Low-cost evaluation of the exchange Fock matrix from Cholesky and density fitting representations of the electron repulsion integrals

Lowering the Scaling of Self-Consistent Field Methods by Combining Tensor Hypercontraction and a Density Difference Ansatz

We present the tensor hypercontraction difference self-consistent field (SCF) method, an approach that reduces the formal computational scaling of traditional naive self-consistent field methods from O ( N 4 ) to O ( N 3 ) with system size N . The scaling reduction is achieved by developing a new technique for constructing the tensor hypercontraction decomposition based on the fundamental approximation made in density fitting. Combining this scheme with the difference self-consistent field methodology, we achieve a method that enables O ( N 3 ) scaling SCF calculations with only O ( N 2 ) storage requirements. Our proof-of-concept numerical tests demonstrate robust performance with errors in total energies below 8 × 10-4 Eh and with sub 1 kcal/mol errors for relative energies.

The Amsterdam Modeling Suite

In this paper, we present the Amsterdam Modeling Suite (AMS), a comprehensive software platform designed to support advanced molecular and materials simulations across a wide range of chemical and physical systems. AMS integrates cutting-edge quantum chemical methods, including Density Functional Theory (DFT) and time-dependent DFT, with molecular mechanics, fluid thermodynamics, machine learning techniques, and more, to enable multi-scale modeling of complex chemical systems. Its design philosophy allows for seamless coupling between components, facilitating simulations that range from small molecules to complex biomolecular and solid-state systems, making it a versatile tool for tackling interdisciplinary challenges, both in industry and in academia. The suite also emphasizes user accessibility, with an intuitive graphical interface, extensive scripting capabilities, and compatibility with high-performance computing environments.

Spatial Signatures of Electron Correlation in Least-Squares Tensor Hypercontraction

Least-squares tensor hypercontraction (LS-THC) has received some attention in recent years as an approach to reduce the significant computational costs of wave function-based methods in quantum chemistry. However, previous work has demonstrated that LS-THC factorization performs disproportionately worse in the description of wave function components (e.g., cluster amplitudes T̂2) than Hamiltonian components (e.g., electron repulsion integrals (pq|rs)). This work develops novel theoretical methods to study the source of these errors in the context of the real-space T̂2 kernel, and reports, for the first time, the existence of a "correlation feature" in the errors of the LS-THC representation of the "exchange-like" correlation energy EX and T̂2 that is remarkably consistent across ten molecular species, three correlated wave functions, and four basis sets. This correlation feature portends the existence of a "pair point kernel" missing in the usual LS-THC representation of the wave function, which critically depends upon pairs of grid points situated close to atoms and with interpair distances between one and two Bohr radii. These findings point the way for future LS-THC developments to address these shortcomings.

Hg-Hg bonding and its influence on the stability of (HgS)n clusters

Pulsed laser ablation of a HgS(s) precursor shows the formation of small cluster ions, (HgS)n=2-4+, together with HgSn=1-8± and [(HgS)n + Sm]±. The computed structure, atomization energy, and HOMO-LUMO gap energy values of the lowest energy ring singlet show stable (HgS)n=2-8. However, the computed bond conductance of the Hg-Hg bond in (HgS)n shows a high value for (HgS)n=2-4 (ξ = 1.072-0.122), whereas it is low for (HgS)n=5-8 (ξ = 0.039-0.006) and decreases significantly as the ring expands, indicating that (HgS)n≥5 is unstable. It evidences that the weak chemical bonding between Hg2+-Hg2+ closed shell (5d10-5d10) electrons plays a significant role in the stability of ring (HgS)n=2-4. Thus, it validates the experimental observation of stable cluster ions up to (HgS)4+. In contrast, the low energy chain triplet (HgS)n=2-8 shows a progressive increase in stability and bond conductance with chain length, indicating sustained mercurophilic interactions in long chain clusters like its crystal structure. Furthermore, the lowest/low energy isomers of HgSn=1-8 have been computed for their energetics, HOMO-LUMO gaps, and electron affinity using DFT-B3LYP/PBE0 methods.

Multi-GPU RI-HF Energies and Analytic Gradients─Toward High-Throughput Ab Initio Molecular Dynamics

This article presents an optimized algorithm and implementation for calculating resolution-of-the-identity Hartree-Fock (RI-HF) energies and analytic gradients using multiple graphics processing units (GPUs). The algorithm is especially designed for high throughput ab initio molecular dynamics simulations of small and medium size molecules (10-100 atoms). Key innovations of this work include the exploitation of multi-GPU parallelism and a workload balancing scheme that efficiently distributes computational tasks among GPUs. Our implementation also employs techniques for symmetry utilization, integral screening, and leveraging sparsity to optimize memory usage. Computational results show that the implementation achieves significant performance improvements, including over 3 × speedups in single GPU AIMD throughput compared to previous GPU-accelerated RI-HF and traditional HF methods. Furthermore, utilizing multiple GPUs can provide superlinear speedup when the additional aggregate GPU memory allows for the storage of decompressed three-center integrals.

Sparse-Stochastic Fragmented Exchange for Large-Scale Hybrid Time-Dependent Density Functional Theory Calculations

We extend our recently developed sparse-stochastic fragmented exchange formalism for ground-state near-gap hybrid DFT to calculate absorption spectra within linear-response time-dependent generalized Kohn-Sham DFT (LR-GKS-TDDFT) for systems consisting of thousands of valence electrons within a grid-based/plane-wave representation. A mixed deterministic/fragmented-stochastic compression of the exchange kernel, here using long-range explicit exchange functionals, provides an efficient method for accurate optical spectra. Both real-time propagation as well as frequency-resolved Casida-equation-type approaches for spectra are presented, and the method is applied to large molecular dyes.

Galván I, Lindh R. A Story of Three Levels of Sophistication in SCF/KS-DFT Orbital Optimization Procedures

In this work, three versions of self-consistent field/Kohn-Sham density functional theory (SCF/KS-DFT) orbital optimization are described and benchmarked. The methods are a modified version of the geometry version of the direct inversion in the iterative subspace approach (which we call r-GDIIS), the modified restricted step rational function optimization method (RS-RFO), and the novel subspace gradient-enhanced Kriging method combined with restricted variance optimization (S-GEK/RVO). The modifications introduced are aimed at improving the robustness and computational scaling of the procedures. In particular, the subspace approach in S-GEK/RVO allows the application to SCF/KS-DFT optimization of a machine learning technique that has proven to be successful in geometry optimizations. The performance of the three methods is benchmarked for a large number of small- to medium-sized organic molecules, at equilibrium structures and close to a transition state, and a second set of molecules containing closed- and open-shell transition metals. The results indicate the importance of the resetting technique in boosting the performance of the r-GDIIS procedure. Moreover, it is demonstrated that already at the inception of the subspace version of GEK to optimize SCF wave functions, it displays superior and robust convergence properties as compared to those of the standard state-of-the-art SCF/KS-DFT optimization methods.

