New coupled-cluster methods with singles, doubles, and noniterative triples for high accuracy calculations of excited electronic states

Use of caps in the auxiliary basis set formulation of the fragment molecular orbital method

An auxiliary polarization formulation of the fragment molecular orbital (FMO) method is developed, combining a basis set correction computed for capped isolated fragments with a polarization obtained from uncapped fragments. For a set of organic and inorganic test systems, it is shown that the total energy and atomic charges are accurately reproduced with respect to full unfragmented calculations. It is demonstrated that the method is accurate for computing electronic excited states. The developed approach is applied to rank the isomers of chignolin from experimental NMR data (PDB: 1UAO) according to their relative energy. Contributions of polarization and basis set effects to pair interactions between fragments are elucidated.

Aufbau Suppressed Coupled Cluster Theory for Electronically Excited States

We introduce an approach to improve single-reference coupled cluster theory in settings where the Aufbau determinant is absent from or plays only a small role in the true wave function. Using a de-excitation operator that can be efficiently hidden within a similarity transform, we create a coupled cluster wave function in which de-excitations work to suppress the Aufbau determinant and produce wave functions dominated by other determinants. Thanks to an invertible and fully exponential form, the approach is systematically improvable, size consistent, size extensive, and, interestingly, size intensive in a granular way that should make the adoption of some ground state techniques, such as local correlation, relatively straightforward. In this initial study, we apply the general formalism to create a state-specific method for orbital-relaxed, singly excited states. We find that this approach matches the accuracy of similar-cost equation-of-motion methods in valence excitations while offering improved accuracy for charge transfer states. We also find the approach to be more accurate than excited-state-specific perturbation theory in both types of states.

Performance of EOM-CCSD(T)(a)*-Based Quartic Force Fields in Computing Fundamental, Anharmonic Vibrational Frequencies of Molecular Electronically Excited States with Application to the Ã1A″ State of :CCH2 (Vinylidene)

Highly accurate anharmonic vibrational frequencies of electronically excited states are not as easily computed as their ground electronic state counterparts, but recently developed approximate triple excited state methods may be changing that. One emerging excited state method is equation of motion coupled cluster theory at the singles and doubles level with perturbative triples computed via the (a)* formalism, EOMEE-CCSD(T)(a)*. One of the most employed means for the ready computation of vibrational anharmonic frequencies for ground electronic states is second-order vibrational perturbation theory (VPT2), a theory based on quartic force fields (QFFs),fourth-order Taylor series expansions of the potential portion of the internuclear Watson Hamiltonian. The combination of these two is herein benchmarked for its performance for use as a means of computing rovibrational spectra of electronically excited states. Specifically, the EOMEE-CCSD(T)(a)* approach employing a complete basis set extrapolation along with core electron inclusion and relativity (the so-called "CcCR" approach) defining the QFF produces anharmonic fundamental vibrational frequencies within 2.83%, on the average, of reported gas-phase experimentally assigned values for the test set including the A ~ 1 A ″ states of HCF, HCCl, HSiF, HNO, and HPO. However, some states have exceptional accuracy in the fundamentals, most notably for ν2 of A ~ 1 A ″ HCCl in which the CcCR QFF value is within 1.8 cm-1 at 927.9 cm-1 (or 0.2%) of the experiment. Additionally, this approach produces rotational constants to, on the absolute average, within 0.41% of available experimental data, showcasing notable accuracy in the computation of rovibronic spectral data. Furthermore, utilizing a hybrid approach composed of harmonic CcCR force constants along with a set of simple EOMEE-CCSD(T)(a)*/aug-cc-pVQZ QFF cubic and quartic force constants is faster than using pure CcCR and better represents those modes that suffer from numerical instability in the anharmonic portion of the QFF, implying that this so-called "CcCR + QZ" QFF approach may be the best for future applications. Finally, complete, rovibrational spectral data are provided for A ~ 1 A 2 :CCH2, a molecule of potential astrochemical interest, in order to aid in its potential future experimental rovibronic characterization.

Analysis of Site Energies and Excitonic Couplings: The Role of Symmetry and Polarization

An excitonic coupling model is developed based on an equation-of-motion coupled cluster combined with the fragment molecular orbital method. The effects of polarization and excitonic coupling on the splitting of quasi-degenerate levels in systems containing multiple chromophores are elucidated on dimers of formaldehyde, water, formic acid, hydrogen fluoride, and carbon monoxide. It is shown that the level structure is mainly determined by the mutual polarization of chromophores and to a lesser extent by the excitonic coupling. The role of symmetry in excitonic coupling in dimers is discussed. The excitonic coupling between all residues in the photoactive yellow protein (PDB: 2PHY) is analyzed.

