Restricted Active Space Configuration Interaction Research Articles

Singlet-Triplet Inversion in Triangular Boron Carbon Nitrides.

The discovery of singlet-triplet (ST) inversion in some π-conjugated triangle-shaped boron carbon nitrides is a remarkable breakthrough that defies Hund's first rule. Deeply rooted in strong electron-electron interactions, ST inversion has garnered significant interest due to its potential to revolutionize triplet harvesting in organic LEDs. Using the well-established Pariser-Parr-Pople model for correlated electrons in π-conjugated systems, we employ a combination of CISDT and restricted active space configuration interaction calculations to investigate the photophysics of several triangular boron carbon nitrides. Our findings reveal that ST inversion in these systems is primarily driven by a network of alternating electron-donor and electron-acceptor groups in the molecular rim, rather than by the triangular molecular structure itself.

Spin–Orbit Couplings of Open-Shell Systems with Restricted Active Space Configuration Interaction

In this work we perform electronic structure calculations to unravel the origin of spin-orbit couplings (SOCs) in open-shell molecules. For that, we select systems displaying di or polyradical character, e.g., trimethylene, and analyze the changes in the magnitude of SOC constants along molecular distortions of ethylene and in the presence of intermolecular interactions between open and closed-shell moieties in the O2-C2H4 system. Calculations were performed by using nonrelativistic wave functions obtained with the restricted active space configuration interaction (RASCI) method, in conjunction with a recent implementation for the calculation of SOC based on the spin-orbit mean field approximation. Our results demonstrate the suitability of RASCI in the calculation of SOCs of open-shell systems, while providing a deep understanding of the relationship between couplings and the nature of the electronic states. Moreover, we introduce a new definition of the SOC constant for the study of molecular aggregates.

RhoDyn: A ρ-TD-RASCI Framework to Study Ultrafast Electron Dynamics in Molecules.

This article presents the program module RhoDyn as part of the OpenMOLCAS project intended to study ultrafast electron dynamics within the density-matrix-based time-dependent restricted active space configuration interaction framework (ρ-TD-RASCI). The formalism allows for the treatment of spin-orbit coupling effects, accounts for nuclear vibrations in the form of a vibrational heat bath, and naturally incorporates (auto)ionization effects. Apart from describing the theory behind and the program workflow, the paper also contains examples of its application to the simulations of the linear L2,3 absorption spectra of a titanium complex, high harmonic generation in the hydrogen molecule, ultrafast charge migration in benzene and iodoacetylene, and spin-flip dynamics in the core excited states of iron complexes.

Two-Component Multireference Restricted Active Space Configuration Interaction for the Computation of L-Edge X-ray Absorption Spectra.

X-ray absorption spectroscopy is a powerful probe of local electronic and nuclear structures, providing insights into chemical processes. The theoretical prediction and interpretation of metal L-edge X-ray absorption spectra are complicated by both relativistic effects, including spin-orbit coupling and the multiconfigurational nature of the states involved. This work details an exact two-component multireference restricted active space (RAS) configuration interaction scheme that uses an exact two-component state-averaged complete active space self-consistent-field method, which includes the spin-orbit coupling in a variational manner, for the accurate description of the electronic structure before using a RAS configuration interaction method to describe the core excited states of the X-ray spectrum. Benchmark calculations are presented for a series of iron-containing complexes, with results showing key features of the spectrum being reproduced, including ligand-to-metal charge transfer and shake-up excitations.

