Hyperpolarizabilities Of Molecules Research Articles

Predict the Polarizability and Order of Magnitude of Second Hyperpolarizability of Molecules by Machine Learning.

In order to determine the polarizability and hyperpolarizability of a molecule, several key parameters need to be known, including the excitation energy of the ground and excited states, the transition dipole moment, and the difference of dipole moment between the ground and excited states. In this study, a machine-learning model was developed and trained to predict the molecular polarizability and second-order hyperpolarizability on a subset of QM9 data set. The density of states was employed as input to the model. The results demonstrated that the machine-learning model effectively estimated both polarizability and the order of magnitude of second-order hyperpolarizability. However, the model was unable to predict the dipole moment and first-order hyperpolarizability, suggesting limitations in its ability to predict the difference of dipole moment between the ground and excited states. The computational efficiency of machine-learning models compared to traditional quantum mechanical calculations enables the possibility of large-scale screening of molecules that satisfy specific requirements using existing databases. This work presents a potential solution for the efficient exploration and analysis of molecules on a larger scale.

Impact of polycyclic aromatic hydrocarbons and heteroatomic bridges (N, S, and O) on optoelectronic properties of 1,3,5‐triazine derivatives: A computational insight

AbstractThe theoretical investigation of four series of 1,3,5‐triazine derivatives (viz.,TN,NTN,STN, andOTNseries), which are substituted with polycyclic aromatic hydrocarbons, is carried out by employing density functional theory and time dependent‐density functional theory. The triazine ring acts as electron acceptor (A) and polycyclic aromatic hydrocarbons act as electron donors (D). The aromatic hydrocarbons like benzene, naphthalene (two fused rings), anthracene (three fused rings), and pyrene (four fused rings) are substituted on 1,3,5‐triazine core by means of a bridging heteroatom N, S, and O in the case ofNTN,STN, andOTNseries of molecules, respectively, whereas polycyclic aromatic hydrocarbons are directly connected to 1,3,5‐triazine in the case ofTNseries of molecules. The present work aims at examining the impact of number of fused aromatic rings and changing the bridging unit between electron acceptor and electron donor on absorption properties, HOMO‐LUMO gap and first hyperpolarizabilities of molecules under study and provides important insights for architecture of organic molecules for applications in organic optoelectronics.

Substituent and solvent effects on geometric and electronic structure of C5H5Ir(PH3)3 iridabenzene: A theoretical insight

Using MPW1PW91 quantum chemical calculations, we report structures, frontier orbital analysis, natural bond analysis, and aromaticity of the C5H5Ir(PH3)3 iridabenzene and XC5H4Ir(PH3)3para-substituted iridabenzenes. The substituent effects were estimated from the donor–acceptor interaction energies of the natural bond orbitals of substituent and iridabenzene frame. Nucleus-independent chemical shift (NICS) has been evaluated to understand the aromaticity. Time dependent density functional theory (TD-DFT) is used to calculate the energy, oscillatory strength and wavelength absorption maxima (λmax) of electronic transitions and their nature. Changes in hyperpolarizability of molecules are studied. Influence of solvent on the structure, frontier orbital energies, λmax, and hyperpolarizability of C5H5Ir(PH3)3 iridabenzene has been studied.

Finding optimal finite field strengths allowing for a maximum of precision in the calculation of polarizabilities and hyperpolarizabilities

The finite field method, widely used for the calculation of static dipole polarizabilities or the first and second hyperpolarizabilities of molecules and polymers, is thoroughly explored. The application of different field strengths and the impact on the precision of the calculations were investigated. Borders could be defined and characterized, establishing a range of feasible field strengths that guarantee reliable numerical results. The quality of different types of meshes to screen the feasible region is assessed. Extrapolation schemes are presented that reduce the truncation error and allow to increase the precision of finite field calculations by one to three orders of magnitude.

Parity-selective enhancement of field-free molecular orientation in an intense two-color laser field

We investigated the characteristics of molecular orientation induced by a nonresonant two-color femtosecond laser field. By analyzing the rotational dynamics of asymmetric linear molecules, we revealed that the critical parameter in characterizing the molecular orientation was the hyperpolarizability of molecules that selected the excitation paths of rotational states between parity-changing and parity-conserving transitions. Especially, in the case of molecules with small hyperpolarizability, a significant enhancement of orientation was achieved at the half-rotational period, instead of the full-rotational period. This deeper understanding of the hyperpolarizability-dependent characteristics of molecular orientation in a two-color scheme can provide an effective method to achieve significantly enhanced field-free orientation for various polar molecules.

