Approximate Coupled Cluster Singles Research Articles

Coupled-cluster treatment of complex open-shell systems: the case of single-molecule magnets.

We investigate the reliability of two cost-effective coupled-cluster methods for computing spin-state energetics and spin-related properties of a set of open-shell transition-metal complexes. Specifically, we employ the second-order approximate coupled-cluster singles and doubles (CC2) method and projection-based embedding that combines equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) with density functional theory (DFT). The performance of CC2 and EOM-CCSD-in-DFT is assessed against EOM-CCSD. The chosen test set includes two hexaaqua transition-metal complexes containing Fe(II) and Fe(III), and a large Co(II)-based single-molecule magnet with a non-aufbau ground state. We find that CC2 describes the excited states more accurately, reproducing EOM-CCSD excitation energies within 0.05 eV. However, EOM-CCSD-in-DFT excels in describing transition orbital angular momenta and spin-orbit couplings. Moreover, for the Co(II) molecular magnet, using EOM-CCSD-in-DFT eigenstates and spin-orbit couplings, we compute spin-reversal energy barriers, as well as temperature-dependent and field-dependent magnetizations and magnetic susceptibilities that closely match experimental values within spectroscopic accuracy. These results underscore the efficiency of CC2 in computing state energies of multi-configurational, open-shell systems and highlight the utility of the more cost-efficient EOM-CCSD-in-DFT for computing spin-orbit couplings and magnetic properties of complex and large molecular magnets.

On the performance of second-order approximate coupled-cluster singles and doubles methods for non-valence anions.

We investigate the capability of several variants of the second-order approximate coupled-cluster singles and doubles (CC2) method to describe dipole-bound, quadrupole-bound, and correlation-bound molecular anions. The binding energy of anions formed by electron attachment to closed-shell molecules is computed using the electron attachment variant of CC2 (EA-CC2), whereas anions with a closed-shell ground state are treated with the standard CC2 method that preserves the number of particles. We find that EA-CC2 captures the binding energies of dipole-bound radical anions quite well, whereas results for other types of non-valence anions are less reliable. We also test the performance of semi-empirical spin-scaling factors for all types of non-valence anions and observe that the spin-scaled CC2 variants generally do not provide more accurate binding energies for dipole-bound anions, while the binding energies of quadrupole-bound and correlation-bound anions are improved. As exemplary applications of EA-CC2, we investigate the dipole-bound anions of the steroids cortisol, progesterone, and testosterone. In addition, we characterize electron attachment to sym-tetracyanonaphthalene, a molecule that supports five anionic states, two of which can be interpreted as hitherto unobserved π-type quadrupole-bound states.

Performance of Common Density Functionals for Excited States of Tetraphenyldibenzoperiflanthene.

Time-dependent density functional theory is the method of choice to efficiently calculate excitation spectra with the functional and basis set choice allowing one to compromise between accuracy and computational cost. In this work, the performance of different functionals as well as the second-order approximate coupled cluster singles and doubles model CC2 is evaluated by comparing the results to experimental results of the example molecule tetraphenyldibenzoperiflanthene (DBP). The choice of the functional has a significant impact on the calculated spectrum of DBP. The performance of a number of different functionals was evaluated, quantified, and, where possible, discussed. The best functional, tuned-CAM-B3LYP, is used to investigate DBP on a surface of hexagonal boron nitride (h-BN). The resulting spectrum shows excellent agreement with experimental results for a monolayer of DBP on h-BN.

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.

Structural changes of 1,2-diphenoxyethane upon electronic excitation from a combined Franck-Condon/rotational constants fit

The geometry changes of the tgt- and the ttt-rotamer of 1,2-diphenoxyethane were determined from a combined fit of line intensities in fluorescence emission spectra, obtained via pumping different vibronic transition, and the changes of rotational constants upon electronic excitation, which were taken from [E.G. Buchanan, P.S. Walsh, D.F. Plusquellic, T.S. Zwier, J. Chem. Phys. 138 (2013) 204313]. The so determined geometry changes are compared to the results of ab initio spin-component-scaled approximate coupled cluster singles and doubles (SCS-CC2) calculations.

Excited States Computation of Models of Phenylalanine Protein Chains: TD-DFT and Composite CC2/TD-DFT Protocols.

