CC2 Methods Research Articles

Stochastic Resolution of Identity to CC2 for Large Systems: Excited State Properties.

We apply a stochastic resolution of identity approximation (sRI) to the CC2 method for the excitation energy calculations. A set of stochastic orbitals are employed to decouple the crucial 4-index electron repulsion integrals and optimize the contraction steps in CC2 response theory. The CC2 response for excitations builds upon sRI-CC2 ground-state calculations, which scales as O(N3), where N is a measure for the system size. Overall, the current algorithm for excited states also allows a sharp scaling reduction from original O(N5) to O(N3). We test the sRI-CC2 for different molecular systems and basis sets, and we show that our sRI-CC2 method can accurately reproduce the results of the deterministic CC2 approach. Our sRI-CC2 exhibits an experimental scaling of O(N2.59) for a series of olefin chains, allowing us to calculate systems with nearly thousands of electrons.

Effect of meso-pentafluorophenyl group on two-photon absorption in heterocorroles and heterocorrins.

Owing to their high reactivity, the meso-positions of corroles and corrins are usually protected by some bulky groups. These groups in addition to the said purpose may also affect the photophysical properties of such systems. However, there is no systematic study in the literature exploring this effect. In this work, we target to answer how the meso-substitution affects the photophysical properties in some heterocorroles and heterocorrins. We considered one of the commonly used substitutions, i.e., pentafluorophenyl (-PFPh), at meso positions of 26 heterocorroles and heterocorrins. We employed the state-of-the-art CC2 method in conjunction with resolution-of-identity approximation to study the charge-transfer and one- and two-photon absorption in these systems. It is further explored using a four-state model that helps in understanding the contribution of various transition dipole moments and their relative orientation. At the end, we also investigated the effect of other substitutions such as -CH3, -CF3, -C2H3, -OMe, -phenyl, and -tolyl on two-photon activity.

Experimental and theoretical study of the cytosine tautomerism through excited states.

The irradiation of water solution of cytosine with UV light (λmax = 254nm) shows oxo-hydroxy tautomerism with a rate constant of 6.297 × 10-3min-1. The order of the reaction implies a tautomeric conversion. After removing the UV light source, we observed a dark reaction with a rate constant of 1.473 × 10-3min-1 which leads to a restoration of the initial tautomer as before the irradiation. The mechanism of oxo-hydroxy tautomerism of cytosine in water solution was studied in the excited state. It was found that the transformations occur along the 1πσ* excited-state reaction paths which link the Franck-Condon geometries of the tautomers and the conical intersections S0/S1 connected with the H-detachment processes of the corresponding bonds. Furthermore, we established that the conical intersections S0/S1 are also mutually accessible along the 1πσ* excited-state reaction paths. The ground-state equilibrium geometries were optimized at the B3LYP/aug-cc-pVDZ level of theory in water environment according to PCM as well as at the CC2/aug-cc-pVDZ level in the gas phase. The TD B3LYP and CC2 methods were applied for the study of the excited states. The tautomerization mechanisms were studied with the use of the linear interpolation in internal coordinates approach using the optimized geometries of tautomers minima and conical intersections S0/S1 at the CASSCF(6,6)/6-31G* level. All calculations were performed with the GAUSSIAN 16 commercial software.

New Implementation of an Equation-of-Motion Coupled-Cluster Damped-Response Framework with Illustrative Applications to Resonant Inelastic X-ray Scattering

We present an implementation of a damped response framework for calculating resonant inelastic X-ray scattering (RIXS) at the equation-of-motion coupled-cluster singles and doubles (CCSD) and second-order approximate coupled-cluster singles and doubles (CC2) levels of theory in the open-source program eT. This framework lays the foundation for future extension to higher excitation methods (notably, the coupled-cluster singles and doubles with perturbative triples, CC3) and to multilevel approaches. Our implementation adopts a fully relaxed ground state and different variants of the core-valence separation projection technique to address convergence issues. Illustrative results are compared with those obtained within the frozen-core core-valence separated approach, available in Q-Chem, as well as with experiment. The performance of the CC2 method is evaluated in comparison with that of CCSD. It is found that, while the CC2 method is noticeably inferior to CCSD for X-ray absorption spectra, the quality of the CC2 RIXS spectra is often comparable to that of the CCSD level of theory, when the same valence excited states are probed. Finally, we present preliminary RIXS results for a solvated molecule in aqueous solution.

