Irreducible Cartesian tensor decomposition: A computational approach.

Cartesian tensors are widely used in physics and chemistry, especially for the formulation of linear and nonlinear spectroscopies as well as for molecular response properties. In this work, we review the problem of irreducible Cartesian tensor (ICT) decomposition of a generic Cartesian tensor of rank n into its irreducible parts, each characterized by a specific symmetry. The matrix formulation of the ICT decomposition is structurally similar to the problem of rotational averaging using isotropic Cartesian tensors. Analogously to the latter, the ICT decomposition can be considered as a problem of selecting a set of permutations of n indices that provides a linearly independent set of mappings between Cartesian tensor subspaces. This selection can be performed using a simple computational approach based on the reduced row echelon form (rref) algorithm. This protocol has been implemented in a computer code used to re-derive the already known ICT decomposition for 2 ≤ n ≤ 4. Finally, for the first time, we performed the explicit ICT decomposition of a Cartesian tensor of rank n = 5.

Three-Dimensional Rotational Averaging Using Irreducible Sets of Linearly Independent Fundamental Isotropic Cartesian Tensors: A Computational Approach.

The theoretical formulation of linear and nonlinear molecular spectroscopies applied to isotropic samples (e.g., liquid or gas solutions) goes through a fundamental step known as the rotational averaging of Cartesian tensors. Rotational averaging of Cartesian tensors is a mathematical procedure from which the expressions for the rotationally invariant observables (e.g., rates or intensities), associated with a given spectroscopic process, can be found. In this work, the mathematical/computational procedure for finding the rotational averages of Cartesian tensors of any rank n, which is based on the use of the fundamental isotropic Cartesian tensors (FICTs), is discussed. Moreover, for the first time, a heuristic computational method for finding a set of linearly independent FICTs is proposed. The procedure has been tested for 2 ≤ n ≤ 12, where most of the linear and nonlinear molecular spectroscopies apply (e.g., one-photon and multiphoton absorption, emission, electronic circular dichroism, Raman optical activity, coherent and incoherent mth-harmonic generation, etc.). Finally, it is shown how this computational procedure can be extended for n > 12.

Third-harmonic scattering optical activity: QED theory, symmetry considerations, and quantum chemistry applications in the framework of response theory.

In this work, expressions for the third-harmonic scattering optical activity (THS-OA) spectroscopic responses are derived by combining molecular quantum electrodynamics (QED) and response theory, allowing their computational implementation. The QED theory of THS-OA presented here is meant to be an extension of a previous study by Andrews [Symmetry 12, 1466 (2020)]. In particular, the THS-OA phenomena are described within the Power-Zienau-Woolley multipolar Hamiltonian by including the electric-dipole, magnetic-dipole, and electric-quadrupole interactions for the absorption as well as the emission processes between the dynamic electromagnetic field (the photons) and matter. Moreover, we derive the expressions for the differential scattering ratios as a function of the scattering angle defined by the wavevectors of the incident and scattered photons. We show how the pure and mixed second hyperpolarizabilities can be obtained in the framework of response theory as specific cases of a generic cubic response function, thus enabling the computational implementation of THS-OA spectroscopy. We prove the origin-independence of the theory for exact wavefunctions. Preliminary computations on a prototype chiral molecule (methyloxirane) are considered together with an analysis of the basis set convergence and of the origin-dependence.

Hyper-Rayleigh scattering optical activity: Theory, symmetry considerations, and quantum chemistry applications.

This work reports on the first computational quantum-chemistry implementation of the hyper-Rayleigh scattering optical activity (HRS-OA), a nonlinear chiroptical phenomenon. First, from the basics of the theory, which is based on quantum electrodynamics, and focusing on the electric dipole, magnetic-dipole, and electric-quadrupole interactions, the equations for the simulation of the differential scattering ratios of HRS-OA are re-derived. Then, for the first time, computations of HRS-OA quantities are presented and analyzed. They have been enacted on a prototypical chiral organic molecule (methyloxirane) at the time-dependent density functional theory level using a broad range of atomic orbital basis sets. In particular, (i) we analyze the basis set convergence, demonstrating that converged results require basis sets with both diffuse and polarization functions, (ii) we discuss the relative amplitudes of the five contributions to the differential scattering ratios, and (iii) we study the effects of origin-dependence and derived the expression of the tensor shifts and we prove the origin-independence of the theory for exact wavefunctions. Our computations show the ability of HRS-OA as a nonlinear chiroptical method, able to distinguish between the enantiomers of the same chiral molecule.