The present benchmark calculations testify to the validity of time-dependent density functional theory (TD-DFT) when exploring the low-lying excited states potential energy surfaces of models of phenylalanine protein chains. Among three functionals suitable for systems exhibiting charge-transfer excited states, LC-ωPBE, CAM-B3LYP, and ωB97X-D, which were tested on a reference peptide system, we selected the ωB97X-D functional, which gave the best results compared to the approximate coupled-cluster singles and doubles (CC2) method. A quantitative agreement for both the geometrical parameters and the vibrational frequencies was obtained for the lowest singlet excited state (a ππ* state) of the series of capped peptides. In contrast, only a qualitative agreement was met for the corresponding adiabatic zero-point vibrational energy (ZPVE)-corrected excitation energies. Two composite protocols combining CC2 and DFT/TD-DFT methods were then developed to improve these calculations. Both protocols substantially reduced the error compared to CC2 and experiment, and the best of both even led to results of CC2 quality at a lower cost, thus providing a reliable alternative to this method for very large systems.

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.

A spin-flip variant of the second-order approximate coupled-cluster singles and doubles method.

We report an implementation of a spin-flip variant of the second-order approximate coupled-cluster singles and doubles (CC2) method. The resolution-of-the-identity approximation or, alternatively, Cholesky decomposition are applied to the electron repulsion integrals. We illustrate the performance of the new method by constructing potential energy curves of H2 and HF and by computing singlet-triplet splittings for various diradicals including some binuclear copper complexes that are of interest as molecular magnets. We find that spin-flip CC2 performs very similarly to the spin-flip variant of the algebraic diagrammatic construction scheme for the polarization propagator of second order (ADC(2)). Application to ozone shows that, depending on the reference state used, spin-flip CC2 erroneously predicts a barrierless symmetric dissociation of this molecule. A similar failure was observed in earlier work for spin-conserving CC2. In contrast, spin-flip ADC(2) and coupled-cluster singles and doubles yield qualitatively correct potential energy surfaces for ozone.

Structural changes of 1-(phenylethynyl)naphthalene upon electronic excitation from Franck–Condon fits of several fluorescence emission spectra

The structural changes of 1-(Phenylethynyl)naphthalene (1-PEN) upon excitation from the ground state to the lowest excited singlet state have been assessed from a combined Franck–Condon-Fit of fluorescence emission spectra after excitation of several vibronic bands of 1-PEN and ab initio calculations. An analysis of the infrared spectrum, the laser induced fluorescence (LIF) spectrum and the fluorescence emission spectra is given on the basis of the approximate coupled cluster singles and doubles model (CC2) within the resolution-of-identity approximation and taking spin-component scaling into account. The excited state structure of 1-PEN is found to be planar, with the major geometry changes upon excitation localized in the naphthalene moiety. Electron density shifts from the naphthyl ring to the phenyl ring upon electronic excitation, leading to an increase of the permanent dipole moment of 1-PEN. The lowest electronically excited state of 1-PEN can be labeled as 1Lb-state, with the 1La-state energetically quasi-degenerate. The geometry changes, determined from the Franck–Condon analysis are in agreement with this assignment.

Limitations of perturbative coupled-cluster approximations for highly accurate investigations of Rb2+

We reveal limitations of several standard coupled-cluster (CC) methods with perturbation-theory based noniterative or approximate iterative treatments of triple excitations when applied to the determination of highly accurate potential energy curves (PECs) of ionic dimers, such as the XΣg+2 electronic ground state of Rb2 +. Such computations are of current interest for the understanding of ion-atom interactions in the ultracold regime. We demonstrate that these CC methods lead to an unphysical long-range barrier for the Rb2 + system. The barrier is small but spoils the long-range behavior of the PEC. The effect is also found for other X2 + systems, such as X = Li, Na, and K. Calculations using a flexible framework for obtaining leading perturbative triples corrections derived using an analytic CC singles and doubles energy derivative formulation demonstrate that the origin of this problem lies in the use of T̂3 amplitudes obtained from approximate CC singles, doubles, and triples amplitude equations. It is shown that the unphysical barrier is related to a symmetry instability of the underlying Hartree-Fock mean-field solution, leading to orbitals representing two +0.5-fold charged ions in the limit of separated fragments. This, in turn, leads to a wrong 1/R asymptote of the interaction potential computed by perturbation-based CC approximations. Physically meaningful perturbative corrections in the long-range tail of the PEC may instead be obtained using symmetry-broken reference determinants.

Simulation and Analysis of the Transient Absorption Spectrum of 4-(N,N-Dimethylamino)benzonitrile (DMABN) in Acetonitrile.

4-(N,N-Dimethylamino)benzonitrile (DMABN) is a well-known model compound for dual fluorescence—in sufficiently polar solvents, it exhibits two distinct fluorescence emission bands. The interpretation of its transient absorption (TA) spectrum in the visible range is the subject of a long-standing controversy. In the present study, we resolve this issue by calculating the TA spectrum on the basis of nonadiabatic molecular dynamics simulations. An unambiguous assignment of spectral signals to specific excited-state structures is achieved by breaking down the calculated spectrum into contributions from twisted and nontwisted molecular geometries. In particular, the much-discussed excited-state absorption band near 1.7 eV (ca. 700 nm) is attributed to the near-planar locally excited (LE) minimum on the S1 state. On the technical side, our study demonstrates that the second-order approximate coupled cluster singles and doubles (CC2) method can be used successfully to calculate the TA spectra of moderately large organic molecules, provided that the system in question does not approach a crossing between the lowest excited state and the singlet ground state within the time frame of the simulation.

