Delving into the catalytic mechanism of molybdenum cofactors: a novel coupled cluster study.

In this work, we use modern electronic structure methods to model the catalytic mechanism of different variants of the molybdenum cofactor (Moco). We investigate the dependence of various Moco model systems on structural relaxation and the importance of environmental effects for five critical points along the reaction coordinate with the DMSO and NO3- substrates. Furthermore, we scrutinize the performance of various coupled-cluster approaches for modeling the relative energies along the investigated reaction paths, focusing on several pair coupled cluster doubles (pCCD) flavors and conventional coupled cluster approximations. Moreover, we elucidate the Mo-O bond formation using orbital-based quantum information measures, which highlight the flow of σM-O bond formation and σN/S-O bond breaking. Our study shows that pCCD-based models are a viable alternative to conventional methods and offer us unique insights into the bonding situation along a reaction coordinate. Finally, this work highlights the importance of environmental effects or changes in the core and, consequently, in the model itself to elucidate the change in activity of different Moco variants.

Toward Reliable Dipole Moments without Single Excitations: The Role of Orbital Rotations and Dynamical Correlation.

The dipole moment is a crucial molecular property linked to a molecular system's bond polarity and overall electronic structure. To that end, the electronic dipole moment, which results from the electron density of a system, is often used to assess the accuracy and reliability of new electronic structure methods. This work analyses electronic dipole moments computed with the pair coupled cluster doubles (pCCD) ansätze and its linearized coupled cluster (pCCD-LCC) corrections using the canonical Hartree-Fock and pCCD-optimized (localized) orbital bases. The accuracy of pCCD-based dipole moments is assessed against experimental and CCSD(T) reference values using relaxed and unrelaxed density matrices and different basis set sizes. Our test set comprises molecules of various bonding patterns and electronic structures, exposing pCCD-based methods to a wide range of electron correlation effects. Additionally, we investigate the performance of pCCD-in-DFT dipole moments of some model complexes. Finally, our work indicates the importance of orbital relaxation in the pCCD model and shows the limitations of the linearized couple cluster corrections in predicting electronic dipole moments of multiple-bonded systems. Most importantly, pCCD with a linearized CCD correction can reproduce the dipole moment surfaces in singly bonded molecules, which are comparable to the multireference ones.

Benchmarking Ionization Potentials from pCCD Tailored Coupled Cluster Models.

The ionization potential (IP) is an important parameter providing essential insights into the reactivity of chemical systems. IPs are also crucial for designing, optimizing, and understanding the functionality of modern technological devices. We recently showed that limiting the CC ansatz to the seniority-zero sector proves insufficient in predicting reliable and accurate ionization potentials within an IP equation-of-motion coupled-cluster formalism. Specifically, the absence of dynamical correlation in the seniority-zero pair coupled cluster doubles (pCCD) model led to unacceptably significant errors of approximately 1.5 eV. In this work, we aim to explore the impact of dynamical correlation and the choice of the molecular orbital basis (canonical vs localized) in CC-type methods targeting 230 ionized states in 70 molecules, comprising small organic molecules, medium-sized organic acceptors, and nucleobases. We focus on pCCD-based approaches as well as the conventional IP-EOM-CCD and IP-EOM-CCSD. Their performance is compared to the CCSD(T) or CCSDT equivalent and experimental reference data. Our statistical analysis reveals that all investigated frozen-pair coupled cluster methods exhibit similar performance, with differences in errors typically within chemical accuracy (1 kcal/mol or 0.05 eV). Notably, the effect of the molecular orbital basis, such as canonical Hartree-Fock or natural pCCD-optimized orbitals, on the IPs is marginal if dynamical correlation is accounted for. Our study suggests that triple excitations are crucial in achieving chemical accuracy in IPs when modeling electron detachment processes with pCCD-based methods.

Accelerating Pythonic Coupled-Cluster Implementations: A Comparison Between CPUs and GPUs.

