Electron correlation effects on the first hyperpolarizability of push-pull π-conjugated systems

The first hyperpolarizability (β) of representative push-pull π-conjugated compounds has been calculated at several levels of approximation to assess the effects of electron correlation. First, the 6-31+G(d) basis set has been shown to give the best balance between accuracy and computational resources for a polyene linker whereas for polyyne linker, the 6-31G(d) basis set is already an optimal choice. As a result of cancellations between higher order contributions, the MP2 method turns out to be the method of choice to predict β of push-pull π-conjugated systems since it closely reproduces the values obtained with the reference CCSD(T) scheme. Moreover, the SDQ-MP4 and CCSD approaches provide rarely improved estimates over MP2 while the MP4 method does not represent an improvement over MP4-SDQ or the SCS-MP2 method, over MP2. Among density functional theory exchange-correlation functionals, LC-BLYP is reliable when characterizing the changes of first hyperpolarizability upon enlarging the π-conjugated linker or upon changing the polyyne linker into a polyene segment. Nevertheless, its reliability is very similar to what can be achieved with the Hartree-Fock method and the MP2 scheme is by far more accurate. On the other hand, the BLYP, B3LYP, and BHandHLYP functionals perform quantitatively better in a number of cases but the trends are poorly described. This is also the case of the B2-PLYP and mPW2-PLYP functionals, which are often the most accurate, though they underestimate the increase of β when going from polyyne to polyene linkers and overestimate the enhancement of β with chain length.     

Monitoring storage time and quality attribute of egg based on electronic nose

The objective of this study was to investigate the potential of an electronic nose (E-nose) technique for monitoring egg storage time and quality attributes. An electronic nose was used to distinguish eggs under cool and room-temperature storage by means of principal component analysis (PCA), linear discriminant analysis (LDA), BP neural network (BPNN) and the combination of a genetic algorithm and BP neural network (GANN). Results showed that the E-nose could distinguish eggs of different storage time under cool and room-temperature storage by LDA, PCA, BPNN and GANN; better prediction values were obtained by GANN than by BPNN. Relationships were established between the E-nose signal and egg quality indices (Haugh unit and yolk factor) by quadratic polynomial step regression (QPSR). The prediction models for Haugh unit and yolk factor indicated a good prediction performance. The Haugh unit model had a standard error of prediction of 3.74 and correlation coefficient 0.91; the yolk factor model had a 0.02 SEP and 0.93 correlation coefficient between predicted and measured values respectively.     

NLO‐X (X = I–III): New Gaussian basis sets for prediction of linear and nonlinear electric properties

New adjusted Gaussian basis sets are proposed for first and second rows elements (H, B, C, N, O, F, Si, P, S, and Cl) with the purpose of calculating linear and mainly nonlinear optical (L–NLO) properties for molecules. These basis sets are new generation of Thakkar‐DZ basis sets, which were recontracted and augmented with diffuse and polarization extrabasis functions. Atomic energy and polarizability were used as reference data for fitting the basis sets, which were further applied for prediction of L–NLO properties of diatomic, H₂, N₂, F₂, Cl₂, BH, BF, BCl, HF, HCl, CO, CS, SiO, PN, and polyatomic, CH₄, SiH₄, H₂O, H₂S, NH₃, PH₃, OCS, NNO, and HCN molecules. The results are satisfactory for all electric properties tested; dipole moment (µ), polarizability (α), and first hyperpolarizability (β), with an affordable computational cost. Three new basis sets are presented and called as NLO‐I (ADZP), NLO‐II (DZP), and NLO‐III (VDZP). The NLO‐III is the best choice to predict L–NLO properties of large molecular systems, because it presents a balance between computational cost and accuracy. The average errors for β at B3LYP/NLO‐III level were of 8% for diatomic molecules and 14% for polyatomic molecules that are within the experimental uncertainty. © 2014 Wiley Periodicals, Inc.     