New physical insights into the supporting subspace factorization of XMS-CASPT2 and generalization to multiple spin states via spin-free formulation

This paper introduces a spin-free formulation of the supporting subspace factorization [C. Song and T. J. Martínez, J. Chem. Phys. 149, 044108 (2018)], enabling a reduction in the computational scaling of the extended multi-state complete active space second-order perturbation (XMS-CASPT2) method for arbitrary spins. Compared to the original formulation that is defined in the spin orbitals and is limited to singlet states, the spin-free formulation in this work treats different spin states equivalently, thus naturally generalizing the idea beyond singlet states. In addition, we will present a new way of deriving the supporting subspace factorization with the purpose of understanding its physical interpretation. In this new derivation, we separate the sources that make CASPT2 difficult into the "same-site interactions" and "inter-site interactions." We will first show how the Kronecker sum can be used to remove the same-site interactions in the absence of inter-site interactions, leading to MP2 energy in dressed orbitals. We will then show how the inter-site interactions can be exactly recovered using Löwdin partition, where the supporting subspace concept will naturally arise. The new spin-free formulation maintains the main advantage of the supporting subspace factorization, i.e., allowing XMS-CASPT2 energies to be computed using highly optimized MP2 energy codes and Fock build codes, thus reducing the scaling of XMS-CASPT2 to the same scaling as MP2. We will present and discuss results that benchmark the accuracy and performance of the new method. To demonstrate how the new method can be useful in studying real photochemical systems, the supporting subspace XMS-CASPT2 is applied to a photoreaction sensitive to magnetic field effects. The new spin-free formulation makes it possible to calculate the doublet and quartet states required in this particular photoreaction mechanism.

The overlooked role of excited anion states in NiO2- photodetachment

Photodetachment spectra of anionic species provide significant insights into the energies and nature of ground and excited states of both the anion and resultant neutral molecules. Direct detachment of the excess electron to the continuum may occur via formally allowed or forbidden transitions (perhaps as the result of intensity borrowing through vibronic coupling). However, alternate indirect pathways are also possible and often overlooked. Here, we report a two-dimensional photoelectron spectral study, combined with correlated electronic structure calculations, to elucidate the nature of photodetachment from NiO2-. The spectra are comprised of allowed and forbidden transitions, in excellent agreement with previously reported slow electron velocity mapped imaging spectra of the same system, which were interpreted in terms of direct detachment. In the current work, the contributions of indirect processes are revealed. Measured oscillations in the branching ratios of the spectral channels clearly indicate non-direct detachment processes, and the electronic structure calculations suggest that excited states of the appropriate symmetry and degeneracy lie slightly above the neutral ground state. Taken together, the results suggest that the origin of the observed forbidden transitions is the result of anion excited states mediating the electron detachment process.

Formulation and Implementation of Frequency-Dependent Linear Response Properties with Relativistic Coupled Cluster Theory for GPU-Accelerated Computer Architectures

We present the development and implementation of relativistic coupled cluster linear response theory (CC-LR), which allows the determination of molecular properties arising from time-dependent or time-independent electric, magnetic, or mixed electric-magnetic perturbations (within a common gauge origin for the magnetic properties) as well as taking into account the finite lifetime of excited states in the framework of damped response theory. We showcase our implementation, which is capable to offload the computationally intensive tensor contractions characteristic of coupled cluster theory onto graphical processing units, in the calculation of (a) frequency-(in)dependent dipole-dipole polarizabilities of IIB atoms and selected diatomic molecules, with a particular emphasis on the calculation of valence absorption cross sections for the I2 molecule; (b) indirect spin-spin coupling constants for benchmark systems such as the hydrogen halides (HX, X = F-I) as well the H2Se-H2O dimer as a prototypical system containing hydrogen bonds; and (c) optical rotations at the sodium D line for hydrogen peroxide analogues (H2Y2, Y = O, S, Se, Te). Thanks to this implementation, we are able to show the similarities in performance, but often the significant discrepancies, between CC-LR and approximate methods such as density functional theory. Comparing standard CC response theory with the flavor based upon the equation of motion formalism, we find that for valence properties such as polarizabilities, the two frameworks yield very similar results across the periodic table as found elsewhere in the literature; for properties that probe the core region, such as spin-spin couplings, on the other hand, we show a progressive differentiation between the two as relativistic effects become more important. Our results also suggest that as one goes down the periodic table, it may become increasingly difficult to measure pure optical rotation at the sodium D line due to the appearance of absorbing states.

Deterministic/Fragmented-Stochastic Exchange for Large-Scale Hybrid DFT Calculations

We develop an efficient approach to evaluate range-separated exact exchange for grid- or plane-wave-based representations within the generalized Kohn-Sham-density functional theory (GKS-DFT) framework. The Coulomb kernel is fragmented in reciprocal space, and we employ a mixed deterministic-stochastic representation, retaining long-wavelength (low-k) contributions deterministically and using a sparse ("fragmented") stochastic basis for the high-k part. Coupled with a projection of the Hamiltonian onto a subspace of valence and conduction states from a prior local-DFT calculation, this method allows for the calculation of the long-range exchange of large molecular systems with hundreds and potentially thousands of coupled valence states delocalized over millions of grid points. We find that even a small number of valence and conduction states is sufficient for converging the HOMO and LUMO energies of the GKS-DFT. Excellent tuning of long-range separated hybrids (RSH) is easily obtained in the method for very large systems, as exemplified here for the chlorophyll hexamer of Photosystem II with 1320 electrons.

Frequency-Dependent Quadratic Response Properties and Two-Photon Absorption from Relativistic Equation-of-Motion Coupled Cluster Theory

We present the implementation of quadratic response theory based upon the relativistic equation-of-motion coupled cluster method. We showcase our implementation, whose generality allows us to consider both time-dependent and time-independent electric and magnetic perturbations, by considering the static and frequency-dependent hyperpolarizability of hydrogen halides (HX, X = F-At), providing comprehensive insights into their electronic response characteristics. Additionally, we evaluated the Verdet constant for noble gases Xe and Rn and discussed the relative importance of relativistic and electron correlation effects for these magneto-optical properties. Finally, we calculate the two-photon absorption cross sections of transition [ns1S0 → (n + 1)s1S0] of Ga+ and In+, which are suggested as candidates for new ion clocks. As our implementation allows for the use of nonrelativistic Hamiltonians as well, we have compared our EOM-QRCC results to the QR-CC implementation in the DALTON code and show that the differences between CC and EOMCC response are in general smaller than 5% for the properties considered. Collectively, the results underscore the versatility of our implementation and its potential as a benchmark tool for other approximated models, such as density functional theory for higher-order properties.

