We present a flexible, automated, and basis-set-insensitive domain-based charge-transfer (CT) decomposition framework that can be combined with any configuration interaction (CI)-type excited-state wave function. Our approach is not based on excited-state densities and allows the excited-state character to be dissected into local and domain-based CT excitations and measures the individual contributions to each excited state. To guarantee a broad applicability, we introduce two domain-accumulation strategies to translate hole-particle substitutions to domain-domain excitations: a strict domain partitioning and a weighted approach suitable for small molecules and a large number of domains. The performance of both schemes is assessed for inter- and intramolecular CT excitations and various basis sets using EOM-CCSD and its simplified counterpart EOM-pCCD+S. Most importantly, the CT character is, to a large extent, basis-set independent, and both domain-accumulation schemes give consistent results. Overall, our framework provides a robust CT analysis and a domain resolution of the excitation character for a variety of computational setups and excited-state models.

Present-day state-of-the-art ab initio many-body calculations on f-block-containing cold molecules rely heavily on perturbative approaches for spin-orbit coupling and exclude a substantial part of the atomic transitions in the f and d shells. Here, we demonstrate the importance of proper relativistic treatment of the f and d shells in Yb-containing diatomics and the inclusion of the f -* d transition to obtain accurate spectra of YbLi+. We focus on state-of-the-art relativistic many-body calculations for the Yb atom's ground and excited states and the YbLi+ potential energy surface. For that purpose, we exploit various quantum many-body methods, namely, a spin-free and four-component implementation of the coupled-cluster singles and doubles (CCSD) model and its equation-of-motion (EOM) extensions, spin-free complete-active-space self-consistent field, and internally contracted multireference (MR) configuration interaction approaches. We oppose scalar relativistic calculations to four-component variants to support the reliability of our EOM-CCSD study and shed new light on the interplay between these systems' spin-orbit coupling and the proper treatment of relativistic effects. Finally, we provide new reference potential-energy curves for ground and excited states. Additionally, we compute spectroscopic constants and analyze the Einstein coefficients.

The balance between localized and delocalized electron distribution in the N,N'-dimethylpiperazine (DMP) molecule in the 3s Rydberg excited state and in the fully ionized DMP+ provides a valuable test of density functionals, in particular the weight of Fock exchange (FE) in hybrid functionals and the scaling of explicit orbital-based self-interaction correction (SIC) applied to less elaborate functionals. We present results of calculations using density functionals of all rungs of Jacob's ladder, ranging from LDA to the DM21 machine learned local hybrid as well as double hybrids. For DMP+, the commonly used hybrid functionals, such as PBE0(0.25) with FE weight of 0.25, as well as PBE0(0.32) with a weight of 0.32, only produce the more delocalized charge. The latter mimics the DM21 energy surface well. However, hybrid functionals with stronger FE, such as BHLYP and PBE0(0.50) as well as some double hybrid functionals, also produce local energy minima corresponding to localized charge. When full SIC is applied to the PBE functional, an energy surface analogous to hybrid functionals with an FE weight of 0.50 is obtained, while the scaling of SIC by 0.50, which has previously been shown to give improved atomization energy and band gap of solids, only produces the more delocalized charge. For the 3s Rydberg excited state of DMP, two types of configurations with a localized hole are obtained in calculations using the PBE0(0.32) functional, in addition to the delocalized hole, but only the latter is found with the PBE functional, showing that a significant reduction of the self-interaction error is needed in order to obtain agreement between density functional calculations and experimental measurements of the Rydberg state.

This work presents an innovative computational study of domain-based charge transfer that leverages the localized orbitals of pair coupled cluster doubles (pCCD). This method enables both directional monitoring and quantitative assessment of charge transfer among donor (D), bridge (B), and acceptor (A) moieties. We applied this approach to a series of newly designed carbazole-based prototypical organic dyes, doping the bridge at positions 1, 2, and 3 with nitrogen, oxygen, and sulfur atoms to generate mono-, di-, and tri-doped variants. Our results demonstrate a clear and progressive enhancement in charge transfer as the degree of nitrogen or oxygen doping increases from mono- to di- to tri-doped systems. For mono-doped dyes, the highest forward charge transfer from donor to bridge to acceptor (D → B → A) occurs when a heteroatom (N or O) is placed in the terminal ring of the bridge, closer to the acceptor. In di-doped dyes, the largest forward charge transfer is observed when heteroatoms occupy both terminal positions, with one atom (N or S) adjacent to the donor and the other (N) near the acceptor. Nitrogen-doped systems consistently outperform their oxygen and sulfur counterparts. Among all variants, the organic dye doped with three nitrogen atoms at the bridge exhibits the most efficient and highest directional donor-to-acceptor charge transfer (42.6%), making it the most promising candidate for potential applications in dye-sensitized solar cells. Finally, our calculations predict weak charge separation in all systems, indicating that charge transfer predominantly occurs from the bridge to the acceptor.