Excited-State-Specific Pseudoprojected Coupled-Cluster Theory

We present an excited-state-specific coupled-cluster approach in which both the molecular orbitals and cluster amplitudes are optimized for an individual excited state. The theory is formulated via a pseudoprojection of the traditional coupled-cluster wavefunction that allows correlation effects to be introduced atop an excited-state mean field starting point. The approach shares much in common with ground-state CCSD, including size extensivity and an N6 cost scaling. Preliminary numerical tests show that, when augmented with N5 cost perturbative corrections for key terms, the method can improve over excited-state-specific second-order perturbation theory in valence, charge transfer, and Rydberg states.

Mass-selected ion-molecule cluster beam apparatus for ultrafast photofragmentation studies

We describe an apparatus for investigating the excited-state dissociation dynamics of mass-selected ion-molecule clusters by mass-resolving and detecting photofragment-ions and neutrals, in coincidence, using an ultrafast laser operating at high repetition rates. The apparatus comprises a source that generates ion-molecule clusters, a time-of-flight spectrometer, and a mass filter that selects the desired anions, and a linear-plus-quadratic reflectron mass spectrometer that discriminates the fragment anions after the femtosecond laser excites the clusters. The fragment neutrals and anions are then captured by two channeltron detectors. The apparatus performance is tested by measuring the photofragments: I-, CF3I-, and neutrals from photoexcitation of the ion-molecule cluster CF3I·I- using femtosecond UV laser pulses with a wavelength of 266 nm. The experimental results are compared with our ground state and excited state electronic structure calculations as well as the existing results and calculations, with particular attention to the generation mechanism of the anion fragments and dissociation channels of the ion-molecule cluster CF3I·I- in the charge-transfer excited state.

Converging high-level coupled-cluster energetics via adaptive selection of excitation manifolds driven by moment expansions

A novel approach to rapidly converging high-level coupled-cluster (CC) energetics in an automated fashion is proposed. The key idea is an adaptive selection of excitation manifolds defining higher--than--two-body components of the cluster operator inspired by CC(P;Q) moment expansions. The usefulness of the resulting methodology is illustrated by molecular examples where the goal is to recover the electronic energies obtained using the CC method with a full treatment of singly, doubly, and triply excited clusters (CCSDT) when the noniterative triples corrections to CCSD fail.

Unitary Coupled Cluster: Seizing the Quantum Moment

Shallow, CNOT-efficient quantum circuits are crucial for performing accurate computational chemistry simulations on current noisy quantum hardware. Here, we explore the usefulness of noniterative energy corrections, based on the method of moments of coupled-cluster theory, for accelerating convergence toward full configuration interaction. Our preliminary numerical results relying on iteratively constructed ansätze suggest that chemically accurate energies can be obtained with substantially more compact circuits, implying enhanced resilience to gate and decoherence noise.

Triple Excitations in Green's Function Coupled Cluster Solver for Studies of Strongly Correlated Systems in the Framework of Self-Energy Embedding Theory

Embedding theories became important approaches used for accurate calculations of both molecules and solids. In these theories, a small chosen subset of orbitals is treated with an accurate method, called an impurity solver, capable of describing higher correlation effects. Ideally, such a chosen fragment should contain multiple orbitals responsible for the chemical and physical behavior of the compound. Handling a large number of chosen orbitals presents a very significant challenge for the current generation of solvers used in the physics and chemistry community. Here, we develop a Green's function coupled cluster singles doubles and triples (GFCCSDT) solver that can be used for a quantitative description in both molecules and solids. This solver allows us to treat orbital spaces that are inaccessible to other accurate solvers. At the same time, GFCCSDT maintains high accuracy of the resulting self-energy. Moreover, in conjunction with the GFCCSD solver, it allows us to test the systematic convergence of computational studies. Developing the CC family of solvers paves the road to fully systematic Green's function embedding calculations in solids. In this paper, we focus on the investigation of GFCCSDT self-energies for a strongly correlated problem of SrMnO₃ solid. Subsequently, we apply this solver to solid MnO showing that an approximate variant of GFCCSDT is capable of yielding a high accuracy orbital resolved spectral function.