Nested gausslet basis sets

We introduce nested gausslet bases, an improvement on previous gausslet bases that can treat systems containing atoms with much larger atomic numbers. We also introduce pure Gaussian distorted gausslet bases, which allow the Hamiltonian integrals to be performed analytically, as well as hybrid bases in which the gausslets are combined with standard Gaussian-type bases. All these bases feature the diagonal approximation for the electron-electron interactions so that the Hamiltonian is completely defined by two Nb × Nb matrices, where Nb ≈ 104 is small enough to permit fast calculations at the Hartree-Fock level. In constructing these bases, we have gained new mathematical insight into the construction of one-dimensional diagonal bases. In particular, we have proved an important theorem relating four key basis set properties: completeness, orthogonality, zero-moment conditions, and diagonalization of the coordinate operator matrix. We test our basis sets on small systems with a focus on high accuracy, obtaining, for example, an accuracy of 2 × 10-5 Ha for the total Hartree-Fock energy of the neon atom in the complete basis set limit.

Galván I, Rivalta I, Aquilante F, Garavelli M, Lindh R, Segarra-Martí J. Characterizing Conical Intersections in DNA/RNA Nucleobases with Multiconfigurational Wave Functions of Varying Active Space Size

We characterize the photochemically relevant conical intersections between the lowest-lying accessible electronic excited states of the different DNA/RNA nucleobases using Cholesky decomposition-based complete active space self-consistent field (CASSCF) algorithms. We benchmark two different basis set contractions and several active spaces for each nucleobase and conical intersection type, measuring for the first time how active space size affects conical intersection topographies in these systems and the potential implications these may have toward their description of photoinduced phenomena. Our results show that conical intersection topographies are highly sensitive to the electron correlation included in the model: by changing the amount (and type) of correlated orbitals, conical intersection topographies vastly change, and the changes observed do not follow any converging pattern toward the topographies obtained with the largest and most correlated active spaces. Comparison across systems shows analogous topographies for almost all intersections mediating population transfer to the dark 1nO/Nπ* states, while no similarities are observed for the "ethylene-like" conical intersection ascribed to mediate the ultrafast decay component to the ground state in all DNA/RNA nucleobases. Basis set size seems to have a minor effect, appearing to be relevant only for purine-based derivatives. We rule out structural changes as a key factor in classifying the different conical intersections, which display almost identical geometries across active space and basis set change, and we highlight instead the importance of correctly describing the electronic states involved at these crossing points. Our work shows that careful active space selection is essential to accurately describe conical intersection topographies and therefore to adequately account for their active role in molecular photochemistry.

A Multiconfigurational Wave Function Implementation of the Frenkel Exciton Model for Molecular Aggregates

We present an implementation of the Frenkel exciton model into the OpenMolcas program package enabling calculations of collective electronic excited states of molecular aggregates based on a multiconfigurational wave function description of the individual monomers. The computational protocol avoids using diabatization schemes and, thus, supermolecule calculations. Additionally, the use of the Cholesky decomposition of the two-electron integrals entering pair interactions enhances the efficiency of the computational scheme. The application of the method is exemplified for two test systems, that is, a formaldehyde oxime and a bacteriochlorophyll-like dimer. For the sake of comparison with the dipole approximation, we restrict our considerations to situations where intermonomer exchange can be neglected. The protocol is expected to be beneficial for aggregates composed of molecules with extended π systems, unpaired electrons such as radicals or transition metal centers, where it should outperform widely used methods based on time-dependent density functional theory.

Real-Time Equation-of-Motion Coupled-Cluster Cumulant Green's Function Method: Heterogeneous Parallel Implementation Based on the Tensor Algebra for Many-Body Methods Infrastructure

We report the implementation of the real-time equation-of-motion coupled-cluster (RT-EOM-CC) cumulant Green's function method [ J. Chem. Phys. 2020, 152, 174113] within the Tensor Algebra for Many-body Methods (TAMM) infrastructure. TAMM is a massively parallel heterogeneous tensor library designed for utilizing forthcoming exascale computing resources. The two-body electron repulsion matrix elements are Cholesky-decomposed, and we imposed spin-explicit forms of the various operators when evaluating the tensor contractions. Unlike our previous real algebra Tensor Contraction Engine (TCE) implementation, the TAMM implementation supports fully complex algebra. The RT-EOM-CC singles (S) and doubles (D) time-dependent amplitudes are propagated using a first-order Adams-Moulton method. This new implementation shows excellent scalability tested up to 500 GPUs using the Zn-porphyrin molecule with 655 basis functions, with parallel efficiencies above 90% up to 400 GPUs. The TAMM RT-EOM-CCSD was used to study core photoemission spectra in the formaldehyde and ethyl trifluoroacetate (ESCA) molecules. Simulations of the latter involve as many as 71 occupied and 649 virtual orbitals. The relative quasiparticle ionization energies and overall spectral functions agree well with available experimental results.

Quantum chemistry simulation of ground- and excited-state properties of the sulfonium cation on a superconducting quantum processor

The computational description of correlated electronic structure, and particularly of excited states of many-electron systems, is an anticipated application for quantum devices. An important ramification is to determine the dominant molecular fragmentation pathways in photo-dissociation experiments of light-sensitive compounds, like sulfonium-based photo-acid generators used in photolithography. Here we simulate the static and dynamical electronic structure of the H3S+ molecule, taken as a minimal model of a triply-bonded sulfur cation, on a superconducting quantum processor of the IBM Falcon architecture. To this end, we generalize a qubit reduction technique termed entanglement forging or EF [A. Eddins et al., Phys. Rev. X Quantum, 2022, 3, 010309], currently restricted to the evaluation of ground-state energies, to the treatment of molecular properties. While in a conventional quantum simulation a qubit represents a spin-orbital, within EF a qubit represents a spatial orbital, reducing the number of required qubits by half. We combine the generalized EF with quantum subspace expansion [W. Colless et al., Phys. Rev. X, 2018, 8, 011021], a technique used to project the time-independent Schrodinger equation for ground- and excited-states in a subspace. To enable experimental demonstration of this algorithmic workflow, we deploy a sequence of error-mitigation techniques. We compute dipole structure factors and partial atomic charges along ground- and excited-state potential energy curves, revealing the occurrence of homo- and heterolytic fragmentation. This study is an important step towards the computational description of photo-dissociation on near-term quantum devices, as it can be generalized to other photodissociation processes and naturally extended in different ways to achieve more realistic simulations.