We introduce a new domain-based charge-transfer analysis tool exploiting the locality of pair Coupled Cluster Doubles orbitals. Unique features of the proposed model include the ability to monitor the direction of the charge flow between different parts or moieties of the system and its quantitative evaluation. We assess the predictive power of our new method for selected dye candidates of dye-sensitized solar cells with different doping and structural arrangements and compare our results for excitation and orbital energies to various density functional approximations and the domain-based local pair natural orbital variant of coupled cluster singles doubles. Our work confirms that the dyes with S-doped bridges are the most promising candidates for dye-sensitized solar cells applications, featuring the largest donor → bridge → acceptor directed charge transfer and the most favorable electrodonating and electroaccepting powers.

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 NO$_3^-$ 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 $\sigma_{\rm M-O}$ bond formation and $\sigma_{\rm N/S-O}$ 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.

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.

We introduce the electron attachment equation-of-motion pair coupled cluster doubles (EA-EOM-pCCD) ansatz, which allows us to inexpensively compute electron affinities, energies of unoccupied orbitals, and electron attachment spectra. We assess the accuracy of EA-EOM-pCCD for a representative data set of organic molecules for which experimental data are available, as well as the electron attachment process in uranyl dichloride. EA-EOM-pCCD provides more reliable energies for electron attachment properties than its ionization potential EOM counterpart. The advantage of EA-EOM-pCCD is demonstrated for rylene and rylene diimide units of different chain lengths, where it outperforms the more elaborate EOM-DLPNO-CCSD flavors, reducing errors by an order of magnitude.

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.

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.

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.

We scrutinize how to accelerate the bottleneck operations of Pythonic coupled cluster implementations performed on a \texttt{NVIDIA} Tesla V100S PCIe 32GB (rev 1a) Graphics Processing Unit (GPU). The \texttt{NVIDIA} Compute Unified Device Architecture (CUDA) API is interacted with via \texttt{CuPy}, an open-source library for Python, designed as a \texttt{NumPy} drop-in replacement for GPUs. The implementation uses the Cholesky linear algebra domain and is done in {PyBEST}, the Pythonic Black-box Electronic Structure Tool -- a fully-fledged modern electronic structure software package. Due to the limitations of Video Memory (VRAM), the GPU calculations must be performed batch-wise. Timing results of some contractions containing large tensors are presented. The \texttt{CuPy} implementation leads to factor 10 speed-up compared to calculations on 36 CPUs. Furthermore, we benchmark several Pythonic routines for time and memory requirements to identify the optimal choice of the tensor contraction operations available. Finally, we compare an example CCSD and pCCD-LCCSD calculation performed solely on CPUs to their CPU--GPU hybrid implementation. Our results indicate a significant speed-up (up to a factor of 16 regarding the bottleneck operations) when offloading specific contractions to the GPU using \texttt{CuPy}.

A potential function is presented for describing a system of flexible H2O molecules based on the single-center multipole expansion (SCME) of the electrostatic interaction. The model, referred to as SCME/f, includes the variation of the molecular quadrupole moment as well as the dipole moment with changes in bond length and angle so as to reproduce results of high-level electronic structure calculations. The multipole expansion also includes fixed octupole and hexadecapole moments, as well as anisotropic dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole polarizability tensors. The model contains five adjustable parameters related to the repulsive interaction and damping functions in the electrostatic and dispersion interactions. Their values are adjusted to reproduce the lowest energy isomers of small clusters, (H2O)n with n = 2-6, as well as measured properties of the ice Ih crystal. Subsequent calculations of the energy difference between the various isomer configurations of the clusters show that SCME/f gives good agreement with results of electronic structure calculations and represents a significant improvement over the previously presented rigid SCME potential function. Analysis of the vibrational frequencies of the clusters and structural properties of ice Ih crystal show the importance of accurately describing the variation of the quadrupole moment with molecular structures.

