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At least 19 records

Structure and dynamics of open-shell nuclei from spherical coupled-cluster theory

We extend the spherical coupled-cluster ab initio method for open-shell nuclei where two nucleons are removed from a shell subclosure. Following the recent implementation of the two-particle-attached approach [Phys. Rev. C 110, 044306 (2024)], we focus on the two-particle-removed method. Using the equations-of-motion framework, we address both nuclear structure and dipole response functions by coupling coupled-cluster theory with the Lorentz integral transform technique. We perform calculations using chiral interactions, including three-nucleon forces, and estimate many-body uncertainties by comparing different coupled-cluster truncation schemes. Here, we validate our approach by studying ground-state energies, excited states, and electric dipole polarizabilities in the oxygen and calcium isotopic chains. For binding energies and selected low-lying excited states, we achieve an accuracy comparable to that of the established closed-shell coupled-cluster theory and generally agree with experiment. Finally, we underestimate experimental data for electric dipole polarizabilities, particularly in calcium isotopes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Accurate energies for ππ* excited states via exchange scaling: the XS-CASSCF method

The state-averaged complete-active space self-consistent field method (SA-CASSCF) is a widely employed electronic structure method used for studying photochemistry and dynamics owing to its ability to provide a reliable description even of complicated cases while still retaining computational efficiency. However, SA-CASSCF suffers from one Achilles heel, related to the description of ionic ππ* excited states, whose energy is often overestimated by 1–2 eV. In light of this challenge, we present the XS-CASSCF method, a new approach based on the idea of exchange scaling (XS) that screens the involved energy terms to improve the excitation energies of singlet ionic ππ* states. First, we illustrate the power of the XS-CASSCF method using hexatriene and para-quinodimethane as examples, showing that it corrects the targeted ionic states while leaving the other states largely unaffected, giving root-mean-square errors (RMSE) below 0.2 eV for the four lowest states in both cases. Subsequently, XS-CASSCF vertical excitation energies are tested against theoretical best estimates for a set of 11 molecules and 56 excited states. XS-CASSCF performs exceptionally well for the ππ* states of hydrocarbons, reducing the RMSE over 21 excitation energies from 0.96 to 0.27 eV. In the challenging subset of molecules with heteroatoms and a larger number of ππ* and nπ* states, we find that improvements can also be obtained, albeit not as pronounced. We conclude with an outlook into more realistic molecular materials focusing on their singlet–triplet (S 1 /T 1 ) gaps, finding that significant improvements can be obtained along the whole range of S 1 /T 1 gaps studied, going from 0.1 eV to more than 1.5 eV. Owing to notable improvements across significant classes of molecules combined with its conceptual simplicity, we believe that XS-CASSCF is a promising addition to the electronic structure toolbox, serving both as a standalone electronic structure method and as a starting point for further correlated treatment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Highly-destabilized ligand field excited states of iron carbene complexes and their relation to charge transfer state lifetimes

Lifetimes of photoexcited charge transfer (CT) states in transition metal chromophores are influenced by low-lying ligand field (LF) excited states, especially for 3d metal complexes. To manipulate interactions between LF and CT states, it is important to be able to control LF excited state energies using tunable synthetic variables. In this report, we use Fe 2p3d L 3 -edge resonant inelastic X-ray scattering (RIXS) to measure LF excited state energies of three homoleptic iron chromophores coordinated by strong-field N-heterocyclic carbenes (NHCs). We investigate the effect of oxidation state and ligand scaffold on LF energies and covalency parameters. A cyclometalated bis(NHC) ligand affords both high LF excited state energies (and thus high 10 Dq) as well as high metal–ligand covalency compared to other iron complexes with very strong-field ligands. However, for the set of complexes investigated, we do not observe meaningful correlation between the LF excited state energies and the CT excited state lifetimes. These results illustrate that targeting long-lived CT excited states necessitates control of multiple molecular excited state properties, with destabilization of the LF excited state energies proving necessary, but insufficient, to control the CT excited state lifetime in Fe carbene complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Excited-State Densities from Time-Dependent Density Functional Response Theory