A configuration interaction correction on top of pair coupled cluster doubles

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

Electronic Excitation of ortho-Fluorothiophenol

ortho-Fluorothiophenol (o-FTP) photodissociates through the well-known πσ* process. The fluorine atom of o-FTP introduces a feature in the photodissociation of o-FTP that does not occur in most other πσ* processes because the fluorine atom can form a hydrogen bond with the hydrogen atom of the SH group. Theoretical computations can serve as a good way to study these reactions because they usually proceed very quickly, and the current spectroscopies cannot probe the details of the processes as thoroughly as theory can. Here we use completely renormalized equation-of-motion coupled cluster theory with single and double excitations and a quasiperturbative treatment of connected triple excitations (CR-EOM-CCSD(T)) and quasidegenerate perturbation theory, in particular extended multistate complete-active-space second-order perturbation theory (XMS- CASPT2), to calculate the four lowest singlet states of o-FTP and hybrid density functional theory to optimize the geometries of the two lowest singlet states. We find that ten active electrons in nine active orbitals are sufficient to provide a good reference function for all four states. We find that the ground electronic state and the first excited singlet state both exhibit strongly bent hydrogen bonds. We also use density functional theory with the Tamm-Dancoff approximation and the SMD solvation model to successfully simulate the electronic spectrum of o-FTP in n-hexane solvent.

Estimation of Excited-State Geometries of Benzene and Fluorobenzene through Vibronic Analyses of Absorption Spectra

The parameters used in theoretical modeling of vibrational patterns within Franck-Condon (FC) approximation can be adjusted to match the vibrationally well-resolved experimental absorption spectrum of molecules. These simulation parameters can then be used to reveal the structural changes occurring between the initial and final states assuming the harmonic oscillator approximation holds for both states. Such a theoretical approach has been applied to benzene and fluorobenzene to disclose the first excited-state geometries of both compounds. The carbon-carbon bond length of benzene in the ¹B_2u state has been calculated as 1.430 Å, which is in very good agreement with the experimental bond length of 1.432 Å. The FC spectral fit method has been exploited to reveal the ¹B₂ state of fluorobenzene as well. Commonly employed density functional theory (DFT) and time-dependent DFT methods have been used to calculate the ground- and excited-state geometries of both compounds, respectively. The comparison of geometrical parameters and vibrational frequencies at the relevant states shows that frequently used hybrid functionals perform quite well in the ground state, whereas their performances drop considerably while predicting the excited-state properties. Among the hybrid functionals studied, TD-B3LYP with 6-31+G(d) basis set can be chosen to calculate the excited-state properties of molecules, albeit with much less anticipation of accuracy from the performance that B3LYP usually shows at the ground state.

High-Level Theoretical Study of the C1Π States of GaCl, GaBr, InCl, and InBr

For the first singlet excited states C¹Π of IIIA group monohalides GaCl, GaBr, InCl, and InBr, a very shallow potential well may exist in the flat potential energy curve, which poses a challenge to the theoretical accuracy. In this study, high-level theoretical calculations have been performed through the Feller-Peterson-Dixon composite approach to study the C¹Π states, and the obtained spectroscopic constants agree well with the known experimental ones. It is found that the C¹Π states are sensitive to the size of basis functions, spin-orbit coupling, and strong correlations mainly due to triple excitations. The final results show that the C¹Π states of GaCl and InCl are quasi-bound with one (v' = 0) and four (v' = 0-3) vibrational levels, respectively, being consistent with the experimental findings, whereas the C¹Π states of GaBr and InBr are repulsive. Our conclusions deny the existence of higher vibrational levels v' = 1 for GaCl, v' > 3 for InCl, and v' ≥ 0 for InBr in previous experimental and theoretical studies of C¹Π.

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.

Quadratic Unitary Coupled-Cluster Singles and Doubles Scheme: Efficient Implementation, Benchmark Study, and Formulation of an Extended Version

An efficient implementation of the quadratic unitary coupled-cluster singles and doubles (qUCCSD) scheme for calculations of electronic ground and excited states using an unrestricted molecular spin-orbital formulation and an efficient tensor contraction library is reported. The accuracy of the qUCCSD scheme and the efficiency of the present implementation are demonstrated using extensive benchmark calculations of excitation energies and an application to S₀ → S₁ vertical excitation energies for cis- and trans-4a,4b-dihydrotriphenylene. The qUCCSD scheme has been shown to provide improved excitation energies compared with the UCC3 scheme formulated based on perturbation theory. A UCC truncation scheme that can provide excitation energies correct through the fourth order is also presented to further improve the accuracy of the qUCCSD scheme.