Restricted active space configuration interaction methods for strong correlation: Recent developments

AbstractIn this review we outline the theory and recent progress of the restricted active space configuration interaction (RASCI) methodology within the hole and particle approximation. The RASCI is a single reference approach based on the splitting of the orbital space in different subsets, in which the target CI space is expressed by the concomitant number of electrons and empty orbitals in each subspace. Initially, the method was born as a spin complete version of the spin‐flip ansatz able to deal with any number of unpaired electrons. Since then, the method has experienced several improvements related to its theoretical foundations, its efficient implementation, in the characterization of RASCI wave functions, and in the calculation of molecular properties. It has shown to be especially suitable for the characterization of medium to large molecular diradicals and polyradicals, and to the study of photophysical processes involving open‐shell species and/or multiexcitonic states, like in the singlet fission reaction. But, despite this success, several limitations emerge from the sever truncation of the excitation operator, which might translate into inaccurate relative energies between different regions of the potential energy surface, and overestimated (or underestimated) excitation energies. These errors are associated with the lack of dynamic correlation, which has motivated the development and implementation of various improvements based on multi‐reference perturbation theory and to blend the RASCI wave function with density functional theory through range separation of electron–electron interactions. Finally, we discuss some of the properties available from RASCI wave functions and give potential future developments.This article is categorized under:Electronic Structure Theory > Ab Initio Electronic Structure MethodsSoftware > Quantum ChemistryQuantum Computing > Theory Development

Calculation of spin-orbit couplings using RASCI spinless one-particle density matrices: Theory and applications.

This work presents the formalism and implementation for calculations of spin-orbit couplings (SOCs) using the Breit-Pauli Hamiltonian and non-relativistic wave functions described by the restricted active space configuration interaction (RASCI) method with general excitation operators of spin-conserving spin-flipping, ionizing, and electron-attaching types. The implementation is based on the application of the Wigner-Eckart theorem within the spin space, which enables the calculation of the entire SOC matrix based on the explicit calculation of just one transition between the two spin multiplets. Numeric results for a diverse set of atoms and molecules highlight the importance of a balanced treatment of correlation and adequate basis sets and illustrate the overall robust performance of RASCI SOCs. The new implementation is a useful addition to the methodological toolkit for studying spin-forbidden processes and molecular magnetism.

Simulating X‐ray absorption spectra with complete active space self‐consistent field linear response methods

AbstractIn this work, two approaches for simulating X‐ray absorption (XA) spectra with the complete active space self‐consistent field (CASSCF) linear response (LR) method are introduced. The first approach employs the well‐known core‐valence separation (CVS) approximation, which is predominantly used by many other electronic structure methods for simulating X‐ray spectra. The second ansatz uses the harmonic Davidson algorithm for finding interior eigenvalues that lie close to a target excitation energy shift and virtually solves a shifted‐and‐inverted (S&I) generalized eigenvalue problem. LR‐CASSCF K‐edge transition energies are systematically blueshifted though have consistently smaller errors than those of the CAS or restricted active space (RAS) configuration interaction (CI) methods. For simple molecules at which the core hole can only be created at a single site, the state‐specific RASSCF or n‐electron valence second‐order perturbation theory/RASCI gave more accurate principal K‐edge excitation energies. If the core hole can be created at multiple sites, the LR‐CASSCF approaches perform much better than RASSCF. Moreover, we observed that the LR‐CASSCF variants were the only MR methods discussed here that predicted correctly the order of O K‐edge features in the ozone molecule and the permanganate ion. The peak separation of edge features in ozone was as accurate as with equation‐of‐motion coupled cluster singles and doubles. The error of the CVS approximation turned out to be very system dependent and in some cases amounted up to 1.0 eV for the K‐edge excitation energies. Those CVS errors are still acceptable if one considers the observed deviation from the experimental reference by 5–11 eV. The deviations made in the XAS intensities were even more pronounced. CVS and the full S&I oscillator strengths could differ even by a factor of 2.8. Since the S&I approach is at least as efficient as the LR‐CASSCF method for valence excitations, future endeavors to improve the accuracy by accounting for dynamic correlation could be built on top of the full S&I approach.

Fragment-Based Restricted Active Space Configuration Interaction with Second-Order Corrections Embedded in Periodic Hartree-Fock Wave Function.

