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.

Consistent Second-Order Treatment of Spin-Orbit Coupling and Dynamic Correlation in Quasidegenerate N-Electron Valence Perturbation Theory.

We present a formulation and implementation of second-order quasidegenerate N-electron valence perturbation theory (QDNEVPT2) that provides a balanced and accurate description of spin-orbit coupling and dynamic correlation effects in multiconfigurational electronic states. In our approach, the energies and wave functions of electronic states are computed by treating electron repulsion and spin-orbit coupling operators as equal perturbations to the nonrelativistic complete active-space wave functions, and their contributions are incorporated fully up to the second order. The spin-orbit effects are described using the Breit-Pauli (BP) or exact two-component Douglas-Kroll-Hess (DKH) Hamiltonians within spin-orbit mean-field approximation. The resulting second-order methods (BP2- and DKH2-QDNEVPT2) are capable of treating spin-orbit coupling effects in nearly degenerate electronic states by diagonalizing an effective Hamiltonian expanded in a compact non-relativistic basis. For a variety of atoms and small molecules across the entire periodic table, we demonstrate that DKH2-QDNEVPT2 is competitive in accuracy with variational two-component relativistic theories. BP2-QDNEVPT2 shows high accuracy for the second- and third-period elements, but its performance deteriorates for heavier atoms and molecules. We also consider the first-order spin-orbit QDNEVPT2 approximations (BP1- and DKH1-QDNEVPT2), among which DKH1-QDNEVPT2 is reliable but less accurate than DKH2-QDNEVPT2. Both DKH1- and DKH2-QDNEVPT2 hold promise as efficient and accurate electronic structure methods for treating electron correlation and spin-orbit coupling in a variety of applications.

Quantifying spin contamination in algebraic diagrammatic construction theory of electronic excitations.

Algebraic diagrammatic construction (ADC) is a computationally efficient approach for simulating excited electronic states, absorption spectra, and electron correlation. Due to their origin in perturbation theory, the single-reference ADC methods may be susceptible to spin contamination when applied to molecules with unpaired electrons. In this work, we develop an approach to quantify spin contamination in the ADC calculations of electronic excitations and apply it to a variety of open-shell molecules starting with either the unrestricted (UHF) or restricted open-shell (ROHF) Hartree-Fock reference wavefunctions. Our results show that the accuracy of low-order ADC approximations [ADC(2) and ADC(3)] significantly decreases when the UHF reference spin contamination exceeds 0.05 a.u. Such strongly spin-contaminated molecules exhibit severe excited-state spin symmetry breaking that contributes to decreasing the quality of computed excitation energies and oscillator strengths. In a case study of phenyl radical, we demonstrate that spin contamination can significantly affect the simulated UV/Vis spectra, altering the relative energies, intensities, and order of electronic transitions. The results presented here motivate the development of spin-adapted ADC methods for open-shell molecules.

Two-State Hydrogen Atom Transfer Reactivity of Unsymmetric [Cu2(O)(NO)]2+ Complexes.

We report the temperature-dependent spin switching of dicopper oxo nitrosyl [Cu2(O)(NO)]2+ complexes and their influence on hydrogen atom transfer (HAT) reactivity. Electron paramagnetic resonance (EPR) and Evans method analysis suggest that [Cu2(O)(NO)]2+ complexes transition from the S = 1/2 to the S = 3/2 state around ca. 202 K. At low temperatures (198 K) where S = 3/2 dominates, a strong correlation between the rate of HAT (kHAT) and the population of the S = 1/2 state was identified (R2 = 0.988), suggesting that the HAT by [Cu2(O)(NO)]2+ complexes proceeds by the S = 1/2 isomer. Installation of functional groups that introduce an unsymmetric secondary coordination environment accelerates the HAT rates through perturbation of the spin equilibria. Given the often unsymmetric coordination sphere of bimetallic active sites in natural proteins, we anticipate that similar strategies could be employed by metalloenzymes to control HAT reactions.

Core-Excited States and X-ray Absorption Spectra from Multireference Algebraic Diagrammatic Construction Theory.

