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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. [ABSTRACT FROM AUTHOR]

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.

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. [ABSTRACT FROM AUTHOR]

In this work, the theory of the modified unit sphere representation (mUSR) has been proposed as a computational tool suitable for the three‐dimensional representation of the pure electric‐dipole [βλμν(−2ω;ω,ω)] as well as of the mixed electric‐dipole/magnetic‐dipole [ αJλμν(−2ω;ω,ω) and βJλμν(−2ω;ω,ω)] or electric‐dipole/electric‐quadrupole [ αKλμνo(−2ω;ω,ω) and βKλμνo(−2ω;ω,ω)] first hyperpolarizabilities. These five quantities are Cartesian tensors and they are responsible for the chiral signal in the chiroptical version of the hyper‐Rayleigh scattering (HRS) spectroscopy, namely the HRS optical activity (HRS‐OA) spectroscopy. For the first time, for each hyperpolarizability, alongside with the three‐dimensional representation of the whole (i.e., reducible) Cartesian tensors, the mUSRs are developed for each of the irreducible Cartesian tensors (ICTs) that constitute them. This scheme has been applied to a series of three (chiral) hexahelicene molecules containing different degrees of electron‐withdrawing (quinone) groups and characterized by the same (positive) handedness. For these molecules, the mUSR shows that, upon substitution, the most remarkable qualitative and semi‐quantitative (enhancement of the molecular responses) effects are obtained for the pure electric‐dipole and for the mixed electric‐dipole/magnetic‐dipole hyperpolarizabilities. [ABSTRACT FROM AUTHOR]

In this work, the HRS-OA circular differential scattering ratios of medium-size chiral molecules, R-carvone and (1R,5R)-α-pinene, has been computed by means of TD-DFT calculations. The results have been discussed as a function of the basis set size. For R-carvone a conformational analysis has been taken into account. In particular, the three most stable conformations of R-carvone present chiral terms that contribute to the HRS-OA circular differential scattering ratio, with opposite signs. Finally, the modified unit sphere representations (mUSR) have been produced for the molecules under study. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this work, the HRS-OA circular differential scattering ratios of medium-size chiral molecules, R -carvone and (1 R ,5 R )-α-pinene, has been computed by means of TD-DFT calculations. The results have been discussed as a function of the basis set size. For R -carvone a conformational analysis has been taken into account. In particular, the three most stable conformations of R -carvone present chiral terms that contribute to the HRS-OA circular differential scattering ratio, with opposite signs. Finally, the modified unit sphere representations (mUSR) have been produced for the molecules under study.