Gauge-origin independent calculations of Jones birefringence

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.

Three-photon circular dichroism: towards a generalization of chiroptical non-linear light absorption

We present the theory of three-photon circular dichroism (3PCD), a novel non-linear chiroptical property not yet described in the literature. We derive the observable absorption cross section including the orientational average of the necessary seventh-rank tensors and provide origin-independent expressions for 3PCD using either a velocity-gauge treatment of the electric dipole operator or a length-gauge formulation using London atomic orbitals. We present the first numerical results for hydrogen peroxide, 3-methylcyclopentanone (MCP) and 4-helicene, including also a study of the origin dependence and basis set convergence of 3PCD. We find that for the 3PCD-brightest low-lying Rydberg state of hydrogen peroxide, the dichroism is extremely basis set dependent, with basis set convergence not being reached before a sextuple-zeta basis is used, whereas for the MCP and 4-helicene molecules, the basis set dependence is more moderate and at the triple-zeta level the 3PCD contributions are more or less converged irrespective of whether the considered states are Rydberg states or not. The character of the 3PCD-brightest states in MCP is characterized by a fairly large charge-transfer character from the carbonyl group to the ring system. In general, the quadrupole contributions to 3PCD are found to be very small.

Ab initio study of the enantio-selective magnetic-field-induced second harmonic generation in chiral molecules

We present a systematic ab initio study of enantio-selective magnetic-field-induced second harmonic generation (MFISHG) on a set of chiral systems ((l)-alanine, (l)-arginine and (l)-cysteine; 3,4-dehydro-(l)-proline; (S)-α-phellandrene; (R,S)- and (S,S)-cystine disulphide; N-(4-nitrophenyl)-(S)-prolinol, N-(4-(2-nitrovinyl)-phenyl)-(S)-prolinol, N-(4-tricyanovinyl-phenyl)-(S)-prolinol, (R)-BINOL, (S)-BINAM and 6-(M)-helicene). The needed electronic frequency dependent cubic response calculations are performed within a density functional theory (DFT) approach. A study of the dependence of the property on the choice of electron correlation, on one-electron basis set extension and on the choice of magnetic gauge origin is carried out on a prototype system (twisted oxygen peroxide). The magnetic gauge dependence analysis is extended also to the molecules of the set. An attempt to analyze the structure-property relationships is also made, based on the results obtained for biphenyl (in a frozen twisted conformation), for prolinol and for some of their derivatives. The strength of the effect is discussed, in order to establish its measurability with a proposed experimental setup.

Jones birefringence in twisted single-mode optical fibers

In this work we analyze the birefringence matrix developed for a twisted fiber in order to identify the basic optical effects that define its birefringence. The study was performed using differential Jones calculus. The resultant differential matrix showed three independent types of birefringence: circular, linear at 0 degrees and linear at 45 degrees (Jones birefringence). We applied this birefringence matrix to the description of the output state of polarization measured for three commercial fibers that due to its higher rigidity present stronger birefringence changes when twisted. The torsion applied to the erbium-doped fiber samples varied from 0 to 1440 degrees.

A density functional theory study of magneto-electric Jones birefringence of noble gases, furan homologues, and mono-substituted benzenes

We report on the results of a systematic ab initio study of the Jones birefringence of noble gases, of furan homologues, and of monosubstituted benzenes, in the gas phase, with the aim of analyzing the behavior and the trends within a list of systems of varying size and complexity, and of identifying candidates for a combined experimental/theoretical study of the effect. We resort here to analytic linear and nonlinear response functions in the framework of time-dependent density functional theory. A correlation is made between the observable (the Jones constant) and the atomic radius for noble gases, or the permanent electric dipole and a structure/chemical reactivity descriptor as the para Hammett constant for substituted benzenes.