Coupled Cluster Research Articles

Cholesky Decomposition-Based Implementation of Relativistic Two-Component Coupled-Cluster Methods for Medium-Sized Molecules.

A Cholesky decomposition (CD)-based implementation of relativistic two-component coupled-cluster (CC) and equation-of-motion CC (EOM-CC) methods using an exact two-component Hamiltonian augmented with atomic-mean-field spin-orbit integrals (the X2CAMF scheme) is reported. The present CD-based implementation of X2CAMF-CC and EOM-CC methods employs atomic-orbital-based algorithms to avoid the construction of two-electron integrals and intermediates involving three and four virtual indices. Our CD-based implementation extends the applicability of X2CAMF-CC and EOM-CC methods to medium-sized molecules with the possibility to correlate around 1000 spinors. Benchmark calculations for uranium-containing small molecules were performed to assess the dependence of the CC results on the Cholesky threshold. A Cholesky threshold of 10-4 is shown to be sufficient to maintain chemical accuracy. Example calculations to illustrate the capability of the CD-based relativistic CC methods are reported for the bond-dissociation energy of the uranium hexafluoride molecule, UF6, with up to quadruple-ζ basis sets, and the lowest excitation energy in the solvated uranyl ion [UO22+(H2O)12].

Robust Tensor Hypercontraction of the Particle-Particle Ladder Term in Equation-of-Motion Coupled Cluster Theory.

One method of representing a high-rank tensor as a (hyper-)product of lower-rank tensors is the tensor hypercontraction (THC) method of Hohenstein et al. This strategy has been found to be useful for reducing the polynomial scaling of coupled-cluster methods by representation of a four-dimensional tensor of electron-repulsion integrals in terms of five two-dimensional matrices. Pierce et al. have already shown that the application of a robust form of THC to the particle-particle ladder (PPL) term reduces the cost of this term in couple-cluster singles and doubles (CCSD) from to with negligible errors in energy with respect to the density-fitted variant. In this work, we have implemented the least-squares variant of THC (LS-THC) which does not require a nonlinear tensor factorization, including the robust form (R-LS-THC), for the calculation of the excitation and electron attachment energies using equation-of-motion coupled cluster methods EOMEE-CCSD and EOMEA-CCSD, respectively. We have benchmarked the effect of the R-LS-THC-PPL approximation on excitation energies using the comprehensive QUEST database and the accuracy of electron attachment energies using the NAB22 database. We find that errors on the order of 1 meV are achievable with a reduction in total calculation time of approximately 5 ×.

Research on sustainable tourism and biodiversity: a bibliometric analysis

ABSTRACT This study intends to analyse sustainable tourism and biodiversity research from a longitudinal point of view from 1995 to 2022. Collected 290 research articles published in the Scopus database and applied rigorous inclusion and exclusion criteria to select them for bibliometric analysis. Bibliometrix and VOSviewer tools were employed to analyse and depict the research. Co-citation of cited references, co-citation on a timeline basis, and bibliometric coupling analysis are performed to examine the trends and patterns. Further, inferred a thematic structure of sustainable tourism and biodiversity, uncovering seven co-citation clusters, twenty co-citation clusters on a timeline basis, and eleven bibliometric coupling clusters. This study offers various perspectives on sustainable tourism and biodiversity research for theoretical and practical advancements.

Composite ab initio vibrational spectroscopy and thermochemistry of low-valency lanthanide compounds: europium dihalides EuX2 (X = F, Cl, Br, I).