Inelastic Neutron Scattering Measurement of the Ground State Tunneling Gap in Tb and Ho Analogues of a Dy Field-Induced Single-Molecule Magnet

Recent advances in single-molecule magnet (SMM) research have placed great value on interpretation of inelastic neutron scattering (INS) data for rare earth (RE)-containing SMMs. Here, we present the synthesis of several rare earth complexes where combined magnetic and INS studies have been performed, supported by ab initio calculations. The reaction of rare earth nitrate salts with 2,2'-bipyridine (2,2'-bpy) and tetrahalocatecholate (X₄Cat^2-, X = Br, Cl) ligands in methanol (MeOH) afforded two new families of compounds [RE(2,2'-bpy)₂(X₄Cat)(X₄CatH)(MeOH)] (X = Br and RE = Y, Eu, Gd, Tb, Dy, Ho, Yb for 1-RE; X = Cl and RE = Y, Tb, Dy, Ho, and Yb for 2-RE). Addition of triethylamine (Et₃N) to the reaction mixture delivered Et₃NH[RE(2,2'-bpy)₂(Br₄Cat)₂] (3-RE, RE = Er and Yb). Interestingly, cerium behaves differently to the rest of the series, generating (2,2'-bpyH)₂[Ce(Br₄Cat)₃(2,2'-bpy)] (4-Ce) with tetravalent Ce(IV) in contrast to the trivalent metal ions in 1-3. The static magnetic properties of 1-RE (RE = Gd, Tb, Dy and Ho) were investigated in conjunction with INS measurements on 1-Y, 1-Tb, and 1-Ho to probe their ground state properties and any crystal field excitations. To facilitate interpretation of the INS spectra and provide insight into the magnetic behavior, ab initio calculations were performed using the single-crystal X-ray diffraction structural data of 1-RE (RE = Tb, Dy and Ho). The ab initio calculations indicate ground doublets dominated by the maximal angular momentum projection states of Kramers type for 1-Dy and Ising type for 1-Tb and 1-Ho. Dynamic magnetic susceptibility measurements indicate that 1-Dy exhibits slow magnetic relaxation in the presence of a small applied magnetic field mainly through Raman pathways. Inelastic neutron scattering spectra exhibit distinct transitions corresponding to crystal field-induced tunneling gaps between the pseudo-doublet ground state components for 1-Tb and 1-Ho, which is one of the first direct experimental measurements with INS of such tunneling transitions in a molecular nanomagnet. The power of high-resolution INS is demonstrated with evidence of two distinct tunneling gaps measurable for the two crystallographically unique Tb coordination environments observed in the single crystal X-ray structure.

Accelerating Linear-Response Time-Dependent Hybrid Density Functional Theory with Low-Rank Decomposition Techniques in the Plane-Wave Basis

We present an efficient low-rank implementation of linear-response time-dependent density functional theory for hybrid functionals (hybrid-LR-TDDFT) within the plane-wave pseudopotential framework. The adaptively compressed exchange (ACE) operator and the natural transition orbitals (NTOs) are introduced to build the low-rank representation of the nonlocal exchange operator in the hybrid-LR-TDDFT Hamiltonian. Numerical tests demonstrate that the ACE approximation significantly reduces the computational cost of applying the nonlocal exchange operator without loss of accuracy, and the NTO approximation can further accelerate the hybrid-LR-TDDFT calculations by introducing an NTO cutoff parameter. This new method enables us to effectively study the excitonic properties of two-dimensional MoS₂ consisting of 216 atoms and ∼1900 electrons with range-separated hybrid functionals on a single graphics processing unit.

Multiconfiguration Pair-Density Functional Theory for Chromium(IV) Molecular Qubits

Pseudotetrahedral organometallic complexes containing chromium(IV) and aryl ligands have been experimentally identified as promising molecular qubit candidates. Here we present a computational protocol based on multiconfiguration pair-density functional theory for computing singlet-triplet gaps and zero-field splitting (ZFS) parameters in Cr(IV) aryl complexes. We find that two multireference methods, multistate complete active space second-order perturbation theory (MS-CASPT2) and hybrid multistate pair-density functional theory (HMS-PDFT), perform better than Kohn-Sham density functional theory for singlet-triplet gaps. Despite the very small values of the ZFS parameters, both multireference methods performed qualitatively well. MS-CASPT2 and HMS-PDFT performed particularly well for predicting the trend in the ratio of the rhombic and axial ZFS parameters, |E/D|. We have also investigated the dependence and sensitivity of the calculated ZFS parameters on the active space and the molecular geometry. The methodologies outlined here can guide future prediction of ZFS parameters in molecular qubit candidates.

Multireference Study of Optically Addressable Vanadium-Based Molecular Qubit Candidates

Molecular electron spin qubits with optical manipulation schemes are some of the most promising candidates for modern quantum technologies. Key values that determine a compound's viability for optical-spin initialization and readout include its singlet-triplet gap and zero-field splitting (ZFS) parameters. Generally, these values are very small in magnitude and are thus difficult to reproduce with theoretical methods. Here, we study a previously identified optically addressable molecular qubit, (C₆F₅)₃trenVCN^tBu (tren = tris(2-aminoethyl)amine), using the complete active space self-consistent field (CASSCF) and post-CASSCF methods: complete active space second-order perturbation theory (CASPT2), multiconfiguration pair-density functional theory (MC-PDFT), and hybrid MC-PDFT (HMC-PDFT). Of those methods, we successfully reproduce the singlet-triplet gap and ZFS parameters with reasonable accuracy using 0.5 HMC-PDFT and CASPT2. Four additional V³⁺ complexes with differing ligands were also investigated. We found that the ligands have minimal effect on the spin properties of the molecule and propose them to be optically addressable qubit candidates. These potential qubits are further analyzed in terms of ab initio ligand field theory (AILFT) to understand the influence of the ligands on the singlet-triplet gap and ZFS parameters.

Efficient implementation of molecular CCSD gradients with Cholesky-decomposed electron repulsion integrals

We present an efficient implementation of ground and excited state coupled cluster singles and doubles (CCSD) gradients based on Cholesky-decomposed electron repulsion integrals. Cholesky decomposition and density fitting are both inner projection methods, and, thus, similar implementation schemes can be applied for both methods. One well-known advantage of inner projection methods, which we exploit in our implementation, is that one can avoid storing large V3 O and V4 arrays by instead considering three-index intermediates. Furthermore, our implementation does not require the formation and storage of Cholesky vector derivatives. The new implementation is shown to perform well, with less than 10% of the time spent calculating the gradients in geometry optimizations. Furthermore, the computational time per optimization cycle is significantly lower compared to other implementations based on an inner projection method. We showcase the capabilities of the implementation by optimizing the geometry of the retinal molecule (C20H28O) at the CCSD/aug-cc-pVDZ level of theory.

