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.

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.

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.

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.

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.

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.

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.

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.

Psi4 1.4: Open-source software for high-throughput quantum chemistry.

PSI4 is a free and open-source ab initio electronic structure program providing implementations of Hartree-Fock, density functional theory, many-body perturbation theory, configuration interaction, density cumulant theory, symmetry-adapted perturbation theory, and coupled-cluster theory. Most of the methods are quite efficient, thanks to density fitting and multi-core parallelism. The program is a hybrid of C++ and Python, and calculations may be run with very simple text files or using the Python API, facilitating post-processing and complex workflows; method developers also have access to most of PSI4's core functionalities via Python. Job specification may be passed using The Molecular Sciences Software Institute (MolSSI) QCSCHEMA data format, facilitating interoperability. A rewrite of our top-level computation driver, and concomitant adoption of the MolSSI QCARCHIVE INFRASTRUCTURE project, makes the latest version of PSI4 well suited to distributed computation of large numbers of independent tasks. The project has fostered the development of independent software components that may be reused in other quantum chemistry programs.

Simulating X-ray Absorption Spectra with Linear-Response Density Cumulant Theory.

We present a new approach for simulating X-ray absorption spectra based on linear-response density cumulant theory (LR-DCT) [ Copan , A. V. ; Sokolov , A. Yu. J. Chem. Theory Comput. 2018 , 14 , 4097 - 4108 ]. Our new method combines the LR-ODC-12 formulation of LR-DCT with core-valence separation approximation (CVS) that allows us to efficiently access high-energy core-excited states. We describe our computer implementation of the CVS-approximated LR-ODC-12 method (CVS-ODC-12) and benchmark its performance by comparing simulated X-ray absorption spectra to those obtained from experiment for several small molecules. Our results demonstrate that the CVS-ODC-12 method shows good agreement with experiment for relative spacings between transitions and their intensities, but the excitation energies are systematically overestimated. When compared to results from excited-state coupled cluster methods with single and double excitations, the CVS-ODC-12 method shows a similar performance for intensities and peak separations, while coupled cluster spectra are less shifted, relative to experiment. An important advantage of CVS-ODC-12 is that its excitation energies are computed by diagonalizing a Hermitian matrix, which enables efficient computation of transition intensities.

Third-order algebraic diagrammatic construction theory for electron attachment and ionization energies: Conventional and Green's function implementation.

We present implementation of second- and third-order algebraic diagrammatic construction (ADC) theory for efficient and accurate computations of molecular electron affinities (EA), ionization potentials (IP), and densities of states [EA-/IP-ADC(n), n = 2, 3]. Our work utilizes the non-Dyson formulation of ADC for the single-particle propagator and reports working equations and benchmark results for the EA-ADC(2) and EA-ADC(3) approximations. We describe two algorithms for solving EA-/IP-ADC equations: (i) conventional algorithm that uses iterative diagonalization techniques to compute low-energy EA, IP, and density of states and (ii) Green's function algorithm (GF-ADC) that solves a system of linear equations to compute density of states directly for a specified spectral region. To assess the accuracy of EA-ADC(2) and EA-ADC(3), we benchmark their performance for a set of atoms, small molecules, and five DNA/RNA nucleobases. As our next step, we demonstrate the efficiency of our GF-ADC implementation by computing core-level K-, L-, and M-shell ionization energies of a zinc atom without introducing the core-valence separation approximation. Finally, we use EA- and IP-ADC methods to compute the bandgaps of equally spaced hydrogen chains Hn with n up to 150, providing their estimates near thermodynamic limit. Our results demonstrate that EA-/IP-ADC(n) (n = 2, 3) methods are efficient and accurate alternatives to widely used electronic structure methods for simulations of electron attachment and ionization properties.

Four-Coordinate Copper Halonitrosyl {CuNO}10 Complexes.