We present a computational scheme for restricted-active-space configuration interaction (RASCI) calculations combined with second-order perturbation theory (RASCI-PT2) on a fragment of a periodic system embedded in the periodic Hartree-Fock (HF) wave function. This method allows one to calculate the electronic structure of localized strongly correlated features in crystals and surfaces. The scheme was implemented via an interface between the Cryscor and Q-Chem codes. To evaluate the performance of the embedding method, we explored dissociation of a fluorine atom from a lithium fluoride surface and partially fluorinated graphane layer. The results show that RASCI and RASCI-PT2 embedded in periodic HF are able to produce well-behaved potential energy surfaces and accurate dissociation energies.

Analytic non-adiabatic couplings for the spin-flip ORMAS method

Analytic non-adiabatic coupling matrix elements (NACME) are derived and implemented for the spin-flip occupation restricted multiple active space configuration interaction (SF-ORMAS-CI) method. SF-ORMAS is a general spin correct implementation of the SF-CI method and has been shown to correctly describe various stationary geometries, including regions of conical intersections. The availability of non-adiabatic coupling allows a fuller examination of non-adiabatic phenomena with the SF-ORMAS method. In this study, the implementation of the NACME is tested using two model systems, MgFH and ethylene. In both cases, the SF-ORMAS method exhibits good qualitative agreement with established multi-reference methods, suggesting that SF-ORMAS is a suitable method for the study of non-adiabatic chemical phenomena.

Magnetic circular dichroism spectra of transition metal complexes calculated from restricted active space wavefunctions.

First principles multiconfigurational restricted active space (RAS) self-consistent field (SCF) or configuration interaction (CI) approaches, augmented with a treatment of spin-orbit coupling by state interaction, were used to calculate the magnetic circular dichroism (MCD) , , and/or for closed- and open-shell transition metal complexes: PdCl42-, PdBr42-, AuCl4-, AuBr4-, MnO4-, CuCl42-, CuBr42-, and Fe(CN)63-. The were determined with a sum-over-states approach. It is shown that reasonably accurate MCD spectra can be obtained directly at a RAS level or at a RAS level augmented with corrections for the dynamic correlation. The sign and magnitude of the individual MCD terms can be unambiguously determined and assigned to particular electronic transitions.

Nonadiabatic scattering of NO off Au3 clusters: A simple and robust diabatic state manifold generation method for multiconfigurational wavefunctions.

The presence of nonadiabatic effects during the interaction of small molecules with metals has been observed experimentally for the last decades. Specially remarkable are the effects found for NO/Au, where experiments have suggested the presence of very strong vibronic coupling during the molecular scattering. However, the accurate inclusion of the nonadiabatic effects in periodic boundary conditions (PBC) theoretical methods remain an unapproachable challenge. Here, aiming to give some theoretical insight to the strong vibronic coupling, we have adopted a pragmatic point of view, taking use of an auxiliary simplified system, NO/Au3 . We show the importance of nonadiabatic coupling, during the scattering of NO from a Au3 cluster, using a diabatic representation of 12 electronic states of the system, including a few charge-transfer states. Our diabatic representation is obtained by rotating the orbital and configuration interaction (CI) vectors of a restricted active space (RAS) wavefunction. We present a strategy for extracting the best effective manifold of states relevant to the system, below some prescribed energy, directly from the RAS CI vectors. This scheme is able to disentangle a large dense manifold of adiabatic states with strong coupling and crossings. This approach is also shown to work for multireference configuration interaction (MRCI). By performing quantum propagations, we observed an increase in vibrational redistribution with increasing initial vibrational or translational energies. We suggest that these nonadiabatic effects should also be present at smaller energies in larger clusters. © 2018 Wiley Periodicals, Inc.

Ultrafast dissipative spin-state dynamics triggered by x-ray pulse trains

Frontiers of attosecond science are constantly shifting, thus addressing more and more intricate effects with increasing resolution. Ultrashort pulses offer a practical way to prepare complex superpositions of quantum states, follow, and steer their dynamics. In this contribution, an ultrafast spin-flip process triggered by sub-femtosecond (fs) excitation and strong spin-orbit coupling between 2p core-excited states of a transition metal complex is investigated using density matrix-based time-dependent restricted active space configuration interaction theory. The effect of the nuclear vibrations is incorporated making use of an electronic system plus vibrational bath partitioning. The differences between isolated sub-fs pulses and pulse trains as well as influence of various pulse characteristics on the initiated dynamics are discussed. The effect under study can be potentially used for ultrafast clocking in sub-few fs experiments.