We report the development and benchmark of multireference algebraic diagrammatic construction theory (MR-ADC) for the simulations of core-excited states and X-ray absorption spectra (XAS). Our work features an implementation that incorporates core-valence separation into the strict and extended second-order MR-ADC approximations (MR-ADC(2) and MR-ADC(2)-X), providing efficient access to high-energy excited states without including inner-shell orbitals in the active space. Benchmark results on a set of small molecules indicate that at equilibrium geometries, the accuracy of MR-ADC is similar to that of single-reference ADC theory when static correlation effects are not important. In this case, MR-ADC(2)-X performs similarly to single- and multireference coupled cluster methods in reproducing the experimental XAS peak spacings. We demonstrate the potential of MR-ADC for chemical systems with multiconfigurational electronic structure by calculating the K-edge XAS spectrum of the ozone molecule with a multireference character in its ground electronic state and the dissociation curve of core-excited molecular nitrogen. For ozone, the MR-ADC results agree well with the data from experimental and previous multireference studies of ozone XAS, in contrast to the results of single-reference methods, which underestimate relative peak energies and intensities. The MR-ADC methods also predict the correct shape of the core-excited nitrogen potential energy curve, and are in good agreement with accurate calculations using driven similarity renormalization group approaches. These findings suggest that MR-ADC(2) and MR-ADC(2)-X are promising methods for the XAS simulations of multireference systems and pave the way for their efficient computer implementation and applications.

Algebraic Diagrammatic Construction Theory for Simulating Charged Excited States and Photoelectron Spectra.

Charged excitations are electronic transitions that involve a change in the total charge of a molecule or material. Understanding the properties and reactivity of charged species requires insights from theoretical calculations that can accurately describe orbital relaxation and electron correlation effects in open-shell electronic states. In this Review, we describe the current state of algebraic diagrammatic construction (ADC) theory for simulating charged excitations and its recent developments. We start with a short overview of ADC formalism for the one-particle Green's function, including its single- and multireference formulations and extension to periodic systems. Next, we focus on the capabilities of ADC methods and discuss recent findings about their accuracy for calculating a wide range of excited-state properties. We conclude our Review by outlining possible directions for future developments of this theoretical approach.

Electronic Structure and Ultrafast Electron Dynamics in CuO Photocatalysts Probed by Surface Sensitive Femtosecond X-ray Absorption Near-Edge Structure Spectroscopy.

CuO is often employed as a photocathode for H2 evolution and CO2 reduction, but observed efficiency is still far below the theoretical limit. To bridge the gap requires understanding the CuO electronic structure; however, computational efforts lack consensus on the orbital character of the photoexcited electron. In this study, we measure the femtosecond XANES spectra of CuO at the Cu M2,3 and O L1 edges to track the element-specific dynamics of electrons and holes. Results show that photoexcitation represents an O 2p to Cu 4s charge transfer state indicating the conduction band electron has primarily Cu 4s character. We also observe ultrafast mixing of Cu 3d and 4s conduction band states mediated by coherent phonons, with Cu 3d character of the photoelectron reaching a maximum of 16%. This is the first observation of the photoexcited redox state in CuO, and results provide a benchmark for theory where electronic structure modeling still relies heavily on model-dependent parametrization.

C(sp3)-H cyanation by a formal copper(iii) cyanide complex.

High-valent metal oxo complexes are prototypical intermediates for the activation and hydroxylation of alkyl C-H bonds. Substituting the oxo ligand with other functional groups offers the opportunity for additional C-H functionalization beyond C-O bond formation. However, few species aside from metal oxo complexes have been reported to both activate and functionalize alkyl C-H bonds. We herein report the first example of an isolated copper(iii) cyanide complex (LCuIIICN) and its C-H cyanation reactivity. We found that the redox potential (E ox) of substrates, instead of C-H bond dissociation energy, is a key determinant of the rate of PCET, suggesting an oxidative asynchronous CPET or ETPT mechanism. Among substrates with the same BDEs, those with low redox potentials transfer H atoms up to a million-fold faster. Capitalizing on this mechanistic insight, we found that LCuIIICN is highly selective for cyanation of amines, which is predisposed to oxidative asynchronous or stepwise transfer of H+/e-. Our study demonstrates that the asynchronous effect of PCET is an appealing tool for controlling the selectivity of C-H functionalization.

Simulating Spin-Orbit Coupling with Quasidegenerate N-Electron Valence Perturbation Theory.

