Efficient Spin-Adapted Implementation of Multireference Algebraic Diagrammatic Construction Theory. I. Core-Ionized States and X-ray Photoelectron Spectra.

We present an efficient implementation of multireference algebraic diagrammatic construction theory (MR-ADC) for simulating core-ionized states and X-ray photoelectron spectra (XPS). Taking advantage of spin adaptation, automatic code generation, and density fitting, our implementation can perform calculations for molecules with more than 1500 molecular orbitals, incorporating static and dynamic correlation in the ground and excited electronic states. We demonstrate the capabilities of MR-ADC methods by simulating the XPS spectra of substituted ferrocene complexes and azobenzene isomers. For the ground electronic states of these molecules, the XPS spectra computed using the extended second-order MR-ADC method (MR-ADC(2)-X) are in a very good agreement with available experimental results. We further show that MR-ADC can be used as a tool for interpreting or predicting the results of time-resolved XPS measurements by simulating the core ionization spectra of azobenzene along its photoisomerization, including the XPS signatures of excited states and the minimum energy conical intersection. This work is the first in a series of publications reporting the efficient implementations of MR-ADC methods.

Simulating transient X-ray photoelectron spectra of Fe(CO)5 and its photodissociation products with multireference algebraic diagrammatic construction theory.

Accurate simulations of transient X-ray photoelectron spectra (XPS) provide unique opportunities to bridge the gap between theory and experiment in understanding the photoactivated dynamics in molecules and materials. However, simulating X-ray photoelectron spectra along a photochemical reaction pathway is challenging as it requires accurate description of electronic structure incorporating core-hole screening, orbital relaxation, electron correlation, and spin-orbit coupling in excited states or at nonequilibrium ground-state geometries. In this work, we employ the recently developed multireference algebraic diagrammatic construction theory (MR-ADC) to investigate the core-ionized states and X-ray photoelectron spectra of Fe(CO)5 and its photodissociation products (Fe(CO)4, Fe(CO)3) following excitation with 266 nm light. The simulated transient Fe 3p and CO 3σ XPS spectra incorporating spin-orbit coupling and high-order electron correlation effects are shown to be in a good agreement with the experimental measurements by Leitner et al. [J. Chem. Phys., 2018, 149, 044307]. Our calculations suggest that core-hole screening, spin-orbit coupling, and ligand-field splitting effects are similarly important in reproducing the experimentally observed chemical shifts in transient Fe 3p XPS spectra of iron carbonyl complexes. Our results also demonstrate that the MR-ADC methods can be very useful in interpreting the transient XPS spectra of transition metal compounds.

Comparison among several vibronic coupling methods.

A comparison of four approaches to account the vibronic coupling in photoabsorption is performed. The methods considered are nuclear ensemble (NE), direct vibronic coupling (DVC), adiabatic Hessian (AH), and vertical gradient (VG). The case study is the symmetry-forbidden [Formula: see text] [Formula: see text]A[Formula: see text] [Formula: see text] [Formula: see text] [Formula: see text]A[Formula: see text] (n [Formula: see text] [Formula: see text]) transition in formaldehyde. Being forbidden in the equilibrium geometry, this transition is entirely induced by vibronic coupling and constitutes an appropriate case to study the performance of different methods. From DVC, it is found that mode 1 (C=O out-of-plane bending) is the most inducing, followed by mode 6 (in-plane C-H asymmetric stretching) and finally by mode 2 (in-plane C-H asymmetric bending). We were able to correlate 17 out of 20 structures obtained from NE with these modes, showing that these two methods, although different in principle, give comparable results. The simulated spectra were obtained for all methods and compared, and each one has its own advantage. In what concerns the transition studied, NE gives the best description of the spectrum, DVC is the only one that easily gives an absolute value for OOS, and AH and VG are the computationally less expensive methods. From the latter two, VG is the less demanding on computational grounds, since it does not require the excited state Hessian.

Electron delocalisation in conjugated sulfur heterocycles probed by resonant Auger spectroscopy.

We propose a novel approach for an indirect probing of conjugation and hyperconjugation in core-excited molecules using resonant Auger spectroscopy. Our work demonstrates that the changes in the electronic structure of thiophene (C4H4S) and thiazole (C3H3NS), occurring in the process of resonant sulfur K-shell excitation and Auger decay, affect the stabilisation energy resulting from π-conjugation and hyperconjugation. The variations in the stabilisation energy manifest themselves in the resonant S KL2,3L2,3 Auger spectra of thiophene and thiazole. The comparison of the results obtained for the conjugated molecules and for thiolane (C4H8S), the saturated analogue of thiophene, has been performed. The experimental observations are interpreted using high-level quantum-mechanical calculations and the natural bond orbital analysis.

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

Correction for 'Simulating X-ray photoelectron spectra with strong electron correlation using multireference algebraic diagrammatic construction theory' by Carlos E. V. de Moura and Alexander Yu. Sokolov, Phys. Chem. Chem. Phys., 2022, 24, 4769-4784, DOI: 10.1039/D1CP05476G.

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

We present 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) [J. Chem. Phys., 2018, 149, 204113] with a core-valence separation (CVS) technique. The resulting CVS-MR-ADC approach has a low computational cost while overcoming many challenges of the conventional multireference theories associated with the calculations of excitations from inner-shell and core molecular orbitals. Our results demonstrate that the CVS-MR-ADC methods are as accurate as single-reference ADC approximations for predicting core ionization energies of weakly-correlated molecules, but are more accurate and reliable for systems with a multireference character, such as a stretched nitrogen molecule, ozone, and isomers of the benzyne diradical. We also highlight the importance of multireference effects for the description of core-hole screening that determines the relative spacing and order of peaks in the XPS spectra of strongly correlated systems.

The problem of hole localization in inner-shell states of N2 and CO2 revisited with complete active space self-consistent field approach.

Potential energy curves for inner-shell states of nitrogen and carbon dioxide molecules are calculated by inner-shell complete active space self-consistent field (CASSCF) method, which is a protocol, recently proposed, to obtain specifically converged inner-shell states at multiconfigurational level. This is possible since the collapse of the wave function to a low-lying state is avoided by a sequence of constrained optimization in the orbital mixing step. The problem of localization of K-shell states is revisited by calculating their energies at CASSCF level based on both localized and delocalized orbitals. The localized basis presents the best results at this level of calculation. Transition energies are also calculated by perturbation theory, by taking the above mentioned MCSCF function as zeroth order wave function. Values for transition energy are in fairly good agreement with experimental ones. Bond dissociation energies for N(2) are considerably high, which means that these states are strongly bound. Potential curves along ground state normal modes of CO(2) indicate the occurrence of Renner-Teller effect in inner-shell states.