Quantum algorithms for electronic structures: basis sets and boundary conditions

The advantages of quantum computers are believed to significantly change the research paradigm of chemical and materials sciences, where computational characterization and theoretical design play an increasingly important role. It is especially desirable to solve the electronic structure problem, a central problem in chemistry and materials science, efficiently and accurately with well-designed quantum algorithms. Various quantum electronic-structure algorithms have been proposed in the literature. In this article, we briefly review recent progress in this direction with a special emphasis on the basis sets and boundary conditions. Compared to classical electronic structure calculations, there are new considerations in choosing a basis set in quantum algorithms. For example, the effect of the basis set on the circuit complexity is very important in quantum algorithm design. Electronic structure calculations should be performed with an appropriate boundary condition. Simply using a wave function ansatz designed for molecular systems in a material system with a periodic boundary condition may lead to significant errors. Artificial boundary conditions can be used to partition a large system into smaller fragments to save quantum resources. The basis sets and boundary conditions are expected to play a crucial role in electronic structure calculations on future quantum computers, especially for realistic systems.

Efficient Implementation of Equation-of-Motion Coupled-Cluster Singles and Doubles Method with the Density-Fitting Approximation: An Enhanced Algorithm for the Particle-Particle Ladder Term

An efficient implementation of the density-fitted equation-of-motion coupled-cluster singles and doubles (DF-EOM-CCSD) method is presented with an enhanced algorithm for the particle-particle ladder (PPL) term, which is the most expensive part of EOM-CCSD computations. To further improve the evaluation of the PPL term, a hybrid density-fitting/Cholesky decomposition (DF/CD) algorithm is also introduced. In the hybrid DF/CD approach, four virtual index integrals are constructed on-the-fly from the DF factors; then, their partial Cholesky decomposition is simultaneously performed. The computational cost of the DF-EOM-CCSD method for excitation energies is compared with that of the resolution of the identity EOM-CCSD (RI-EOM-CCSD) (from the Q-chem 5.3 package). Our results demonstrate that DF-EOM-CCSD excitation energies are significantly accelerated compared to RI-EOM-CCSD. There is more than a 2-fold reduction for the C₈H₁₈ molecule in the cc-pVTZ basis set with the restricted Hartree-Fock (RHF) reference. This cost savings results from the efficient evaluation of the PPL term. In the RHF based DF-EOM-CCSD method, the number of flops (NOF) is 1/4O²V⁴, while that of RI-EOM-CCSD was reported (Epifanovsky et al. J. Chem. Phys. 2013, 139, 134105) to be 5/8O²V⁴ for the PPL contraction term. Further, the NOF of VVVV-type integral transformation is 1/2V⁴N_aux in our case, while it appears to be V⁴N_aux for RI-EOM-CCSD. Hence, our implementation is 2.5 and 2.0 times more efficient compared to RI-EOM-CCSD for these expensive terms. For the unrestricted Hartree-Fock (UHF) reference, our implementation maintains its enhanced performance and provides a 1.8-fold reduction in the computational time compared to RI-EOM-CCSD for the C₇H₁₆ molecule. Our results indicate that our DF-EOM-CCSD implementation is 1.7 and 1.4 times more efficient compared with RI-EOM-CCSD for average computational cost per EOM-CCSD iteration. Moreover, our results show that the new hybrid DF/CD approach improves upon the DF algorithm, especially for large molecular systems. Overall, we conclude that the new hybrid DF/CD PPL algorithm is very promising for large-sized chemical systems.

New Light on an Old Story: Breaking Kasha's Rule in Phosphorescence Mechanism of Organic Boron Compounds and Molecule Design

In this work, the phosphorescence mechanism of (E)-3-(((4-nitrophenyl)imino)methyl)-2H-thiochroman-4-olate-BF2 compound (S-BF2) is investigated theoretically. The phosphorescence of S-BF2 has been reassigned to the second triplet state (T2) by the density matrix renormalization group (DMRG) method combined with the multi-configurational pair density functional theory (MCPDFT) to approach the limit of theoretical accuracy. The calculated radiative and non-radiative rate constants support the breakdown of Kasha's rule further. Our conclusion contradicts previous reports that phosphorescence comes from the first triplet state (T1). Based on the revised phosphorescence mechanism, we have purposefully designed some novel compounds in theory to enhance the phosphorescence efficiency from T2 by replacing substitute groups in S-BF2. Overall, both S-BF2 and newly designed high-efficiency molecules exhibit anti-Kasha T2 phosphorescence instead of the conventional T1 emission. This work provides a useful guidance for future design of high-efficiency green-emitting phosphors.

Straightforward and Accurate Automatic Auxiliary Basis Set Generation for Molecular Calculations with Atomic Orbital Basis Sets

Density fitting (DF), also known as the resolution of the identity (RI), is a widely used technique in quantum chemical calculations with various types of atomic basis sets─Gaussian-type orbitals, Slater-type orbitals, as well as numerical atomic orbitals─to speed up density functional, Hartree-Fock (HF), and post-HF calculations. Traditionally, custom auxiliary basis sets are hand-optimized for each orbital basis set; however, some automatic schemes have also been suggested. In this work, we propose a simple yet numerically stable automated scheme for forming auxiliary basis sets with the help of a pivoted Cholesky decomposition, which is applicable to any type of atomic basis function. We exemplify the scheme with proof-of-concept calculations with Gaussian basis sets and show that the proposed approach leads to negligible DF/RI errors in HF and second-order Møller-Plesset (MP2) total energies of the non-multireference part of the W4-17 test set when used with orbital basis sets of at least polarized triple-ζ quality. The results are promising for future applications employing Slater-type orbitals or numerical atomic orbitals, as well as schemes based on the use of local fitting approaches. Global fitting approaches can also be used, in which case the high-angular-momentum functions produced by the present scheme can be truncated to minimize the computational cost.

Modelling Photoionisation in Isocytosine: Potential Formation of Longer-Lived Excited State Cations in its Keto Form

Studying the effects of UV and VUV radiation on non-canonical DNA/RNA nucleobases allows us to compare how they release excess energy following absorption with respect to their canonical counterparts. This has attracted much research attention in recent years because of its likely influence on the origin of our genetic lexicon in prebiotic times. Here we present a CASSCF and XMS-CASPT2 theoretical study of the photoionisation of non-canonical pyrimidine nucleobase isocytosine in both its keto and enol tautomeric forms. We analyse their lowest energy cationic excited states including 2 π + , 2 n O + and 2 n N + and compare these to the corresponding electronic states in cytosine. Investigating lower-energy decay pathways we find - unexpectedly - that keto-isocytosine+ presents a sizeable energy barrier potentially inhibiting decay to its cationic ground state, whereas enol-isocytosine+ features a barrierless and consequently ultrafast pathway analogous to the one previously found for the canonical (keto) form of cytosine+ . Dynamic electron correlation reduces the energy barrier in the keto form substantially (by ∼1 eV) but it is nevertheless still present. We additionally compute the UV/Vis absorption signals of the structures encountered along these decay channels to provide spectroscopic fingerprints to assist future experiments in monitoring these intricate photo-processes.

