Frequency dispersion of the first hyperpolarizabilities of reference molecules for nonlinear optics

Liquid Water: When Hyperpolarizability Fluctuations Boost and Reshape the Second Harmonic Scattering Intensities

Second harmonic scattering (SHS) is a method of choice to investigate the molecular structure of liquids. While a clear interpretation of SHS intensity exists for diluted solutions of dyes, the scattering due to solvents remains difficult to interpret quantitatively. Here, we report a quantum mechanics/molecular mechanics (QM/MM) approach to model the polarization-resolved SHS intensity of liquid water, quantifying different contributions to the signal. We point out that the molecular hyperpolarizability fluctuations and correlations cannot be neglected. The intermolecular orientational and hyperpolarizability correlations up to the third solvation layer strongly increase the scattering intensities and modulate the polarization-resolved oscillation that is predicted here by QM/MM without fitting parameters. Our approach can be generalized to other pure liquids to provide a quantitative interpretation of SHS intensities in terms of short-range molecular ordering.

Recent Advances in Cartesian-Grid DFT in Atoms and Molecules

In the past several decades, density functional theory (DFT) has evolved as a leading player across a dazzling variety of fields, from organic chemistry to condensed matter physics. The simple conceptual framework and computational elegance are the underlying driver for this. This article reviews some of the recent developments that have taken place in our laboratory in the past 5 years. Efforts are made to validate a viable alternative for DFT calculations for small to medium systems through a Cartesian coordinate grid- (CCG-) based pseudopotential Kohn–Sham (KS) DFT framework using LCAO-MO ansatz. In order to legitimize its suitability and efficacy, at first, electric response properties, such as dipole moment (μ), static dipole polarizability (α), and first hyperpolarizability (β), are calculated. Next, we present a purely numerical approach in CCG for proficient computation of exact exchange density contribution in certain types of orbital-dependent density functionals. A Fourier convolution theorem combined with a range-separated Coulomb interaction kernel is invoked. This takes motivation from a semi-numerical algorithm, where the rate-deciding factor is the evaluation of electrostatic potential. Its success further leads to a systematic self-consistent approach from first principles, which is desirable in the development of optimally tuned range-separated hybrid and hyper functionals. Next, we discuss a simple, alternative time-independent DFT procedure, for computation of single-particle excitation energies, by means of “adiabatic connection theorem” and virial theorem. Optical gaps in organic chromophores, dyes, linear/non-linear PAHs, and charge transfer complexes are faithfully reproduced. In short, CCG-DFT is shown to be a successful route for various practical applications in electronic systems.

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.

In situ reversible redox switching of first hyperpolarizability of bimetallic ruthenium complexes

In this article we report the reversible redox switching of first hyperpolarizability of bimetallic ruthenium complexes bridged by bipyridyl tetrazine (bptz) ligands by second harmonic light scattering experiments (SHLS). We have synthesised [RuII(acac)₂(CH₃CN)₂] and [(acac)₂Ru-bptz-Ru(acac)₂] complexes and measured their first hyperpolarizabilities as a function of in situ electrochemical oxidation/reduction of the metal centres. As a result of the oxidation of ruthenium centre from Ru(ii) to Ru(iii), the molecular hyperpolarizability of the complexes went up. The mixed-valence intermediate bimetallic complex and not the fully oxidized complex exhibit the highest β value of 780 × 10^-30 esu. We also demonstrated that the hyperpolarizability is reversible with the change of the oxidation state of the metal and both the complexes are stable for several cycles of redox switching. The experimental results are also supported by calculations.

Coupled-cluster sum-frequency generation nonlinear susceptibilities of methyl (CH3) and methylene (CH2) groups