Triple electron-electron-proton excitations and second-order approximations in nuclear-electronic orbital coupled cluster methods.

The accurate description of nuclear quantum effects, such as zero-point energy, is important for modeling a wide range of chemical and biological processes. Within the nuclear-electronic orbital (NEO) approach, such effects are incorporated in a computationally efficient way by treating electrons and select nuclei, typically protons, quantum mechanically with molecular orbital techniques. Herein, we implement and test a NEO coupled cluster method that explicitly includes the triple electron-electron-proton excitations, where two electrons and one proton are excited simultaneously, using automatic differentiation Our calculations show that this NEO-CCSDTeep method provides highly accurate proton densities and proton affinities, outperforming any previously studied NEO method. These examples highlight the importance of the triple electron-electron-proton excitations for an accurate description of nuclear quantum effects. Additionally, we also implement and test the second-order approximate coupled cluster with singles and doubles (NEO-CC2) method as well as its scaled-opposite-spin (SOS) versions. The NEO-SOS'-CC2 method, which scales the electron-proton correlation energy as well as the opposite-spin and same-spin components of the electron-electron correlation energy, achieves nearly the same accuracy as the NEO-CCSDTeep method for the properties studied. Because of its low computational cost, this method will enable a wide range of chemical and photochemical applications for large molecular systems. This work sets the stage for a variety of developments and applications within the NEO framework.

A similarity transformed second-order approximate coupled cluster method for the excited states: Theory, implementation, and benchmark.

We present a novel and cost-effective approach of using a second similarity transformation of the Hamiltonian to include the missing higher-order terms in the second-order approximate coupled cluster singles and doubles (CC2) model. The performance of the newly developed ST-EOM-CC2 model has been investigated for the calculation of excitation energies of valence, Rydberg, and charge-transfer excited states. The method shows significant improvement in the excitation energies of Rydberg and charge-transfer excited states as compared to the conventional CC2 method while retaining the good performance of the latter for the valence excited state. This method retains the charge-transfer separability of the charge-transfer excited states, which is a significant advantage over the traditional CC2 method. A second order many-body perturbation theory variant of the new method is also proposed.

Optical Spectra of Oligofurans: A Theoretical Approach to the Transition Energies, Reorganization Energies, and the Vibronic Activity.

There is experimental evidence of high vibronic activity that accompanies the allowed transition between the ground state and the lowest electronic singlet excited state of oligofurans that contain two, three, and four furan rings. The absorption and emission spectra of the three lowest oligofurans measured at liquid nitrogen temperature show distinct fine structures that are reproduced using the projection-based model of vibronic coupling (with Dushinsky rotation included) parameterized utilizing either Density Functional Theory (DFT, with several different exchange-correlation functionals) or ab initio (CC2) quantum chemistry calculations. Using as a reference the experimental data concerning the electronic absorption and fluorescence for the eight lowest oligofurans, we first analyzed the performance of the exchange-correlation functionals for the electronic transition energies and the reorganization energies. Subsequently, we used the best functionals alongside with the CC2 method to explore how the reorganization energies are distributed among the totally symmetric vibrations, identify the normal modes that dominate in the fine structures present in the absorption and emission bands, and trace their evolution with the increasing number of rings in the oligofuran series. Confrontation of the simulated spectra with the experiment allows for the verification of the performance of the selected DFT functionals and the CC2 method.

How to Predict Excited State Geometry by Using Empirical Parameters Obtained from Franck-Condon Analysis of Optical Spectrum.

Excited state geometries of molecules can be calculated with highly reliable wavefunction schemes. Most of such schemes, however, are applicable to small molecules and can hardly be viewed as error-free for excited state geometries. In this study, a theoretical approach is presented in which the excited state geometries of molecules can be predicted by using vibrationally resolved experimental absorption spectrum in combination with the theoretical modelling of vibrational pattern based on Franck-Condon approximation. Huang-Rhys factors have been empirically determined and used as input for revealing the structural changes occurring between the ground and the excited state geometries upon photoexcitation. Naphthalene molecule has been chosen as a test case to show the robustness of the proposed theoretical approach. Predicted 1B2u excited state geometry of the naphthalene has similar but slightly different bond length alternation pattern when compared with the geometries calculated with CIS, B3LYP, and CC2 methods. Excited state geometries of perylene and pyrene molecules are also determined with the presented theoretical approach. This powerful method can be applied to other molecules and specifically to relatively large molecules rather easily as long as vibrationally resolved experimental spectra are available to use.