Using Redox-Active Ligands to Generate Actinide Ligand Radical Species

Using a redox-active dioxophenoxazine ligand, DOPO (DOPO = 2,4,6,8-tetra-tert-butyl-1-oxo-1H-phenoxazine-9-olate), a family of actinide (U, Th, Np, and Pu) and Hf tris(ligand) coordination compounds was synthesized. The full characterization of these species using ¹H NMR spectroscopy, electronic absorption spectroscopy, SQUID magnetometry, and X-ray crystallography showed that these compounds are analogous and exist in the form M(DOPO^q)₂(DOPO^sq), where two ligands are of the oxidized quinone form (DOPO^q) and the third is of the reduced semiquinone (DOPO^sq) form. The electronic structures of these complexes were further investigated using CASSCF calculations, which revealed electronic structures consistent with metals in the +4 formal oxidation state and one unpaired electron localized on one ligand in each complex. Furthermore, f orbitals of the early actinides show a sizable bonding overlap with the ligand 2p orbitals. Notably, this is the first example of a plutonium-ligand radical species and a rare example of magnetic data being recorded for a homogeneous plutonium coordination complex.

Modeling magnetic interactions in high-valent trinuclear [Mn3(IV)O4]4+ complexes through highly compressed multi-configurational wave functions

In this work we apply a quantum chemical framework, recently designed in our laboratories, to rationalize the low-energy electronic spectrum and the magnetic properties of an homo-valent trinuclear [Mn₃^(IV)O₄]⁴⁺ model of the oxygen-evolving center in photosystem II. The method is based on chemically motivated molecular orbital unitary transformations, and the optimization of spin-adapted many-body wave functions, both for ground- and excited-states, in the transformed MO basis. In this basis, the configuration interaction Hamiltonian matrix of exchange-coupled multi-center clusters is extremely sparse and characterized by a unique block diagonal structure. This property leads to highly compressed wave functions (oligo- or single-reference) and crucially enables state-specific optimizations. This work is the first showing that compression and selective targeting of ground- and excited-states wave functions is possible for systems with three magnetic centers that are not exactly half-filled, and that potentially exhibit frustrated spin interactions. The reduced multi-reference character of the wave function greatly simplifies the interpretation of the ground- and excited-state electronic structures, and provides a route for the direct rationalization of magnetic interactions in these compounds, often considered a challenge in polynuclear transition-metal chemistry. In this study, strong electron correlation effects have explicitly been described by conventional and stochastic multiconfigurational methodologies, while dynamic correlation effects have been accounted for by multiconfigurational second order perturbation theory, CASPT2. Ab initio results for the [Mn₃^(IV)O₄]⁴⁺ system have been mapped to a three-site Heisenberg model with two magnetic coupling constants. The magnetic coupling constants and the temperature dependence of the effective magnetic moment predicted by the ab initio calculations are in good agreement with the available experimental data, and confirm the antiferromagnetic interaction among the three magnetic centers, while providing a simple and rigorous description of the noncollinearity of the local spins, that characterize most of the low-energy states for this system.

An improved chain of spheres for exchange algorithm

In the present work, we describe a more accurate and efficient variant of the chain-of-spheres algorithm (COSX) for exchange matrix computations. Higher accuracy for the numerical integration is obtained with new grids that were developed using global optimization techniques. With our new default grids, the average absolute energy errors are much lower than 0.1 kcal/mol, which is desirable to achieve "chemical accuracy." Although the size of the new grids is increased by roughly a factor of 2.5, the excellent efficiency of the original COSX implementation is still further improved in most cases. The evaluation of the analytic electrostatic potential integrals was significantly accelerated by a new implementation of rolled-out versions of the Dupuis-Rys-King and Head-Gordon-Pople algorithms. Compared to our earlier implementation, a twofold speedup is obtained for the frequently used triple-ζ basis sets, while up to a 16-fold speedup is observed for quadruple-ζ basis sets. These large gains are a consequence of both the more efficient integral evaluation and the intermediate exchange matrix computation in a partially contracted basis when generally contracted shells occur. With our new RIJCOSX implementation, we facilitate accurate self-consistent field (SCF) binding energy calculations on a large supra-molecular complex composed of 320 atoms. The binding-energy errors with respect to the fully analytic results are well below 0.1 kcal/mol for the cc-pV(T/Q)Z basis sets and even smaller than for RIJ with fully analytic exchange. At the same time, our RIJCOSX SCF calculation even with the cc-pVQZ basis and the finest grid is 21 times faster than the fully analytic calculation.

Model protein excited states: MRCI calculations with large active spaces vs CC2 method

Benchmarking calculations on excited states of models of phenylalanine protein chains are presented to assess the ability of alternative methods to the standard and most commonly used multiconfigurational wave function-based method, the complete active space self-consistent field (CASSCF), in recovering the non-dynamical correlation for systems that become not affordable by the CASSCF. The exploration of larger active spaces beyond the CASSCF limit is benchmarked through three strategies based on the reduction in the number of determinants: the restricted active space self-consistent field, the generalized active space self-consistent field (GASSCF), and the occupation-restricted multiple active space (ORMAS) schemes. The remaining dynamic correlation effects are then added by the complete active space second-order perturbation theory and by the multireference difference dedicated configuration interaction methods. In parallel, the approximate second-order coupled cluster (CC2), already proven to be successful for small building blocks of model proteins in one of our previous works [Ben Amor et al., J. Chem. Phys. 148, 184105 (2018)], is investigated to assess its performances for larger systems. Among the different alternative strategies to CASSCF, our results highlight the greatest efficiency of the GASSCF and ORMAS schemes in the systematic reduction of the configuration interaction expansion without loss of accuracy in both nature and excitation energies of both singlet ππ^* and nπ^* _CO excited states with respect to the equivalent CASSCF calculations. Guidelines for an optimum applicability of this scheme to systems requiring active spaces beyond the complete active space limit are then proposed. Finally, the extension of the CC2 method to such large systems without loss of accuracy is demonstrated, highlighting the great potential of this method to treat accurately excited states, mainly single reference, of very large systems.