In Silico Ultrafast Nonlinear Spectroscopy Meets Experiments: The Case of Perylene Bisimide Dye.

Spectroscopy simulations are of paramount importance for the interpretation of experimental electronic spectra, the disentangling of overlapping spectral features, and the tracing of the microscopic origin of the observed signals. Linear and nonlinear simulations are based on the results drawn from electronic structure calculations that provide the necessary parameterization of the molecular systems probed by light. Here, we investigate the applicability of excited-state properties obtained from linear-response time-dependent density functional theory (TDDFT) in the description of nonlinear spectra by employing the pseudowavefunction approach and compare them with benchmarks from highly accurate RASSCF/RASPT2 calculations and with high temporal resolution experimental results. As a test case, we consider the prediction of femtosecond transient absorption and two-dimensional electronic spectroscopy of a perylene bisimide dye in solution. We find that experimental signals are well reproduced by both theoretical approaches, showing that the computationally cheaper TDDFT can be a suitable option for the simulation of nonlinear spectroscopy of molecular systems that are too large to be treated with higher-level RASSCF/RASPT2 methods.

Characterization of ß-turns by electronic circular dichroism spectroscopy: a coupled molecular dynamics and time-dependent density functional theory computational study.

Electronic circular dichroism is one of the most used spectroscopic techniques for peptide and protein structural characterization. However, while valuable experimental spectra exist for α-helix, ß-sheet and random coil secondary structures, previous studies showed important discrepancies for ß-turns, limiting their use as a reference for structural studies. In this paper, we simulated circular dichroism spectra for the best-characterized ß-turns in peptides, namely types I, II, I' and II'. In particular, by combining classical molecular dynamics simulations and state-of-the-art quantum time-dependent density functional theory (with the polarizable embedding multiscale model) computations, two common electronic circular dichroism patterns were found for couples of ß-turn types (namely, type I/type II' and type II/type I'), at first for a minimal di-peptide model (Ace-Ala-Ala-NHMe), but also for all sequences tested with non-aromatic residues in the central positions. On the other hand, as expected, aromatic substitution causes important perturbations to the previously found ECD patterns. Finally, by applying suitable approximations, these patterns were subsequently rationalized based on the exciton chirality rule. All these results provide useful predictions and pave the way for a possible experimental characterization of ß-turns based on circular dichroism spectroscopy.

Rational design of novel fluorescent analogues of cholesterol: a "step-by-step" computational study.

In this paper we show a theoretical rational design approach on a series of intrinsically fluorescent analogues of cholesterol (FLACs), called polyene-sterols (P-sterols), followed by a step-by-step selection of potential candidates, employing, sequentially, state-of-the-art quantum mechanical (QM) computations of the optical properties (single- and multiphoton absorption electronic spectroscopies and emission), molecular dynamics (MD) simulations in model membranes, and multiscale approaches (polarizable embedding). This selection converged to a promising candidate that shows simultaneously interesting single- and multiphoton absorption properties as well as emitting properties and good abilities to mimic cholesterol order effects in model membranes.

Revisiting absorption and electronic circular dichroism spectra of cholesterol in solution: a joint experimental and theoretical study.

Cholesterol is doubtless one of the most studied bio-molecules, which unfortunately features low emitting properties, precluding its in vivo study by fluorescence experiments. The design of fluorescent analogues of cholesterol is thus an appealing challenge in biochemistry, which simultaneously requires minor changes in its chemical structure (to retain main biological properties) and considerable enhancement of light emission. To this aim, the photochemical behaviour of the native molecule has to be deeply understood. In this work, we focused our attention on the electronic absorption of cholesterol in several common organic solutions, combining experimental (through ultraviolet-visible and electronic circular dichroism spectroscopy) and theoretical approaches (at the time-dependent density functional theory level) in order to solve the important discrepancies previously reported in the literature on the maximum absorption wavelengths and on the nature (Rydberg and/or π → π*) of the associated electronic transition.