Experimental and Theoretical Study of the Ultrafast Dynamics of a Ni2 Dy2 -Compound in DMF After UV/Vis Photoexcitation

We present a combined experimental and theoretical study of the ultrafast transient absorption spectroscopy results of a {Ni₂Dy₂}‐compound in DMF, which can be considered as a prototypic molecule for single molecule magnets. We apply state‐of‐the‐art ab initio quantum chemistry to quantitatively describe the optical properties of an inorganic complex system comprising ten atoms to form the chromophoric unit, which is further stabilized by surrounding ligands. Two different basis sets are used for the calculations to specifically identify two dominant peaks in the ground state. Furthermore, we theoretically propagate the compound's correlated many‐body wavefunction under the influence of a laser pulse as well as relaxation processes and compare against the time‐resolved absorption spectra. The experimental data can be described with a time constant of several hundreds of femtoseconds attributed to vibrational relaxation and trapping into states localized within the band gap. A second time constant is ascribed to the excited state while trap states show lifetimes on a longer timescale. The theoretical propagation is performed with the density‐matrix formalism and the Lindblad superoperator, which couples the system to a thermal bath, allowing us to extract relaxation times from first principles.

Excited-State Dynamics of a Substituted Fluorene Derivative. The Central Role of Hydrogen Bonding Interactions with the Solvent

Substituted fluorene structures have demonstrated unusual photochemical properties. Previous reports on the substituted fluorene Schiff base FR0-SB demonstrated super photobase behavior with a ΔpKb of ∼14 upon photoexcitation. In an effort to understand the basis for this unusual behavior, we have examined the electronic structure and relaxation dynamics of the structural precursor of FR0-SB, the aldehyde FR0, in protic and aprotic solvents using time-resolved fluorescence spectroscopy and quantum chemical calculations. The calculations show three excited singlet states in relatively close energetic proximity. The spectroscopic data are consistent with relaxation dynamics from these electronic states that depend on the presence and concentration of solvent hydroxyl functionality. These results underscore the central role of solvent hydrogen bonding to the FR0 aldehyde oxygen in mediating the relaxation dynamics within this molecule.

Unitary coupled-cluster based self-consistent polarization propagator theory: A quadratic unitary coupled-cluster singles and doubles scheme

The development of a quadratic unitary coupled-cluster singles and doubles (qUCCSD) based self-consistent polarization propagator method is reported. We present a simple strategy for truncating the commutator expansion of the unitary version of coupled-cluster transformed Hamiltonian H̄. The qUCCSD method for the electronic ground state includes up to double commutators for the amplitude equations and up to cubic commutators for the energy expression. The qUCCSD excited-state eigenvalue equations include up to double commutators for the singles-singles block of H̄, single commutators for the singles-doubles and doubles-singles blocks, and the bare Hamiltonian for the doubles-doubles block. Benchmark qUCCSD calculations of the ground-state properties and excitation energies for representative molecules demonstrate significant improvement of the accuracy and robustness over the previous UCC3 scheme derived using Møller-Plesset perturbation theory.

Internal Conversion between Bright (11Bu+) and Dark (21Ag-) States in s-trans-Butadiene and s-trans-Hexatriene

Internal conversion (IC) between the two lowest singlet excited states, 1¹B_u⁺ and 2¹A_g^-, of s-trans-butadiene and s-trans-hexatriene is investigated using a series of single- and multi- reference wave function and density functional theory (DFT) methodologies. Three independent types of the equation-of-motion coupled-cluster (EOMCC) theory capable of providing an accurate and balanced description of one- as well as two-electron transitions, abbreviated as δ-CR-EOMCC(2,3), DIP-EOMCC(4h2p){N_o}, and DEA-EOMCC(4p2h){N_u} or DEA-EOMCC(3p1h,4p2h){N_u}, consistently predict that the 1¹B_u⁺/2¹A_g^- crossing in both molecules occurs along the bond length alternation coordinate. However, the analogous 1¹B_u⁺ and 2¹A_g^- potentials obtained with some multireference approaches, such as CASSCF and MRCIS(D), as well as with the linear-response formulation of time-dependent DFT (TDDFT), do not cross. Hence, caution needs to be exercised when studying the low-lying singlet excited states of polyenes with conventional multiconfigurational methods and TDDFT. The multistate many-body perturbation theory methods, such as XMCQDPT2, do correctly reproduce the curve crossing. Among the simplest and least expensive computational methodologies, the DFT approaches that incorporate the contributions of doubly excited configurations, abbreviated as MRSF (mixed reference spin-flip) TDDFT and SSR(4,4), accurately reproduce our best EOMCC results. This is highly promising for nonadiabatic molecular dynamics simulations in larger systems.