Model protein excited states: MRCI calculations with large active spaces vs CC2 method.

Benchmarking calculations on excited states of models of phenylalanine protein chains are presented to assess the ability of alternative methods to the standard and most commonly used multiconfigurational wave function-based method, the complete active space self-consistent field (CASSCF), in recovering the non-dynamical correlation for systems that become not affordable by the CASSCF. The exploration of larger active spaces beyond the CASSCF limit is benchmarked through three strategies based on the reduction in the number of determinants: the restricted active space self-consistent field, the generalized active space self-consistent field (GASSCF), and the occupation-restricted multiple active space (ORMAS) schemes. The remaining dynamic correlation effects are then added by the complete active space second-order perturbation theory and by the multireference difference dedicated configuration interaction methods. In parallel, the approximate second-order coupled cluster (CC2), already proven to be successful for small building blocks of model proteins in one of our previous works [Ben Amor et al., J. Chem. Phys. 148, 184105 (2018)], is investigated to assess its performances for larger systems. Among the different alternative strategies to CASSCF, our results highlight the greatest efficiency of the GASSCF and ORMAS schemes in the systematic reduction of the configuration interaction expansion without loss of accuracy in both nature and excitation energies of both singlet ππ* and nπ* CO excited states with respect to the equivalent CASSCF calculations. Guidelines for an optimum applicability of this scheme to systems requiring active spaces beyond the complete active space limit are then proposed. Finally, the extension of the CC2 method to such large systems without loss of accuracy is demonstrated, highlighting the great potential of this method to treat accurately excited states, mainly single reference, of very large systems.

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.

An Ab Initio Computational Study of Electronic and Structural Factors in the Isomerization of Donor-Acceptor Stenhouse Adducts.

In this work, the photochemically and thermally induced isomerization of multiple donor-acceptor Stenhouse adducts (DASAs) of the first, second, and third generation is studied by means of state-of-the-art ab initio electronic structure methods leading to new insight into multiple facets of the reaction mechanism. Importantly, prior to any studies of the reaction mechanism, a set of test calculations demonstrate the suitability of the applied ADC(2) and CC2 methods in the present context. An important aspect in this regard is the availability of electronic energies and gradients under implicit consideration of solvent effects. On the basis of calculated reaction energies and barriers as well as a thorough analysis of the wave function compositions, interesting features of the reaction mechanism are deduced. For example, the closed form of second- and third-generation DASAs can be significantly stabilized by π - π interactions between the donor and acceptor termini when certain structural requirements are fulfilled. The central point of this work concerns the delicate balance between neutral and zwitterionic resonance structures that governs the relative barrier height for the crucial C2-C3 and C3-C4 bond rotations. Finally, a set of calculations on yet unreported derivatives highlights how this balance and hence the barrier heights can be tuned through variation of the donor-acceptor strength as well as the solvent polarity.

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.

Benchmarking Correlated Methods for Frequency-Dependent Polarizabilities: Aromatic Molecules with the CC3, CCSD, CC2, SOPPA, SOPPA(CC2), and SOPPA(CCSD) Methods.