In this work, we benchmark several Python routines for time and memory requirements to identify the optimal choice of the tensor contraction operations available. We scrutinize how to accelerate the bottleneck tensor operations of Pythonic coupled-cluster implementations in the Cholesky linear algebra domain, utilizing a NVIDIA Tesla V100S PCIe 32GB (rev 1a) graphics processing unit (GPU). The NVIDIA compute unified device architecture API interacts with CuPy, an open-source library for Python, designed as a NumPy drop-in replacement for GPUs. Due to the limitations of video memory, the GPU calculations must be performed batch-wise. Timing results of some contractions containing large tensors are presented. The CuPy implementation leads to a factor of 10-16 speed-up of the bottleneck tensor contractions compared to computations on 36 central processing unit (CPU) cores. Finally, we compare example CCSD and pCCD-LCCSD calculations performed solely on CPUs to their CPU-GPU hybrid implementation, which leads to a speed-up of a factor of 3-4 compared to the CPU-only variant.

Geminal-Based Strategies for Modeling Large Building Blocks of Organic Electronic Materials.

We elaborate on unconventional electronic structure methods based on geminals and their potential to advance the rapidly developing field of organic photovoltaics (OPVs). Specifically, we focus on the computational advantages of geminal-based methods over standard approaches and identify the critical aspects of OPV development. Examples are reliable and efficient computations of orbital energies, electronic spectra, and van der Waals interactions. Geminal-based models can also be combined with quantum embedding techniques and a quantum information analysis of orbital interactions to gain a fundamental understanding of the electronic structures and properties of realistic OPV building blocks. Furthermore, other organic components present in, for instance, dye-sensitized solar cells (DSSCs) represent another promising scope of application. Finally, we provide numerical examples predicting the properties of a small building block of OPV components and two carbazole-based dyes proposed as possible DSSC sensitizers.

Static embedding with pair coupled cluster doubles based methods.

Quantum embedding methods have recently been significantly developed to model large molecular structures. This work proposes a novel wave function theory in a density functional theory (WTF-in-DFT) embedding scheme based on pair-coupled cluster doubles (pCCD)-type methods. While pCCD can reliably describe strongly-correlated systems with mean-field-like computational cost, the large extent of the dynamic correlation can be accounted for by (linearized) coupled-cluster corrections on top of the pCCD wave function. Here we focus on the linearized coupled-cluster singles and doubles (LCCSD) ansatz for electronic ground states and its extension to excited states within the equation of motion (EOM) formalism. We test our EOM-pCCD-LCCSD-in-DFT approach for the vertical excitation energies of the hydrogen-bonded water-ammonia complex, micro-solvated thymine, and uranyl tetrahalides (UO2X42-, X = F, Cl, Br). Furthermore, we assess the quality of the embedding potential using an orbital entanglement and correlation analysis. The approximate embedding models successfully capture changes in the excitation energies going from bare fragments to supramolecular structures and represent a promising computational method for excited states in large molecular systems.

The relationship between structure and excited-state properties in polyanilines from geminal-based methods.

We employ state-of-the-art quantum chemistry methods to study the structure-to-property relationship in polyanilines (PANIs) of different lengths and oxidation states. Specifically, we focus on leucoemeraldine, emeraldine, and pernigraniline in their tetramer and octamer forms. We scrutinize their structural properties, HOMO and LUMO energies, HOMO-LUMO gaps, and vibrational and electronic spectroscopy using various Density Functional Approximations (DFAs). Furthermore, the accuracy of DFAs is assessed by comparing them to experimental and wavefunction-based reference data. We perform large-scale orbital-optimized pair-Coupled Cluster Doubles (oo-pCCD) calculations for ground and electronically excited states and conventional Configuration Interaction Singles (CIS) calculations for electronically excited states in all investigated systems. The EOM-pCCD+S approach with pCCD-optimized orbitals allows us to unambiguously identify charge transfer and local transitions across the investigated PANI systems-an analysis not possible within a delocalized canonical molecular orbital basis obtained, for instance, by DFAs. We show that the low-lying part of the emeraldine and pernigraniline spectrum is dominated by charge transfer excitations and that polymer elongation changes the character of the leading transitions. Furthermore, we augment our study with a quantum informational analysis of orbital correlations in various forms of PANIs.

Benchmarking ionization potentials using the simple pCCD model.