Time-Dependent Long-Range-Corrected Double-Hybrid Density Functionals with Spin-Component and Spin-Opposite Scaling: A Comprehensive Analysis of Singlet-Singlet and Singlet-Triplet Excitation Energies

Following the work on spin-component and spin-opposite scaled (SCS/SOS) global double hybrids for singlet-singlet excitations by Schwabe and Goerigk [ J. Chem. Theory Comput. 2017, 13, 4307-4323] and our own works on new long-range corrected (LC) double hybrids for singlet-singlet and singlet-triplet excitations [ J. Chem. Theory Comput. 2019, 15, 4735-4744 and J. Chem. Phys. 2020, 153, 064106], we present new LC double hybrids with SCS/SOS that demonstrate further improvement over previously published results and methods. We introduce new unscaled and scaled versions of different global and LC double hybrids based on Becke88 or PBE exchange combined with LYP, PBE, or P86 correlation. For singlet-singlet excitations, we cross-validate them on six benchmark sets that cover small to medium-sized chromophores with different excitation types (local-valence, Rydberg, and charge transfer). For singlet-triplet excitations, we perform the cross-validation on three different benchmark sets following the same analysis as in our previous work in 2020. In total, 203 excitations are analyzed. Our results confirm and extend those of Schwabe and Goerigk regarding the superior performance of SCS and SOS variants compared to their unscaled parents by decreasing mean absolute deviations, root-mean-square deviations, or error spans by more than half and bringing absolute mean deviations closer to zero. Our SCS/SOS variants are shown to be highly efficient and robust for the computation of vertical excitation energies, which even outperform specialized double hybrids that also contain an LC in their perturbative part. In particular, our new SCS/SOS-ωPBEPP86 and SCS/SOS-ωB88PP86 functionals are four of the most accurate and robust methods tested in this work, and we fully recommend them for future applications. However, if the relevant SCS and SOS algorithms are not available to the user, we suggest ωPBEPP86 as the best unscaled method in this work.

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.

(T)+EOM Quartic Force Fields for Theoretical Vibrational Spectroscopy of Electronically Excited States

(T)+EOM quartic force fields (QFFs) are proposed for ab initio rovibrational properties of electronically excited states of small molecules. The (T)+EOM method is a simple treatment of the potential surface of the excited state using a composite energy from the CCSD(T) energy for the ground-state configuration and the EOM-CCSD excitation energy for the target state. The method is benchmarked with two open-shell species, HOO and HNF, and two closed-shell species, HNO and HCF. A (T)+EOM QFF with a complete basis set extrapolation (C) and corrections for core correlation (cC) and scalar relativity (R), dubbed (T)+EOM/CcCR, achieves a mean absolute error (MAE) as low as 1.6 cm^-1 for the à ²A' state of HOO versus an established benchmark QFF with CCSD(T)-F12b/cc-pVTZ-F12 (F12-TZ) for this variationally accessible electronically excited state. The MAE for anharmonic frequencies for (T)+EOM/CcCR versus F12-TZ for HNF is 7.5 cm^-1. The closed-shell species are compared directly with the experiment, where a simpler (T)+EOM QFF using the aug-cc-pVTZ basis set compares more favorably than the more costly (T)+EOM/CcCR, suggesting a possible influence of decreasing accuracy with basis set size. Scans along internal coordinates are also provided which show reasonable modeling of the potential surface by (T)+EOM compared to benchmark QFFs computed for variationally accessible electronic states. The agreement between (T)+EOM/CcCR with F12-TZ and CcCR benchmarks is also shown to be quite accurate for rotational constants and geometries, with an MAE of 0.008 MHz for the rotational constants of (T)+EOM/CcCR versus CcCR for à ²A' HOO and agreement within 0.003 Å for bond lengths.

