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The iterative subspace algorithm to solve the complex linear response equation of damped coupled cluster response theory presented, up to CCSD level, by Kauczor et al., J. Chem. Phys., 2013, 139, 211102, and recently extended to the solution of the complex left response multipliers by Faber and Coriani, J. Chem. Theory Comput., 2019, 15, 520, has been modified to include a core-valence separation projection step in the iterative procedure. This allows one to overcome serious convergence issues that specifically manifest themselves at the CCSD level when addressing core-related spectroscopic effects using large basis sets. The spectra, obtained adopting the new scheme for X-ray absorption and circular dichroism, as well as resonant inelastic-X-ray scattering, are presented and discussed. Core-valence separated results for non-resonant X-ray emission are also reported.

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.

The absorption and magnetic circular dichroism (MCD) spectra of purine and of the purine nucleobases adenine and guanine have been calculated in gas phase at the Coupled Cluster Singles and Doubles (CCSD) and Resolution-of-Identity Singles and Approximate Doubles (RI-CC2) levels of theory. Exploiting a new development in the Turbomole program package for computing vertical excitation energies and Faraday B terms in an implicit solvent approximated by the conductor-like screening model (COSMO) at the CC2 level, we have investigated the solvent effects on the relative positions of the ππ∗ and nπ∗ electronic transitions in these three molecules and compared them to the corresponding vacuum results. In the case of adenine we included also specific solvent effects with a small water cluster. The spectra obtained with the implicit model COSMO are in qualitative agreement with those obtained with explicit water molecules both with and without inclusion of the bulk solvent effects via the continuum solvent model. This suggests that the inclusion of the electrostatic contributions of the solvent can provide a sufficiently accurate description of the absorption spectra for adenine. The results for purine, adenine, and guanine show that after the inclusion of bulk solution the ππ ∗ states shift to lower energies while at the same time nπ∗ states show a reversed behavior. The computed MCD spectra show the characteristic bi-signate profile found experimentally in all cases, despite, for adenine, remarkable differences in the origin of the individual peaks for different computational methods. Therefore, the ability (or inability) of MCD for determining the relative stability of the La and Lb states is critically re-assessed. According to our best estimate for adenine in aqueous solution the La state is more stable than Lb.

A coupled cluster protocol rooted in damped response theory is presented for computing Resonant Inelastic X-ray Scattering spectra of molecules in gas-phase. Working equations are reported for both linear (i.e., equation-of-motion) and nonlinear parametrizations of the coupled-cluster wave function response. A simple scheme to compute nonresonant X-ray Emission Spectra is also proposed. Illustrative results are presented for water.

The Dalton Project provides a uniform platform access to the underlying full-fledged quantum chemistry codes Dalton and LSDalton as well as the PyFraME package for automatized fragmentation and parameterization of complex molecular environments. The platform is written in Python and defines a means for library communication and interaction. Intermediate data such as integrals are exposed to the platform and made accessible to the user in the form of NumPy arrays, and the resulting data are extracted, analyzed, and visualized. Complex computational protocols that may, for instance, arise due to a need for environment fragmentation and configuration-space sampling of biochemical systems are readily assisted by the platform. The platform is designed to host additional software libraries and will serve as a hub for future modular software development efforts in the distributed Dalton community.

A computational expression for the Faraday A term of magnetic circular dichroism (MCD) is derived within coupled cluster response theory and alternative computational expressions for the B term are discussed. Moreover, an approach to compute the (temperature-independent) MCD ellipticity in the context of coupled cluster damped response is presented, and its equivalence with the stick-spectrum approach in the limit of infinite lifetimes is demonstrated. The damped response approach has advantages for molecular systems or spectral ranges with a high density of states. Illustrative results are reported at the coupled cluster singles and doubles level and compared to time-dependent density functional theory results., Submitted to J. Chem. Phys. on May 10, 2020

NMR shielding and spin–spin coupling constants of cis and trans isomers of FNNF have been determined to near-quantitative accuracy from ab initio calculations. The FNNF system, containing multiple N–F bonds and fluorine atoms, provides a severe test of computational methods. Coupled-cluster methods were used with large basis sets and complete basis set (CBS) extrapolations of the equilibrium geometry results, with vibrational and relativistic corrections. Shielding constants were calculated with basis sets as large as aug-cc-pCV7Z, together with coupled-cluster expansions up to CCSDT, at the all-electron CCSD(T)/aug-cc-pCVQZ optimized geometries. Spin–spin coupling constants have been determined with specialized versions of the correlation consistent basis sets ccJ-pVXZ, further augmented with diffuse functions. All-electron coupled-cluster methods up to CC3 were applied in these calculations. The results of this work highlight the application of state-of-the-art theoretical techniques, and provide the most accurate NMR properties of FNNF to date, which can serve to guide and supplement NMR experimentation.