While copper nitrosyl complexes are implicated in numerous biological systems, isolable examples remain limited. In this report, we show that [Cl3 CuNO]- , with a {CuNO}10 electron configuration, can be generated by nitrite reduction at a copper(I) dichloride anion or by nitric oxide addition to a copper(II) trichloride precursor. The bromide analogue, [Br3 CuNO]- was synthesized analogously, and both copper halonitrosyl complexes were characterized by X-ray diffraction and a variety of spectroscopic methods. Experimental data and multireference (CASSCF/NEVPT2) calculations provide strong evidence for a CuII -NO. ground state. Both [Cl3 CuNO]- and [Br3 CuNO]- release and recapture NO. reversibly, and exhibit nitrosative reactivities toward a wide range of biological nucleophiles, such as amines, alcohols, and thiols.

Multi-reference algebraic diagrammatic construction theory for excited states: General formulation and first-order implementation.

We present a multi-reference generalization of the algebraic diagrammatic construction (ADC) theory [J. Schirmer, Phys. Rev. A 26, 2395 (1982)] for excited electronic states. The resulting multi-reference ADC (MR-ADC) approach can be efficiently and reliably applied to systems, which exhibit strong electron correlation in the ground or excited electronic states. In contrast to conventional multi-reference perturbation theories, MR-ADC describes electronic transitions involving all orbitals (core, active, and external) and enables efficient computation of spectroscopic properties, such as transition amplitudes and spectral densities. Our derivation of MR-ADC is based on the effective Liouvillian formalism of Mukherjee and Kutzelnigg [Many-Body Methods in Quantum Chemistry (Springer, 1989), pp. 257-274], which we generalize to multi-determinant reference states. We discuss a general formulation of MR-ADC, perform its perturbative analysis, and present an implementation of the first-order MR-ADC approximation, termed MR-ADC(1), as a first step in defining the MR-ADC hierarchy of methods. We show results of MR-ADC(1) for the excitation energies of the Be atom, an avoided crossing in LiF, and doubly excited states in C2 and outline directions for our future developments.

Time-dependent N-electron valence perturbation theory with matrix product state reference wavefunctions for large active spaces and basis sets: Applications to the chromium dimer and all-trans polyenes.

In earlier work [A. Y. Sokolov and G. K.-L. Chan, J. Chem. Phys. 144, 064102 (2016)], we introduced a time-dependent formulation of the second-order N-electron valence perturbation theory (t-NEVPT2) which (i) had a lower computational scaling than the usual internally contracted perturbation formulation and (ii) yielded the fully uncontracted NEVPT2 energy. Here, we present a combination of t-NEVPT2 with a matrix product state (MPS) reference wavefunction (t-MPS-NEVPT2) that allows us to compute uncontracted dynamic correlation energies for large active spaces and basis sets, using the time-dependent density matrix renormalization group algorithm. In addition, we report a low-scaling MPS-based implementation of strongly contracted NEVPT2 (sc-MPS-NEVPT2) that avoids computation of the four-particle reduced density matrix. We use these new methods to compute the dissociation energy of the chromium dimer and to study the low-lying excited states in all-trans polyenes (C4H6 to C24H26), incorporating dynamic correlation for reference wavefunctions with up to 24 active electrons and orbitals.

A time-dependent formulation of multi-reference perturbation theory.

We discuss the time-dependent formulation of perturbation theory in the context of the interacting zeroth-order Hamiltonians that appear in multi-reference situations. As an example, we present a time-dependent formulation and implementation of second-order n-electron valence perturbation theory. The resulting time-dependent n-electron valence second-order perturbation theory (t-NEVPT2) method yields the fully uncontracted n-electron valence perturbation wavefunction and energy, but has a lower computational scaling than the usual contracted variants, and also avoids the construction of high-order density matrices and the diagonalization of metrics. We present results of t-NEVPT2 for the water, nitrogen, carbon, and chromium molecules and outline directions for the future.