The first vibrational sum frequency generation (SFG) spectra based on molecular properties calculated at the coupled cluster singles and doubles (CCSD) level of approximation have been simulated for interfacial model alkyl chains, providing benchmark data for comparisons with approximate methods, including density functional theory (DFT). The approach proceeds in three steps. In the first two steps, the molecular spectral properties are determined: the vibrational normal modes and frequencies and then the derivatives of the dipole moment and of the polarizability with respect to the normal coordinates. These derivatives are evaluated with a numerical differentiation approach, of which the accuracy was monitored using Romberg's procedure. Then, in the last step, a three-layer model is employed to evaluate the macroscopic second-order nonlinear optical responses and thereby the simulated SFG spectra of the alkyl interface. Results emphasize the following facts: (i) the dipole and polarizability derivatives calculated at the DFT level with the B3LYP exchange-correlation functional can differ, with respect to CCSD, by as much as ±10 to 20% and ±20 to 50% for the CH₃ and CH₂ vibrations, respectively; (ii) these differences are enhanced when considering the SFG intensities as well as their variations as a function of the experimental configuration (ppp versus ssp) and as a function of the tilt and rotation angles, defining the orientation of the alkyl chain at the interface; (iii) these differences originate from both the vibrational normal coordinates and the Cartesian derivatives of the dipole moment and polarizability; (iv) freezing the successive fragments of the alkyl chain strongly modifies the SFG spectrum and enables highlighting the delocalization effects between the terminal CH₃ group and its neighboring CH₂ units; and finally (v) going from the free chain to the free methyl model, and further to C_3v constraints on leads to large variations of two ratios that are frequently used to probe the molecular orientation at the interface, the (r + r)/r⁺ ratio for both antisymmetric and symmetric CH₃ vibrations and the I_ppp/I_ssp ratio.

Synthesis, structural characterization and computational study of a novel amino chalcone: a potential nonlinear optical material

The interest for novel chalcone-based materials in nonlinear optics is dependent on strong second harmonic generation in organic systems.

Performance of Hybrid DFT Compared to MP2 Methods in Calculating Nonlinear Optical Properties of Divinylpyrene Derivative Molecules

A series of divinyl-pyrene derivatives of the form D-vinyl-pyrene-vinyl-A, in which D corresponds to an electron donor group and A to an electron acceptor group, were studied in this work. The first purpose was to determine the optimal HF % exchange as incorporated in a range of hybrid functionals (M06HF, M062X, M06L, CAM-B3LYP, PBE0, BMK, and B3LYP) capable to produce, reliably and as close as possible to those obtained from MP2 calculations, NLO parameters and, in particular, first-order static hyperpolarizabilities. The CAM-B3LYP functional was revealed to be the most suitable one. The pair N(CH₃)₂/NO₂ was then determined as the most efficient pair of groups in producing appreciable NLO responses. The effect of the substitution position on the pyrene moiety was also investigated, whereby aligning the two substituents involving the D and A groups in the direction of the dipole moment as in the (1,6 DVP) derivatives was shown to be most favorable for increasing the NLO parameters.

Challenging compounds for calculating molecular second hyperpolarizabilities: the triplet state of the trimethylenemethane diradical and two derivatives

The second hyperpolarizability γ of trimethylenemethane (TMM) and two 1,3-dipole derivatives (NXA and OXA) in their triplet ground state has been evaluated at the UCCSD(T) level with the d-aug-cc-pVDZ extended basis set, highlighting that γ decreases from TMM to NXA and OXA, following the opposite order of their permanent dipole moments. These results are then used to benchmark a broad range of levels of approximation. So, the UMP2, UMP4, and UCCSD methods can be used to characterize γ of TMM and NXA but not of OXA. In that case, the large field-induced charge transfer contribution is difficult to handle using the MPn methods and only the UCCSD method provides values close to the UCCSD(T) reference. Turning to the performance of DFT with typical exchange-correlation functionals, the UM06-2X functional, which contains 54% of HF exchange, performs very well with a maximum of 4.5% of difference with respect to the reference values. On the other hand, employing less HF exchange leads to an overestimation of the responses whereas range-separated hybrids generally underestimate the second hyperpolarizabilities. Finally, the use of spin-projected methods for these 1,3-dipole triplet molecules has a little impact since the spin contamination is almost negligible.

Investigating the first hyperpolarizability of liquid carbon tetrachloride

Sequential QMMM calculations have been carried out to investigate the first hyperpolarizability of liquid CCl₄.

Hyperpolarizability dispersion measured for (CH3)2O

The third-order nonlinear-optical susceptibility of dimethyl ether, (CH3)2O, has been measured in the gas phase over the wavelength range 488 nm < λ < 1064 nm using the technique of gas-phase electric-field-induced second-harmonic generation with periodic phase matching and with N2 as the reference gas. Measurements span a range of temperature, which allows for separation of the temperature-independent second hyperpolarizability term from the temperature-dependent first hyperpolarizability term. The dispersion curves of the isotropically averaged first and second hyperpolarizabilities (β and γ) are deduced.

The first hyperpolarizability of nitrobenzene in benzene solutions: investigation of the effects of electron correlation within the sequential QM/MM approach

Molecular polarization due to solvation amplifies the impact of electron correlation on the first hyperpolarizability of nitrobenzene.