A sum-over-state scheme of analysis of hyperpolarizabilities and its application to spiroconjugated molecular system

The static first and second hyperpolarizabilities of a number of spiromolecules with varying degree of polarity have been calculated at the HF and MP2 level using the 6-31+G* basis set and the B3LYP/6-31+G* optimized geometry. The variation of mean second hyperpolarizability in these molecular systems has been explained in terms of the ground state dipole moment, mean linear polarizability and second-order polarizability. A number of relationships among these quantities have been derived in the framework of the sum-over-state scheme and the generalized Thomas–Kuhn sum rule. The spiroconjugation results in the significant increase of the mean polarizability. The appreciable enhancement of first hyperpolarizability due to the spiroconjugation between two dipolar monomer units has been accounted for the rather significant increase of the mean polarizability tensor and the ground state dipole moment. The relatively larger value of the average second hyperpolarizability of the spiroconjugated molecules compared to that of the corresponding monomers arises from the rather significant increase of the nonaxial component γ _xxyy . The replacement of spirocarbon by spirosilicon results in the enhancement of the cubic polarizability manifold. The donor–acceptor substituted spirocompounds are predicted to be the superior third-order nonlinear optical (NLO) phores. The nature of π-conjugation in the monomer units around the spirocenter shows a strong modulation of the NLO properties of spirocompounds. The influence of electron correlation on the NLO properties at the MP2 level has been found to be rather significant.     

Modulation of the Second Order Nonlinear Optical Properties of Helical Graphene Nanoribbons Through Introducing Azulene Defects or/and BN Units

The current study has obtained excellent potential nonlinear optical(NLO) materials by combining density functional theory methods with sum-over-states model to predict the second order NLO properties of helical graphene nanoribbons(HGNs) through introducing azulene defects or/and BN units. The introduction of these functional groups deforms the pristine HGN (compression or tension) and enhances obviously the static first hyperpolarizability(<b₀>) of system by up to two orders of magnitude. The tensor components along the helical axis of HGNs play a dominant role in the total <b₀>. The azulene defects and the BN units polarize the pristine HGN to different degrees, and the azulenes and contiguous benzenes are involved in the major electron excitations with significant contributions to <b₀> but the BN units are not. The BN-doped chiral HGNs have good kinetic stability and strong second order NLO properties(6.84×10⁵×10^-30 esu), and can be a potential candidate of high-performance second order NLO materials. The predicted two-dimensional second order NLO spectra provide useful information for further exploration of those helicenes for electro-optic applications.     

Ab initio potential-energy surfaces for complex, multichannel systems using modified novelty sampling and feedforward neural networks

A neural network/trajectory approach is presented for the development of accurate potential-energy hypersurfaces that can be utilized to conduct ab initio molecular dynamics (AIMD) and Monte Carlo studies of gas-phase chemical reactions, nanometric cutting, and nanotribology, and of a variety of mechanical properties of importance in potential microelectromechanical systems applications. The method is sufficiently robust that it can be applied to a wide range of polyatomic systems. The overall method integrates ab initio electronic structure calculations with importance sampling techniques that permit the critical regions of configuration space to be determined. The computed ab initio energies and gradients are then accurately interpolated using neural networks (NN) rather than arbitrary parametrized analytical functional forms, moving interpolation or least-squares methods. The sampling method involves a tight integration of molecular dynamics calculations with neural networks that employ early stopping and regularization procedures to improve network performance and test for convergence. The procedure can be initiated using an empirical potential surface or direct dynamics. The accuracy and interpolation power of the method has been tested for two cases, the global potential surface for vinyl bromide undergoing unimolecular decomposition via four different reaction channels and nanometric cutting of silicon. The results show that the sampling methods permit the important regions of configuration space to be easily and rapidly identified, that convergence of the NN fit to the ab initio electronic structure database can be easily monitored, and that the interpolation accuracy of the NN fits is excellent, even for systems involving five atoms or more. The method permits a substantial computational speed and accuracy advantage over existing methods, is robust, and relatively easy to implement.     

