction of short-range corrected functionals is described. The application of these calculations to study large systems through the use of efficient implementations of TDDFT will be highlighted, with the use of these methods illustrated through studies of ionic liquids and transition metal complexes. The extension of TDDFT to calculate XES through the use of a reference determinant for the core-ionized state will be described, and the factors that affect the accuracy of the computed spectra discussed. The application of these approaches will be illustrated through the study of a range of organic molecules and transition metal complexes, which also show how going beyond the dipole approximation in determining the transition intensities can be critical. The application of these approaches to the simulation of the RIXS spectrum of water will also be described, highlighting how ultrafast dynamics on the femtoscale time scale are evident in the measured spectra. In these calculations, the description of the core-ionized and core-excited states becomes increasingly important, and the role of the basis set in accurately describing these states will be explored.

Generalized single excitation configuration interaction: an investigation into the impact of the inclusion of non-orthogonality on the calculation of core-excited states

In this paper, we investigate different non-orthogonal generalizations of the configuration interaction with single substitutions (CIS) method and their impact on the calculation of core-excited states.

Molecular inner-shell photoabsorption/photoionization cross sections at core-valence-separated coupled cluster level: Theory and examples

Oxygen, nitrogen, and carbon K-shell photoabsorption and photoionization cross sections have been calculated within core-valence-separated coupled cluster (CC) linear response theory for a number of molecular systems, namely, water, ammonia, ethylene, carbon dioxide, acetaldehyde, furan, and pyrrole. The cross sections below and above the K-edge core ionization thresholds were obtained, on the same footing, from L² basis set calculations of the discrete electronic pseudospectrum yielded by an asymmetric-Lanczos-based formulation of CC linear response theory at the CC singles and doubles (CCSD) and CC singles and approximate doubles (CC2) levels. An analytic continuation procedure for both discrete and continuum cross sections as well as a Stieltjes imaging procedure for the photoionization cross section were applied and the results critically compared.

X-ray Absorption Near-Edge Structure Spectroscopy of a Stable 6-Oxoverdazyl Radical and Its Diamagnetic Precursor

The electronic structure of 1,3,5-triphenyl-6-oxoverdazyl, a heteroatom-rich stable organic radical, and its diamagnetic 1,3,5-triphenyl-6-oxotetrazane precursor are probed using X-ray absorption near-edge structure (XANES) spectroscopy. The N K-edge XANES spectra of the 6-oxoverdazyl radical contain strong N 1s → π* resonances for each set of equivalent nitrogen atoms. The fact that these resonances are absent from the analogous spectra of the 6-oxotetrazane, whereas the O K-edge and C K-edge XANES spectra of both species are very similar, demonstrates that the unpaired electron of the radical is localized primarily on the N atoms of the 6-oxoverdazyl heterocycle. The O K-edge XANES spectra of both species contain strong O 1s → π* (C═O) peaks, but the peak of the radical is red-shifted by 0.5 eV relative to that of the 6-oxotetrazane, which indicates that the C═O bond in the radical is part of a larger π-conjugated system. The proposed interpretations of the XANES spectra are aided by density-functional calculations.

Characterisation of the electronic structure of galvinoxyl free radical by variable energy UPS, XPS and NEXAFS spectroscopy

UPS, XPS and NEXAFS spectra of persistent free radical galvinoxyl are assigned using theoretical ΔDFT and TDDFT methods.