The electron-detachment energy is measured by the ionization potential (IP). As a result, it is a fundamental, observable and important molecular electronic signature in photoelectron spectroscopy. A precise theoretical prediction of electron-detachment energies or ionization potentials is essential for organic optoelectronic systems like transistors, solar cells, or light-emitting diodes. In this work, we benchmark the performance of the recently presented IP variant of the equation-of-motion pair coupled cluster doubles (IP-EOM-pCCD) model to determine IPs. Specifically, the predicted ionization energies are compared to experimental results and higher-order coupled cluster theories based on statistically assessing 201 electron-detached states of 41 organic molecules for three different molecular orbital basis sets and two sets of particle-hole operators. While IP-EOM-pCCD features a reasonable spread and skewness of ionization energies, its mean error and standard deviation differ by up to 1.5 eV from reference data. Our study, thus, highlights the importance of dynamical correlation to reliably predict IPs from a pCCD reference function in small organic molecules.

A configuration interaction correction on top of pair coupled cluster doubles.

Numerous numerical studies have shown that geminal-based methods are a promising direction to model strongly correlated systems with low computational costs. Several strategies have been introduced to capture the missing dynamical correlation effects, which typically exploit a posteriori corrections to account for correlation effects associated with broken-pair states or inter-geminal correlations. In this article, we scrutinize the accuracy of the pair coupled cluster doubles (pCCD) method extended by configuration interaction (CI) theory. Specifically, we benchmark various CI models, including, at most double excitations against selected CC corrections as well as conventional single-reference CC methods. A simple Davidson correction is also tested. The accuracy of the proposed pCCD-CI approaches is assessed for challenging small model systems such as the N2 and F2 dimers and various di- and triatomic actinide-containing compounds. In general, the proposed CI methods considerably improve spectroscopic constants compared to the conventional CCSD approach, provided a Davidson correction is included in the theoretical model. At the same time, their accuracy lies between those of the linearized frozen pCCD and frozen pCCD variants.

Geminal-based electronic structure methods in quantum chemistry. Toward a geminal model chemistry.

In this review, we discuss the recent progress in developing geminal-based theories for challenging problems in quantum chemistry. Specifically, we focus on the antisymmetrized geminal power, generalized valence bond, antisymmetrized product of strongly orthogonal geminals, singlet-type orthogonal geminals, the antisymmetric product of 1-reference orbital geminal, also known as the pair coupled cluster doubles ansatz, and geminals constructed from Richardson-Gaudin states. Furthermore, we review various corrections to account for the missing dynamical correlation effects in geminal models and possible extensions to target electronically excited states and open-shell species. Finally, we discuss some numerical examples and present-day challenges for geminal-based models, including a quantitative and qualitative analysis of wave functions, and software availability.

Resolving the π-assisted U-N σf-bond formation using quantum information theory.

We model the potential energy profiles of the UO2 (NCO)Cl2- → NUOCl2- + CO2 reaction pathway [Y. Gong, V. Vallet, M. del Carmen Michelini, D. Rios and J. K. Gibson, J. Phys. Chem. A, 2014, 118, 325-330] using different pair coupled-cluster doubles (pCCD) methods. Specifically, we focus on pCCD and pCCD-tailored coupled cluster models in predicting relative energies for the various intermediates and transition states along the reaction coordinate. Furthermore, we augment our study on energetics with an orbital-pair correlation analysis of the complete reaction pathway that features two distinct paths. Our analysis of orbital correlations sheds new light on the formation and breaking of respective bonds between the uranium, oxygen, and nitrogen atoms along the reaction coordinates where the "yl" bond is broken and a nitrido compound formed. Specifically, the strengthening of the U-N σf-bond is assisted by a π-type interaction that is delocalized over the C-N-U backbone of the UO2 (NCO)Cl2- complex.

Assessing the Accuracy of Tailored Coupled Cluster Methods Corrected by Electronic Wave Functions of Polynomial Cost.