Applicability of hybrid density functional theory methods to calculation of molecular hyperpolarizability

The donor/acceptor (D/A) substituted pi-conjugated organic molecules possess extremely fast nonlinear optical (NLO) response time that is purely electronic in origin. This makes them promising candidates for optoelectronic applications. In the present study, we utilized four hybrid density functionals (B3LYP, B97-2, PBE0, BMK), Hartree-Fock, and second order Moller-Plesset correlation energy correction, truncated at second-order (MP2) methods with different basis sets to estimate molecular first hyperpolarizability (beta) of D/A-substituted benzenes and stilbenes (D=OMe, OH, NMe(2), NH(2); A=NO(2), CN). The results of density functional theory (DFT) calculations are compared to those of MP2 method and to the experimental data. We addressed the following questions: (1) the accurate techniques to compare calculated results to each other and to experiment, (2) the choice of the basis set, (3) the effect of molecular planarity, and (4) the choice of the method. Comparison of the absolute values of hyperpolarizabilities obtained computationally and experimentally is complicated by the ambiguities in conventions and reference values used by different experimental groups. A much more tangible way is to compare the ratios of beta's for two (or more) given molecules of interest that were calculated at the same level of theory and measured at the same laboratory using the same conventions and reference values. Coincidentally, it is the relative hyperpolarizabilities rather than absolute ones that are of importance in the rational molecular design of effective NLO materials. This design includes prediction of the most promising candidates from particular homologous series, which are to be synthesized and used for further investigation. In order to accomplish this goal, semiquantitative level of accuracy is usually sufficient. Augmentation of the basis set with polarization and diffuse functions changes beta by 20%; however, further extension of the basis set does not have significant effect. Thus, we recommend 6-31+G(*) basis set. We also show that the use of planar geometry constraints for the molecules, which can somewhat deviate from planarity in the gas phase, leads to sufficient accuracy (with an error less than 10%) of predicted values. For all the molecules studied, MP2 values are in better agreement with experiment, while DFT hybrid methods overestimate beta values. BMK functional gives the best agreement with experiment, with systematic overestimation close to the factor of 1.4. We propose to use the scaled BMK results for prediction of molecular hyperpolarizability at semiquantitative level of accuracy.     

How does hybrid bridging core modification enhance the nonlinear optical properties in donor‐π‐acceptor configuration? A case study of dinitrophenol derivatives

This study spotlights the fundamental insights about the structure and static first hyperpolarizability (β) of a series of 2,4‐dinitrophenol derivatives (1–5), which are designed by novel bridging core modifications. The central bridging core modifications show noteworthy effects to modulate the optical and nonlinear optical properties in these derivatives. The derivative systems show significantly large amplitudes of first hyperpolarizability as compared to parent system 1 , which are 4, 46, 66, and 90% larger for systems 2, 3, 4 , and 5 , respectively, at Moller–Plesset (MP2)/6‐31G* level of theory. The static first hyperpolarizability and frequency dependent coupled‐perturbed Kohn–Sham first hyperpolarizability are calculated by means of MP2 and density functional theory methods and compared with respective experimental values wherever possible. Using two‐level model with full‐set of parameters dependence of transition energy (ΔΕ), transition dipole moment (μ⁰) as well as change in dipole moment from ground to excited state (Δμ), the origin of increase in β amplitudes is traced from the change in dipole moment from ground to excited state. The causes of change in dipole moments are further discovered through sum of Mulliken atomic charges and intermolecular charge transfer spotted in frontier molecular orbitals analysis. Additionally, analysis of conformational isomers and UV‐Visible spectra has been also performed for all designed derivatives. Thus, our present investigation provides novel and explanatory insights on the chemical nature and origin of intrinsic nonlinear optical (NLO) properties of 2,4‐dinitrophenol derivatives. © 2014 Wiley Periodicals, Inc.     