We present the first implementation of spin-orbit coupling effects in fully internally contracted second-order quasidegenerate N-electron valence perturbation theory (SO-QDNEVPT2). The SO-QDNEVPT2 approach enables the computations of ground- and excited-state energies and oscillator strengths combining the description of static electron correlation with an efficient treatment of dynamic correlation and spin-orbit coupling. In addition to SO-QDNEVPT2 with the full description of one- and two-body spin-orbit interactions at the level of two-component Breit-Pauli Hamiltonian, our implementation also features a simplified approach that takes advantage of spin-orbit mean-field approximation (SOMF-QDNEVPT2). The accuracy of these methods is tested for the group 14 and 16 hydrides, 3d and 4d transition metal ions, and two actinide dioxides (neptunyl and plutonyl dications). The zero-field splittings of group 14 and 16 molecules computed using SO-QDNEVPT2 and SOMF-QDNEVPT2 are in good agreement with the available experimental data. For the 3d transition metal ions, the SO-QDNEVPT2 method is significantly more accurate than SOMF-QDNEVPT2, while no substantial difference in the performance of two methods is observed for the 4d ions. Finally, we demonstrate that for the actinide dioxides the results of SO-QDNEVPT2 and SOMF-QDNEVPT2 are in good agreement with the data from previous theoretical studies of these systems. Overall, our results demonstrate that SO-QDNEVPT2 and SOMF-QDNEVPT2 are promising multireference methods for treating spin-orbit coupling with a relatively low computational cost.

Electrochemical Strategy for Proton Relay Installation Enhances the Activity of a Hydrogen Evolution Electrocatalyst.

A new method to install a proton relay that enhances the reactivity near an active catalytic site for H2 production is reported, afforded by the electrochemical reduction and protonation of one of the ligands in the paddlewheel Rh2(II,II) hydrogen evolution complex, cis-[Rh2(DPhF)2(bncn)2]2+ (Rh-bncn; DPhF = N,N'-diphenylformamidinate, bncn = benzo[c]cinnoline). An electrochemical reversible prewave is observed for Rh-bncn at potentials more positive than the first bncn-centered reduction couple in the presence of strong acids, observed at -0.72 V vs Fc+/0 (Fc = ferrocene) in the cyclic voltammograms (CVs) in DMF (0.1 M TBAPF6). The origin of this prewave is shown to arise from a precatalytic transformation that originates from a concerted proton-electron transfer (CPET) event occurring at one of the bridging bncn ligands. Through electrochemical analysis, CV simulations, and electronic structure calculations, a reaction mechanism is elucidated. In this system, the electrochemically formed N-H bond on the reduced bncn ligand serves as a proton relay in the H2 formation reaction through a cooperative interligand pathway involving one of the bridging DPhF ligands after a second reduction step, accessible at approximately -1.15 V vs Fc+/0. Since calculations show that hydrogen evolution takes place at the bridging ligands and does not involve the dirhodium core, it is predicted that more abundant metal centers can be incorporated into this ligand scaffold, leading to new candidates for electrocatalytic hydrogen reduction. As such, this work delineates a new design strategy to incorporate proton relays in molecular bimetallic hydrogen evolution electrocatalysts to achieve higher efficiency.

Non-Dyson Algebraic Diagrammatic Construction Theory for Charged Excitations in Solids.

We present the first implementation and applications of non-Dyson algebraic diagrammatic construction theory for charged excitations in three-dimensional periodic solids (EA/IP-ADC). The EA/IP-ADC approach has a computational cost similar to the ground-state Møller-Plesset perturbation theory, enabling efficient calculations of a variety of crystalline excited-state properties (e.g., band structure, band gap, density of states) sampled in the Brillouin zone. We use EA/IP-ADC to compute the quasiparticle band structures and band gaps of several materials (from large-gap atomic and ionic solids to small-gap semiconductors) and analyze the errors of EA/IP-ADC approximations up to the third order in perturbation theory. Our work also reports the first-ever calculations of ground-state properties (equation-of-state and lattice constants) of three-dimensional crystalline systems using a periodic implementation of third-order Møller-Plesset perturbation theory (MP3).

Quantifying and reducing spin contamination in algebraic diagrammatic construction theory of charged excitations.

Algebraic diagrammatic construction (ADC) theory is a computationally efficient and accurate approach for simulating electronic excitations in chemical systems. However, for the simulations of excited states in molecules with unpaired electrons, the performance of ADC methods can be affected by the spin contamination in unrestricted Hartree-Fock (UHF) reference wavefunctions. In this work, we benchmark the accuracy of ADC methods for electron attachment and ionization of open-shell molecules with the UHF reference orbitals (EA/IP-ADC/UHF) and develop an approach to quantify the spin contamination in charged excited states. Following this assessment, we demonstrate that the spin contamination can be reduced by combining EA/IP-ADC with the reference orbitals from restricted open-shell Hartree-Fock (ROHF) or orbital-optimized Møller-Plesset perturbation (OMP) theories. Our numerical results demonstrate that for open-shell systems with strong spin contamination in the UHF reference, the third-order EA/IP-ADC methods with the ROHF or OMP reference orbitals are similar in accuracy to equation-of-motion coupled cluster theory with single and double excitations.