An Open-Shell Coronoid with Hybrid Chichibabin-Schlenk Conjugation

A hexaradicaloid molecule with alternating Kekulé and non-Kekulé connectivities between adjacent spin centers was obtained by fusing two classic conjugation motifs, found respectively in the Chichibabin and Schlenk hydrocarbons, into a coronoid structure. 1 H NMR, ESR and SQUID experiments, combined with computational analyses reveal that the system has a singlet ground state, characterized by a significant hexaradicaloid character ( γ 0 = 0.826, γ 1 = γ 2 = 0.773). It possesses multiple thermally accessible high-spin states (up to the septet), with uniform energy gaps of ca 1.0 kcal/mol between consecutive multiplicities. In line with its open-shell character, the coronoid has a small electronic bandgap of ca. 0.8 eV and undergoes two consecutive one-electron oxidations at low potentials, yielding cationic forms with extended near-infrared absorption. The hexaradicaloid, which combines open-shell and macrocyclic contributions to its π conjugation, provides an example of a design strategy for multistate spin switches and redox-amphoteric NIR dyes.

A critical analysis of least-squares tensor hypercontraction applied to MP3

The least-squares tensor hypercontraction (LS-THC) approach is a promising method of reducing the high polynomial scaling of wavefunction methods, for example, those based on many-body perturbation theory or coupled cluster. Here, we focus on LS-THC-MP3 and identify four variants with differing errors and efficiency characteristics. The performance of LS-THC-MP3 is analyzed for regular test systems with up to 40 first-row atoms. We also analyze the size-extensivity/size-consistency and grid- and basis set dependence of LS-THC-MP3. Overall, the errors observed are favorably small in comparison with standard density fitting, and a more streamlined method of generating grids via pruning is suggested. A practical crossover (the point at which LS-THC-MP3 is cheaper than the canonical method) is achieved around 240 correlated electrons. Despite several drawbacks of LS-THC that have been identified: an initial non-linearity of error when increasing system size, poor description of angular correlation, and a potentially large increase in error with the basis set size, the results show that LS-THC has significant potential for practical application to MP3 and other wavefunction methods.

From NWChem to NWChemEx: Evolving with the Computational Chemistry Landscape

Since the advent of the first computers, chemists have been at the forefront of using computers to understand and solve complex chemical problems. As the hardware and software have evolved, so have the theoretical and computational chemistry methods and algorithms. Parallel computers clearly changed the common computing paradigm in the late 1970s and 80s, and the field has again seen a paradigm shift with the advent of graphical processing units. This review explores the challenges and some of the solutions in transforming software from the terascale to the petascale and now to the upcoming exascale computers. While discussing the field in general, NWChem and its redesign, NWChemEx, will be highlighted as one of the early codesign projects to take advantage of massively parallel computers and emerging software standards to enable large scientific challenges to be tackled.

Energy and analytic gradients for the orbital-optimized coupled-cluster doubles method with the density-fitting approximation: An efficient implementation

Efficient implementations of the orbital-optimized coupled-cluster doubles (or simply "optimized CCD," OCCD, for short) method and its analytic energy gradients with the density-fitting (DF) approach, denoted by DF-OCCD, are presented. In addition to the DF approach, the Cholesky-decomposed variant (CD-OCCD) is also implemented for energy computations. The computational cost of the DF-OCCD method (available in a plugin version of the DFOCC module of PSI4) is compared with that of the conventional OCCD (from the Q-CHEM package). The OCCD computations were performed with the Q-CHEM package in which OCCD are denoted by OD. In the conventional OCCD method, one needs to perform four-index integral transformations at each of the CCD iterations, which limits its applications to large chemical systems. Our results demonstrate that DF-OCCD provides dramatically lower computational costs compared to OCCD, and there are almost eightfold reductions in the computational time for the C₆H₁₄ molecule with the cc-pVTZ basis set. For open-shell geometries, interaction energies, and hydrogen transfer reactions, DF-OCCD provides significant improvements upon DF-CCD. Furthermore, the performance of the DF-OCCD method is substantially better for harmonic vibrational frequencies in the case of symmetry-breaking problems. Moreover, several factors make DF-OCCD more attractive compared to CCSD: (1) for DF-OCCD, there is no need for orbital relaxation contributions in analytic gradient computations; (2) active spaces can readily be incorporated into DF-OCCD; (3) DF-OCCD provides accurate vibrational frequencies when symmetry-breaking problems are observed; (4) in its response function, DF-OCCD avoids artificial poles; hence, excited-state molecular properties can be computed via linear response theory; and (5) symmetric and asymmetric triples corrections based on DF-OCCD [DF-OCCD(T)] have a significantly better performance in near degeneracy regions.

Quantum Information and Algorithms for Correlated Quantum Matter

Discoveries in quantum materials, which are characterized by the strongly quantum-mechanical nature of electrons and atoms, have revealed exotic properties that arise from correlations. It is the promise of quantum materials for quantum information science superimposed with the potential of new computational quantum algorithms to discover new quantum materials that inspires this Review. We anticipate that quantum materials to be discovered and developed in the next years will transform the areas of quantum information processing including communication, storage, and computing. Simultaneously, efforts toward developing new quantum algorithmic approaches for quantum simulation and advanced calculation methods for many-body quantum systems enable major advances toward functional quantum materials and their deployment. The advent of quantum computing brings new possibilities for eliminating the exponential complexity that has stymied simulation of correlated quantum systems on high-performance classical computers. Here, we review new algorithms and computational approaches to predict and understand the behavior of correlated quantum matter. The strongly interdisciplinary nature of the topics covered necessitates a common language to integrate ideas from these fields. We aim to provide this common language while weaving together fields across electronic structure theory, quantum electrodynamics, algorithm design, and open quantum systems. Our Review is timely in presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum matter with applications in grand-challenge problems. Looking to the future, at the intersection of quantum information science and algorithms for correlated quantum matter, we envision seminal advances in predicting many-body quantum states and describing excitonic quantum matter and large-scale entangled states, a better understanding of high-temperature superconductivity, and quantifying open quantum system dynamics.

Bioinspired Nickel Complexes Supported by an Iron Metalloligand

Nature utilizes multimetallic sites in metalloenzymes to enable multielectron chemical transformations at ambient conditions and low overpotentials. One such example of multimetallic cooperativity can be found in the C-cluster of Ni-carbon monoxide dehydrogenase (CODH), which interconverts CO and CO₂. Toward a potential functional model of the C-cluster, a family of Ni-Fe bimetallic complexes was synthesized that contain direct metal-metal bonding interactions. The complexes were characterized by X-ray crystallography, various spectroscopies (NMR, EPR, UV-vis, Mössbauer), and theoretical calculations. The Ni-Fe bimetallic system has a reversible Fe(III)/Fe(II) redox couple at -2.10 V (vs Fc⁺/Fc). The Fe-based "redox switch" can turn on CO₂ reactivity at the Ni(0) center by leveraging the Ni→Fe dative interaction to attenuate the Ni(0) electron density. The reduced Ni(0)Fe(II) species mediated the formal two-electron reduction of CO₂ to CO, providing a Ni-CO adduct and CO₃^2- as products. During the reaction, an intermediate was observed that is proposed to be a Ni-CO₂ species.