Intramolecular Charge Transfer and Local Excitation in Organic Fluorescent Photoredox Catalysts Explained by RASCI-PDFT

We investigate the electronically excited states of two recently synthesized organic fluorescent photoredox catalysts of the dihydrophenazine family. The mixed charge transfer and local excitation behavior of dark and bright transitions is unveiled by multiconfiguration pair-density functional theory (MC-PDFT) based on a restricted active space configuration interaction (RASCI) wave function (RASCI-PDFT). The RASCI-PDFT calculations give an accurate description of the experimental optical absorption spectra with active spaces too large for conventional complete active space self-consistent-field calculations. These results were achieved by the inclusion of many valence orbitals in the active space and their optimization within a cost-effective restricted active space self-consistent field framework without a RAS2 subspace, followed by calculations at the RASCI level including orbitals in RAS2. This novel strategy can be extended to systems that need a large number of orbitals in the active space.

Short-range density functional correlation within the restricted active space CI method.

In the present work, I introduce a hybrid wave function-density functional theory electronic structure method based on the range separation of the electron-electron Coulomb operator in order to recover dynamic electron correlations missed in the restricted active space configuration interaction (RASCI) methodology. The working equations and the computational algorithm for the implementation of the new approach, i.e., RAS-srDFT, are presented, and the method is tested in the calculation of excitation energies of organic molecules. The good performance of the RASCI wave function in combination with different short-range exchange-correlation functionals in the computation of relative energies represents a quantitative improvement with respect to the RASCI results and paves the path for the development of RAS-srDFT as a promising scheme in the computation of the ground and excited states where nondynamic and dynamic electron correlations are important.

Density matrix-based time-dependent configuration interaction approach to ultrafast spin-flip dynamics

ABSTRACTRecent developments in attosecond spectroscopy yield access to the correlated motion of electrons on their intrinsic timescales. Spin-flip dynamics is usually considered in the context of valence electronic states, where spin–orbit coupling is weak and processes related to the electron spin are usually driven by nuclear motion. However, for core-excited states, where the core-hole has a nonzero angular momentum, spin–orbit coupling is strong enough to drive spin-flips on a much shorter timescale. Using density matrix-based time-dependent restricted active space configuration interaction including spin–orbit coupling, we address an unprecedentedly short spin-crossover for the example of L-edge (2p→3d) excited states of a prototypical Fe(II) complex. This process occurs on a timescale, which is faster than that of Auger decay (∼4 fs) treated here explicitly. Modest variations of carrier frequency and pulse duration can lead to substantial changes in the spin-state yield, suggesting its control by soft X-ray light.

Relativistic extended-coupled-cluster method for the magnetic hyperfine structure constant

This article deals with the general implementation of 4-component spinor relativistic extended coupled cluster (ECC) method to calculate first order property of atoms and molecules in their open-shell ground state configuration. The implemented relativistic ECC is employed to calculate hyperfine structure (HFS) constant of alkali metals (Li, Na, K, Rb and Cs), singly charged alkaline earth metal atoms (Be+, Mg+, Ca+ and Sr+) and molecules (BeH, MgF and CaH). We have compared our ECC results with the calculations based on restricted active space configuration interaction (RAS-CI) method. Our results are in better agreement with the available experimental values than those of the RAS-CI values.

Re-appraisal of the hyperfine-structure constants in YbF: relativistic configuration interaction approach

Ab initio calculation of the spin rotational Hamiltonian parameters A and Ad has been performed using a fully-relativistic restricted active space (RAS) configuration interaction (CI) method for the YbF molecule. These calculations lead to the results for the hyperfine-structure constants as A = 6725 MHz, and Ad = 86 MHz, which agree favorably well with some previous correlated calculations and experimental findings. The convergence behavior of the parameters A and Ad with respect to the size of the active space and basis set has been tested satisfactorily for the reliability of the present results (within an uncertainty of ∼7%). Further, we believe that the theoretical estimates of some symmetry violating interaction constants like Wd can also be predicted with similar accuracy using the RASCI method.