While the variational principle for excited-state energies leads to a route to obtaining excited-state densities from time-dependent density functional theory, relatively little attention has been paid to the quality of the resulting densities in real space obtained with different exchange-correlation functional approximations or how nonadiabatic approximations developed for energies of states of double-excitation character perform for their densities. Here we derive an expression directly in real space for the excited-state density, which includes the case of nonadiabatic kernels and consequently is able, for the first time, to yield densities of states of double-excitation character. Under some well-defined simplifications, we compare the performance of the local-density approximation and exact-exchange approximation, which are in a sense at the opposite extremes of the fundamental functional approximations, on local and charge-transfer excitations in one-dimensional model systems and show that the dressed Time-Dependent Density Functional Theory (TDDFT) approach gives good densities of double excitations.

approximation

Strategic Lifetime Tuning of Visible-Light Absorbing Two-Coordinate Metal Complexes

This paper highlights how the singlet and triplet amide ligand centered ( 1,3 LC) and interligand charge transfer ( 1,3 ICT) states in (carbene)M(amide), M = Cu, Au (cMa) complexes influence the excited state properties when the triplet states are close in energy. To that end we prepared a set of five cMa complexes, in which the amide (i.e., 5H-benzo[b]carbazole, H-BnCz) was kept constant giving a 3 LC energy of ca. 2.15 eV. Four different carbene ligands were selected to develop M BnCz Carbene complexes which have energies for the ICT state that vary from being either markedly higher, lower, or close to the energy of the 3 LC state on the amide ligand. Steady-state and time-resolved spectroscopic studies show that the emission spectrum of the cMa complex mirrors the phosphorescence of the parent H-BnCz amide and has a luminescence decay lifetime in the millisecond regime when the lowest energy excited state is 3 LC. When the lowest energy states are 1,3 ICT in nature, the emission band is broad and featureless, giving a lifetime in the nanosecond regime. As the 3 LC and 1,3 ICT states have comparable energies, dynamic equilibrium between the states is observed with the luminescence consisting of a mixture of 3 LC and 1,3 ICT transitions. The measured lifetime of this equilibrating system is between 45 and 350 μs depending on the solvent, for both copper- and gold-based cMa complexes. Furthermore, these complexes demonstrate the ability to “park” the excited state population in the 3 LC state, allowing it to act as a reservoir for thermally activated emission, while still maintaining a very rapid equilibrium between LC and ICT states.

14 SOLAR ENERGY

Spin-State and Reorganization Energy Considerations for Metal-Centered Photoredox Catalysis

Transition-metal complexes featuring metal-centered excited states have recently emerged as mechanistically distinct platforms for selective photochemistry, including photoredox catalysis. Among these, Co(III) complexes have demonstrated productive photoinduced electron transfer via the 3 T 1 metal-centered state. In contrast, photoreactivity from the 5 T 2 metal-centered state in Fe(II) polypyridyl complexes remains limited. Building on our prior report concerning reactivity associated with the 5 T 2 state in [Fe(tren(py) 3 )] 2+ (tren(py) 3 = tris(2-pyridylmethyliminoethyl)-amine), we introduced stronger-field ligands in an effort to increase excited-state energies of Fe(II) polypyridyl complexes and enhance reactivity. Despite achieving nanosecond-scale excited-state lifetimes and favorable thermodynamic driving forces, no photoreactivity was observed. Reinvestigation of the observations previously reported for [Fe(tren(py) 3 )] 2+ revealed interactions between the metal complex and the substrate in their respective ground states that mimicked dynamic quenching of the chromophore, prompting a reassessment of mechanistic considerations inherent in leveraging reductive chemistry from the 5 T 2 excited state of Fe(II). Our analysis indicates that electron transfer from the 5 T 2 excited state of a low-spin d6 metal is subject to significant barriers both in terms of reorganization energies and spin conservation that undermines its ability to act as an electron donor for photoredox catalysis. In contrast, ligand fields that are sufficient to stabilize the 3 T 1 excited state have available to them numerous spin-allowed and, in certain cases, near-barrierless pathways to engage in excited-state electron transfer (both oxidative and reductive depending on the identity of the metal). These results highlight the critical role of spin-state changes and their associated reorganization energy requirements in metal-centered photoredox catalysis.