We present a novel approach for computing resonant inelastic X-ray scattering (RIXS) cross sections within the equation-of-motion coupled-cluster (EOM-CC) framework. The approach is based on recasting the sum-over-states expressions for RIXS moments into closed-form expressions by using damped response theory. Damped response formalism allows one to circumvent problems of divergent behavior of response equations in the resonant regime. However, the convergence of response equations in the X-ray frequency range is often erratic due to the electronically metastable (i.e., resonant) nature of the virtual core-excited states embedded in the valence ionization continuum. We circumvent this problematic behavior by extending the core–valence separation (CVS) scheme, which decouples the valence-excited and core-excited configurations of the excitation manifold, into the response domain. The accuracy of the CVS-enabled damped response theory, implemented within the EOM-EE-CCSD (EOM-CC for excitation energies with single and double excitations) framework, is assessed by comparison against standard damped EOM-EE-CCSD response calculations. The capabilities of the new approach are illustrated by calculations of RIXS cross sections for benzene and benzene radical cation.

We present a novel approach for computing resonant inelastic X-ray scattering (RIXS) cross sections within the equation-of-motion coupled-cluster (EOM-CC) framework. The approach is based on recasting the sum-over-state expressions for RIXS moments into a compact form by using damped response theory. Damped response formalism allows one to circumvent problems of divergent behavior of the response equation in the resonant regime. However, the convergence of response equations in the X-ray frequency range is often erratic due to the resonant nature of the virtual core-excited states embedded in the valence ionization continuum. We demonstrate that this problematic behavior can be avoided by extending the core-valence separation (CVS) scheme, which decouples the valence-occupied and core-occupied excitation manifolds, into the response domain. The accuracy of the CVS-enabled damped response theory, implemented within the EOM-EE-CCSD (EOM-CC for excitation energies with single and double excitations) framework, is assessed by comparison against damped EOM-EE-CCSD response calculations. The capabilities of the new approach are illustrated by calculations of RIXS cross sections for benzene and benzene radical cation.

We present the first analytical implementation of CC3 second derivatives using the spin-unrestricted approach. This allows, for the first time, the calculation of nuclear spin–spin coupling constants (SSCC) relevant to NMR spectroscopy at the CC3 level of theory in a fully analytical manner. CC3 results for the SSCCs of a number of small molecules and their fluorine substituted derivatives are compared with the corresponding coupled cluster singles and doubles (CCSD) results obtained using specialized basis sets. For one-bond couplings the change when going from CCSD to CC3 is typically 1–3%, but much higher corrections were found for 1JCN in FCN, 15.7%, and 1JOF in OF2, 6.4%. The changes vary significantly in the case of multibond couplings, with differences of up to 10%, and even 13.6% for 3JFH in fluoroacetylene. Calculations at the coupled cluster singles, doubles, and triples (CCSDT) level indicate that the most important contributions arising from connected triple excitations in the coupled cluster ...

The method and basis set dependence of zero-point vibrational corrections (ZPVCs) to nuclear magnetic resonance shielding constants and anisotropies has been investigated using water as a test system. A systematic comparison has been made using the Hartree–Fock, second-order Møller–Plesset perturbation theory (MP2), coupled cluster singles and doubles (CCSD), coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)) and Kohn–Sham density functional theory with the B3LYP exchange-correlation functional methods in combination with the second-order vibrational perturbation theory (VPT2) approach for the vibrational corrections. As basis sets, the correlation consistent basis sets cc-pVXZ, aug-cc-pVXZ, cc-pCVXZ and aug-cc-pCVXZ with X = D, T, Q, 5, 6 and the polarisation consistent basis sets aug-pc-n and aug-pcS-n with n = 1, 2, 3, 4 were employed. Our results show that basis set convergence of the vibrational corrections is not monotonic and that very large basis sets are needed before a reasonable extrapolation to the basis set limit can be performed. Furthermore, our results suggest that coupled cluster methods and a decent basis set are required before the error of the electronic structure approach is lower than the inherent error of the VPT2 approximation.

Singlet fission is a photophysical process in which an optically excited singlet exciton is converted into two triplet excitons. Singlet fission sensitized solar cells are expected to display a greatly enhanced power conversion efficiency compared to conventional single-junction cells, but the efficient design of such devices relies on the selection of materials capable of harvesting triplets generated in the fission chromophore. To this aim, the possibility of measuring triplet exciton dynamics with chemical selectivity paves the way for the rational design of complex heterojunctions, with optimized triplet conversion. Here we exploit the chemical sensitivity of X-ray absorption spectroscopy to track triplet exciton dynamics at the picosecond timescale in multilayer films of pentacene, the archetypal singlet fission material. We experimentally identify the signature of the triplet exciton in the Carbon K-edge absorption spectrum and measure its lifetime of about 300 ps. Our results are supported by state-of-the-art ab initio calculations. Excitons are neutral quasiparticles, which are investigated as a potential component to improve the performance of photovoltaic cells however it is first necessary to develop methods to achieve multiexciton generation such as singlet fission. To this end the authors theoretically and experimentally demonstrate long-lived triplet exciton states via singlet fission enabled by the intermolecular coupling geometries in pentacene films.

