Perspective: multi-configurational methods in bio-inorganic chemistry.

Transition metal ions play crucial roles in the structure and function of numerous proteins, contributing to essential biological processes such as catalysis, electron transfer, and oxygen binding. However, accurately modeling the electronic structure and properties of metalloproteins poses significant challenges due to the complex nature of their electronic configurations and strong correlation effects. Multiconfigurational quantum chemistry methods are, in principle, the most appropriate tools for addressing these challenges, offering the capability to capture the inherent multi-reference character and strong electron correlation present in bio-inorganic systems.

Variational Pair-Density Functional Theory: Dealing with Strong Correlation at the Protein Scale.

Multiconfigurational pair-density functional theory (MC-PDFT) offers a promising solution to the challenges faced by traditional density functional theory (DFT) in addressing molecular systems containing transition metals, open-shells, or strong correlations in general. By utilizing both the density and on-top pair-density, MC-PDFT can make use of a more flexible multiconfigurational wave function to capture the necessary static correlation, while the pair-density functional also includes the effect of dynamic correlation. So far, MC-PDFT has been used after a multiconfigurational self-consistent field (MCSCF) step, using the orbitals and configuration interaction coefficients from the converged MCSCF wave function to compute PDFT energies and properties.

Multiconfigurational Pair-Density Functional Theory Is More Complex than You May Think.

Multiconfigurational pair-density functional theory (MC-PDFT) is a promising way to describe both strong and dynamic correlations in an inexpensive way. The functionals in MC-PDFT are often "translated" from standard spin density functionals. However, these translated functionals can in principle lead to "translated spin densities" with a nonzero imaginary component.

Complex Linear Response Functions for a Multiconfigurational Self-Consistent Field Wave Function in a High Performance Computing Environment.

We present novel developments for the highly efficient evaluation of complex linear response functions of a multiconfigurational self-consistent field (MCSCF) wave function as implemented in MultiPsi. Specifically, expressions for the direct evaluation of linear response properties at given frequencies using the complex polarization propagator (CPP) approach have been implemented, within both the Tamm-Dancoff approximation (TDA) and the random phase approximation (RPA). Purely real algebra with symmetric and antisymmetric trial vectors in a shared subspace is used wherein the linear response equations are solved.

The OpenMolcas : A Community-Driven Approach to Advancing Computational Chemistry.

The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.

Complete Active Space Methods for NISQ Devices: The Importance of Canonical Orbital Optimization for Accuracy and Noise Resilience.

To avoid the scaling of the number of qubits with the size of the basis set, one can divide the molecular space into active and inactive regions, which is also known as complete active space methods. However, selecting the active space alone is not enough to accurately describe quantum mechanical effects such as correlation. This study emphasizes the importance of optimizing the active space orbitals to describe correlation and improve the basis-dependent Hartree-Fock energies.

Soft X-ray signatures of cationic manganese-oxo systems, including a high-spin manganese(V) complex.

Manganese-oxo species catalyze key reactions, including C-H bond activation or dioxygen formation in natural photosynthesis. To better understand relevant reaction intermediates, we characterize electronic states and geometric structures of [MnO] manganese-oxo complexes that represent a wide range of manganese oxidation states. To this end, we apply soft X-ray spectroscopy in a cryogenic ion trap, combined with multiconfigurational wavefunction calculations.

Unravelling the mechanism of pH-regulation in dinoflagellate luciferase.

Dinoflagellates are the dominant source of bioluminescence in coastal waters. The luminescence reaction involves the oxidation of luciferin by a luciferase enzyme, which only takes place at low pH. The pH-dependence has previously been linked to four conserved histidines.

Exact semi-classical light-matter interaction operator applied to two-photon processes with strong relativistic effects.

X-ray processes involve interactions with high-energy photons. For these short wavelengths, the perturbing field cannot be treated as constant, and there is a need to go beyond the electric-dipole approximation. The exact semi-classical light-matter interaction operator offers several advantages compared to the multipole expansion such as improved stability and ease of implementation.

Origin of core-to-core x-ray emission spectroscopy sensitivity to structural dynamics.