charge transfer

A Spectrochemical Series for Electron Spin Relaxation

Controlling the rate of electron spin relaxation in paramagnetic molecules is essential for contemporary applications in molecular magnetism and quantum information science. However, the physical mechanisms of spin relaxation remain incompletely understood, and new spectroscopic observables play an important role in evaluating spin dynamics mechanisms and structure–property relationships. Here, we use cryogenic magnetic circular dichroism (MCD) spectroscopy and pulse electron paramagnetic resonance (EPR) in tandem to examine the impact of ligand field (d–d) excited states on spin relaxation rates. We employ a broad scope of square-planar Cu(II) compounds with varying ligand field strength, including CuS 4 , CuN 4 , CuN 2 O 2 , and CuO 4 first coordination spheres. An unexpectedly strong correlation exists between spin relaxation rates and the average d–d excitation energy (R 2 = 0.97). The relaxation rate trends as the inverse 11th power of the excited-state energies, whereas simplified theoretical models predict only an inverse second power dependence. These experimental results directly implicate ligand field excited states as playing a critical role in the ground-state spin relaxation mechanism. Furthermore, ligand field strength is revealed to be a particularly powerful design principle for spin dynamics, enabling formation of a spectrochemical series for spin relaxation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Cerium Dimer Anion and the Contribution of 4f Electrons to Lanthanide Metal–Metal Bonds

Direct metal−metal bonding between lanthanide atoms has been challenging to observe. We report on the first spectroscopic characterization of the cerium dimer anion (Ce 2 − ) and its neutral analog (Ce 2 ) in the gas phase, achieved using photoelectron and ultrafast spectroscopy combined with high-level quantum chemistry calculations. The electron affinity of Ce 2 is 0.24 eV, from which a dissociation energy of 2.21 eV is derived for Ce 2 − . The wave-packet dynamics upon photodetachment are studied and yield vibrational frequencies for electronically excited Ce 2 . Ce 2 − exhibits a conventional metal−metal triple bond with minimal contribution from 4f electrons. However, evidence of 4f-electron participation in bonding is identified for the low-energy excited states only 0.1 eV higher. The results challenge the assumption of inert 4f electrons in metal−metal bonding, and we propose a promising strategy for forming stable lanthanide−lanthanide bonds involving significant 4f-electron contributions.

Anions

Cyclometallated Co(III) Complexes with Lowest-Energy Charge Transfer Excited States Accessible with Visible Light

The Co(III) complexes, cis-[Co(ppy) 2 (L)]PF 6 , where ppy = 2-phenylpyridine and L = bpy (2,2′-bipyridine; 1), phen (1,10-phenanthroline; 2), and DAP (1,12-diazaperylene; 3), are reported and their photophysical properties were investigated to evaluate their potential as sensitizers for applications that include solar energy conversion schemes and photoredox catalysis. Calculations show that cyclometallation in the cis-[Co(ppy) 2 (L)]PF 6 series affords strong Co(dπ)/ppy(π) orbital interactions that result in a Co/ppy(π*) highest occupied molecular orbital (HOMO) and a lowest unoccupied molecular orbital (LUMO) localized on the diimine ligand, L(π*). Complexes 1–3 exhibit relatively invariant oxidation potentials, whereas the reduction event is dependent on the identity of the diimine ligand, L, consistent with the theoretical predictions. For 3 a broad Co/ppy(π*) → L(π*) metal/ligand-to-ligand charge transfer (ML-LCT) absorption band is observed in CH 3 CN with a maxima at 507 nm, extending beyond 600 nm. Upon excitation of the 1ML-LCT transition, transient absorption features consistent with the population of a 3 ML-LCT excited state with lifetimes, τ, of 3.0 ps, 4.6 and 42 ps for 1, 2 and 3 in CH 3 CN respectively are observed. Upon irradiation with 505 nm, 3 is able to reduce methyl viologen (MV 2+ ), an electron acceptor commonly in photocatalytic schemes. Here, to our knowledge, 3 represents the first heteroleptic molecular Co(III) complex that combines cyclometallation with a diimine ligand with lowest-lying metal-to-ligand charge transfer excited states able to undergo photoinduced charge transfer with low-energy green light. As such, the structural design of 3 represents an important step toward d6 photosensitizers based on earth abundant metals.