Geometry dependence of excitonic couplings and the consequences for configuration-space sampling.

Excitonic coupling plays a key role for the understanding of excitonic energy transport (EET) in, for example, organic photovoltaics. However, the calculation of realistic systems is often beyond the applicability range of accurate wavefunction methods so that lower-scaling semi-empirical methods are used to model EET events. In the present work, the distance and angle dependence of excitonic couplings of dimers of selected organic molecules are evaluated for the semi-empirical long-range corrected density functional based tight binding (LC-DFTB) method and spin opposite scaled second order approximate coupled cluster singles and doubles (SOS-CC2). While semi-empirically scaled methods can lead to slightly increased deviations for excitation energies, the excitonic couplings and their dependence on the dimer geometry are reproduced. LC-DFTB yields a similar accuracy range as density-functional theory (DFT) employing the ωB97X functional while the computation time is reduced by several orders of magnitude. The dependence of the exchange contributions to the excitonic couplings on the dimer geometry is analyzed assessing the calculation of Coulombic excitonic couplings from monomer local excited states only, which reduces the computational effort significantly. The present work is a necessary first step toward the simulation of excitonic energy transport using semi-empirical methods.

Spin contamination in MP2 and CC2, a surprising issue

When calculating the spin multiplicity at either the second-order Møller-Plesset (MP2) or the iterative second-order approximate coupled-cluster singles and doubles (CC2) levels of theory using the same strategy for the calculation of the expectation value as in regular CC theory together with the usual definitions of the MP2 and CC2 density matrices, artificial spin contamination occurs in closed-shell molecules. Non-intuitively, for open-shell systems, results at the MP2 or CC2 levels of theory based on this procedure even suggest stronger contamination at the correlated level than for the Hartree-Fock reference, although treatment of electron correlation should lower spin contamination. In this Communication, the reasons behind this inconsistency are investigated and a solution is proposed, which removes spin contamination for closed-shell molecules and leads to physically meaningful results for open-shell cases. Additionally, we show that CC2 significantly outperforms MP2 in describing systems with a strongly spin-contaminated reference with a performance similar to that of full coupled-cluster with singles and doubles substitutions (CCSD).

A quantum chemical study of excited states and thermally activated delayed fluorescence in tetracyanoquinodimethane

It has recently been reported that tetracyanoquinodimethane (TCNQ) shows thermally activated delayed fluorescence (TADF). Here, we report quantum chemical study using the second-order approximate coupled-cluster singles and doubles (CC2) calculations to understand the excitation energy and the optimized geometry for the excited singlet and triplet states. The ground state geometry is optimized with the CC2 and second-order Møller-Plesset perturbation theory. The spin–orbit coupling (SOC) matrix elements computed by time-dependent density functional theory show that the electronic coupling via SOC between the S1 state and the triplet state is small. The contribution of the intersystem crossing between the singlet and triplet states to the TADF process is not suggested by the calculations. The adiabatic energy gap between the ground and T1 states for TCNQ is predicted to be 0.98 eV.

Structural changes upon electronic excitation in 1,3-dimethoxybenzene from Franck-Condon/rotational constants fits of the fluorescence emission spectra[formula omitted

The geometry changes of two rotamers of 1,3-dimethoxybenzene were determined from a combined fit of line intensities in fluorescence emission spectra, obtained via pumping different vibronic transition and the changes of rotational constants upon electronic excitation. The so determined changes are compared to the results of ab initio approximate coupled cluster singles and doubles (CC2) calculations. The bond length variations in the aromatic ring follow the calculated electron density differences from the coupled cluster wavefunctions and are in agreement with excitation to an 1Lb-state for the C2v symmetric B-conformer.

Comparison of Reaction Field Schemes for Coupling Continuum Solvation Models with Wave Function Methods for Excitation Energies.