Theoretical studies on nonlinear optical properties of formaldehyde oligomers by ab initio and density functional theory methods

The first and second hyperpolarizability beta and gamma are obtained for formaldehyde oligomers (H2CO)n (n = 1-7) using computational methods. We have used the finite field (FF) approach and hyperpolarizability density analysis (HDA) to predict the microscopic first and second nonlinear hyperpolarizability of the formaldehyde oligomers. The spatial contributions of electrons to the hyperpolarizability by using plots of HDA are presented. It has been found from the numerical stability checking of the hyperpolarizability calculations that the calculated values by FF method are more stable than those by HDA approach. The values of beta are zero when n is even as the molecule possesses centrosymmetry, and when n is odd, the differences among beta values are not clear. The gamma values are increased with increase in n.     

Performance of density functional theory in computing nonresonant vibrational (hyper)polarizabilities

A set of exchange‐correlation functionals, including BLYP, PBE0, B3LYP, BHandHLYP, CAM‐B3LYP, LC‐BLYP, and HSE, has been used to determine static and dynamic nonresonant (nuclear relaxation) vibrational (hyper)polarizabilities for a series of all‐trans polymethineimine (PMI) oligomers containing up to eight monomer units. These functionals are assessed against reference values obtained using the Møller–Plesset second‐order perturbation theory (MP2) and CCSD methods. For the smallest oligomer, CCSD(T) calculations confirm the choice of MP2 and CCSD as appropriate for assessing the density functionals. By and large, CAM‐B3LYP is the most successful, because it is best for the nuclear relaxation contribution to the static linear polarizability, intensity‐dependent refractive index second hyperpolarizability, static second hyperpolarizability, and is close to the best for the electro‐optical Pockels effect first hyperpolarizability. However, none of the functionals perform satisfactorily for all the vibrational (hyper)polarizabilities studied. In fact, in the case of electric field‐induced second harmonic generation all of them, as well as the Hartree–Fock approximation, yield the wrong sign. We have also found that the Pople 6–31+G(d) basis set is unreliable for computing nuclear relaxation (hyper)polarizabilities of PMI oligomers due to the spurious prediction of a nonplanar equilibrium geometry. © 2013 Wiley Periodicals, Inc.     

Improving the accuracy of density-functional theory calculation: the genetic algorithm and neural network approach

The combination of genetic algorithm and neural network approach (GANN) has been developed to improve the calculation accuracy of density functional theory. As a demonstration, this combined quantum mechanical calculation and GANN correction approach has been applied to evaluate the optical absorption energies of 150 organic molecules. The neural network approach reduces the root-mean-square (rms) deviation of the calculated absorption energies of 150 organic molecules from 0.47 to 0.22 eV for the TDDFTB3LYP6-31G(d) calculation, and the newly developed GANN correction approach reduces the rms deviation to 0.16 eV.     

Density Functional Theory Investigation on the Second‐Order Nonlinear Optical Properties of Chlorobenzyl‐o‐Carborane Derivatives

The structures and second‐order nonlinear optical (NLO) properties of a series of chlorobenzyl‐o‐carboranes derivatives ( 1 – 12 ) containing different push‐pull groups have been studied by density functional theory (DFT) calculation. Our theoretical calculations show that the static first hyperpolarizability (β_tot) values gradually increase with increasing the π‐conjugation length and the strength of electron donor group. Especially, compound 12 exhibits the largest β_tot (62.404×10^?30 esu) by introducing tetrathiafulvalene (TTF), which is about 76 times larger than that of compound 1 containing aryl. This means that the appropriate structural modification can substantially increase the first hyperpolarizabilities of the studied compounds. For the sake of understanding the origin of these large NLO responses, the frontier molecular orbitals (FMOs), electron density difference maps (EDDMs), orbital energy and electronic transition energy of the studied compounds are analyzed. According to the two‐state model, the lower transition energy plays an important role in increasing the first hyperpolarizability values. This study may evoke possible ways to design preferable NLO materials.     