Assessment of the Density-Fitted Second-Order Quasidegenerate Perturbation Theory for Transition Energies: Accurate Computations of Singlet-Triplet Gaps for Charge-Transfer Compounds

Organic light-emitting diodes (OLEDs) have been of significant interest because of their superior performance and low cost of production. Thermally activated delayed fluorescence (TADF) has attracted significant interest in the OLED technology because it improves the efficiency of OLEDs by harvesting triplet excitons. Therefore, the accurate computation of singlet-triplet transition energies (ΔE_S1-T1) of charge-transfer molecules is very important. However, the accurate computation of the ΔE_S1-T1 values is a challenging problem for single-reference methods because of the multireference character of excited states. In this research, an assessment of density-fitted second-order quasidegenerate perturbation theory (DF-QDPT2) [Bozkaya, U.; J. Chem. Theory Comput. 2019, 15, 4415-4429] for singlet-triplet transition energies (ΔE_S1-T1) of charge-transfer compounds is presented. The performance of the DF-QDPT2 method has been compared with those of several density-functional theory functionals, such as B3LYP, PBE0, M06-2X, ωB97X-D, and MN15; density-fitted state-averaged CASSCF (DF-SA-CASSCF); and single-state single-reference second-order perturbation theory (SS-SR-CASPT2) methods. For the TADF molecules considered, the DF-QDPT2 method provides a mean absolute error (MAE) of 0.13 eV, while the MAE values of DF-SA-CASSCF and SS-SR-CASPT2 are 0.65 and 0.74 eV, respectively. The performances of B3LYP and PBE0 are slightly better than that of DF-QDPT2, while M06-2X and ωB97X-D provide noticeably higher errors compared with DF-QDPT2. Furthermore, the standard CASSCF without state-averaging yields dramatic errors with an MAE value of 3.0 eV. Our results demonstrate that eigenvalues of the DF-QDPT2-effective Hamiltonian can be reliably used for the prediction of singlet-triplet transition energies, while eigenvalues of DF-CASSCF/DF-SA-CASSCF fail to provide accurate predictions. Overall, we conclude that the DF-QDPT2 method emerges as a very useful tool for the computation of excited-state properties.

Ab initio study on the excited states of pyrene and its derivatives using multi-reference perturbation theory methods

Low-lying singlet excited states of pyrene derivatives originated from the 1La and 1Lb states of pyrene have decisive influences on their absorption and fluorescence emission behaviors. Calculation of these excited states with quantitative accuracy is required for the theoretical design of pyrene derivatives tailored to target applications; this has been a long-standing challenge for ab initio quantum chemical calculations. In this study, we explore an adequate computational scheme through calculations of pyrene and its phenyl-substituted derivatives using multi-reference perturbation theory (MRPT) methods. All valence π orbitals on the pyrene moiety were assigned to the active orbitals. Computational load was reduced by restricting the electron excitations within the active orbitals in the preparation of reference configuration space. A generalized multi-configuration quasi-degenerate perturbation theory (GMCQDPT) was adopted to treat the reference space other than the complete active space. The calculated 1La and 1Lb excitation energies of pyrene are in good agreement with the experimental values. Calculations of 1,3,6,8-tetraphenyl pyrene suggest that the energetic ordering of 1La and 1Lb is inverted through tetraphenyl substitution and its lowest singlet excited state is the 1La parentage of pyrene, which is consistent with the experimentally deduced scheme. These results are not readily obtained by MRPT calculations with a limited number of active orbitals and single-reference theory calculations. Diphenyl pyrenes (DPPy) were also calculated at the same level of theory to investigate the dependence on the substitution positions of phenyl groups.

Probing competing relaxation pathways in malonaldehyde with transient X-ray absorption spectroscopy

Excited-state intramolecular hydrogen transfer (ESIHT) is a fundamental reaction relevant to chemistry and biology. Malonaldehyde is the simplest example of ESIHT, yet only little is known experimentally about its excited-state dynamics. Several competing relaxation pathways have been proposed, including internal conversion mediated by ESIHT and C[double bond, length as m-dash]C torsional motion as well as intersystem crossing. We perform an in silico transient X-ray absorption spectroscopy (TRXAS) experiment at the oxygen K-edge to investigate its potential to monitor the proposed ultrafast decay pathways in malonaldehyde upon photoexcitation to its bright S₂(ππ*) state. We employ both restricted active space perturbation theory and algebraic-diagrammatic construction for the polarization propagator along interpolated reaction coordinates as well as representative trajectories from ab initio multiple spawning simulations to compute the TRXAS signals from the lowest valence states. Our study suggests that oxygen K-edge TRXAS can distinctly fingerprint the passage through the H-transfer intersection and the concomitant population transfer to the S₁(nπ*) state. Potential intersystem crossing to T₁(ππ*) is detectable from reappearance of the double pre-edge signature and reversed intensities. Moreover, the torsional deactivation pathway induces transient charge redistribution from the enol side towards the central C-atom and manifests itself as substantial shifts of the pre-edge features. Given the continuous advances in X-ray light sources, our study proposes an experimental route to disentangle ultrafast excited-state decay channels in this prototypical ESIHT system and provides a pathway-specific mapping of the TRXAS signal to facilitate the interpretation of future experiments.

Asymmetric Density Fitting with Modified Cholesky Decomposition Applied to Second-Order Electron Propagator

Computation of molecular orbital electron repulsion integrals (MO-ERIs) as a transformation from atomic orbital ERIs (AO-ERIs) is the bottleneck of second-order electron propagator calculations when a single orbital is studied. In this contribution, asymmetric density fitting is combined with modified Cholesky decomposition to generate efficiently the required MO-ERIs. The key point of the presented algorithms is to keep track of integrals through partial contractions performed on three-center AO-ERIs; these contractions are stored in RAM instead of the AO-ERIs. Two implementations are provided, an in-core, which reduces the arithmetic and memory scaling factors as compared to the four-center AO-ERIs contraction method, and a semidirect, which overcomes memory limitations by evaluating antisymmetrized MO-ERIs in batches. On the numerical side, the proposed approach is fast and stable. The bad effects due to ill conditioning, namely, several negative and close to zero eigenvalues due to machine round off errors of the matrix associated with the density fitting process, are effectively controlled by means of a modified Cholesky factorization that avoids the matrix inversion needed to perform the asymmetrical density fitting implementation. The numerical experience presented shows that the in-core implementation is highly competitive to perform calculations on medium and large basis sets, while the semidirect implementation has small variations in time by changes in the available memory. The general applicability is illustrated on a set of selected relatively large-size molecules.