A coupled cluster protocol rooted in damped response theory is presented for computing Resonant Inelastic X-Ray Scattering spectra of molecules in gas-phase. Working equations are reported for both linear (i.e., equation-of-motion) and non-linearparametrizations of the coupled-cluster wavefunction response. A simple scheme tocompute non-resonant X-ray emission spectra is also proposed. Illustrative results arepresented for water.

The basis set convergence of nuclear spin-spin coupling constants (SSCC) calculated at the coupled cluster singles and doubles (CCSD) level has been investigated for ten difficult molecules. Eight of the molecules contain fluorine atoms and nine contain double or triple bonds. Results obtained using the ccJ-pVXZ, X=D,T,Q,5, hierarchy of basis sets of Benedikt et al. [J. Chem. Phys. 129, 064111 (2008)], converge rather slowly towards the basis set limit, but fast convergence can be obtained by adding diffuse functions, in particular for couplings across several bonds. The pcJ-n basis sets of Jensen [J. Chem. Theory Comput. 2, 1360 (2006)] exhibit large contraction errors for one-bond couplings, but in their uncontracted form they perform better than the ccJ-pVXZ basis sets. For multi-bond couplings, however, diffuse functions should be used, and when including these the two hierarchies show similar performance. The ccJ-pVXZ basis sets with diffuse functions included (aug-ccJ-pVXZ) show consistent performance across all types of SSCCs, with the triple zeta (X=T) basis set yielding sufficiently good results for most purposes.

Correction for ‘How to stay out of trouble in RIXS calculations within equation-of-motion coupled-cluster damped response theory? Safe hitchhiking in the excitation manifold by means of core–valence separation’ by Kaushik D. Nanda et al., Phys. Chem. Chem. Phys., 2020, 22, 2629–2641, DOI: 10.1039/c9cp03688a.

The demand for high precision calculations of NMR shieldings (or their related values, chemical shifts δ) and spin–spin coupling constants facilitating and supporting detailed interpretations of NMR spectra increases hand in hand with the development of computational techniques and hardware resources. Highly sophisticated calculations including even relativistic effects are nowadays possible for these properties. However, NMR parameters depend not only on molecular structure and environment but also on molecular flexibility and temperature and the apparent success of theoretical predictions for molecular equilibrium geometries creates a demand for zero-point vibrational and temperature corrections. In this chapter we describe briefly the theory behind rovibrational corrections and review then some important contributions to this field.

We present zero-point vibrational corrections to the indirect nuclear spin-spin coupling constants in ethyne, ethene, cyclopropene and allene. The calculations have been carried out both at the level of the second order polarization propagator approximation (SOPPA) employing a new implementation in the DALTON program, at the density functional theory level with the B3LYP functional employing also the Dalton program and at the level of coupled cluster singles and doubles (CCSD) theory employing the implementation in the CFOUR program. Specialized coupling constant basis sets, aug-cc-pVTZ-J, have been employed in the calculations. We find that on average the SOPPA results for both the equilibrium geometry values and the zero-point vibrational corrections are in better agreement with the CCSD results than the corresponding B3LYP results. Furthermore we observed that the vibrational corrections are in the order of 5 Hz for the one-bond carbon-hydrogen couplings and about 1 Hz or smaller for the other couplings apart from the one-bond carbon-carbon coupling (11 Hz) and the two-bond carbon-hydrogen coupling (4 Hz) in ethyne. However, not for all couplings lead the inclusion of zero-point vibrational corrections to better agreement with experiment.

The vicinal indirect nuclear spin–spin coupling constant (SSCC) between the two fluorine atoms in difluoroethyne has been reinvestigated. This coupling has previously proved to be difficult to calculate accurately. In this study we have therefore systematically investigated the dependence of this coupling on the choice of one-electron basis set, the choice of correlated wave function method and the inclusion of zero-point vibrational and temperature corrections. All terms of the SSCC have been evaluated at the second-order polarization propagator, SOPPA and SOPPA(CCSD), and coupled cluster singles and doubles (CCSD) levels of theory and for the most correlation dependent term, the paramagnetic spin–orbit contribution (PSO), also at the very accurate CC3 level. We find that in order to get results that are well converged with respect to the basis set, one needs to use special SSCC optimized basis sets of at least quadruple zeta quality and with added diffuse functions. Furthermore, the PSO term is not yet converged at the CCSD level as shown by the CC3 calculations. Finally, it is shown that vibrational effects are very important, as they are in this case of the same order of magnitude as the equilibrium geometry value of the coupling constant. Only by using a converged basis set and including both vibrational and higher order correlation effects can we obtain agreement with the experimental value for this coupling.