Nonlinear optical properties of polydiacetylene with donor-acceptor substitution block

The elongation finite-field (elongation-FF) method is applied to donor/acceptor substituted polydiacetylenes (PDAs) for the estimation of substituent effects on nonlinear optical (NLO) properties. The first hyperpolarizability (beta) and the second hyperpolarizability (gamma) of PDA with separated donor and acceptor substitution blocks have much larger values than those of the other substituted PDAs. For the PDAs with donor and acceptor substitution blocks, the relationship between the NLO properties and the block period is examined. It is shown, from the local density of states, that gamma of a system with a quantum well structure has a maximum value at a certain block size. This indicates that by tuning the size of proper block it is possible to achieve the largest gamma value in block polymers. Furthermore, the through-space/bond interaction analysis is performed to examine the pi-conjugation effects on the NLO properties for particular substituted PDA. It is demonstrated by our quantitative analysis that beta is affected by electron transfers in the molecule, and the quantum well structure is critical for gamma improvement.     

BAND NN: A Deep Learning Framework for Energy Prediction and Geometry Optimization of Organic Small Molecules

Recent advances in artificial intelligence along with the development of large data sets of energies calculated using quantum mechanical (QM)/density functional theory (DFT) methods have enabled prediction of accurate molecular energies at reasonably low computational cost. However, machine learning models that have been reported so far require the atomic positions obtained from geometry optimizations using high-level QM/DFT methods as input in order to predict the energies and do not allow for geometry optimization. In this study, a transferable and molecule size-independent machine learning model bonds (B), angles (A), nonbonded (N) interactions, and dihedrals (D) neural network (BAND NN) based on a chemically intuitive representation inspired by molecular mechanics force fields is presented. The model predicts the atomization energies of equilibrium and nonequilibrium structures as sum of energy contributions from bonds (B), angles (A), nonbonds (N), and dihedrals (D) at remarkable accuracy. The robustness of the proposed model is further validated by calculations that span over the conformational, configurational, and reaction space. The transferability of this model on systems larger than the ones in the data set is demonstrated by performing calculations on selected large molecules. Importantly, employing the BAND NN model, it is possible to perform geometry optimizations starting from nonequilibrium structures along with predicting their energies. © 2019 Wiley Periodicals, Inc.     

Polycyclic aromatic hydrocarbon-substituted push–pull chromophores: an investigation of optoelectronic and nonlinear optical properties using experimental and theoretical approaches

A series of new push–pull chromophores were synthesized in moderate to very high yields (65%–97%) by treating TCNE and TCNQ with alkynes substituted by electron-rich diethylaniline and polycyclic aromatic hydrocarbons. Some of the chromophores exhibit strong intramolecular charge-transfer bands in the near-IR region with λ_max values between 695 and 749 nm. With the help of experimental and theoretical analysis, it is concluded that the trend in λ _max values is affected by PAH substituents sterically, not electronically. Steric constraints led to the increased dihedral angles, reducing conjugation efficiencies. The absorption properties of push-pull compounds have been investigated in solvents possessing different polarities. All chromophores exhibited positive solvatochromism. As an additional proof of efficient charge-transfer in push–pull chromophores, quinoid character (dr) values were predicted using calculated bond lengths. Remarkably, substantial dr values (0.045–0.049) were predicted for donor diethylaniline rings in all compounds. The effects of various polycyclic aromatic hydrocarbons on optical and nonlinear optical properties were also studied by computational methods. Several parameters, such as band gaps, Mulliken electronegativity, chemical hardness and softness, dipole moments, average polarizability, first hyperpolarizability, were predicted for chromophores at the B3LYP/6-31++G(d,p) level of theory. The predicted first hyperpolarizability β_(tot) values vary between 198 to 538 × 10^–30 esu for the reported push–pull chromophores in this study. The highest predicted β_(tot) value in this study is 537.842 × 10^–30 esu, 8150 times larger than the predicted β_(tot) value of benchmark NLO material urea, suggests possible utilization of these chromophores in NLO devices. The charge-transfer character of the synthesized structures was further confirmed by HOMO-LUMO depictions and electrostatic potential maps.     