A benchmark study of several correlated second-order methods for frequency-dependent polarizabilities has been carried out. For the benchmark, a set of 14 (hetero)aromatic medium-sized molecules has been chosen. For the first time, CC3 polarizabilities are reported for these molecules using Sadlej's polarized triple-ζ basis set, and for a subset of these molecules the polarizabilities were obtained at the CC3 level also with the larger aug-cc-pVTZ basis set. These CC3 values are used as the reference values for benchmarking the second-order methods: SOPPA, SOPPA(CC2), SOPPA(CCSD), CC2, as well as CCSD. The influence of different basis sets, aug-cc-pVDZ, aug-cc-pVTZ, aug-cc-pVQZ, d-aug-cc-pVTZ, and Sadlej's polarized triple-ζ basis set, on static and frequency-dependent polarizabilities was investigated for the full set of molecules at the SOPPA level. It was found that the choice of basis set had a somewhat greater influence on the frequency-dependent polarizabilities than on the static polarizabilities, but all effects were small. The aug-cc-pVTZ basis set performed adequately for both static and frequency-dependent polarizabilities, having an insignificant offset from the values obtained with the larger d-aug-cc-pVTZ and aug-cc-pVQZ basis sets. Comparing the second-order methods, SOPPA, SOPPA(CC2), SOPPA(CCSD), CC2, as well as CCSD, to the CC3 reference values, it was found that the best performing method was CCSD, as expected. The SOPPA method, on the contrary, outperformed the CC2 method, suggesting the use of SOPPA rather than CC2 for polarizabilities, at least for these kinds of molecules. The SOPPA results were found to improve further when the Møller-Plesset correlation coefficients in the wave function were replaced by coupled-cluster amplitudes in the SOPPA(CC2) and SOPPA(CCSD) methods. Finally, a comparison was made for a small subset of the molecules between experimental data and calculated polarizabilities. It shows that, for this set of molecules, the trend in the performance of the different second-order methods does not depend on whether the reference values are calculated CC3 values or experimental values.

CC2 Benchmark for Models of Phenylalanine Protein Chains: 0-0 Transition Energies and IR Signatures of the ππ* Excited State.

Extensive benchmarking calculations are presented to assess the accuracy of the standard approximate coupled cluster singles and doubles method (CC2) in studying ππ* excited states properties of model protein chains containing a phenylalanine residue, namely capped peptides, whose ground state conformers adopt the prototypical secondary structural features of proteins. First, the dependence with the basis set of the CC2 excitation energies, CC2 geometry optimizations, and amide A region frequencies of the lowest ππ* excited state in a reference system, the N-acetylphenylalaninylamide, are investigated, and the results are compared with experimental data. Second, at the best level of theory determined, the CC2/aug(N,O,π)-cc-pVDZ//CC2/cc-pVDZ level, a series of capped peptides of increasing size and containing residues of different nature are investigated. Along the series, compared to the experimental values, a mean absolute error of 0.10 eV is achieved for the 0-0 transition energies with a systematic overestimation. In addition, mode-dependent linear scaling functions for the calculated frequencies of the amide A region have been determined from the set of 95 experimental frequencies available; they lead to a quantitative simulation of the observed shifts of the amide A region frequencies upon ππ* excitation (root-mean-square deviation of 5 cm-1). These results confirm the reliability of the CC2 method to characterize the lowest ππ* excited state of such medium-sized systems, emphasizing this class of theoretical approaches as a relevant spectroscopic tool, including for tasks as difficult as conformational assignment.

Accuracy of Spin-Component Scaled ADC(2) Excitation Energies and Potential Energy Surfaces.

In a recent paper of this journal ( Tajti ; ; Szalay . J. Chem. Theory Comput. 2019 , 15 , 5523 ), we have shown that failures of the CC2 method to describe Rydberg excited states as well as potential energy surfaces of certain valence excited states can be cured by spin-component scaled (SCS) versions SCS-CC2 and SOS-CC2 to a large extent. In this paper, the related and popular second-order algebraic diagrammatic construction (ADC(2)) method and its SCS variants are inspected with the previously established methodology. The results reflect the similarity of the CC2 and ADC(2) models, showing identical problems in the case of the canonical form and the same improvement when spin-component scaling is applied.

Multilevel CC2 and CCSD Methods with Correlated Natural Transition Orbitals.

In the multilevel coupled cluster approach, an active orbital space is treated at a higher level of coupled cluster theory than the remaining inactive orbitals. We introduce the multilevel CC2 method where CC2 is used for the active orbital space. Furthermore, we present a simplified formulation of the multilevel CCSD method where CCSD is used for the active space. The simplification lies in the evaluation of the CC2 amplitudes in the inactive space; these CC2 amplitudes have previously been determined iteratively. We use correlated natural transition orbitals to determine the active orbital spaces. The convergence of the multilevel CC2 and multilevel CCSD valence excitation energies is established with proof-of-concept calculations. The methods are also applied to two larger systems: p-nitroaniline in water and amoxicillin. The calculations on the p-nitroaniline-water system illustrate the usefulness of multilevel coupled cluster methods for molecules in solution and for charge transfer excitations.