A Lanczos-chain driven approach for calculating damped vibrational configuration interaction response functions

We present an approach based on the Lanczos method for calculating the vibrational configuration interaction response functions necessary for evaluating the pure vibrational contributions to the polarizabilities and first hyperpolarizabilities of molecules. The method iteratively builds a tridiagonal representation of the central response matrix, which is subsequently used for solving the response equations. From the same chain, the response functions can be evaluated approximately for any frequency as well as using any complex damping factor. Applications to formaldehyde, cyclopropene, and uracil illustrate the concepts presented.

Analytic Calculations of Vibrational Hyperpolarizabilities in the Atomic Orbital Basis

We present an analytic scheme for the calculation of pure vibrational contributions to linear and nonlinear optical properties such as the polarizability and the first and second hyperpolarizabilities. The formalism is fully expressed in terms of a perturbation- and time-dependent atomic orbital basis, using the elements of the density matrix in the atomic orbital basis as the basic variables. We calculate perturbed densities up to third order with respect to the electric field in accordance with the n + 1 rule, and the approach is therefore applicable for the calculation of pure vibrational contributions involving all vibrational coordinates in large molecular complexes. In the case of static electric fields, we therefore only need to calculate 19 response equations, independent of the size of the molecule. If we can determine the molecular energy and force field, the calculation of pure vibrational contributions to the nonlinear optical properties of the molecule is therefore a rather straightforward task. We illustrate the implementation by calculating pure vibrational contributions to the first and second hyperpolarizabilities of molecules containing up to 66 atoms using basis sets of good quality.

Nonlinear optical response from periodic molecular structures

The explicit expressions of all independent components of the molecular crystal nonlinear susceptibility (NS) tensor (of any order) are given through the independent components of hyperpolarizability (HP) tensors of the constituting molecules. This expression has a polynomial form of convolutions of HP components and includes local field tensor components; each product contains from 1 to k−1 HP cofactors of all preceding ranks, and k is NS rank. The Bloembergen-Armstrong formula for the first NS and Hurst-Munn for the second NS are particular cases of this expression. The reciprocal equation for molecular HP in terms of crystal NS is also presented. The Lorentz formula of the phenomenological reaction field theory is derived from the microscopic crystal Hartree-Fock HP equations with the Madelung polarization potential included. The derivation is based on the expansion of the Madelung polarization interaction over the inter-ion distances. The second order term of this expansion is expressed through the Lorentz tensor components. The expansion is obtained due to a convenient method of calculation of the Madelung crystal sums. This technique enabled to reformulate for a molecular crystal the existing computational quantum methods for lone molecules. In particular, Hartree-Fock equations for HP of molecules are adjusted for the optical properties of molecular crystals and layers. The illustrative examples, demonstrating various aspects of the mentioned techniques, are presented.

Fixing chiral molecules in space by intense two-color phase-locked laser fields

A new scheme is proposed to uniquely orient molecules of arbitrary symmetry with respect to the laboratory frame by the interaction of a phase-locked superposition of intense, ( ω , 2 ω ) two-color laser fields whose polarization directions cross each other obliquely with the polarizability and hyperpolarizability of molecules. Applicability of the present scheme is demonstrated for l-alanine by deriving theoretically the quasi-stationary states created adiabatically in a long laser pulse. The results show that a sufficiently high degree of 3D orientation can be achieved in the moderate laser-intensity range ( 10 12 – 10 13 W/cm 2 ) when the initial rotational temperature is as low as 10 - 1 K.

Hartree-Fock Calculations of Optical Hyperpolarizability of Molecules, Fullerenes, and Carbon Nanotubes Interacting With Ionic Crystal Surface

The matrix form of TDHF theory for HP is summarized and illustrated by π-electronic applications. The description of intermolecular interaction in crystals by means of the Madelung method is given. A technique of the Lorentz tensor calculation is improved and applied to compare with the direct Hartree-Fock computation of various hyperpolarizabilities. A microscopic explanation of SHG by fullerene C60 is presented. The possibility of SHG by finite length carbon nanotubes is discussed.