Recently, coherent structural dynamics in the excited state of an iron photosensitizer was observed through oscillations in the intensity of K x-ray emission spectroscopy (XES). Understanding the origin of the unexpected sensitivity of core-to-core transitions to structural dynamics is important for further development of femtosecond time-resolved XES methods and, we believe, generally necessary for interpretation of XES signals from highly non-equilibrium structures that are ubiquitous in photophysics and photochemistry. Here, we use multiconfigurational wavefunction calculations combined with atomic theory to analyze the emission process in detail.

Toward a Computational Ecotoxicity Assay.

Thousands of anthropogenic chemicals are released into the environment each year, posing potential hazards to human and environmental health. Toxic chemicals may cause a variety of adverse health effects, triggering immediate symptoms or delayed effects over longer periods of time. It is thus crucial to develop methods that can rapidly screen and predict the toxicity of chemicals to limit the potential harmful impacts of chemical pollutants.

Simulations of valence excited states in coordination complexes reached through hard X-ray scattering.

Hard X-ray spectroscopy selectively probes metal sites in complex environments. Resonant inelastic X-ray scattering (RIXS) makes it is possible to directly study metal-ligand interactions through local valence excitations. Here multiconfigurational wavefunction simulations are used to model valence K pre-edge RIXS for three metal-hexacyanide complexes by coupling the electric dipole-forbidden excitations with dipole-allowed valence-to-core emission.

Core-level nonlinear spectroscopy triggered by stochastic X-ray pulses.

Stochastic processes are highly relevant in research fields as different as neuroscience, economy, ecology, chemistry, and fundamental physics. However, due to their intrinsic unpredictability, stochastic mechanisms are very challenging for any kind of investigations and practical applications. Here we report the deliberate use of stochastic X-ray pulses in two-dimensional spectroscopy to the simultaneous mapping of unoccupied and occupied electronic states of atoms in a regime where the opacity and transparency properties of matter are subject to the incident intensity and photon energy.

OpenMolcas: From Source Code to Insight.

In this Article we describe the OpenMolcas environment and invite the computational chemistry community to collaborate. The open-source project already includes a large number of new developments realized during the transition from the commercial MOLCAS product to the open-source platform. The paper initially describes the technical details of the new software development platform.

Efficient calculations of a large number of highly excited states for multiconfigurational wavefunctions.

Electronically excited states play important roles in many chemical reactions and spectroscopic techniques. In quantum chemistry, a common technique to solve excited states is the multiroot Davidson algorithm, but it is not designed for processes like X-ray spectroscopy that involves hundreds of highly excited states. We show how the use of a restricted active space wavefunction together with a projection operator to remove low-lying electronic states offers an efficient way to reach single and double-core-hole states.

Tracing the 267 nm-Induced Radical Formation in Dimethyl Disulfide Using Time-Resolved X-ray Absorption Spectroscopy.

Disulfide bonds are pivotal for the structure, function, and stability of proteins, and understanding ultraviolet (UV)-induced S-S bond cleavage is highly relevant for elucidating the fundamental mechanisms underlying protein photochemistry. Here, the near-UV photodecomposition mechanisms in gas-phase dimethyl disulfide, a prototype system with a S-S bond, are probed by ultrafast transient X-ray absorption spectroscopy. The evolving electronic structure during and after the dissociation is simultaneously monitored at the sulfur L-edges and the carbon K-edge with 100 fs (FWHM) temporal resolution using the broadband soft X-ray spectrum from a femtosecond high-order harmonics light source.

Molecular Orbital Simulations of Metal 1s2p Resonant Inelastic X-ray Scattering.

For first-row transition metals, high-resolution 3d electronic structure information can be obtained using resonant inelastic X-ray scattering (RIXS). In the hard X-ray region, a K pre-edge (1s→3d) excitation can be followed by monitoring the dipole-allowed Kα (2p→1s) or Kβ (3p→1s) emission, processes labeled 1s2p or 1s3p RIXS. Here the restricted active space (RAS) approach, which is a molecular orbital method, is used for the first time to study hard X-ray RIXS processes.

Viewing the Valence Electronic Structure of Ferric and Ferrous Hexacyanide in Solution from the Fe and Cyanide Perspectives.