Recent Rydberg spectroscopy measurements of a diamine molecule, N,N′-dimethylpiperazine (DMP), indicate the existence of a localized electronic state as well as a delocalized electronic state. This implies that the cation, DMP+, can similarly have its positive charge either localized on one of the N atoms or delocalized over both. This interpretation of the experiments has, however, been questioned based on coupled cluster calculations. In this article, results of high-level multireference configuration interaction calculations are presented where a localized state of DMP+ is indeed found to be present with an energy barrier separating it from the delocalized state. The energy difference between the two states is in excellent agreement with the experimental estimate. The results presented here, therefore, support the original interpretation of the experiments and illustrate a rare shortcoming of CCSD(T), the “gold standard” of quantum chemistry. These results have implications for the development of density functionals, as most functionals fail to produce the localized state.

The relative stability of a localized and delocalized electronic state in the same molecule, the N,N' -Dimethylpiperazine cation, is calculated at various levels of theory up to multireference configuration interaction (MRCI+Q). This system has received a great deal of attention because of recent experimental studies of corresponding Rydberg states of the molecule and the failure of most density functional approximations to produce a metastable localized state. A cut through the energy surface involving two dihedral angles is generated at the level of MRCI+Q as well as Hartree-Fock (HF), Möller-Plesset second order perturbation theory (MP2), coupled cluster theory with and without perturbative triple excitations (CCSD and CCSD(T)) and complete active space self-consistent field calculations with and without perturbative correction (CASSCF and NEVPT2). Remarkably, while CCSD produces a localized state, CCSD(T) does not, and similarly, large active-space CASSCF does while NEVPT2 does not. The inclusion of dynamic correlation in a perturbative way thus adversely affects the accuracy of the calculation, most notably for CCSD(T), the 'golden standard'. The MRCI+Q results are in close correspondence with the experimental results, as well as CAS(19,20) DMRG-CASSCF calculations. The results presented here establish a benchmark system for the study of electronic state localization.

Quantum chemical calculations for two TiO2 nanoparticle cluster models (rutile-(TiO2)(n) with n = 20, and anatase-(TiO2)(n) with n = 92), selected to represent different nanoparticle size regimes, are used to elucidate structural influences on the electronic properties. Structural and electronic properties were obtained using a variety of computational methods and structure optimisation schemes, including a comparison of results for several different density functional theory functionals, as well as complementary Hartree-Fock and semi-empirical calculations. The results demonstrate a strong dependence of electronic properties, such as the optical band gap of importance for photoelectrochemical and photocatalytic applications, on the structure of the nanocrystal. From a methodological point of view, the calculations also provide useful information of broader significance about the viability of different computational schemes to efficiently obtain reliable computational results for intrinsically nanostructured materials.[GRAPHICS].

Surface interactions of water with nano-TiO2 and structurally related group IV metal dioxide nanoparticles have been investigated using density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations. The investigated clusters include 46 and 92 unit models of TiO2 (i.e., (TiO2)46 and (TiO2)92) of the three low-energy polymorphs of TiO2: anatase, rutile, and brookite. The investigation also includes studies of corresponding rutile-type clusters of three structurally related forms of group IV oxides: SnO2, GeO2, and SiO2. The calculations demonstrate the strong influence of water surface adsorption on several important nanoparticle properties including structure, charge distribution, and electronic structure for all investigated materials. Significant differences between the various materials are also revealed by the calculations, including an unusual stability of the electronic structure of TiO2 in the environment of particular relevance for its photoelectrochemical and photocatalytic applications.

Density functional theory (DFT) and time-dependent DFT calculations have been performed on a set of 34 titanium dioxide clusters ((TiO2)(n) with n125) to investigate structural and electronic properties of nanostructured TiO2 (nano-TiO2) materials. The investigated clusters include models of the three low-energy polymorphic forms of TiO2 anatase, rutile, and brookite. A systematic comparison of clusters of increasing size show clear trends for emerging bulk properties in the investigated systems as the surface-to-bulk ratio changes from small clusters dominated by undercoordinated surface atoms to more realistic model nanocrystals with significant bulk components. Differences and similarities in terms of atomic coordination, structural stability, and electronic properties for the three different polymorphic forms of nano-TiO2 are discussed. The calculations provide evidence for emerging polymorphism with increasing cluster sizes so that the different TiO2 forms can be clearly distinguished based on structural characteristics associated with the local bonding environment of the constituent atoms. (c) 2013 Wiley Periodicals, Inc.