Kβ mainline X-ray emission spectroscopy as an experimental probe of metal-ligand covalency.

The mainline feature in metal Kβ X-ray emission spectroscopy (XES) has long been recognized as an experimental marker for the spin state of the metal center. However, even within a series of metal compounds with the same nominal oxidation and spin state, significant changes are observed that cannot be explained on the basis of overall spin. In this work, the origin of these effects is explored, both experimentally and theoretically, in order to develop the chemical information content of Kβ mainline XES. Ligand field expressions are derived that describe the behavior of Kβ mainlines for first row transition metals with any dn count, allowing for a detailed analysis of the factors governing mainline shape. Further, due to limitations associated with existing computational approaches, we have developed a new methodology for calculating Kβ mainlines using restricted active space configuration interaction (RAS–CI) calculations. This approach eliminates the need for empirical parameters and provides a powerful tool for investigating the effects that chemical environment exerts on the mainline spectra. On the basis of a detailed analysis of the intermediate and final states involved in these transitions, we confirm the known sensitivity of Kβ mainlines to metal spin state via the 3p–3d exchange coupling. Further, a quantitative relationship between the splitting of the Kβ mainline features and the metal–ligand covalency is established. Thus, this study furthers the quantitative electronic structural information that can be extracted from Kβ mainline spectroscopy.

Second-order perturbative corrections to the restricted active space configuration interaction with the hole and particle approach.

Second-order corrections to the restricted active space configuration interaction (RASCI) with the hole and particle truncation of the excitation operator are developed. Theoretically, the computational cost of the implemented perturbative approach, abbreviated as RASCI(2), grows like its single reference counterpart in MP2. Two different forms of RASCI(2) have been explored, that is the generalized Davidson-Kapuy and the Epstein-Nesbet partitions of the Hamiltonian. The preliminary results indicate that the use of energy level shift of a few tenths of a Hartree might systematically improve the accuracy of the RASCI(2) energies. The method has been tested in the computation of the ground state energy profiles along the dissociation of the hydrogen fluoride and N2 molecules, the computation of correlation energy in the G2/97 molecular test set, and in the computation of excitation energies to low-lying states in small organic molecules.

Time-dependent multiconfiguration methods for the numerical simulation of photoionization processes of many-electron atoms

Numerical simulations present an indispensable way to the understanding of complex physical processes. In quantum mechanics where the theoretical description is given in terms of the time-dependent Schrodinger equation the road is, however, difficult for any but the simplest systems. This is particularly true if one considers photoionization processes of atoms and molecules which, at the same time, require an accurate description of bound and continuum states and, therefore, an extensive region of space to be sampled during the calculation. As a consequence, direct simulations of photoionization processes are currently only feasible for systems containing up to three electrons. Despite this fundamental restriction, many physical effects can be essentially described by single- and two-electron models, among them are high-order harmonic generation and non-sequential double-ionization of atoms and molecules. A plethora of numerical investigations have been performed on atomic and molecular hydrogen and helium in the last two decades, and these have had a strong impact on the current understanding of photoionization. On the other hand, there are processes which are characterized by the interplay of a larger number of electrons, such as tunnel ionization, the Auger effect and, to give a more recent example, the temporal delay between the photo-emission of electrons from different shells of neon and krypton. The many-electron character of these effects complicates the accurate, time-resolved simulation and, so far, no universally applicable method exists. This review presents two theoretical methods which are promising candidates for closing this gap–the multiconfigurational time-dependent Hartree-Fock (MCTDHF) method and the time-dependent restricted active space configuration interaction (TD-RASCI) method. Both represent the wavefunction in a linear subspace of the many-body Hilbert space and follow particular strategies to avoid the exponential problem. This makes it possible to treat a much larger number of electrons than with the direct techniques mentioned above.