We address in this work the question to which extend reaction field schemes for correlated wave function methods give accurate excitation energies and, at the same time, physically consistent potential energy surfaces. The performance of the perturbation on energy (PTE), perturbation on energy and density (PTED), and post-SCF reaction field schemes is compared for the algebraic diagrammatic construction through second-order, ADC(2), as electronic structure and the conductor-like screening model COSMO as solvation model. The conditions on reaction field schemes to give physically consistent potential energies surfaces are discussed at the example of 4-(N,N-dimethylamino)benzonitrile, which is used as a test case to assess the artifacts introduced by state-specific contributions to the effective Hamiltonian. To evaluate the accuracy for excitation energies, we use two benchmark sets with data in gas phase and solution for ππ* and nπ* electronic transitions. The experimental solvatochromic shifts are compared to the corresponding calculated values at the COSMO-ADC(2) level with the PTE scheme within the frozen solvent approximation, PTED with the linear response (LR) and corrected linear response (cLR) and post-SCF with LR schemes and with the approximate coupled-cluster singles and doubles method CC2 combined with COSMO in the post-SCF (LR) scheme. The PTE scheme gives at the COSMO-ADC(2) level less accurate solvent shifts than the PTED(LR), PTED(cLR), and post-SCF(LR) schemes. The most accurate prediction of solvatochromism is obtained with the post-SCF(LR) scheme. In most cases, PTED(cLR) performs similar to post-SCF, although its nonlinear perturbative correction causes problems for potential energy surfaces.

Analytical nuclear gradients for electron-attached and electron-detached states for the second-order algebraic diagrammatic construction scheme combined with frozen-density embedding

In the present work, we report the derivation and implementation of vertical ionization potentials (IPs) and electron affinities (EAs) for embedded wavefunction methods as well as the corresponding analytical nuclear gradients. Vertical transitions have been implemented for CIS(D∞), the second-order algebraic diagrammatic construction [ADC(2)] scheme, and the second-order approximate coupled-cluster singles and doubles method. For all methods, density fitting is applied to facilitate reduced memory and disk storage requirements. Analytical nuclear gradients have been derived and implemented for CIS(D∞) and ADC(2) both with and without frozen-density embedding (FDE). The objective of the reported method is to study the properties of organic semiconductors in which charge is transported along molecular stacks in molecular crystals. The accuracy of the implemented methods is, therefore, assessed using stacked dimers of small model systems. Albeit second-order methods can yield noticeable errors with respect to reference methods in terms of absolute IP and EA values, they show a significantly improved accuracy for the shift of the IP and EA values at different intermolecular distances relative to the monomers. Besides reducing the computational costs, the FDE ansatz introduces furthermore a significant conceptual difference as it enables control over which subsystem is ionized, allowing for the calculation of transfer integrals for the interacting (embedded) systems. The new implementation is finally applied to tetraazaperopyrenes, used as organic semiconductors, to study charge-localization and long-range polarization in particular.

How accurate are TD-DFT excited-state geometries compared to DFT ground-state geometries?

In this work, we take a different angle to the benchmarking of time-dependent density functional theory (TD-DFT) for the calculation of excited-state geometries by extensively assessing how accurate such geometries are compared to ground-state geometries calculated with ordinary DFT. To this end, we consider 20 medium-sized aromatic organic compounds whose lowest singlet excited states are ideally suited for TD-DFT modeling and are very well described by the approximate coupled-cluster singles and doubles (CC2) method, and then use this method and six different density functionals (BP86, B3LYP, PBE0, M06-2X, CAM-B3LYP, and ωB97XD) to optimize the corresponding ground- and excited-state geometries. The results show that although each hybrid functional reproduces the CC2 excited-state bond lengths very satisfactorily, achieving an overall root mean square error of 0.011 Å for all 336 bonds in the 20 molecules, these errors are distinctly larger than those of only 0.004-0.006 Å with which the hybrid functionals reproduce the CC2 ground-state bond lengths. Furthermore, for each functional employed, the variation in the error relative to CC2 between different molecules is found to be much larger (by at least a factor of 3) for the excited-state geometries than for the ground-state geometries, despite the fact that the molecules/states under investigation have rather uniform chemical and spectroscopic character. Overall, the study finds that even in favorable circumstances, TD-DFT excited-state geometries appear intrinsically and comparatively less accurate than DFT ground-state ones.

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.

Noniterative Doubles Corrections to the Random Phase and Higher Random Phase Approximations: Singlet and Triplet Excitation Energies.

The second‐order noniterative doubles‐corrected random phase approximation (RPA) method has been extended to triplet excitation energies and the doubles‐corrected higher RPA method as well as a shifted version for calculating singlet and triplet excitation energies are presented here for the first time. A benchmark set consisting of 20 molecules with a total of 117 singlet and 71 triplet excited states has been used to test the performance of the new methods by comparison with previous results obtained with the second‐order polarization propagator approximation (SOPPA) and the third order approximate coupled cluster singles, doubles and triples model CC3. In general, the second‐order doubles corrections to RPA and HRPA significantly reduce both the mean deviation as well as the standard deviation of the errors compared to the CC3 results. The accuracy of the new methods approaches the accuracy of the SOPPA method while using only 10–60% of the calculation time. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.