Tailored coupled cluster theory represents a computationally inexpensive way to describe static and dynamical electron correlation effects. In this work, we scrutinize the performance of various coupled cluster methods tailored by electronic wave functions of polynomial cost. Specifically, we focus on frozen-pair coupled cluster (fpCC) methods, which are tailored by pair-coupled cluster doubles (pCCD), and coupled cluster theory tailored by matrix product state wave functions optimized by the density matrix renormalization group (DMRG) algorithm. As test system, we selected a set of various small- and medium-sized molecules containing diatomics (N2, F2, C2, CN+, CO, BN, BO+, and Cr2) and molecules (ammonia, ethylene, cyclobutadiene, benzene, hydrogen chains, rings, and cuboids) for which the conventional single-reference coupled cluster singles and doubles (CCSD) method is not able to produce accurate results for spectroscopic constants, potential energy surfaces, and barrier heights. Most importantly, DMRG-tailored and pCCD-tailored approaches yield similar errors in spectroscopic constants and potential energy surfaces compared to accurate theoretical and/or experimental reference data. Although fpCC methods provide a reliable description for the dissociation pathway of molecules featuring single and quadruple bonds, they fail in the description of triple or hextuple bond-breaking processes or avoided crossing regions.

Open-shell extensions to closed-shell pCCD.

The pair coupled cluster doubles (pCCD) ansatz represents an inexpensive but accurate single-reference method to describe multi-reference problems. By construction, pCCD remains, however, applicable to closed-shell systems. For the first time, we present extensions to pCCD that allow us to target open-shell molecules with up to 4 unpaired electrons. Although requiring only modest computational cost, our methods approach chemical accuracy for some challenging cases, while their performance is comparable to more expensive models like DMRG or CCSD(T).

Orbital entanglement and correlation from pCCD-tailored coupled cluster wave functions.

Wave functions based on electron-pair states provide inexpensive and reliable models to describe quantum many-body problems containing strongly correlated electrons, given that broken-pair states have been appropriately accounted for by, for instance, a posteriori corrections. In this article, we analyze the performance of electron-pair methods in predicting orbital-based correlation spectra. We focus on the (orbital-optimized) pair-coupled cluster doubles (pCCD) ansatz with a linearized coupled-cluster (LCC) correction. Specifically, we scrutinize how orbital-based entanglement and correlation measures can be determined from a pCCD-tailored CC wave function. Furthermore, we employ the single-orbital entropy, the orbital-pair mutual information, and the eigenvalue spectra of the two-orbital reduced density matrices to benchmark the performance of the LCC correction for the one-dimensional Hubbard model with the periodic boundary condition as well as the N2 and F2 molecules against density matrix renormalization group reference calculations. Our study indicates that pCCD-LCC accurately reproduces the orbital-pair correlation patterns in the weak correlation limit and for molecules close to their equilibrium structure. Hence, we can conclude that pCCD-LCC predicts reliable wave functions in this regime.

Mixed uranyl and neptunyl cation-cation interaction-driven clusters: structures, energetic stability, and nuclear quadrupole interactions.

We present a state-of-the-art quantum chemical study of mixed cation-cation interaction (CCI) driven complexes composed of uranyl and neptunyl units. Specifically, we consider the stability of the D-shaped and T-shaped structural rearrangements in CCIs, various oxidation states of the uranium and neptunium atom (v and vi), as well as a different number of unpaired electrons. Furthermore, we scrutinize the nuclear quadrupole interactions of the bare actinyl subunits and the most stable mixed CCI clusters. The electric field gradients (and nuclear quadrupole coupling constants) of neptunyls are reported for the first time. The characteristic features of the nuclear quadrupole interactions for the bare neptunyl ions are very similar to those predicted for uranyls. When the CCI clusters are formed, a considerable asymmetry is introduced compared to the bare actinyl cations. Most importantly, we are able to distinguish different types of CCIs with respect to their structural arrangement and their total charge by analyzing the electric field gradients at the uranium and neptunium nuclei.

Assessing the accuracy of simplified coupled cluster methods for electronic excited states in f0 actinide compounds.

