Communication: X-ray absorption spectra and core-ionization potentials within a core-valence separated coupled cluster framework

We present a simple scheme to compute X-ray absorption spectra (e.g., near-edge absorption fine structure) and core ionisation energies within coupled cluster linear response theory. The approach exploits the so-called core-valence separation to effectively reduce the excitation space to processes involving at least one core orbital, and it can be easily implemented within any pre-existing coupled cluster code for low energy states. We further develop a perturbation correction that incorporates the effect of the excluded part of the excitation space. The correction is shown to be highly accurate. Test results are presented for a set of molecular systems for which well converged results in full space could be generated at the coupled cluster singles and doubles level of theory only, but the scheme is straightforwardly generalizable to all members of the coupled cluster hierarchy of approximations, including CC3

Damped (linear) response theory within the resolution-of-identity coupled cluster singles and approximate doubles (RI-CC2) method

An implementation of a complex solver for the solution of the response equations required to compute the complex response functions of damped response theory is presented for the resolution-of-identity (RI) coupled-cluster singles and approximate doubles CC2 method. The implementation uses a partitioned formulation that avoids the storage of double excitation amplitudes to make it applicable to large molecules. The solver is the keystone element for the development of the damped coupled-cluster response formalism for linear and nonlinear effects in resonant frequency regions at the RI-CC2 level of theory. Illustrative results are reported for the one-photon absorption cross section of C60, the electronic circular dichroism of $n$-helicenes ($n$ = 5, 6, 7), and the $C_6$ dispersion coefficients of a set of selected organic molecules and fullerenes.Comment: Submitted to J. Chem. Phys., Dec. 202

nuclear spin circular dichroism in fullerenes a computational study

Chemically different carbons in C70 give distinct signals in nuclear spin circular dichroism spectroscopy, a novel candidate for high-resolution identification of chemical compounds

Vibrationally Resolved Coupled Cluster X-Ray Absorption Spectra from Vibrational Configuration Interaction Anharmonic Calculations

Vibrationally resolved near-edge x-ray absorption spectra at the K-edge for a number of small molecules have been computed from anharmonic vibrational configuration interaction calculations of the Franck-Condon factors. The potential energy surfaces for ground and core-excited states were obtained at the core-valence separated CC2, CCSD, CCSDR(3), and CC3 levels of theory, employing the Adaptive Density-Guided Approach (ADGA) scheme to select the single points at which to perform the energy calculations. We put forward an initial attempt to include pair-mode coupling terms to describe the potential of polyatomic molecule

Circular and linear magnetic birefringences in xenon at λ=1064\lambda = 1064 nm

The circular and linear magnetic birefringences corresponding to the Faraday and the Cotton-Mouton effects, respectively, have been measured in xenon at $\lambda = 1064$ nm. The experimental setup is based on time dependent magnetic fields and a high finesse Fabry-Perot cavity. Our value of the Faraday effect is the first measurement at this wavelength. It is compared to theoretical predictions. Our uncertainty of a few percent yields an agreement at better than 1$\sigma$ with the computational estimate when relativistic effects are taken into account. Concerning the Cotton-Mouton effect, our measurement, the second ever published at $\lambda = 1064$ nm, agrees at better than $1\sigma$ with theoretical predictions. We also compare our error budget with those established for other experimental published values

Molecular response properties in equation of motion coupled cluster theory: A time-dependent perspective

Molecular response properties for ground and excited states and for transitions between these states are defined by solving the time-dependent Schr\uf6dinger equation for a molecular system in a field of a time-periodic perturbation. In equation of motion coupled cluster (EOM-CC) theory, molecular response properties are commonly obtained by replacing, in configuration interaction (CI) molecular response property expressions, the energies and eigenstates of the CI eigenvalue equation with the energies and eigenstates of the EOM-CC eigenvalue equation. We show here that EOM-CC molecular response properties are identical to the molecular response properties that are obtained in the coupled cluster\u2013configuration interaction (CC-CI) model, where the time-dependent Schr\uf6dinger equation is solved using an exponential (coupled cluster) parametrization to describe the unperturbed system and a linear (configuration interaction) parametrization to describe the time evolution of the unperturbed system. The equivalence between EOM-CC and CC-CI molecular response properties only holds when the CI molecular response property expressions\u2014from which the EOM-CC expressions are derived\u2014are determined using projection and not using the variational principle. In a previous article [F. Paw\u142owski, J. Olsen, and P. J\uf8rgensen, J. Chem. Phys. 142, 114109 (2015)], it was stated that the equivalence between EOM-CC and CC-CI molecular response properties only held for a linear response function, whereas quadratic and higher order response functions were mistakenly said to differ in the two approaches. Proving the general equivalence between EOM-CC and CC-CI molecular response properties is a challenging task, that is undertaken in this article. Proving this equivalence not only corrects the previous incorrect statement but also first and foremost leads to a new, time-dependent, perspective for understanding the basic assumptions on which the EOM-CC molecular response property expressions are founded. Further, the equivalence between EOM-CC and CC-CI molecular response properties highlights how static molecular response properties can be obtained from finite-field EOM-CC energy calculations

Relation between molecular electronic structure and nuclear spin-induced circular dichroism

The recently theoretically described nuclear spin-induced circular dichroism (NSCD) is a promising method for the optical detection of nuclear magnetization. NSCD involves both optical excitations of the molecule and hyperfine interactions and, thus, it offers a means to realize a spectroscopy with spatially localized, high-resolution information. To survey the factors relating the molecular and electronic structure to the NSCD signal, we theoretically investigate NSCD of twenty structures of the four most common nucleic acid bases (adenine, guanine, thymine, cytosine). The NSCD signal correlates with the spatial distribution of the excited states and couplings between them, reflecting changes in molecular structure and conformation. This constitutes a marked difference to the nuclear magnetic resonance (NMR) chemical shift, which only reflects the local molecular structure in the ground electronic state. The calculated NSCD spectra are rationalized by means of changes in the electronic density and by a sum-over-states approach, which allows to identify the contributions of the individual excited states. Two separate contributions to NSCD are identified and their physical origins and relative magnitudes are discussed. The results underline NSCD spectroscopy as a plausible tool with a power for the identification of not only different molecules, but their specific structures as well.Peer reviewe

A computational protocol for the study of circularly polarized phosphorescence and circular dichroism in spin-forbidden absorption

We present a computational methodology to calculate the intensity of circular dichroism (CD) in spin-forbidden absorption and of circularly polarized phosphorescence (CPP) signals, a manifestation of the optical activity of the triplet-singlet transitions in chiral compounds. The protocol is based on the response function formalism and is implemented at the level of time-dependent density functional theory. It has been employed to calculate the spin-forbidden circular dichroism and circularly polarized phosphorescence signals of valence n -> pi* and n <- pi* transitions, respectively, in several chiral enones and diketones. Basis set effects in the length and velocity gauge formulations have been explored, and the accuracy achieved when employing approximate (mean-field and effective nuclear charge) spin-orbit operators has been investigated. CPP is shown to be a sensitive probe of the triplet excited state structure. In many cases the sign of the spin-forbidden CD and CPP signals are opposite. For the beta,gamma-enones under investigation, where there are two minima on the lowest triplet excited state potential energy surface, each minimum exhibits a CPP signal of a different sign

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 $e^T$. 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