Modeling nonlinear optics of nanosystems with sum-over-states model

Three-stage strategies (ladder rule, few state model (FSM), and parallelization) were proposed to improve the computational efficiency of the sum-over-states (SOS) model in nonlinear optics (NLO) modeling. Ladder rule decomposes NLO coefficients of the nth state into the (n-1)th term and the contribution from the (n-1)th to the nth state without loss of rigor in theory. FSM singles out the states with substantial contribution to NLO. Those strategies are universal to all (including revised and simplified) SOS models. The computing cost reduces roughly to C/(n(i-1)) (C is a constant and i is the rank (order) of the NLO coefficients).     

Second-order Nonlinearities of CdS Nanoparticles Studied by Hyper-Rayleigh Scattering Technique

Optical nonlinearities of semiconductor nanoparticles are of great interest recently. So fartheir third-order nonlinear optical (NLO) properties have been widely studied. However,there are only few studies on second-order NLO properties, because it is believed that thecentrosymmetry or near-centrosymmetry of spherical nanoparticles eliminate their firstorder hyperpolarizability 6 values to'zero or near zero. And for a long time it remains aproblem to directly study the second-order=NLO pro…     

Synthesis, spectroscopic studies and nonlinear optical behavior of N,N′-bis(2-hydroxy-1-naphthylmethylidene)-1-methyl-1,2-diaminoethane-N,N′,O,O′-nickel(II)

A Schiff base complex N,N′-bis(2-hydroxy-1-naphthylmethylidene)-1-methyl-1,2- diaminoethane-N,N′,O,O′-nickel(II) has been synthesized. The title compound has been characterized by FT-IR and UV–vis spectroscopies. The UV–vis experiments indicate that the compound has solvatochromism in the UV region, implying non-zero molecular first hyperpolarizability. To investigate microscopic second-order nonlinear optical (NLO) behavior of the examined complex, the electric dipole moments (μ) and the first static hyperpolarizabilities (β) were computed using Finite Field second-order Møller Plesset (FF MP2) perturbation procedure. According to ab initio quantum mechanical calculations, the title complex exhibits non-zero β values, revealing microscopic second-order NLO behavior.     

Quantum chemical research on structures, linear and nonlinear optical properties of the Li@n-acenes salt (n = 1, 2, 3, and 4)

On the basis of the n-acenes (n = 1, 2, 3 and 4), the α-Li@n-acenes and β-Li@n-acenes salts were selected to investigate how increasing the number n of conjugated benzenoid rings affects the linear and nonlinear optical responses. The α-Li@n-acenes and β-Li@n-acenes salts are obtained by a lithium atom substituting the α-H and β-H, respectively. In the present work, both ab initio (HF and MP2) and DFT (B3LYP, BhandHLYP, M05-2X, and CAM-B3LYP) methods are adopted to calculate the polarizability (α(0)) and first hyperpolarizability (β(tot)) of the α-Li@n-acenes and β-Li@n-acenes salts. MP2 results show that the α(0) values of both classes of lithium salts increase with increasing number n of conjugated benzenoid rings. Interestingly, we found that the β(tot) values of α-Li@n-acenes and β-Li@n-acenes salts take on opposite trends: the β(tot) values of α-Li@n-acenes are decreasing slowly (2187 for α-Li@benzene > 1978 for α-Li@naphthalene > 1898 for α-Li@anthrecene > 1830 au for α-Li@tetracene) and inceasing remarkably (2738 for β-Li@naphthalene < 3186 for β-Li@anthrecene < 3314 au for β-Li@tetracene) for β-Li@n-acenes. Furthermore, we found that the β(tot) values (2738-3314 au) of the β-Li@n-acenes are larger than those of the α-Li@n-acenes (1830-2187 au). On the other hand, comparing the results of different methods, the β(tot) values obtained by the M05-2X and CAM-B3LYP methods reproduce the polarizability and first hyperpolarizability of the α-Li@n-acenes and β-Li@n-acenes salts well, which test and verify the results of the MP2 method. Our present work may be beneficial to development of high-performance organic NLO optical materials.