Consistent Franck–Condon modeling of geometry changes for the S0→S1(ππ*) excitation in anthranilic acid: LIF spectroscopy aided by CC2 or TDDFT vibrations

Experimentally-based evaluation of the changes of equilibrium geometry for the S0→S1(ππ*) excitation in anthranilic acid via fitting of Franck–Condon factors is tested for reliability. The modeling is based on the experimental band intensities in the LIF spectrum that are transformed into geometry changes with the aid of the vibrational modes computed using both the CC2 method (the perturbative approximation to CCSD coupled-cluster) and TDDFT(B3LYP). This modeling is a challenging task not only for quantitative spectroscopy, but also for the quantum chemistry calculations, since the adequate reproduction of vibrational modes for the excited state requires a balanced treatment of the π-electronic conjugation and dynamic electron correlation. The most reliable approach (LIF+CC2 Franck–Condon fitting) predicts a dramatic shortening of the O···H distance by 31 ± 1.5 pm, from 1.91 Å in the ground state to 1.60 Å in the excited state. The changes in bond alternation in the H-chelate ring (around 5 pm according to the LIF+CC2 fit) and the shortening of the O···H bond are typically 1 pm larger than modeled with the LIF+TDDFT fit. Changes of valence angles of magnitude around 5° are larger by 0.5°-1.0° according to LIF+CC2 FC fit than the LIF+DFT fit. Consistency of the obtained results shows that the Franck-Condon fitting provides a reliable, experimentally-based approach to evaluation of the excitation-related geometry changes. It has been achieved owing to the quantitatively reliable spectroscopic results and vibrational analysis computed using the quantum chemistry methods that are able to provide correct description of the excited-state vibrational modes involving the intramolecular hydrogen bond.

Theoretical insights on nonradiative deactivation mechanisms of protonated xanthine

The nonradiative deactivation mechanisms of the lowest 1ππ excited states in four protonated isomers of the 7H- and 9H-xanthine, based on the MP2, CC2, ADC(2) and CASSCF theoretical methods have been investigated. It has been predicted that out-of-plane driving coordinates are effectively responsible for photostability of these systems at the Franck-Condon region of the 1ππ* excited state, while the NH or OH stretching coordinates can be suggested to play the deactivation role in the higher energetic range based on the 1πσ* state. The different deactivation mechanisms provide significant supports for photostability of protonated xanthine in the wide range of UV radiation as well as its neutral homologue. Also, from spectroscopy points of view, no significant alteration in the 1ππ*-S0 electronic transition has been predicted to occur following protonation.

Ab Initio Study of Phosphorescence of Hetero[8]Circulenes

Quantum chemical calculations of phosphorescence lifetime are performed for the first time by ab initio CC2 and TD-DFT methods for hetero[8]circulenes bearing Si and Ge atoms. According to the results of calculations, a lower value of τphos for tetragermatetrathia[8]circulene (II) originates from two factors: almost 29 times more distorted main macrocycle II and almost four times larger spin-orbit coupling matrix element between T1 and S0 by virtue of heavier Ge atoms as compared to Si. The τphos values calculated by CC2 ideally agree with its experimental value; the difference is less than 2 and 0.3 s for tetrasilatetrathia[8]circulene (I) and tetragermatetrathia[8]circulene (II) molecules, respectively. The agreement of the lifetimes calculated by TD-DFT is only within an order of magnitude. The main intramolecular decay channel of the T1 state is internal conversion between T1 and S0 owing to simultaneous spin-orbit and nonadiabatic interaction of their wavefunctions.

Predicting absorption spectra of silver‐ligand complexes

AbstractThe detailed structures of most of ligand‐stabilized metal nanoclusters (NCs) remain unknown due to the absence of crystal structure data for them. In such a situation, quantum‐chemical modeling is of particular interest. We compared the performance of different theoretical methods of geometry optimization and absorption spectra calculation for silver‐thiolate complexes. We showed that the absorption spectra calculated with the ADC(2) method were consistent with the spectra obtained with CC2 method. Three DFT functionals (B3LYP, CAM‐B3LYP, and M06‐2X) failed to reproduce the CC2 absorption spectra of the silver‐thiolate complexes.