Interference of coherently scattered signals in the laser SRS-CARS monitoring of hydrogen concentration in gas mixtures

The possibility of measuring the hydrogen impurity concentration in dense gas mixtures by coherent anti-Stokes Raman scattering (CARS) is studied. In this technique, biharmonic laser pumping based on stimulated Raman scattering (SRS) in compressed hydrogen is used. Because of the interference between the coherent scattering components from buffer gas molecules and molecules of the impurity to be detected, the signal recorded may depend on the hydrogen concentration by a parabolic law, which has a minimum and makes the results uncertain. It is shown that this uncertainty can be removed if the frequency of the biharmonic laser pump, which is produced by the SRS oscillator, somewhat differs from the frequency of molecular oscillations of hydrogen in the test mixture. A sensitivity of 5 ppm is obtained as applied to the hydrogen-air mixture under normal pressure. The coefficients of the nonresonance cubic hyperpolarizability of molecules and atoms are measured relative to nitrogen in a number of gas media.

The influence of solvent on the two-photon absorption cross section and hyperpolarizability of molecules exhibiting large solvatochromic shifts

A theoretical approach to the effect of influence of solute/solvent interaction on the electronic contributions to the two-photon absorption cross section (δ) is presented. The solvent effect was included via a discrete quantum-mechanical Langevin dipoles/Monte Carlo method. The calculations of δ were performed for the first excited singlet state connected with the intramolecular charge transfer (CT). The results of calculations demonstrate the existence of the significant solvent effect on the two-photon absorption cross section (δ) of the charge-transfer chromophore (p-nitroaniline) exhibiting large solvatochromic shifts. The results of quantum-chemical calculations are analyzed based on the simple two-state model.

Incoherent subharmonic light scattering in isotropic media

Incoherent subharmonic light scattering in isotropic media is a new kind of nonlinear light scattering, which involves single input photon and multiple output photons of equal frequency. We investigate theoretically the dependence of the subharmonic scattering intensity on the hyperpolarizability of molecules and the incident intensity using nonlinear optics theory similar to that used for Hyper-Rayleigh scattering and degenerate optical parametric oscillators. It is derived that the subharmonic scattering intensities grow exponentially or superexponentially with the hyperpolarizability of molecules and the incident intensity.

Floquet gauge-invariant coupled perturbation theory in calculations of the optical susceptibilities of molecules

A trial wave function applied in variational calculations of the dynamic hyperpolarizabilities of molecules in the Floquet theory is analyzed. It is proved that, when a variational parameter is introduced into the phase multiplier of the trial function, the two methods of description of the interaction between a molecule and a field of a light wave in the dipole approximation with the use of scalar or vector potentials turn out to be identical, as in the rigorous theory. The concept of the gauge-invariant Floquet method as a method of approximate calculation in a finite basis is introduced. Based on the Floquet theory, this method yields identical results in both gauges. A system of equations for the variational parameters is obtained in terms of the suggested method. The perturbation theory is developed on the basis of this system of equations, and the formulas for the first and second derivatives of the Fourier component of the electronic dipole moment of the molecule are derived. These formulas, in combination with the formulas of numerical differentiation, allow one to calculate the dynamic polarizabilities and the first and second hyperpolarizabilities of molecules with the use of the gauge-invariant method.

Intensity-carrying modes important for vibrational polarizabilities and hyperpolarizabilities of molecules: derivation from the algebraic properties of formulas and applications.

The intensity-carrying mode (ICM) theory is developed for analyzing the vibrational motions that mainly contribute to vibrational polarizabilities and hyperpolarizabilities, which are important for describing intermolecular electrostatic interactions and nonlinear optical properties of molecules. The ICMs are derived from dipole derivatives, polarizability derivatives, and first hyperpolarizability derivatives by using algebraic properties of intensity formulas. The way to obtain explicit forms of ICMs, including the optimization method of the basis of the ICM vector space, is discussed in detail. One- and two-dimensional models are constructed on the basis of the ICMs. The theory is applied to three molecules (a push-pull type polyene, a streptocyanine dye cation, and a symmetric neutral polyene) taken as typical examples. It is shown that the ICM theory provides a reasonable picture on the vibrational polarization properties of these molecules. On the basis of this result, the validity of the valence-bond charge transfer (VB-CT) model, which is a one-dimensional model and is widely used to describe the electronic and vibrational properties of dye molecules, is also discussed.