The valence-excited states of ferric and ferrous hexacyanide ions in aqueous solution were mapped by resonant inelastic X-ray scattering (RIXS) at the Fe L2,3 and N K edges. Probing of both the central Fe and the ligand N atoms enabled identification of the metal- and ligand-centered excited states, as well as ligand-to-metal and metal-to-ligand charge-transfer excited states. Ab initio calculations utilizing the RASPT2 method were used to simulate the Fe L2,3-edge RIXS spectra and enabled quantification of the covalencies of both occupied and empty orbitals of π and σ symmetry.

Analytical State-Average Complete-Active-Space Self-Consistent Field Nonadiabatic Coupling Vectors: Implementation with Density-Fitted Two-Electron Integrals and Application to Conical Intersections.

Analytical state-average complete-active-space self-consistent field derivative (nonadiabatic) coupling vectors are implemented. Existing formulations are modified such that the implementation is compatible with Cholesky-based density fitting of two-electron integrals, which results in efficient calculations especially with large basis sets. Using analytical nonadiabatic coupling vectors, the optimization of conical intersections is implemented within the projected constrained optimization method.

Benzophenone Ultrafast Triplet Population: Revisiting the Kinetic Model by Surface-Hopping Dynamics.

The photochemistry of benzophenone, a paradigmatic organic molecule for photosensitization, was investigated by means of surface-hopping ab initio molecular dynamics. Different mechanisms were found to be relevant within the first 600 fs after excitation; the long-debated direct (S1 → T1) and indirect (S1 → T2 → T1) mechanisms for population of the low-lying triplet state are both possible, with the latter being prevalent. Moreover, we established the existence of a kinetic equilibrium between the two triplet states, never observed before.

Simulations of iron K pre-edge X-ray absorption spectra using the restricted active space method.

The intensities and relative energies of metal K pre-edge features are sensitive to both geometric and electronic structures. With the possibility to collect high-resolution spectral data it is important to find theoretical methods that include all important spectral effects: ligand-field splitting, multiplet structures, 3d-4p orbital hybridization, and charge-transfer excitations. Here the restricted active space (RAS) method is used for the first time to calculate metal K pre-edge spectra of open-shell systems, and its performance is tested against on six iron complexes: [FeCl6](n-), [FeCl4](n-), and [Fe(CN)6](n-) in ferrous and ferric oxidation states.

Molcas 8: New capabilities for multiconfigurational quantum chemical calculations across the periodic table.

In this report, we summarize and describe the recent unique updates and additions to the Molcas quantum chemistry program suite as contained in release version 8. These updates include natural and spin orbitals for studies of magnetic properties, local and linear scaling methods for the Douglas-Kroll-Hess transformation, the generalized active space concept in MCSCF methods, a combination of multiconfigurational wave functions with density functional theory in the MC-PDFT method, additional methods for computation of magnetic properties, methods for diabatization, analytical gradients of state average complete active space SCF in association with density fitting, methods for constrained fragment optimization, large-scale parallel multireference configuration interaction including analytic gradients via the interface to the Columbus package, and approximations of the CASPT2 method to be used for computations of large systems. In addition, the report includes the description of a computational machinery for nonlinear optical spectroscopy through an interface to the QM/MM package Cobramm.

Cost and sensitivity of restricted active-space calculations of metal L-edge X-ray absorption spectra.

The restricted active-space (RAS) approach can accurately simulate metal L-edge X-ray absorption spectra of first-row transition metal complexes without the use of any fitting parameters. These characteristics provide a unique capability to identify unknown chemical species and to analyze their electronic structure. To find the best balance between cost and accuracy, the sensitivity of the simulated spectra with respect to the method variables has been tested for two models, [FeCl6 ](3-) and [Fe(CN)6 ](3-) .

Analytical gradients of the state-average complete active space self-consistent field method with density fitting.

An efficient implementation of the state-averaged complete active space self-consistent field (SA-CASSCF) gradients employing density fitting (DF) is presented. The DF allows a reduction both in scaling and prefactors of the different steps involved. The performance of the algorithm is demonstrated on a set of molecules ranging up to an iron-Heme b complex which with its 79 atoms and 811 basis functions is to our knowledge the largest SA-CASSCF gradient computed.

Correction: Orbital entanglement and CASSCF analysis of the Ru-NO bond in a Ruthenium nitrosyl complex.

Correction for ‘Orbital entanglement and CASSCF analysis of the Ru–NO bond in a Ruthenium nitrosyl complex’ by Leon Freitag , 2015, DOI: ; 10.1039/c4cp05278a.