Energy

The Impact of Carotenoid Energy Levels on the Exciton Dynamics and Singlet–Triplet Annihilation in Isolated Bacterial Light-Harvesting 2 Complexes

The light-harvesting 2 (LH2) complex of purple phototrophic bacteria plays a critical role in absorbing solar energy and distributing the excitation energy. Exciton dynamics within LH2 complexes are controlled by the structural arrangement and energy levels of the bacteriochlorophyll (BChl) and carotenoid (Car) pigments. However, there is still debate over the competing light-harvesting versus energy-dissipation pathways. In this work, we compared five variants of the LH2 complex from genetically modified strains of Rhodobacter sphaeroides, all containing the same BChls but different Cars with increasing conjugation: zeta-carotene (N = 7; LH2 Zeta ), neurosporene (N = 9; LH2 Neu ), spheroidene (N = 10; LH2 Spher ), lycopene (N = 11; LH2 Lyco ), and spirilloxanthin (N = 13; LH2 Spir ). Absorption measurements confirmed that the Car excited-state energy decreased with increasing conjugation. Similarly, fluorescence spectra showed that the B850 BChl emission peak had an increasing red shift from LH2 Zeta →(LH2 Neu /LH2 Spher )→LH2 Lyco →LH2 Spir . In contrast, time-resolved fluorescence and ultrafast transient absorption (fs-TA) revealed similar excited-state lifetimes (∼1 ns) for all complexes except LH2 Spir (∼0.7 ns). From fs-TA analysis, an additional ∼7 ps nonradiative dissipation step from B850 BChl was observed for LH2 Zeta . Further, singlet− singlet and singlet−triplet annihilation studies showed a ∼50% average fluorescence lifetime reduction in LH2Zeta at high laser power and high repetition rate, compared to ∼10−15% reductions in LH2 Neu /LH2 Spher /LH2 Lyco and minimal lifetime change in LH2 Spir . In LH2 Zeta , the fastest decay component (<50 ps) became prominent at high repetition rates, consistent with strong singlet−triplet annihilation. Nanosecond TA measurements revealed long-lived (>40 μs) BChl triplet states in LH2 Zeta and signs of damage caused by singlet oxygen, whereas other LH2s showed faster triplet quenching (∼18 ns) by Cars. These findings highlight a key design principle of LH2 complexes: the Car triplet energy must be significantly lower than the BChl triplet energy to efficiently quench BChl triplets that otherwise act as potent “trap states,” causing exciton annihilation in laser-based experiments or photodamage in native membranes.

Absorption

Challenging excited states from adaptive quantum eigensolvers: subspace expansions vs. state-averaged strategies

The prediction of electronic structure for strongly correlated molecules represents a promising application for near-term quantum computers. Significant attention has been paid to ground state wavefunctions, but excited states of molecules are relatively unexplored. In this work, we consider the adaptive, problem-tailored (ADAPT)-variational quantum eigensolver (VQE) algorithm, a single-reference approach for obtaining ground states, and its state-averaged generalization for computing multiple states at once. We demonstrate for both rectangular and linear H4, as well as for BeH2, that this approach, which we call multistate-objective, Ritz-eigenspectral (MORE)-ADAPT-VQE, can make better use of small excitation manifolds than an analogous method based on a single-reference ADAPT-VQE calculation, q-sc-EOM. In particular, MORE-ADAPT-VQE is able to accurately describe both avoided crossings and crossings between states of different symmetries. In addition to more accurate excited state energies, MORE-ADAPT-VQE can recover accurate transition dipole moments in situations where traditional ADAPT-VQE and q-sc-EOM struggle. These improvements suggest a promising direction toward the use of quantum computers for difficult excited state problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Atomic ionization: sd energy imbalance and Perdew–Zunger self-interaction correction energy penalty in 3d atoms

To accurately describe the energetics of transition metal systems, density functional approximations (DFAs) must provide a balanced description of s- and d- electrons. One measure of this is the sd transfer error, which has previously been defined as E ( 3 d n − 1 4 s 1 ) − E ( 3 d n − 2 4 s 2 ) . Theoretical concerns have been raised about this definition due to its evaluation of excited-state energies using ground-state DFAs. A more serious concern appears to be strong correlation in the 4s 2 configuration. Here, we define a ground-state measure of the sd energy imbalance, based on the errors of s- and d-electron second ionization energies of the 3d atoms, that effectively circumvents the aforementioned problems. We find an improved performance as we move from the local spin density approximation (LSDA) to the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) to the regularized and restored Strongly Constrained and Appropriately Normed (r 2 SCAN) meta-GGA for first-row transition metal atoms. However, we find large (∼2 eV) ground-state sd energy imbalances when applying a Perdew–Zunger 1981 self-interaction correction. This is attributed to an “energy penalty” associated with the noded 3d orbitals. A local scaling of the self-interaction correction to LSDA results in a balance of s- and d-errors.