We scrutinize the performance of different variants of equation of motion coupled cluster (EOM-CC) methods to predict electronic excitation energies and excited state potential energy surfaces in closed-shell actinide species. We focus our analysis on various recently presented pair coupled cluster doubles (pCCD) models [J. Chem. Phys., 2016, 23, 234105 and J. Chem. Theory Comput., 2019, 15, 18-24] and compare their performance to the conventional EOM-CCSD approach and to the completely renormalized EOM-CCSD with perturbative triples ansatz. Since the single-reference pCCD model allows us to efficiently describe static/nondynamic electron correlation, while dynamical electron correlation is accounted for a posteriori, the investigated pCCD-based methods represent a good compromise between accuracy and computational cost. Such a feature is particularly advantageous when modelling electronic structures of actinide-containing compounds with stretched bonds. Our work demonstrates that EOM-pCCD-based methods reliably predict electronic spectra of small actinide building blocks containing thorium, uranium, and protactinium atoms. Specifically, the standard errors in adiabatic and vertical excitation energies obtained by the conventional EOM-CCSD approach are reduced by a factor of 2 when employing the EOM-pCCD-LCCSD variant resulting in a mean error of 0.05 eV and a standard deviation of 0.25 eV.

Benchmarking the Accuracy of Seniority-Zero Wave Function Methods for Noncovalent Interactions.

In this paper, we scrutinize the ability of seniority-zero wave function-based methods to model different types of noncovalent interactions, such as hydrogen bonds, dispersion, and mixed noncovalent interactions as well as prototypical model systems with various contributions of dynamic and static electron correlation effects. Specifically, we focus on the pair Coupled Cluster Doubles (pCCD) ansatz combined with two different flavors of dynamic energy corrections, (i) based on a perturbation theory correction and (ii) on a linearized coupled cluster ansatz on top of pCCD. We benchmark these approaches against the A24 data set [ Rezác and Hobza J. Chem. Theory Comput. 2013 , 9 , 2151 - 2155 .] extrapolated to the basis set limit and some model noncovalent complexes that feature covalent bond breaking. By dissecting different types of interactions in the A24 data set within the Symmetry-Adapted Perturbation Theory (SAPT) framework, we demonstrate that pCCD can be classified as a dispersion-free method. Furthermore, we found that both flavors of post-pCCD approaches represent encouraging and computationally more efficient alternatives to standard electronic structure methods to model weakly bound systems, resulting in small statistical errors. Finally, a linearized coupled cluster correction on top of pCCD proved to be most reliable for the majority of investigated systems, featuring smaller nonparallelity errors compared to perturbation-theory-based approaches.

Elucidating cation-cation interactions in neptunyl dications using multi-reference ab initio theory.

Understanding the binding mechanism in neptunyl clusters formed due to cation-cation interactions is of crucial importance in nuclear waste reprocessing and related areas of research. Since experimental manipulations with such species are often rather limited, we have to rely on quantum-chemical predictions of their electronic structures and spectroscopic parameters. In this work, we present a state-of-the-art quantum chemical study of the T-shaped and diamond-shaped neptunyl(v) and neptunyl(vi) dimers. Specifically, we scrutinize their molecular structures, (implicit and explicit) solvation effects, the interplay of static and dynamical correlation, and the influence of spin-orbit coupling on the ground state and lowest-lying excited states for different total spin states and total charges of the neptunyl dications. Furthermore, we use the picture of interacting orbitals (quantum entanglement and correlation analysis) to identify strongly correlated orbitals in the cation-cation complexes that should be included in complete active space calculations. Most importantly, our study highlights the complex interplay of correlation effects and relativistic corrections in the description of the ground and lowest-lying excited states of neptunyl dications.

Targeting Doubly Excited States with Equation of Motion Coupled Cluster Theory Restricted to Double Excitations.

The accurate description of doubly excited states using conventional electronic structure methods is remarkably challenging, primarily because such excited states require the inclusion of doubly or higher excited configurations or the application of multireference methods. We present a new approach to target electronically excited states that feature a double-electron transfer. Our method uses the equation of motion (EOM) formalism with a pair coupled cluster doubles (pCCD) reference function, where dynamical correlation is accounted for by a linearized coupled cluster correction with singles and doubles (LCCSD). Specifically, our proposed EOM-pCCD-LCCSD model represents a simplification of the conventional EOM-CCSD approach, where the electron-pair amplitudes of CCSD are tailored by pCCD. The performance of EOM-pCCD-LCCSD is assessed for the lowest-lying excited states in CH+ and all-trans polyenes. In contrast to conventional EOM-CC methods with at most double excitations, EOM-pCCD-LCCSD predicts the right order of states in polyenes with excitation energies closest to experiment, outperforming even highly accurate methods such as the density matrix renormalization group algorithm.