NMR parameters of FNNF as a test for coupled-cluster methods: CCSDT shielding and CC3 spin-spin coupling.

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.

Correction: 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.

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: .

Dalton Project: A Python platform for molecular- and electronic-structure simulations of complex systems.

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.

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.

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.

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.

Core-valence-separated coupled-cluster-singles-and-doubles complex-polarization-propagator approach to X-ray spectroscopies.

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.

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.

Spin adapted implementation of EOM-CCSD for triplet excited states: Probing intersystem crossings of acetylacetone at the carbon and oxygen K-edges.

We present an equation of motion coupled cluster singles and doubles approach for computing transient absorption spectra from a triplet excited state. The implementation determines the left and right excitation vectors by explicitly spin-adapting the triplet excitation space. As an illustrative application, we compute transient state X-ray absorption spectra at the carbon and oxygen K-edges for the acetylacetone molecule.

Resonant Inelastic X-ray Scattering and Nonesonant X-ray Emission Spectra from Coupled-Cluster (Damped) Response Theory.

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.

UV Absorption and Magnetic Circular Dichroism Spectra of Purine, Adenine, and Guanine: A Coupled Cluster Study in Vacuo and in Aqueous Solution.

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 [Formula: see text] 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 also included 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 the 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 solvation, 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 bisignate 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 to determine the relative stability of the La and Lb states is critically reassessed. According to our best estimate for adenine in aqueous solution, the La state is more stable than Lb.

RPA(D) and HRPA(D): Two new models for calculations of NMR indirect nuclear spin-spin coupling constants.

In this article, the RPA(D) and HRPA(D) models for the calculation of linear response functions are presented. The performance of the new RPA(D) and HRPA(D) models is compared to the performance of the established RPA, HRPA, and SOPPA models in calculations of indirect nuclear spin-spin coupling constants using the CCSD model as a reference. The doubles correction offers a significant improvement on both the RPA and HRPA models; however, the improvement is more dramatic in the case of the RPA model. For all coupling types investigated in this study, the results obtained using the HRPA(D) model are comparable in accuracy to those given by the SOPPA model, while requiring between 30% and 90% of the calculation time needed for SOPPA. The RPA(D) model, while of slightly lower accuracy compared to the CCSD model than HRPA(D), offered calculation times of only approximately 25% of those required for SOPPA for all the investigated molecules. © 2018 Wiley Periodicals, Inc.

Importance of Triples Contributions to NMR Spin-Spin Coupling Constants Computed at the CC3 and CCSDT Levels.

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 expansion are accounted for at the CC3 level. Thus, we believe that the CC3 method will become the standard approach for the calculation of reference values of nuclear spin-spin coupling constants.

Spin-orbit ZORA and four-component Dirac-Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers.

Hartree-Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange-correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin-orbit zeroth-order regular approximation Hamiltonian in combination with the large Slater-type basis set QZ4P as well as with the four-component Dirac-Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization-consistent basis sets aug-pcSseg-4 for He, Ne and Ar, aug-pcSseg-3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero-point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed.

On the discrepancy between theory and experiment for the F-F spin-spin coupling constant of difluoroethyne.

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.