A unique diversity in chemical properties of lanthanide compounds making them very useful in various important applications stems not least from the existence of less common Ln oxidation states, in particular +2. However, the molecular properties of low-valency lanthanide compounds are not yet well studied even for the most stable divalent Ln-containing species, such as europium dihalides. In this paper, highly accurate molecular structures, vibrational spectra, and atomisation energies of the europium dihalides EuX2 (X = F, Cl, Br, I) are obtained at the complete basis set CCSD(T) level. All of the EuX2 species are calculated to be non-linear (C2v) exhibiting a regular increase in X-Eu-X bond angle on passing through the halogen series (F → Cl → Br → I), from 117° in EuF2 to 141° in EuI2, which is accompanied by a rapid decrease in the barriers to linearity, h = E(D∞h) - E(C2v), from 2180 cm-1 to 166 cm-1, respectively. The Eu-X bonds in EuX2 appear to be longer but energetically stronger than those in the respective monohalides EuX, whose properties are studied in this work at the same level of theory as EuX2. The performance of the Ln 4f-in-core pseudopotential (PP) approximation for EuX2 is assessed by comparing the Eu PP-based coupled-cluster (CC) calculations with all-electron CC benchmarks. Incorporating the Eu 4f electrons into the PP is shown to cause large errors: up to 10 deg. in X-Eu-X bond angles, 80% in barriers to linearity, and 0.05 Å in the Eu-X bond lengths, which proves the necessity of an explicit treatment of 4f electrons if high accuracy is the goal. The present results set a benchmark in the field of low-valency lanthanide chemistry, in particular for the calibration of DFT functionals.

Coupling Clustering and Channeling Contrast in the Scanning Electron Microscope

Coupling Clustering and Channeling Contrast in the Scanning Electron Microscope

Spin-flip equation-of-motion coupled cluster method with singles, doubles and (full) triples: computational implementation and some pilot applications.

We present our computational implementation of the spin-flip (SF) equation-of-motion (EOM) coupled-cluster (CC) method with singles, doubles, and (full) triples (SDT) within Q-CHEM. The inclusion of triples not only enhances the quantitative accuracy of the SF-EOM-CCSD method but also provides correct qualitative trends in the energy gaps between strongly degenerate states. To assess the accuracy, we compare our SF-EOM-CCSDT results with full configuration interaction (FCI) and complete-active-space self-consistent field second-order (CASSCF-SO) CI benchmarks to study the adiabatic energy gaps in CH2 and NH2+ diradicals, vertical excitation energies in CH radicals and the bond dissociation of the HF molecule. We have implemented SF-EOM-CCSDT using both the conventional double precision (DP) and the single precision (SP) algorithms. The use of SP does not introduce any significant errors in energies and energy gaps, and, due to low cost (relative to DP), turns out to be a promising approach to widen the applicability of EOM-CCSDT to bigger molecules.

Synergistic effect of heterogeneous single atoms and clusters for improved catalytic performance

Electrocatalytic water splitting provides an efficient method for the production of hydrogen. In electrocatalytic water splitting, the oxygen evolution reaction (OER) involves a kinetically sluggish four-electron transfer process, which limits the efficiency of electrocatalytic water splitting. Therefore, it is urgent to develop highly active OER catalysts to accelerate reaction kinetics. Coupling single atoms and clusters in one system is an innovative approach for developing efficient catalysts that can synergistically optimize the adsorption and configuration of intermediates and improve catalytic activity. However, research in this area is still scarce. Herein, we constructed a heterogeneous single-atom cluster system by anchoring Ir single atoms and Co clusters on the surface of Ni(OH)<sub>2</sub> nanosheets. Ir single atoms and Co clusters synergistically improved the catalytic activity toward the OER. Specifically, Co<sub><i>n</i></sub>Ir<sub>1</sub>/Ni(OH)<sub>2</sub> required an overpotential of 255 mV at a current density of 10 mA·cm<sup>−2</sup>, which was 60 mV and 67 mV lower than those of Co<sub><i>n</i></sub>/Ni(OH)<sub>2</sub> and Ir<sub>1</sub>/Ni(OH)<sub>2</sub>, respectively. The turnover frequency of Co<sub><i>n</i></sub>Ir<sub>1</sub>/Ni(OH)<sub>2</sub> was 0.49 s<sup>−1</sup>, which was 4.9 times greater than that of Co<sub><i>n</i></sub>/Ni(OH)<sub>2</sub> at an overpotential of 300 mV.