Hyper-Rayleigh scattering in the Fourier domain for higher precision: Correcting for multiphoton fluorescence with demodulation and phase data

An improved experimental technique for the suppression of the multiphoton fluorescence contribution in hyper-Rayleigh scattering experiments for the determination of the first hyperpolarizability of molecules in solution is presented. This improvement allows for a better correction for the fluorescence artifact, so as to eliminate any overestimation for the value of the first hyperpolarizability. The measurement of the demodulation only of the fluorescence as a function of modulation frequency [Olbrechts et al., Rev. Sci. Instrum. 69, 2233 (1998)] is now complemented by the measurement of the phase lag between the intermediate scattering and the time-delayed fluorescence. From the simultaneous data reduction of demodulation and phase shift toward the hyperpolarizability, fluorescence contribution, and fluorescence lifetime, an improvement in precision of 1 order of magnitude is demonstrated. This level of precision has been used to show the relative impact of f-orbital filling and ligands on the molecular second-order nonlinear optical response of lanthanide complexes containing a hemicyanine chromophore.

Generalized integral-screening for efficient calculations of nonlinear optical properties of large molecules

We describe the implementation of integral screening in the integral-direct SCF calculation of cubic response functions. The screening is applied to all computational steps that involve the construction of Fock matrices or one-index transformed Fock matrices. We apply this implementation to study the length dependence of the polarizability and second hyperpolarizability of diphenylpolyenes. It is demonstrated that calculations of the second hyperpolarizability of molecules containing more than 140 atoms are now accessible by ab initio methods on a time scale that makes it of interest in real applications.

FEMTOSECOND HYPER-RAYLEIGH SCATTERING STUDY OF SPATIAL ORIENTATIONAL CORRELATIONS BETWEEN CHROMOPHORES

Since the introduction of Hyper-Rayleigh scattering (HRS) as a measurement technique for the first hyperpolarizability of molecules in solution,1 the importance of fluctuations was realized.2 For isotropic solutions, a combination of the spatial and temporal orientational fluctuations causes the instantaneous and local deviation from macroscopic centrosymmetry, necessary to observe a second-order signal. The fluctuations in the spatial orientational distribution function of nonlinear optical chromophores cause an HRS signal that fluctuates as a function of position in solid samples. The correlation length, characterizing the decay of the autocorrelation function of this fluctuating signal, indicates the degree of spatial correlation between these chromophores. The development of femtosecond HRS was instrumental for the study of orientational correlations.3

Hyper-Rayleigh Scattering (Hrs) In Isotropic Media

ABSTRACTIn this paper some of the more important Hyper Rayleigh Scattering (HRS) Measurements performed in our laboratory are reviewed. The results of experiments conducted on polymers, the protein Bacteriorhodopsin, retinal derivatives and octopoles are presented. Basic HRS theory, along with a brief description of the HRS set-up, is also included.We demonstrate that the experimental simplicity of HRS allows for an accurate determination of the first hyperpolarizability of molecules that could not have been measured by the more traditional Electric Field Induced Second Harmonic Generation (EFISHG) technique.

Hyperpolarizabilities of molecules with frequency dependence and electron correlation

Frequency dependent second hyperpolarizabilities of N2 and the prototype organic molecule trans-butadiene are reported using generalized time dependent Hartree–Fock (TDHF) theory for several frequencies of applied fields. A monotonic increase of the values (positive dispersion) is observed for every nonlinear optical process in a range of frequencies for the applied field. Correlation effects are estimated using a second-order many body perturbation theory and coupled cluster singles and doubles relaxed density method for the analytical determination of the induced dipole moment. Such hybrid results for DC-induced second harmonic generation provide reasonable values in comparison with experiment for N2. However, dispersion and correlation effects in trans-butadiene are both found to be large and could be nonadditive.