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.

New and Efficient Implementation of CC3

We present a new and efficient implementation of the closed shell coupled cluster singles and doubles with perturbative triples method (CC3) in the electronic structure program eT. Asymptotically, a ground state calculation has an iterative cost of 4nV4nO3 floating point operations (FLOP), where nV and nO are the number of virtual and occupied orbitals, respectively. The Jacobian and transpose Jacobian transformations, required to iteratively solve for excitation energies and transition moments, both require 8nV4nO3 FLOP. We have also implemented equation of motion (EOM) transition moments for CC3. The EOM transition densities require recalculation of triples amplitudes, as nV3nO3 tensors are not stored in memory. This results in a noniterative computational cost of 10nV4nO3 FLOP for the ground state density and 26nV4nO3 FLOP per state for the transition densities. The code is compared to the CC3 implementations in CFOUR, DALTON, and PSI4. We demonstrate the capabilities of our implementation by calculating valence and core excited states of l-proline.

The Trip to the Density Functional Theory Zoo Continues: Making a Case for Time-Dependent Double Hybrids for Excited-State Problems

This account is written for general users of time-dependent density functional theory (TD-DFT) methods as well as chemists who are unfamiliar with the field. It includes a brief overview of conventional TD-DFT approaches and recommendations for applications to organic molecules based on our own experience. The main emphasis of this work, however, lies in providing the first in-depth review of time-dependent double-hybrid density functionals. They were first established in 2007 with very promising follow-up studies in the subsequent four years before developments or applications became scarce. The topic has regained more interest since 2017, and this account reviews those latest developments led by our group. These developments have shown unprecedented robustness for a variety of different types of electronic excitations when compared to more conventional TD-DFT methods. In particular, time-dependent double hybrids do not suffer from artificial ghost states and are able to reproduce exciton-coupled absorption spectra. Our latest methods include range separation and belong to the currently best TD-DFT methods for singlet-singlet excitations in organic molecules. While there is still room for improvement and further development in this space, we hope that this account encourages users to adjust their computational protocols to such new methods to provide more real-life testing and scenarios.

Valence Bond Alternative Yielding Compact and Accurate Wave Functions for Challenging Excited States. Application to Ozone and Sulfur Dioxide

A novel state-averaged version of ab initio nonorthogonal valence bond method is described, for the sake of accurate theoretical studies of excited states in the valence bond framework. With respect to standard calculations in the molecular orbital framework, the state-averaged breathing-orbital valence bond (BOVB) method has the advantage to be free from the penalizing constraint for the ground and excited state(s) to share the same unique set of orbitals. The ability of the BOVB method to faithfully describe excited states and to compute accurate transition energies from the ground state is tested on the five lowest-lying singlet electronic states of ozone and sulfur dioxide, among which 1¹B₂ and 2¹A₁ are the challenging ones. As the 1¹A₂, 1¹B₁, and 1¹B₂ states are of different symmetries than the ground state, they can be calculated at the state-specific BOVB level. On the other hand, the 2¹A₁ states and the 1¹A₁ ground states, which are of like symmetry, are calculated with the state-averaged BOVB technique. In all cases, the calculated vertical energies are close to the experimental values when available, and at par with the most sophisticated calculations in the molecular framework, despite the extreme compactness of the BOVB wave functions, made of no more than 5-9 valence bond structures in all cases. The features that allow the combination of compactness and accuracy in challenging cases are analyzed. For the "ionic" 1¹B₂ states, which are the site of important charge fluctuations, it is because of the built-in dynamic correlation inherent to the BOVB method. For the 2¹A₁ ones, this is the fact that these states have the degree of freedom of having different orbitals than the ground states, even though they are of like symmetry and calculated simultaneously using the newly implemented state-average BOVB algorithm. Finally, the description of the excited states in terms of Lewis structures is insightful, rationalizing the fast ring closure for the 2¹A₁ state of ozone and predicting some diradical character in the so-called "ionic" 1¹B₂ states.

