Coupled cluster evaluation of the second and third harmonic scattering responses of small molecules

A quantum chemical investigation of the second hyperpolarizability of p-nitroaniline

Recent measurements of the third harmonic scattering responses of molecules have given a new impetus for computing molecular second hyperpolarizabilities (γ) and for deducing structure-property relationships. This paper has employed a variety of wavefunction and density functional theory methods to evaluate the second hyperpolarizability of the p-nitroaniline prototypical push-pull π-conjugated molecule, addressing also numerical aspects, such as the selection of an integration grid and the impact of the order of differentiation vs the achievable accuracy by using the Romberg quadrature. The reliability of the different methods has been assessed by comparison to reference Coupled-Cluster Singles and Doubles with perturbative treatment of the Triples results. On the one hand, among wavefunction methods, the MP2 scheme offers the best accuracy/cost ratio for computing the static γ. On the other hand, using density functional theory, γ remains a challenging property to compute because all conventional, global hybrid or range-separated hybrid, exchange-correlation functionals underestimate static γ values by at least 15%. Even tuning the range-separating parameter to minimize the delocalization errors does not enable to improve the γ values. Nevertheless, the original double-hybrid B2-PLYP functional, which benefits from 27% of PT2 correlation and 53% Hartree-Fock exchange, provides accurate estimates of static γ values. Unfortunately, the best performing exchange-correlation functionals for γ are not necessarily reliable for the first hyperpolarizability, β, and vice versa. In fact, the β of p-nitroaniline (pNA) could be predicted, with a good accuracy, with several hybrid exchange-correlation functionals (including by tuning the range-separating parameter), but these systematically underestimate γ. As for γ, the MP2 wavefunction method remains the best compromise to evaluate the first hyperpolarizability of pNA at low computational cost.

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.

Unraveling the Symmetry Effects on the Second-Order Nonlinear Optical Responses of Molecular Switches: The Case of Ruthenium Complexes

Owing to their odd order, second-order nonlinear optical (NLO) responses are very sensitive to symmetry. Therefore, within hyper-Rayleigh scattering (HRS) technique, the symmetry impacts the amplitude of the molecular responses, the HRS first hyperpolarizability (β_HRS), and the depolarization ratio (DR). Starting from a challenging octupolar structure bearing six ruthenium(II) ammine centers π-conjugated via quaterpyridyl moieties to a tris-chelated zinc(II) core, together with its Λ shape and one-dimensional analogues built by replacing one or two Ru-quaterpyridyl moieties with bipyridine moieties, (time-dependent) density functional theory calculations have been enacted to unravel the symmetry-NLO response relationships as well as their Ru^II/III redox-triggered switching effects. The one-dimensional and Λ-shaped NLOphores present β_HRS values ∼3 times larger than those of the octupolar system, for both Ru oxidation states. However, using the few-state valence bond-charge transfer models demonstrates that the β_HRS response of the octupolar complex cation can become larger than those of its one-dimensional and Λ-shaped analogues provided stronger donor-acceptor groups are employed. In parallel, the DRs decrease from a strong dipolar character (DR ≈ 6) for the one-dimensional chromophore to a weaker dipolar character (DR ≈ 5) for the Λ-shaped one and to a clear octupolar character (DR ≈ 1.7) for the last one. In all cases, the β responses originate mostly from metal-to-ligand charge transfer excited states, as revealed using a new scheme for analyzing the variations in electron density upon excitation. The Ru^II/III oxidations lead to a strong decrease in the β_HRS responses, which is attributed to the loss of the donor character of the Ru centers and therefore to the reduction of the push-pull π-conjugation. These results demonstrate that the NLO contrast and the NLO switching behavior of these Ru cations are maintained for the different molecular symmetries. Finally, the character of the β responses of the oxidized species, as revealed by the DR values, further evidences a clear evolution from dipolar to octupolar NLOphores.

First Hyperpolarizability of Water in Bulk Liquid Phase: Long-Range Electrostatic Effects Included via the Second Hyperpolarizability

The molecular first hyperpolarizability β contributes to second-order optical non-linear signals collected from molecular liquids. For the Second Harmonic Generation (SHG) response, the first hyperpolarizability β (2ω,ω,ω) often depends on...

First hyperpolarizability of water at the air-vapor interface: a QM/MM study questions standard experimental approximations

Surface Second-Harmonic Generation (S-SHG) experiments provide a unique approach to probe interfaces. One important issue for S-SHG is how to interpret the S-SHG intensities at the molecular level. Established frameworks commonly assume that each molecule emits light according to an average molecular hyperpolarizability tensor β(-2ω,ω,ω). However, for water molecules, this first hyperpolarizability is known to be extremely sensitive to their environment. We have investigated the molecular first hyperpolarizability of water molecules within the liquid-vapor interface, using a quantum description with explicit, inhomogeneous electrostatic embedding. The resulting average molecular first hyperpolarizability tensor depends on the distance relative to the interface, and it practically respects the Kleinman symmetry everywhere in the liquid. Within this numerical approach, based on the dipolar approximation, the water layer contributing to the Surface Second Harmonic Generation (S-SHG) intensity is less than a nanometer. The results reported here question standard interpretations based on a single, averaged hyperpolarizability for all molecules at the interface. Not only the molecular first hyperpolarizability tensor significantly depends on the distance relative to the interface, but it is also correlated to the molecular orientation. Such hyperpolarizability fluctuations may impact the S-SHG intensity emitted by an aqueous interface.

Theoretical Study on Third-Order Nonlinear Optical Properties for One-Hole-Doped Diradicaloids

We investigate the relationships between open-shell character and longitudinal static second hyperpolarizabilities γ for one-hole-doped diradicaloids using the strong-correlated ab initio molecular orbital methods and simple one-dimensional (1D) three-site two-electron (3s-2e) models. As examples of one-hole-doped diradicaloids, we examine H₃ ⁺, methyl radical trimer cation ((CH₃)₃ ⁺), silyl radical trimer cation ((SiH₃)₃ ⁺), and 1,2,3,5-dithiadizolyl trimer cation (DTDA₃ ⁺). For H₃ ⁺, the static γ exhibits negative values and shows a monotonic increase in amplitude with an increase in the open-shell character defined by a neighbor-site interaction (y _S). On the other hand, it is found for (CH₃)₃ ⁺, (SiH₃)₃ ⁺, and DTDA₃ ⁺ that the static γ value exhibits similar behavior to that for H₃ ⁺ up to an intermediate y _S value, while it takes the negative maximum at a large y _S value, followed by a decrease in γ amplitude, and subsequently, γ changes to positive values with a drastic increase for larger y _S values. For example, in DTDA₃ ⁺, the negative/positive γ values, -69 × 10⁵/700 × 10⁵ au at y _S = 0.75/0.87, exhibit significant enhancements in amplitude, 2.4/24 times as large as that (-29 × 10⁵ au) at intermediate y _S = 0.59 as is often the case in DTDA₂. Using the 1D 3s-2e valence-bond configuration interaction model, these sign inversions and drastic increase in the amplitude of γ are found to originate in the differences in Coulomb interactions between valence electrons, between valence and core electrons, and between valence electrons and nuclei. These results contribute to pave the way for the construction of novel control guidelines for the amplitude and sign of γ for one-hole-doped diradicaloids.