Science & Technology - Other Topics

Advancing quantum simulations of the nuclear shell model with Gray-code–based resource-efficient protocols

Background: Some of the computational limitations in solving the nuclear many-body problem could be overcome by utilizing quantum computers. The nuclear shell-model calculations providing deeper insights into the properties of atomic nuclei are one such case with high demand for resources, as the size of the Hilbert space grows exponentially with the number of particles involved. Quantum algorithms are being developed to overcome these challenges and advance such calculations. Purpose: To develop quantum circuits for the nuclear shell-model, leveraging the capabilities of noisy intermediate-scale quantum (NISQ) devices. Here, we aim to minimize resource requirements (specifically in terms of qubits and gates) and strive to reduce the impact of noise by employing relevant mitigation techniques. Methods: We achieve noise resilience by designing an optimized Ansatz for the variational quantum eigensolver (VQE) based on Givens rotations and incorporating qubit-ADAPT-VQE in combination with variational quantum deflation (VQD) to compute ground and excited states, incorporating the zero-noise extrapolation mitigation technique. Furthermore, the qubit requirements are significantly reduced by mapping the basis states to qubits using Gray-code encoding and generalizing transformations of fermionic operators to efficiently represent many-body states. Results: By employing the resource-efficient protocols, we achieve the ground and excited state energy levels of 38 Ar and 6 Li with better accuracy. These energy levels are presented for noiseless simulations, noisy conditions, and after applying noise mitigation techniques. Results are compared for Jordan-Wigner and Gray-code encoding using VQE, qubit-ADAPT-VQE, and VQD. Conclusions: Our work highlights the potential of resource-efficient protocols to leverage the full potential of NISQ devices in scaling the nuclear shell model calculations, offering a pathway toward more complex quantum simulations in nuclear physics. This approach establishes a framework for studying other nuclear systems with improved quantum resource efficiency, marking a significant advancement in applying quantum computing to realistic nuclear physics applications.

Physics - Nuclear physics and radiation physics

Block Lanczos algorithm for lattice QCD spectroscopy and matrix elements

Recent work introduced a new framework for analyzing correlation functions with improved convergence and signal-to-noise properties, as well as rigorous quantification of excited-state effects, based on the Lanczos algorithm and spurious eigenvalue filtering with the Cullum-Willoughby test. Here, we extend this framework to the analysis of correlation-function matrices built from multiple interpolating operators in lattice quantum chromodynamics (QCD) by constructing an oblique generalization of the block Lanczos algorithm, as well as a new physically motivated reformulation of the Cullum-Willoughby test that generalizes to block Lanczos straightforwardly. The resulting block Lanczos method directly extends generalized eigenvalue problem (GEVP) methods, which can be viewed as applying a single iteration of block Lanczos. Block Lanczos provides qualitative and quantitative advantages over GEVP methods analogous to the benefits of Lanczos over the standard effective mass, including faster convergence to ground- and excited-state energies, explicitly computable two-sided error bounds, straightforward extraction of matrix elements of external currents, and asymptotically constant signal-to-noise. No fits or statistical inference are required. Proof-of-principle calculations are performed for noiseless mock-data examples as well as two-by-two proton correlation-function matrices in lattice QCD.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Equation-of-motion internally contracted multireference unitary coupled-cluster theory

The accurate computation of excited states remains a challenge in electronic structure theory, especially for systems with a ground state that requires a multireference treatment. In this work, we introduce a novel equation-of-motion (EOM) extension of the internally contracted multireference unitary coupled-cluster framework (ic-MRUCC), termed EOM-ic-MRUCC. EOM-ic-MRUCC follows the transform-then-diagonalize approach, in analogy to its non-unitary counterpart. By employing a projective approach to optimize the ground state, the method retains additive separability and proper scaling with system size. We show that excitation energies are size-intensive if the EOM operator satisfies the “killer” and the projective conditions. Furthermore, we propose to represent changes in the reference state upon electron excitation via projected many-body operators that span the active orbitals and show that the EOM equations formulated in this way are invariant with respect to active orbital rotations. We test the EOM-ic-MRUCC method truncated to single and double excitations by computing the potential energy curves for several excited states of a BeH2 model system, the HF molecule, and water undergoing symmetric dissociation. Across these systems, our method delivers accurate excitation energies and potential energy curves within 5 mE h (∼0.14 eV) from full configuration interaction. Here, we find that truncating the Baker–Campbell–Hausdorff series to fourfold commutators contributes negligible errors (on the order of 10 −5 E h or less), offering a practical route to highly accurate excited-state calculations with reduced computational overhead.