Isoenergetic two-photon excitation enhances solvent-to-solute excited-state proton transfer

Two-photon excitation (TPE) is an attractive means for controlling chemistry in both space and time. Since isoenergetic one- and two-photon excitations (OPE and TPE) in non-centrosymmetric molecules are allowed to reach the same excited state, it is usually assumed that they produce similar excited-state reactivity. We compare the solvent-to-solute excited-state proton transfer of the super photobase FR0-SB following isoenergetic OPE and TPE. We find up to 62% increased reactivity following TPE compared to OPE. From steady-state spectroscopy, we rule out the involvement of different excited states and find that OPE and TPE spectra are identical in non-polar solvents but not in polar ones. We propose that differences in the matrix elements that contribute to the two-photon absorption cross sections lead to the observed enhanced isoenergetic reactivity, consistent with the predictions of our high-level coupled-cluster-based computational protocol. We find that polar solvent configurations favor greater dipole moment change between ground and excited states, which enters the probability for TPE as the absolute value squared. This, in turn, causes a difference in the Franck-Condon region reached via TPE compared to OPE. We conclude that a new method has been found for controlling chemical reactivity via the matrix elements that affect two-photon cross sections, which may be of great utility for spatial and temporal precision chemistry.

NWChem: Past, present, and future

Specialized computational chemistry packages have permanently reshaped the landscape of chemical and materials science by providing tools to support and guide experimental efforts and for the prediction of atomistic and electronic properties. In this regard, electronic structure packages have played a special role by using first-principle-driven methodologies to model complex chemical and materials processes. Over the past few decades, the rapid development of computing technologies and the tremendous increase in computational power have offered a unique chance to study complex transformations using sophisticated and predictive many-body techniques that describe correlated behavior of electrons in molecular and condensed phase systems at different levels of theory. In enabling these simulations, novel parallel algorithms have been able to take advantage of computational resources to address the polynomial scaling of electronic structure methods. In this paper, we briefly review the NWChem computational chemistry suite, including its history, design principles, parallel tools, current capabilities, outreach, and outlook.

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.

Quantum computation solves a half-century-old enigma: Elusive vibrational states of magnesium dimer found

The high-lying vibrational states of the magnesium dimer (Mg₂), which has been recognized as an important system in studies of ultracold and collisional phenomena, have eluded experimental characterization for half a century. Until now, only the first 14 vibrational states of Mg₂ have been experimentally resolved, although it has been suggested that the ground-state potential may support five additional levels. Here, we present highly accurate ab initio potential energy curves based on state-of-the-art coupled-cluster and full configuration interaction computations for the ground and excited electronic states involved in the experimental investigations of Mg₂. Our ground-state potential unambiguously confirms the existence of 19 vibrational levels, with ~1 cm^-1 root mean square deviation between the calculated rovibrational term values and the available experimental and experimentally derived data. Our computations reproduce the latest laser-induced fluorescence spectrum and provide guidance for the experimental detection of the previously unresolved vibrational levels.

Approximate equation-of-motion coupled-cluster methods for electron affinities of closed-shell molecules

We investigate performance of the equation-of-motion coupled-cluster method at the single and doubles level (EOM-CCSD) and a series of approximate methods based on EOM-CCSD on electron affinities (EA) of closed-shell cations and neutral molecules with positive and negative EAs in this work. Our results confirm that P-EOM-MBPT2 can provide reasonable EAs when molecules with significant multireference character are not considered and its mean absolute error on EAs of these molecules is around or less than 0.2 eV. Its accuracy is comparable to that of the more expensive EOM-CCSD(2) method. Results of EOM-CCSD(2), P-EOM-MBPT2, and CIS(D_∞) indicate that the [[H, a_c ⁺], T₂] term in the 1h2p-1h block is more important on EAs than the term neglected in the 1h2p-1h2p block in P-EOM-MBPT2. We proposed an economical method where EAs from CIS(D_∞) are corrected by treating this [[H, a_c ⁺], T₂] term in the 1h2p-1h block perturbatively [corr-CIS(D_∞)]. EAs with corr-CIS(D_∞) agree very well with those of P-EOM-MBPT2 with a difference of less than 0.02 eV. Computational scaling of this method is N⁴ for the iterative part and N⁵ for some non-iterative steps. Its storage requirement is only of OV³. Corr-CIS(D_∞) is an economical and reliable method on EAs, and it can be applied to EAs of large molecules.