Generating Predictive Chemical Kinetic Models for Quaternary Ammonium Monomers Chemical Degradation in Anion Exchange Membrane

It is widely accepted that the high cost of Proton Exchange Membrane (PEM) fuel cells (FC) is a major inhibitor of the transition to extensive commercialization of hydrogen-fueled FCs. One known alternative to this technology is Anion Exchange Membrane (AEM), greatly reducing the need for precious metals, e.g., platinum, and allowing a wider choice of lower cost polymeric materials1. Although research in the field of AEM has greatly evolved recently, AEM-FCs still lack sufficient durability and cell longevity. The current major challenge revolves around the chemical and structural stability of polymers constructing the membrane, which undergo different degradation reactions under cell operating conditions. A widely investigated AEM monomer is Benzyl trimethylammonium (BTMA), a quaternary ammonium (QA) cation, in which the positively charged nitrogen atom enables the selective transfer of hydroxide ions through the membrane2. BTMA degradation occurs in several reaction paths, the main one involving a nucleophilic attack of the hydroxide at the benzylic carbon atom, resulting in complete displacement of the functional group (Fig. 1a). Recently, it has also been shown that low hydration levels of hydroxide, evidently more relevant to the FC’s environment, have an immense impact on the reduced stability of BTMA3,4. Despite the elaborate research done on BTMA degradation, as well as on other QA monomers, complete understanding of the chemical mechanisms affecting the stability of AEM-FCs is still lacking. Modeling these mechanisms can assist in facilitating practical implementation of this promising technology, discovering novel chemically-stable ionomers, while saving time and resources in trial-and-error efforts.The goal of this research is to develop an automated workflow for generating and refining predictive chemical kinetic models describing chemical degradation of AEM monomers, by combining several computational tools, and tailoring them to suit our specific needs. The first is the Reaction Mechanism Generator (RMG) software, which automatically generates chemical kinetic models by utilizing a basic comprehension of chemical reactions5. RMG derives its data from “libraries” of kinetic and thermodynamic parameters based on the literature, and from estimations schemes based on group or decision trees. Since RMG currently does not support ion chemistry, it is required to add this feature to the software, along with solvation corrections, while extending its estimation schemes. To achieve this, accurate kinetic and thermodynamic parameters of the species and reactions of interest are necessary.The present work focuses on describing BTMA degradation. Preliminary results for the temperature-dependent rate coefficient and thermodynamic properties were obtained using the Automated Rate Calculator (ARC) software6. This tool facilitates electronic structure calculations relevant for chemical kinetic modeling, by automatically spawning, tracking, and analyzing relevant computations. We computed the BTMA + OH– reaction rate coefficient at a low hydration level (λ=1) at the ωB97xD/Def2-TZVP level of theory, and compared it to the experimental results obtained at three different temperatures (Fig. 1b). The calculations were performed using the SMD solvation model with DMSO as the solvent, in accordance with the experimental conditions. Our preliminary results show some agreement with experimental measurements, and we expect this agreement to improve by calculating single-point energies using the more accurate coupled-cluster (CC) theory.The methods developed to generate a chemical kinetic model for BTMA, can then be applied for other potential QA monomers. Furthermore, an additional software called The Tandem Tool (T3), can be used to perform model refinement, through a process of iterations between RMG and ARC, creating the desired automated model generation workflow. This process is designed to obtain quantum mechanics-based calculated parameters for significant species and reactions in the model, chosen using sensitivity analysis. Altogether, this work can create a powerful tool, providing insights on known AEM ionomers, as well as the flexibility to investigate additional polymeric materials, with minimal experimental resources.

Isomerism of : Accurate structural, energetic, and spectroscopic characterization.

A recent work [Ye et al. Mon. Not. R. Astron. Soc. 2023, 525, 1158] on the gas-phase formation of t-HC(O)SH, already detected in the interstellar medium, pointed out that the trans form of HC(S)OH is a potential candidate for astronomical observations. Prompted by these results, the family of isomers has been investigated from an energetic point of view using a double-hybrid density functional in combination with a partially augmented triple-zeta basis set. This preliminary study showed that the most stable species of the family are the cis and trans forms of HC(O)SH and HC(S)OH. For their structural and spectroscopic characterization, a composite scheme based on coupled cluster (CC) calculations that incorporates up to the quadruple excitations and accounts for the extrapolation to the complete basis set limit and core correlation effects has been employed. This approach opens to the prediction of rotational constants with an accuracy of 0.1%. A hybrid scheme, based on harmonic frequencies computed using the CC singles, doubles and a perturbative treatment of triples method (CCSD(T)) in conjunction with a quadruple-zeta basis set, allowed us to obtain fundamental vibrational frequencies with a mean absolute error of about 1%.