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.

Multireference Algebraic Diagrammatic Construction Theory for Excited States: Extended Second-Order Implementation and Benchmark.

We present an implementation and benchmark of new approximations in multireference algebraic diagrammatic construction theory for simulations of neutral electronic excitations and UV/vis spectra of strongly correlated molecular systems (MR-ADC). Following our work on the first-order MR-ADC approximation [J. Chem. Phys. 2018, 149, 204113], we report the strict and extended second-order MR-ADC methods (MR-ADC(2) and MR-ADC(2)-X) that combine the description of static and dynamic electron correlation in the ground and excited electronic states without relying on state-averaged reference wave functions. We present an extensive benchmark of the new MR-ADC methods for excited states in several small molecules, including the carbon dimer, ethylene, and butadiene. Our results demonstrate that, for weakly correlated electronic states, the MR-ADC(2) and MR-ADC(2)-X methods outperform the third-order single-reference ADC approximation and are competitive with the results from equation-of-motion coupled cluster theory. For states with multireference character, the performance of the MR-ADC methods is similar to that of an N-electron valence perturbation theory. In contrast to conventional multireference perturbation theories, the MR-ADC methods have many attractive features, such as a straightforward and efficient calculation of excited-state properties and a direct access to excitations outside of the frontier (active) orbitals.

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.

Assessing the orbital-optimized unitary Ansatz for density cumulant theory.

The previously proposed Ansatz for density cumulant theory that combines orbital-optimization and a parameterization of the 2-electron reduced density matrix cumulant in terms of unitary coupled cluster amplitudes (OUDCT) is carefully examined. Formally, we elucidate the relationship between OUDCT and orbital-optimized unitary coupled cluster theory and show the existence of near-zero denominators in the stationarity conditions for both the exact and some approximate OUDCT methods. We implement methods of the OUDCT Ansatz restricted to double excitations for numerical study, up to the fifth commutator in the Baker-Campbell-Hausdorff expansion. We find that methods derived from the Ansatz beyond the previously known ODC-12 method tend to be less accurate for equilibrium properties and less reliable when attempting to describe H2 dissociation. New developments are needed to formulate more accurate density cumulant theory variants.

Extended Second-Order Multireference Algebraic Diagrammatic Construction Theory for Charged Excitations.

We report a new implementation of multireference algebraic diagrammatic construction theory (MR-ADC) for simulations of electron attachment and ionization in strongly correlated molecular systems (EA/IP-MR-ADC). Following our recent work on IP-MR-ADC [J. Chem. Theory Comput. 2019, 15, 5908], we present the first implementation of the second-order MR-ADC method for electron attachment (EA-MR-ADC(2)) and two extended second-order approximations (EA- and IP-MR-ADC(2)-X) that incorporate a partial treatment of third-order electron correlation effects. Introducing a small approximation for the second-order amplitudes of the effective Hamiltonian, our implementation of EA- and IP-MR-ADC(2)-X has a low O(M5) computational scaling with the basis set size M. Additionally, we describe an efficient algorithm for solving the first-order amplitude equations in MR-ADC and partially contracted second-order N-electron valence perturbation theory (NEVPT2) which completely avoids computation of the four-particle reduced density matrices without introducing any approximations or imaginary-time propagation. For a benchmark set of eight small molecules, a carbon dimer, and a twisted ethylene, we demonstrate that EA- and IP-MR-ADC(2)-X achieve an accuracy similar to that of strongly contracted NEVPT2 while having a lower computational scaling with the active space size and providing efficient access to transition properties.

Recent developments in the PySCF program package.

PySCF is a Python-based general-purpose electronic structure platform that supports first-principles simulations of molecules and solids as well as accelerates the development of new methodology and complex computational workflows. This paper explains the design and philosophy behind PySCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PySCF as a development environment. We then summarize the capabilities of PySCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PySCF across the domains of quantum chemistry, materials science, machine learning, and quantum information science.