Ab Initio Linear and Pump-Probe Spectroscopy of Excitons in Molecular Crystals

Linear and nonlinear spectroscopies are powerful tools used to investigate the energetics and dynamics of electronic excited states of both molecules and crystals. While highly accurate ab initio calculations of molecular spectra can be performed relatively routinely, extending these calculations to periodic systems is challenging. Here, we present calculations of the linear absorption spectrum and pump-probe two-photon photoemission spectra of the naphthalene crystal using equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD). Molecular acene crystals are of interest due to the low-energy multiexciton singlet states they exhibit, which have been studied extensively as intermediates involved in singlet fission. Our linear absorption spectrum is in good agreement with experiment, predicting a first exciton absorption peak at 4.4 eV, and our two-photon photoemission spectra capture the qualitative behavior of multiexciton states, whose double-excitation character cannot be captured by current methods. The simulated pump-probe spectra provide support for existing interpretations of two-photon photoemission experiments in closely related acene crystals such as tetracene and pentacene.

Quantum algorithm for simulating molecular vibrational excitations

We introduce a quantum algorithm for simulating molecular vibrational excitations during vibronic transitions. The algorithm is used to simulate vibrational excitations of pyrrole and butane during photochemical and mechanochemical excitations.

Proton Abstraction Mediates Interactions between the Super Photobase FR0-SB and Surrounding Alcohol Solvent

We report on the motional and proton transfer dynamics of the super photobase FR0-SB in the series of normal alcohols C1 (methanol) through C8 (n-octanol) and ethylene glycol. Steady-state and time-resolved fluorescence data reveal that the proton abstraction dynamics of excited FR0-SB depend on the identity of the solvent and that the transfer of the proton from solvent to FR0-SB*, forming FR0-HSB⁺*, fundamentally alters the nature of interactions between the excited molecule and its surroundings. In its unprotonated state, solvent interactions with FR0-SB* are consistent with slip limit behavior, and in its protonated form, intermolecular interactions are consistent with a much stronger interaction of FR0-HSB⁺* with the deprotonated solvent RO^-. We understand the excited-state population dynamics in the context of a kinetic model involving a transition state wherein FR0-HSB⁺* is still bound to the negatively charged alkoxide, prior to solvation of the two charged species. Data acquired in ethylene glycol confirm the hypothesis that the rotational diffusion dynamics of FR0-SB* are largely mediated by solvent viscosity while proton transfer dynamics are mediated by the lifetime of the transition state. Taken collectively, our results demonstrate that FR0-SB* extracts solvent protons efficiently and in a predictable manner, consistent with a ca. 3-fold increase in dipole moment upon photoexcitation as determined by ab initio calculations based on the equation-of-motion coupled-cluster theory.

ωB2PLYP and ωB2GPPLYP: The First Two Double-Hybrid Density Functionals with Long-Range Correction Optimized for Excitation Energies

Double-hybrid density functionals are currently the most accurate density functionals for ground-state properties and electronic excitations. Nevertheless, the lack of a long-range correction scheme makes them unreliable when it comes to long-range excitations. For this reason, we propose the first two time-dependent double-hybrid functionals with correct asymptotic long-range behavior named ωB2PLYP and ωB2GPPLYP. Herein, we demonstrate their excellent performance and show that they are the most accurate and robust time-dependent density functional theory methods for electronic excitation energies. They provide a balanced description of local-valence, Rydberg, and charge-transfer states. They are also able to tackle the difficult first two transitions in polycyclic aromatic hydrocarbons and show very promising results in a preliminary study on transition-metal compounds, exemplified for titanium dioxide clusters. This work shows that double hybrids can be systematically improved also for excitation energies, and further work in this field is warranted.

State-Dependent Fragmentation of Protonated Uracil and Uridine

Action spectroscopy using photon excitation in the VUV range (photon energy 4.5-9 eV) was performed on protonated uracil (UraH⁺) and uridine (UrdH⁺). The precursor ions with m/ z 113 and m/ z 245, respectively, were produced by an electrospray ionization source and accumulated inside a quadrupole ion trap mass spectrometer. After irradiation with tunable synchrotron radiation, product ion mass spectra were obtained. Fragment yields as a function of excitation energy show several maxima that can be attributed to the photoexcitation into different electronic states. For uracil, vertically excited states were calculated using the equation-of-motion coupled cluster approach and compared to the observed maxima. This allows to establish correlations between electronic states and the resulting fragment masses and can thus help to disentangle the complex de-excitation and fragmentation pathways of nucleic acid building blocks. Photofragmentation of the nucleoside uridine shows a significantly lower variety of fragments, indicating stabilization of the nucleobase by the attached sugar.