Effect of vibrational resonances and dynamic polarizability on the Raman spectrum of furfural: A vibrational coupled cluster study

The Raman spectrum of furfural is computed and analyzed using the Vibrational Coupled Cluster Method (VCCM). Furfural has immense applications in organic synthesis, electrocatalysis and energy conversion process. The experimental Raman spectrum of furfural is congested and broad, even in the medium energy regions like C-C stretching and CO stretching regions. We extensively analyze the Fermi and higher quanta resonance effects on the Raman spectrum by examining the VCCM wavefunctions. In addition, a systematic study on the effect of incident frequency on the anharmonic Raman activity is carried out by comparing the results with incident wavelengths 325.0 nm and 632.8 nm against static polarizability.

PyBEST: Improved functionality and enhanced performance

PyBEST: Improved functionality and enhanced performance

Combining state-of-the-art quantum chemistry and machine learning make gold standard potential energy surfaces accessible for medium-sized molecules

Developing full-dimensional machine-learned potentials with the current “gold-standard” coupled-cluster (CC) level is challenging for medium-sized molecules due to the high computational cost. Consequently, researchers are often bound to use lower-level electronic structure methods such as density functional theory or second-order Møller–Plesset perturbation theory (MP2). Here, we demonstrate on a representative example that gold-standard potentials can now be effectively constructed for molecules of 15 atoms using off-the-shelf hardware. This is achieved by accelerating the CCSD(T) computations via the accurate and cost-effective frozen natural orbital (FNO) approach. The Δ-machine learning (Δ-ML) approach is employed with the use of permutationally invariant polynomials to fit a full-dimensional potential energy surface of the acetylacetone molecule, but any other effective descriptor and ML approach can similarly benefit from the accelerated data generation proposed here. Our benchmarks for the global minima, H-transfer TS, and many high-lying configurations show the excellent agreement of FNO-CCSD(T) results with conventional CCSD(T) while achieving a significant time advantage of about a factor of 30–40. The obtained Δ-ML PES shows high fidelity from multiple perspectives including energetic, structural, and vibrational properties. We obtain the symmetric double well H-transfer barrier of 3.15 kcal/mol in excellent agreement with the direct FNO-CCSD(T) barrier of 3.11 kcal/mol as well as with the benchmark CCSD(F12*)(T+)/CBS value of 3.21 kcal/mol. Furthermore, the tunneling splitting due to H-atom transfer is calculated using a 1D double-well potential, providing improved estimates over previous ones obtained using an MP2-based PES. The methodology introduced here represents a significant advancement in the efficient and precise construction of potentials at the CCSD(T) level for molecules above the current limit of 15 atoms.

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.

Coupled cluster cavity Born-Oppenheimer approximation for electronic strong coupling.

Chemical and photochemical reactivity, as well as supramolecular organization and several other molecular properties, can be modified by strong interactions between light and matter. Theoretical studies of these phenomena require the separation of the Schrödinger equation into different degrees of freedom as in the Born-Oppenheimer approximation. In this paper, we analyze the electron-photon Hamiltonian within the cavity Born-Oppenheimer approximation (CBOA), where the electronic problem is solved for fixed nuclear positions and photonic parameters. In particular, we focus on intermolecular interactions in representative dimer complexes. The CBOA potential energy surfaces are compared with those obtained using a polaritonic approach, where the photonic and electronic degrees of freedom are treated at the same level. This allows us to assess the role of electron-photon correlation and the accuracy of CBOA.

New Mechanistic Insights into the Primary Thermolysis Reactions of 1,3,4,6-Tetranitrooctahydroimidazo-[4,5-d]imidazole (BCHMX) from Predictive Local Coupled Cluster Calculations.

Theoretical studies of the decomposition mechanism of energetic materials quite often scrutinize only the primary thermolysis reactions. However, the secondary reactions are crucial, inter alia, for proper building of the combustion models and understanding the autocatalytic processes. In the present study, we applied predictive DLPNO-CCSD(T) calculations to elucidate the kinetics and decomposition mechanism of a novel promising energetic material, 1,3,4,6-tetranitrooctahydroimidazo [4,5-d] imidazole (BCHMX). We identified eight previously unknown BCHMX conformers, both cis and trans in accordance to the spatial position of the H atoms bonded to a carbon bridge. Among them, the relative enthalpies of cis isomers lie in the narrow range ∼10 kJ mol-1 rendering them thermally accessible in the course of decomposition. The radical N-NO2 bond cleavage via one of the novel conformers is the dominant primary decomposition channel of BCHMX with the kinetic parameters Ea = 168.4 kJ mol-1 and log(A, s-1) = 18.5. We also resolved several contradictory assumptions on the mechanism and key intermediates of BCHMX thermolysis. To get a deeper understanding of the decomposition mechanism, we examined a series of unimolecular and bimolecular secondary channels of BCHMX. Among the former reactions, the C-C bond unzipping followed by another radical elimination of a nitro group is the most energetically favorable pathway with an activation barrier ∼113 kJ mol-1. However, contrary to the literature assumptions, the bimolecular H atom abstraction from a pristine BCHMX molecule by a primary nitramine radical product, not the nitro one, followed by another NO2 radical elimination, is the most important bimolecular secondary thermolysis reaction of BCHMX at lower temperatures. The isokinetic temperature of the bimolecular and unimolecular secondary reactions is ∼620 K. Unimolecular reactions might be important in dilute solutions, where bimolecular reactions are suppressed. The secondary reactions considered in the present work might be pertinent in the case of related energetic nitramines (e.g., RDX, HMX, and CL-20).

Capturing Weak Interactions in Surface Adsorbate Systems at Coupled Cluster Accuracy: A Graph-Theoretic Molecular Fragmentation Approach Improved through Machine Learning.

The accurate and efficient study of the interactions of organic matter with the surface of water is critical to a wide range of applications. For example, environmental studies have found that acidic polyfluorinated alkyl substances, especially perfluorooctanoic acid (PFOA), have spread throughout the environment and bioaccumulate into human populations residing near contaminated watersheds, leading to many systemic maladies. Thus, the study of the interactions of PFOA with water surfaces became important for the mitigation of their activity as pollutants and threats to public health. However, theoretical study of the interactions of such organic adsorbates on the surface of water, and their bulk concerted properties, often necessitates the use of ab initio methods to properly incorporate the long-range electronic properties that govern these extended systems. Notable theoretical treatments of "on-water" reactions thus far have employed hybrid DFT and semilocal DFT, but the interactions involved are weak interactions that may be best described using post-Hartree-Fock theory. Here, we aim to demonstrate the utility of a graph-theoretic approach to molecular fragmentation that accurately captures the critical "weak" interactions while maintaining an efficient ab initio treatment of the long-range periodic interactions that underpin the physics of extended systems. We apply this graph-theoretical treatment to study PFOA on the surface of water as a model system for the study of weak interactions seen in the wide range of surface interactions and reactions. The approach divides a system into a set of vertices, that are then connected through edges, faces, and higher order graph theoretic objects known as simplexes, to represent a collection of locally interacting subsystems. These subsystems are then used to construct ab initio molecular dynamics simulations and for computing multidimensional potential energy surfaces. To further improve the computational efficiency of our graph theoretic fragmentation method, we use a recently developed transfer learning protocol to construct the full system potential energy from a family of neural networks each designed to accurately model the behavior of individual simplexes. We use a unique multidimensional clustering algorithm, based on the k-means clustering methodology, to define our training space for each separate simplex. These models are used to extrapolate the energies for molecular dynamics trajectories at PFOA water interfaces, at less than one-tenth the cost as compared to a regular molecular fragmentation-based dynamics calculation with excellent agreement with couple cluster level of full system potential energies.

Unitary coupled-cluster for quantum computation of molecular properties in a strong magnetic field.

In truncated coupled-cluster (CC) theories, non-variational and/or generally complex ground-state energies can occur. This is due to the non-Hermitian nature of the similarity transformed Hamiltonian matrix in combination with CC truncation. For chemical problems that deal with real-valued Hamiltonian matrices, complex CC energies rarely occur. However, for complex-valued Hamiltonian matrices, such as those that arise in the presence of strong magnetic fields, complex CC energies can be regularly observed unless certain symmetry conditions are fulfilled. Therefore, in the presence of magnetic fields, it is desirable to pursue CC methods that are guaranteed to give upper-bound, real-valued energies. In this work, we present the first application of unitary CC to chemical systems in a strong magnetic field. This is achieved utilizing the variational quantum eigensolver algorithm applied to the unitary coupled-cluster singles and doubles (UCCSD) method. We benchmark the method on the H2 molecule in a strong magnetic field and then calculate UCCSD energies for the H4 molecule as a function of both geometry and field angle. We show that while standard CCSD can yield generally complex energies that are not an upper-bound to the true energy, UCCSD always results in variational and real-valued energies. We also show that the imaginary components of the CCSD energy are largest in the strongly correlated region. Last, the UCCSD calculations capture a large percentage of the correlation energy.

Modulation of the NLO properties of p-coumaric acid by the solvent effects and proton dissociation

Solute-solvent interactions and deprotonation effects have been related to second-order nonlinear optical response modulators. This work takes advantage of sequential Monte Carlo/Quantum mechanics together with Time-Dependent Density Functional Theory, Coupled Cluster methods, and the hyper-Rayleigh scattering formalism to investigate how these effects influence the stability and optical response of p-coumaric acid (pCA) and its anionic and diionic forms. The solvent influences the chromophores in different ways, inducing bathochromic and hypsochromic solvatochromism so for the neutral pCA molecule as for its deprotonated derivatives. The results indicate a high sensitivity of the nonlinear optics (NLO) parameters with relation to proton dissociation. Ionization of the carboxyl group produces the lowest values of the first frequency-dependent hyperpolarizability (βHRS), while phenolic deprotonation leads to the highest values. The results show that proton removal can be used as a switch that modulates the NLO response within a wide range of values (159.15≤βHRS≤4393.97 au) greater than those reported for reference NLO chromophores like urea (37.3 au) and p-nitroaniline (74.3 au). Thermochemical analysis of enthalpies and Gibbs free energies indicate that both monoionic forms of the pCA molecule are the most stable in gas or water solvents. Furthermore, these structures represent the limits of NLO modulation in the gas and solvent phases. Analysis of the projected density of states and mapping of the molecular electrostatic potential indicate that increased contributions from conduction electrons found in the aromatic ring are the mechanism by which deprotonation enhances the NLO response. All the results show that ionic pCA forms are promising in the functionalization of optoelectronic devices.

Benchmark Study of the Electronic States of the LiRb Molecule: Ab Initio Calculations with the Fock Space Coupled Cluster Approach.

Accurate potential energy curves (PECs) are determined for the twenty-two electronic states of LiRb. In contrast to previous studies, the applied approach relies on the first principle calculations involving correlation among all electrons. The current methodology is founded on the multireference coupled cluster (CC) scheme constructed within the Fock space (FS) formalism, specifically for the (2,0) sector. The FS methodology is established within the framework of the intermediate Hamiltonian formalism and offers an intruder-free, efficient computational scheme. This method has a distinctive feature that, when applied to the doubly ionized system, provides the characteristics of the neutral case. This proves especially beneficial when investigating PECs in situations where a closed-shell molecule dissociates into open-shell fragments, yet its double positive ion forms closed-shell species. In every instance, we successfully computed continuous PECs spanning the entire range of interatomic distances, from the equilibrium to the dissociation limit. Moreover, the spectroscopic characteristic of various electronic states is presented, including relativistic effects. Relativistic corrections included at the third-order Douglas-Kroll level have a non-negligible effect on the accuracy of the determined spectroscopic constants.

Triplet Excited States with Multilevel Coupled Cluster Theory.

We extend the multilevel coupled cluster framework with triplet excitation energies at the singles and perturbative doubles (MLCC2) and singles and doubles (MLCCSD) levels of theory. In multilevel coupled cluster theory, we partition the orbitals and restrict the higher-order excitations in the cluster operator to a set of active orbitals. With an appropriate choice of these orbitals, the multilevel approach can give significant computational savings while maintaining the high accuracy of standard coupled cluster theory. In this work, we generated active orbitals from approximate correlated natural transition orbitals (CNTOs). The CNTOs form a compact orbital space specifically tailored to describe the triplet excited states of interest. We compare the performance of MLCCSD and MLCC2, in terms of cost and accuracy, to those of their standard coupled cluster counterparts (CC2 and CCSD) and finally show proof-of-concept calculations of the singlet-triplet gaps of molecules that are of interest for their potential use in organic light-emitting diodes.