74 ATOMIC AND MOLECULAR PHYSICS

Toward a Balanced Description of Ground and Excited States with Transcorrelated F12 Methods

By correlating only the 1-particle states occupied in the reference determinant, the conventional design for the single-reference R12/F12 explicitly correlated methods biases them toward the ground-state description, thereby making the treatment of response properties of the ground state, and energies and other properties of excited states less robust. While the use of multireference methods and/or extensions of the standard SP-projected geminals can achieve a more balanced description of ground and excited states, here we show that the same goals can be achieved by extending the action of F12 correlators to the occupied and valence unoccupied 1-particle states only. This design choice reflects the strong dependence of the optimal correlation length scale of the F12 ansatz on the orbital energies/structure, and helps to avoid the unphysical raising of the ground-state energy if the F12 geminals are used to correlate pairs of all 1-particle states. The improved F12 geminal design is incorporated into the unitary transcorrelation framework to produce a unitary 2-body Hamiltonian that incorporates the short-range dynamical correlation physics for ground and low-energy excited states in a balanced manner. This explicitly correlated effective Hamiltonian reduces the basis set requirement on the correlation-consistent basis cardinal number by 1 or more over the uncorrelated counterpart for the description of ground-state coupled-cluster singles and doubles (CCSD) energies, vertical excitation energies, and harmonic vibrational frequencies of equation-of-motion CCSD low-energy excited states.

Hamiltonians

Ligand substituents modulate excited-state lifetime and energy-transfer reactivity in Cu( I ) photosensitizers supported by salicylaldimine and isocyanide ligands

The design of earth-abundant molecular photosensitizers with desirable photophysical properties and good excited-state reactivity is critical for sustainable photochemical applications. Herein, we report a new family of three-coordinate heteroleptic Cu(I) complexes supported by monoanionic salicylaldimine (N^O) chelating ligands and aryl isocyanides. By systematically tuning the steric bulk on each ligand, we establish clear structure–property relationships that govern the excited-state lifetimes and photocatalytic performance metrics of these complexes. Increasing steric congestion on the salicylaldimine ligand, which contributes to the HOMO, results in faster nonradiative decay and shortens excited-state lifetimes. In contrast, introducing steric bulk on the isocyanide ligand, where the LUMO is primarily localized, suppresses nonradiative decay, most likely by inhibiting excited-state geometric relaxation, thereby extending the lifetime up to 375 ns. These photophysical trends correlate directly with performance in triplet–triplet energy transfer (TTET) photocatalysis, where longer-lived complexes enable faster E/Z isomerization of trans-stilbene. This work demonstrates that remote steric modulation of ligand frameworks offers a simple yet powerful strategy for tuning the excited-state dynamics and catalytic properties of this new class of Cu(I) photosensitizers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

COLUMBUS─An Efficient and General Program Package for Ground and Excited State Computations Including Spin–Orbit Couplings and Dynamics

The COLUMBUS program system provides the tools for performing high-level multireference (MR) computations, including the multireference configuration interaction (MRCI) method and its multireference averaged quadratic coupled cluster (MR-AQCC) extension, allowing computations on a wide range of fascinating atomic and molecular systems, including the treatment of open-shells and complicated excited state phenomena. The inclusion of spin−orbit coupling (SOC) directly within the MRCI step enables the description of systems containing heavy elements, such as lanthanides and actinides, whose properties are strongly influenced by SOC. Analytic energy gradients and nonadiabatic couplings at the correlated MRCI level provide the foundation for a variety of dynamics studies, giving insight into ultrafast photochemistry. New and ongoing method developments in COLUMBUS include the computation of spin densities, improved descriptions of ionic states, enhancements to the AQCC method, and the porting of COLUMBUS to graphical processing units (GPUs). New external interfaces enable an enhanced description of electronic resonances and molecules in strong laser fields. This work highlights these new developments while providing a detailed account of the diverse applications of COLUMBUS in recent years.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH