Iterative and non-iterative triple excitation corrections in coupled-cluster methods for excited electronic states: the EOM-CCSDT-3 and EOM-CCSD(T̃) methods

Fock Space Coupled-Cluster Method for the Ground and Excited States of the NaMg+ Molecular Cation

This study presents a theoretical investigation of the potential energy curves (PECs) and spectroscopic constants of the NaMg+ molecular cation using the intermediate Hamiltonian Fock space coupled-cluster method with singles and doubles within the (2,0) sector [IH-FS-CCSD(2,0)]. The NaMg+ cation has gained scientific interest due to its potential applications in ultracold chemistry, yet it remains experimentally unexplored. We computed 20 lowest-lying PECs and assigned them to 10 dissociation limits. Our results demonstrated high accuracy, and computed curves are smooth and continuous over the entire range of interatomic distances. The study validates the effectiveness of the IH-FS-CCSD(2,0) method in describing PECs of diatomic molecular cations composed of alkali and alkaline earth metals and provides a solid theoretical foundation for further studies of NaMg+ and similar systems.

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.

A mountaineering strategy to excited states: Accurate vertical transition energies and benchmarks for substituted benzenes

In an effort to expand the existing QUEST database of accurate vertical transition energies [Véril et al. WIREs Comput. Mol. Sci. 2021, 11, e1517], we have modeled more than 100 electronic excited states of different natures (local, charge-transfer, Rydberg, singlet, and triplet) in a dozen of mono- and di-substituted benzenes, including aniline, benzonitrile, chlorobenzene, fluorobenzene, nitrobenzene, among others. To establish theoretical best estimates for these vertical excitation energies, we have employed advanced coupled-cluster methods including iterative triples (CC3 and CCSDT) and, when technically possible, iterative quadruples (CC4). These high-level computational approaches provide a robust foundation for benchmarking a series of popular wave function methods. The evaluated methods all include contributions from double excitations (ADC(2), CC2, CCSD, CIS(D), EOM-MP2, STEOM-CCSD), along with schemes that also incorporate perturbative or iterative triples (ADC(3), CCSDR(3), CCSD(T)(a)  ⋆ , and CCSDT-3). This systematic exploration not only broadens the scope of the QUEST database but also facilitates a rigorous assessment of different theoretical approaches in the framework of a homologous chemical series, offering valuable insights into the accuracy and reliability of these methods in such cases. We found that both ADC(2.5) and CCSDT-3 can provide very consistent estimates, whereas among less expensive methods SCS-CC2 is likely the most effective approach. Importantly, we show that some lower order methods may offer reasonable trends in the homologous series while providing quite large average errors, and vice versa. Consequently, benchmarking the accuracy of a model based solely on absolute transition energies may not be meaningful for applications involving a series of similar compounds.

Magnetic Dipole Transition in ^{48}Ca

The magnetic dipole transition strength B(M1) of ^{48}Ca is dominated by a single resonant state at an excitation energy of 10.23 MeV. Experiments disagree about B(M1) and this impacts our understanding of spin flips in nuclei. We performed ab initio computations based on chiral effective field theory and found that B(M1:  0^{+}→1^{+}) lies in the range from 7.0 to 10.2  μ_{N}^{2}. This is consistent with a (γ,n) experiment but larger than results from (e,e^{'}) and (p,p^{'}) scattering. Two-body currents yield no quenching of the B(M1) strength and continuum effects reduce it by about 10%. For a validation of our approach, we computed magnetic moments in ^{47,49}Ca and performed benchmark calculations in light nuclei.

First observation of 28O

Subjecting a physical system to extreme conditions is one of the means often used to obtain a better understanding and deeper insight into its organization and structure. In the case of the atomic nucleus, one such approach is to investigate isotopes that have very different neutron-to-proton (N/Z) ratios than in stable nuclei. Light, neutron-rich isotopes exhibit the most asymmetric N/Z ratios and those lying beyond the limits of binding, which undergo spontaneous neutron emission and exist only as very short-lived resonances (about 10-21 s), provide the most stringent tests of modern nuclear-structure theories. Here we report on the first observation of 28O and 27O through their decay into 24O and four and three neutrons, respectively. The 28O nucleus is of particular interest as, with the Z = 8 and N = 20 magic numbers1,2, it is expected in the standard shell-model picture of nuclear structure to be one of a relatively small number of so-called 'doubly magic' nuclei. Both 27O and 28O were found to exist as narrow, low-lying resonances and their decay energies are compared here to the results of sophisticated theoretical modelling, including a large-scale shell-model calculation and a newly developed statistical approach. In both cases, the underlying nuclear interactions were derived from effective field theories of quantum chromodynamics. Finally, it is shown that the cross-section for the production of 28O from a 29F beam is consistent with it not exhibiting a closed N = 20 shell structure.

Dark Doubly Excited States with Modified Coupled Cluster Models: A Reliable Compromise between Cost and Accuracy?

To treat doubly excited states, the treatment of triple excitations is considered necessary in the framework of equation-of-motion coupled cluster (EOM-CC) methods. We investigate models without explicit triples and seek quantitative measure for the performance of EOM based on CC with singles and doubles (CCSD) or modified CCSD (Distinguishable Cluster Approximation) approaches for states with predominant double excitation character. We also test the efficacy of including triples in perturbative manner through EOM-CCSD(T) and in an iterative way through EOM-CCSDT-3 method. Extended similarity transformed EOM-CCSD(EXT-STEOM-CCSD) method is also tested and provides superior quality results at comparatively low cost. We use the QUEST2 benchmark set of double excitations proposed by Loos et al. [ J. Chem. Theory Comput.2019, 15, 1939] to investigate the performance of methods such as EOM-CCSD, EOM-DCSD, EXT-STEOM-CCSD, ΔCCSD, and ΔDCSD. We also test a tailored CC approach, ΔpairCCD-TCCSD.

Density functionals for core excitations

The core excitation energies and related principal ionization energies are obtained for selected molecules using several density functionals and compared with benchmark equation-of-motion coupled cluster (EOM-CC) results. Both time-dependent and time-independent formulations of excitation spectra in the time-dependent density functional theory and the EOM-CC are employed to obtain excited states that are not always easily accessible with the time-independent method. Among those functionals, we find that the QTP(00) functional, which is only parameterized to reproduce the five IPs of water, provides excellent core IPs and core excitation energies, consistently yielding better excitation and ionization energies. We show that orbital eigenvalues of KS density functional theory play an important role in determining the accuracy of the excitation and photoelectron spectra.

Oscillator Strengths in the Framework of Equation of Motion Multilevel CC3

We present an efficient implementation of the equation of motion oscillator strengths for the closed-shell multilevel coupled cluster singles and doubles with perturbative triples method (MLCC3) in the electronic structure program e^T. The orbital space is split into an active part treated with CC3 and an inactive part computed at the coupled cluster singles and doubles (CCSD) level of theory. Asymptotically, the CC3 contribution scales as floating-point operations, where n_V is the total number of virtual orbitals while n_v and n_o are the number of active virtual and occupied orbitals, respectively. The CC3 contribution, thus, only scales linearly with the full system size and can become negligible compared to the cost of CCSD. We demonstrate the capabilities of our implementation by calculating the ultraviolet–visible spectrum of azobenzene and a core excited state of betaine 30 with more than 1000 molecular orbitals.

The intermediate state approach for doubly excited dark states in EOM-coupled-cluster theory

Solution of dark, doubly excited states using equation-of-motion coupled-cluster (EOM-CC) usually equires at least triple excitations or even quadruples beyond the standard singles and doubles (EOM-CCSD) for an appropriate treatment. A new route to obtain these doubly excited states using EOM-CCSD is demonstrated. Traditionally, EOM-CC is performed on a closed shell reference state that has a well-described single reference CC wavefunction. In this Communication, we attempt to use low spin open-shell states such as the MS = 0 triplet and open-shell singlet as a reference state. Using this intermediate excited state as a reference state provides us with the benefit of obtaining a doubly excited state, as a single excitation at the cost of EOM-CCSD.

Assessing the Performances of CASPT2 and NEVPT2 for Vertical Excitation Energies

Methods able to simultaneously account for both static and dynamic electron correlations have often been employed, not only to model photochemical events but also to provide reference values for vertical transition energies, hence allowing benchmarking of lower-order models. In this category, both the complete-active-space second-order perturbation theory (CASPT2) and the N-electron valence state second-order perturbation theory (NEVPT2) are certainly popular, the latter presenting the advantage of not requiring the application of the empirical ionization-potential-electron-affinity (IPEA) and level shifts. However, the actual accuracy of these multiconfigurational approaches is not settled yet. In this context, to assess the performances of these approaches, the present work relies on highly accurate (±0.03 eV) aug-cc-pVTZ vertical transition energies for 284 excited states of diverse character (174 singlet, 110 triplet, 206 valence, 78 Rydberg, 78 n → π*, 119 π → π*, and 9 double excitations) determined in 35 small- to medium-sized organic molecules containing from three to six non-hydrogen atoms. The CASPT2 calculations are performed with and without IPEA shift and compared to the partially contracted (PC) and strongly contracted (SC) variants of NEVPT2. We find that both CASPT2 with IPEA shift and PC-NEVPT2 provide fairly reliable vertical transition energy estimates, with slight overestimations and mean absolute errors of 0.11 and 0.13 eV, respectively. These values are found to be rather uniform for the various subgroups of transitions. The present work completes our previous benchmarks focused on single-reference wave function methods ( J. Chem. Theory Comput. 2018, 14, 4360; J. Chem. Theory Comput. 2020, 16, 1711), hence allowing for a fair comparison between various families of electronic structure methods. In particular, we show that ADC(2), CCSD, and CASPT2 deliver similar accuracies for excited states with a dominant single-excitation character.

Charge-Transfer Excitations within Density Functional Theory: How Accurate Are the Most Recommended Approaches?

The performance of the most recent density functionals is assessed for charge-transfer (CT) excitations using comprehensive intra- and intermolecular CT benchmark sets with high-quality reference values. For this comparison, the state-of-the-art range-separated (RS) and long-range-corrected (LC) double hybrid (DH) approaches are selected, and global DH and LC hybrid functionals are also inspected. The correct long-range behavior of the exchange–correlation (XC) energy is extensively studied, and various CT descriptors are compared as well. Our results show that the most robust performance is attained by RS-PBE-P86/SOS-ADC(2), as it is suitable to describe both types of CT excitations with outstanding accuracy. Furthermore, concerning the intramolecular transitions, unexpectedly excellent results are obtained for most of the global DHs, but their limitations are also demonstrated for bimolecular complexes. Despite the outstanding performance of the LC-DH methods for common intramolecular excitations, serious deficiencies are pointed out for intermolecular CT transitions, and the wrong long-range behavior of the XC energy is revealed. The application of LC hybrids to such transitions is not recommended in any respect.

Accurate Spectral Properties within Double-Hybrid Density Functional Theory: A Spin-Scaled Range-Separated Second-Order Algebraic-Diagrammatic Construction-Based Approach

Our second-order algebraic-diagrammatic construction [ADC(2)]-based double-hybrid (DH) ansatz (J. Chem. Theory Comput. 2019, 15, 4440. DOI: 10.1021/acs.jctc.9b00391) is combined with range-separation techniques. In the present scheme, both the exchange and the correlation contributions are range-separated, while spin-scaling approaches are also applied. The new methods are thoroughly tested for the most popular benchmark sets including 250 singlet and 156 triplet excitations, as well as 80 oscillator strengths. It is demonstrated that the range separation for the correlation contributions is highly recommended for both the genuine and the ADC(2)-based DH approaches. Our results show that the latter scheme slightly but consistently outperforms the former one for single excitation dominated transitions. Furthermore, states with larger fractions of double excitations are assessed as well, and challenging charge-transfer excitations are also discussed, where the recently proposed spin-scaled long-range corrected DHs fail. The suggested iterative fourth-power scaling RS-PBE-P86/SOS-ADC(2) method, using only three adjustable parameters, provides the most robust and accurate excitation energies within the DH theory. In addition, the relative error of the oscillator strengths is reduced by 65% compared to the best genuine DH functionals.

A Mountaineering Strategy to Excited States: Highly Accurate Energies and Benchmarks for Bicyclic Systems

Pursuing our efforts to define highly accurate estimates of the relative energies of excited states in organic molecules, we investigate, with coupled-cluster methods including iterative triples (CC3 and CCSDT), the vertical excitation energies of 10 bicyclic molecules (azulene, benzoxadiazole, benzothiadiazole, diketopyrrolopyrrole, furofuran, phthalazine, pyrrolopyrrole, quinoxaline, tetrathiafulvalene, and thienothiophene). In total, we provide aug-cc-pVTZ reference vertical excitation energies for 91 excited states of these relatively large systems. We use these reference values to benchmark various wave function methods, i.e., CIS(D), EOM-MP2, CC2, CCSD, STEOM-CCSD, CCSD(T)(a)*, CCSDR(3), CCSDT-3, ADC(2), ADC(2.5), and ADC(3), as well as some spin-scaled variants of both CC2 and ADC(2). These results are compared to those obtained previously on smaller molecules. It turns out that while the accuracy of some methods is almost unaffected by system size, e.g., CIS(D) and CC3, the performance of others can significantly deteriorate as the systems grow, e.g., EOM-MP2 and CCSD, whereas others, e.g., ADC(2) and CC2, become more accurate for larger derivatives.

Three-Body Excitations in Fock-Space Coupled-Cluster: Fourth Order Perturbation Correction to Electron Affinity and Its Relation to Bondonic Formalism

In this paper, we present a formulation of highly correlated Fock-space multi-reference coupled-cluster (FSMRCC) methods, including approximate triples on top of the FSMRCC with singles and doubles, which correct the electron affinities by at least at third and up to the fourth order in perturbation. We discuss various partial fourth-order schemes, which are reliable and yet computationally more efficient than the full fourth-order triples scheme. The third-order scheme is called MRCCSD+T^*(3). We present two approximate fourth-order schemes, MRCCSD+T^*−a(4) and MRCCSD+T^*(4). The results that are presented allow one to choose an appropriate fourth-order scheme, which is less expensive and right for the problem. All these schemes are based on the effective Hamiltonian scheme, and provide a direct calculation of the vertical electron affinities. We apply these schemes to a prototype Li₂ molecule, using four different basis sets, as well as BeO and CH⁺. We have calculated the vertical electron affinities of Li₂ at the geometry of the neutral Li₂ molecule. We also present the vertical ionization potentials of the Li₂ anion at the geometry of the anion ground state. We have also shown how to calculate adiabatic electron affinity, though in that case we lose the advantages of direct calculation. BeO has been examined in two basis sets. For CH⁺, four different basis sets have been used. We have presented the partial fourth-order schemes to the EA in all the basis sets. The results are analyzed to illustrate the importance of triples, as well as highlight computationally efficient partial fourth-order schemes. The choice of the basis set on the electron affinity calculation is also emphasized. Comparisons with available experimental and theoretical results are presented. The general fourth-order schemes, which are conceptually equivalent with the Fock-space multi-reference coupled-cluster singles, doubles, and triplets (MRCCSD+T) methods, based on bondonic formalism, are also presented here in a composed way, for quantum electronic affinity.

Spin-Scaled Range-Separated Double-Hybrid Density Functional Theory for Excited States

Our recently presented range-separated (RS) double-hybrid (DH) time-dependent density functional approach [J. Chem. Theory Comput. 17, 927 (2021)] is combined with spin-scaling techniques. The proposed spin-component-scaled (SCS) and scaled-opposite-spin (SOS) variants are thoroughly tested for almost 500 excitations including the most challenging types. This comprehensive study provides useful information not only about the new approaches but also about the most prominent methods in the DH class. The benchmark calculations confirm the robustness of the RS-DH ansatz, while several tendencies and deficiencies are pointed out for the existing functionals. Our results show that the SCS variant consistently improves the results, while the SOS variant preserves the benefits of the original RS-DH method reducing its computational expenses. It is also demonstrated that, besides our approaches, only the nonempirical functionals provide balanced performance for general applications, while particular methods are only suggested for certain types of excitations.

Stationary Points on Potential Energy Surface of Cyclic C3H3 with Coupled-Cluster Approaches and Density Functional Theory

Cyclic C₃H₃ is the simplest cyclic hydrocarbon, but its configuration is complicated. The ground ²E″ state at the equilateral triangle geometry with D_3h symmetry undergoes both Jahn-Teller (JT) distortion and pseudo-Jahn-Teller (PJT) distortion to structures with C_3v, C_2v, C_s, or C₂ symmetry. Previous works using complete active space self-consistent field (CASSCF) or multiconfiguration SCF (MCSCF) differ on the characteristics of these structures. To clarify the characteristics of these stationary points on the potential energy surface (PES) of this radical, coupled-cluster methods CCSD, CCSD(T), and EOMEA/IP-CCSD as well as density functional theory are employed to calculate their geometries, harmonic frequencies, and relative energies. Deformations between these stationary points due to JT and PJT effects are analyzed in detail. Most of the results with these methods are consistent with each other, except for the b₂ mode of the ²B₁ state with C_2v symmetry. CCSD and CCSD(T) provide an imaginary frequency for this vibrational mode, while it is calculated to be real with the other methods as well as with EOM-CCSDT-3. This may be related to unstable reference in CCSD and CCSD(T) calculations. On the other hand, most of the employed exchange-correlation functionals provide reliable results on the characteristics of these stationary points. Our results show that the ²A' state with C_s symmetry is the only minimum structure on the PES of cyclic C₃H₃. The ²A₂ and ²B₁ states of the C_2v structure are second-order saddle points, while both the ²A state of the C₂ structure and the ²A″ state of the C_s structure are transition states connecting the global minimum ²A' state.

A Simple Range-Separated Double-Hybrid Density Functional Theory for Excited States

A simple and robust range-separated (RS) double-hybrid (DH) time-dependent density functional approach is presented for the accurate calculation of excitation energies of molecules within the Tamm-Dancoff approximation. The scheme can be considered as an excited-state extension of the ansatz proposed by Toulouse and co-workers [J. Chem. Phys. 2018, 148, 164105], which is based on the two-parameter decomposition of the Coulomb potential, for which both the exchange and correlation contributions are range-separated. A flexible and efficient implementation of the new scheme is also presented, which facilitates its extension to any combination of exchange and correlation functionals. The performance of the new approximation is tested for singlet excitations on several benchmark compilations and thoroughly compared to that of representative DH, RS hybrid, and RS DH functionals. The one-electron basis set dependence and computation times are also assessed. Our results show that the new approach improves on standard DHs in most cases, and it can provide a more robust and accurate alternative. In addition, on average, it noticeably surpasses the existing RS hybrid and RS DH functionals.

Reinterpreting the vibrational structure in the electronic spectrum of the propargyl cation (H2C3H+) using an efficient and accurate quantum model

The B̃¹A₁ ← X̃¹A₁ absorption spectra of propargyl cations H₂C₃H⁺ and D₂C₃D⁺ were simulated by an efficient two-dimensional (2D) quantum model, which includes the C-C stretch (v₅) and the C≡C stretch (v₃) vibrational modes. The choice of two modes was based on a scheme that can identify the active modes quantitively by examining the normal coordinate displacements (∆Q) directly based on the ab initio equilibrium geometries and frequencies of the X̃¹A₁ and B̃¹A₁ states of H₂C₃H⁺. The spectrum calculated by the 2D model was found to be very close to those calculated by all the higher three-dimensional (3D) quantum models (including v₅, v₃, and another one in 12 modes of H₂C₃H⁺), which validates the 2D model. The calculated B̃¹A₁ ← X̃¹A₁ absorption spectra of both H₂C₃H⁺ and D₂C₃D⁺ are in fairly good agreement with experimental results.

Improved Description of Charge-Transfer Potential Energy Surfaces via Spin-Component-Scaled CC2 and ADC(2) Methods

The molecular level understanding of electronic transport properties depends on the reliable theoretical description of charge-transfer (CT)-type electronic states. In this paper, the performance of spin-component-scaled variants of the popular CC2 and ADC(2) methods is evaluated for CT states, following benchmark strategies of earlier studies that revealed a compromised accuracy of the unmodified models. In addition to statistics on the accuracy of vertical excitation energies at equilibrium and infinite separation of bimolecular complexes, potential energy surfaces of the ammonia-fluorine complex are also reported. The results show the capability of spin-component-scaled approaches to reduce the large errors of their regular counterparts to a significant extent, outperforming even the coupled-cluster single and double method in many cases. The cost-effective scaled-opposite-spin variants are found to provide a remarkably good agreement with the CCSDT-3 reference data, thereby being recommended methods of choice in the study of charge-transfer states.

Equation-of-motion coupled-cluster theory for double electron attachment with spin-orbit coupling

We report implementation of the equation-of-motion coupled-cluster (EOM-CC) method for double electron-attachment (DEA) with spin-orbit coupling (SOC) at the CC singles and doubles (CCSD) level using a closed-shell reference in this work. The DEA operator employed in this work contains two-particle and three-particle one-hole excitations, and SOC is included in post-Hartree-Fock treatment. Time-reversal symmetry and spatial symmetry are exploited to reduce computational cost. The EOM-DEA-CCSD method with SOC allows us to investigate SOC effects of systems with two-unpaired electrons. According to our results on atoms, double ionization potentials (DIPs), excitation energies (EEs), and SO splittings of low-lying states are calculated reliably using the EOM-DEA-CCSD method with SOC. Its accuracy is usually higher than that of EOM-CCSD for EEs or DIPs if the same target can be reached from single excitations by choosing a proper closed-shell reference. However, performance of the EOM-DEA-CCSD method with SOC on molecules is not as good as that for atoms. Bond lengths for the ground and the several lowest excited states of GaH, InH, and TlH are underestimated pronouncedly, although reasonable EEs are obtained, and splittings of the ³Σ^- state from the π² configuration are calculated to be too small with EOM-DEA-CCSD.

A New Benchmark Set for Excitation Energy of Charge Transfer States: Systematic Investigation of Coupled Cluster Type Methods

The numerous existing publications on benchmarking quantum chemistry methods for excited states rarely include Charge Transfer (CT) states, although many interesting phenomena in, e.g., biochemistry and material physics involve the transfer of electrons between fragments of the system. Therefore, it is timely to test the accuracy of quantum chemical methods for CT states, as well. In this study we first propose a new benchmark set consisting of dimers having low-energy CT states. On this set, the vertical excitation energy has been calculated with Coupled Cluster methods including triple excitations (CC3, CCSDT-3, CCSD(T)(a)*), as well as with methods including full or approximate doubles (CCSD, STEOM-CCSD, CC2, ADC(2), EOM-CCSD(2)). The results show that the popular CC2 and ADC(2) methods are much less accurate for CT states than for valence states. On the other hand, EOM-CCSD seems to have similar systematic overestimation of the excitation energies for both types of states. Among the triples methods the novel EOM-CCSD(T)(a)* method including noniterative triple excitations is found to stand out with its consistently good performance for all types of states, delivering essentially EOM-CCSDT quality results.

Third-Order Unitary Coupled Cluster (UCC3) for Excited Electronic States: Efficient Implementation and Benchmarking

The efficient implementation of the third-order unitary coupled-cluster scheme (UCC3) for the calculation of excited electronic states is reported. The UCC3 scheme and its second-order UCC2 variant have been benchmarked and compared to Jacquemin's recently introduced, as well as Thiel's well-established, benchmark sets for excitation energies and oscillator strengths. For the latter, the calculation of 134 excited singlet and 71 excited triplet states of 28 small- to medium-sized organic molecules has revealed that UCC2 exhibits a mean error and standard deviation of 0.36 ± 0.41 eV for singlet states and 0.22 ± 0.21 eV for triplet states, whereas UCC3 revealed an accuracy of 0.06 ± 0.27 eV for singlet and -0.22 ± 0.15 eV for triplet states. In addition, the oscillator strengths obtained with effective transition moments correct through second order in perturbation theory are in very good agreement with literature data.

Recent developments in the general atomic and molecular electronic structure system

A discussion of many of the recently implemented features of GAMESS (General Atomic and Molecular Electronic Structure System) and LibCChem (the C++ CPU/GPU library associated with GAMESS) is presented. These features include fragmentation methods such as the fragment molecular orbital, effective fragment potential and effective fragment molecular orbital methods, hybrid MPI/OpenMP approaches to Hartree-Fock, and resolution of the identity second order perturbation theory. Many new coupled cluster theory methods have been implemented in GAMESS, as have multiple levels of density functional/tight binding theory. The role of accelerators, especially graphical processing units, is discussed in the context of the new features of LibCChem, as it is the associated problem of power consumption as the power of computers increases dramatically. The process by which a complex program suite such as GAMESS is maintained and developed is considered. Future developments are briefly summarized.

The Quest for Highly Accurate Excitation Energies: A Computational Perspective

We provide an overview of the successive steps that made it possible to obtain increasingly accurate excitation energies with computational chemistry tools, eventually leading to chemically accurate vertical transition energies for small- and medium-size molecules. First, we describe the evolution of ab initio methods employed to define benchmark values, with the original Roos CASPT2 method, then the CC3 method as in the renowned Thiel set, and more recently the resurgence of selected configuration interaction methods. The latter method has been able to deliver consistently, for both single and double excitations, highly accurate excitation energies for small molecules, as well as medium-size molecules with compact basis sets. Second, we describe how these high-level methods and the creation of representative benchmark sets of excitation energies have allowed the fair and accurate assessment of the performance of computationally lighter methods. We conclude by discussing possible future theoretical and technological developments in the field.

A Mountaineering Strategy to Excited States: Highly Accurate Energies and Benchmarks for Medium Sized Molecules

Following our previous work focusing on compounds containing up to 3 non-hydrogen atoms [J. Chem. Theory Comput. 2018, 14, 4360-4379], we present here highly accurate vertical transition energies obtained for 27 molecules encompassing 4, 5, and 6 non-hydrogen atoms: acetone, acrolein, benzene, butadiene, cyanoacetylene, cyanoformaldehyde, cyanogen, cyclopentadiene, cyclopropenone, cyclopropenethione, diacetylene, furan, glyoxal, imidazole, isobutene, methylenecyclopropene, propynal, pyrazine, pyridazine, pyridine, pyrimidine, pyrrole, tetrazine, thioacetone, thiophene, thiopropynal, and triazine. To obtain these energies, we use equation-of-motion/linear-response coupled cluster theory up to the highest technically possible excitation order for these systems (CC3, EOM-CCSDT, and EOM-CCSDTQ) and selected configuration interaction (SCI) calculations (with tens of millions of determinants in the reference space), as well as the multiconfigurational n-electron valence state perturbation theory (NEVPT2) method. All these approaches are applied in combination with diffuse-containing atomic basis sets. For all transitions, we report at least CC3/aug-cc-pVQZ vertical excitation energies as well as CC3/aug-cc-pVTZ oscillator strengths for each dipole-allowed transition. We show that CC3 almost systematically delivers transition energies in agreement with higher-level methods with a typical deviation of ±0.04 eV, except for transitions with a dominant double excitation character where the error is much larger. The present contribution gathers a large, diverse, and accurate set of more than 200 highly accurate transition energies for states of various natures (valence, Rydberg, singlet, triplet, n → π*, π → π*, ...). We use this series of theoretical best estimates to benchmark a series of popular methods for excited state calculations: CIS(D), ADC(2), CC2, STEOM-CCSD, EOM-CCSD, CCSDR(3), CCSDT-3, CC3, and NEVPT2. The results of these benchmarks are compared to the available literature data.

Adventures in DFT by a wavefunction theorist

The attraction density functional theory (DFT) has for electronic structure theory is that it is easier to do computationally than ab initio, correlated wavefunction methods, due to its effective one-particle structure. On the contrary, ab initio theorists insist on the ability to converge to the right answer in appropriate limits, but this requires a treatment of the reduced two-particle density matrix. DFT avoids that by appealing to an "existence" theorem (not a constructive one) that all its effects are subsummed into a DFT functional of the one-particle density. However, the existence of thousands of DFT functionals emphasizes that there is no satisfactory way to systematically improve the Kohn-Sham (KS) version as most changes in parameterization or formulation seldom lead to a new functional that is genuinely better than others. Some researchers in the DFT community try to address this issue by imposing conditions rigorously derived from exact DFT considerations, but to date, no one has shown how this route will ever lead to converged results even for the ground state, much less for all the other electronic states obtained from time-dependent DFT that are critically important for chemistry. On the contrary, coupled-cluster (CC) theory and its equation-of-motion extensions provide rigorous results for both that KS-DFT methods are attempting to emulate. How to use them and their exact formal properties to tie CC theory to an effective one-particle form is the target of this perspective. This route addresses the devil's triangle of KS-DFT problems: the one-particle spectrum, self-interaction, and the integer discontinuity.

Equation of motion coupled-cluster for core excitation spectra: Two complementary approaches

This paper presents core excitation spectra from coupled-cluster (CC) theory obtained from both a time-independent and a new time-dependent formalism. The conventional time-independent CC formulation for excited states is the equation-of-motion (EOM-CC) method whose eigenvalues and eigenvectors describe the core excited states. An alternative computational procedure is offered by a time-dependent CC description. In that case, the dipole transition operator is expressed in the CC effective Hamiltonian form and propagated with respect to time. The absorption spectrum is obtained from the CC dipole autocorrelation function via a Fourier transformation. Comparisons are made among the time-dependent results obtained from second-order perturbation theory, to coupled cluster doubles and their linearized forms (CCD and LCCD), to CC singles and doubles (CCSD) and the linearized form (LCCSD). In the time-independent case, considerations of triples (EOM-CCSDT) and quadruples (EOM-CCSDTQ) are used to approach sub-electron volt accuracy. A particular target is the allyl radical, as an example of an open-shell molecule. As the results have to ultimately be the same, the two procedures offer a complementary approach toward analyzing experimental results.

How Robust is the N=34 Subshell Closure? First Spectroscopy of ^{52}Ar

The first γ-ray spectroscopy of ^{52}Ar, with the neutron number N=34, was measured using the ^{53}K(p,2p) one-proton removal reaction at ∼210  MeV/u at the RIBF facility. The 2_{1}^{+} excitation energy is found at 1656(18) keV, the highest among the Ar isotopes with N>20. This result is the first experimental signature of the persistence of the N=34 subshell closure beyond ^{54}Ca, i.e., below the magic proton number Z=20. Shell-model calculations with phenomenological and chiral-effective-field-theory interactions both reproduce the measured 2_{1}^{+} systematics of neutron-rich Ar isotopes, and support a N=34 subshell closure in ^{52}Ar.

Green's function coupled cluster formulations utilizing extended inner excitations

In this paper, we analyze new approximations of the Green's function coupled cluster (GFCC) method where locations of poles are improved by extending the excitation level of inner auxiliary operators. These new GFCC approximations can be categorized as the GFCC-i(n, m) method, where the excitation level of the inner auxiliary operators (m) used to describe the ionization potential and electron affinity effects in the N - 1 and N + 1 particle spaces is higher than the excitation level (n) used to correlate the ground-state coupled cluster wave function for the N-electron system. Furthermore, we reveal the so-called "n + 1" rule in this category [or the GFCC-i(n, n + 1) method], which states that in order to maintain size-extensivity of the Green's function matrix elements, the excitation level of inner auxiliary operators X _p (ω) and Y _q (ω) cannot exceed n + 1. We also discuss the role of the moments of coupled cluster equations that in a natural way assures these properties. Our implementation in the present study is focused on the first approximation in this GFCC category, i.e., the GFCC-i(2,3) method. As our first practice, we use the GFCC-i(2,3) method to compute the spectral functions for the N₂ and CO molecules in the inner and outer valence regimes. In comparison with the Green's function coupled cluster singles, doubles results, the computed spectral functions from the GFCC-i(2,3) method exhibit better agreement with the experimental results and other theoretical results, particularly in terms of providing higher resolution of satellite peaks and more accurate relative positions of these satellite peaks with respect to the main peak positions.