Finite Field Calculations Research Articles

First- and Second-Order Polarizabilities of Simple Merocyanines. An Experimental and Theoretical Reassessment of the Two-Level Model

Taking four merocyanines [(CH3)2N-(CHCH)n-C(CH 3)O; n = 1-4] (Mc1-4) as test D-A systems, we performed a close experimental and theoretical examination of the two level model with reference to its ability to provide correct predictions of both absolute values and dependence on the conjugation path length of first- and second-order molecular polarizabilities. By (1)H NMR spectroscopy merocyanines Mc1-4 were found to be approximately 1:1 mixtures of two planar conformers with cis and trans arrangements of the C(CH 3)O electron-acceptor group and all trans structure of the polyene like fragment. The degree of bond length alternancy (BLA) in the -(CHCH)n- fragment, was quantified by extensive full geometry optimizations at both semiempirical and ab initio level. DFT (6-31G**/B3LYP) optimized geometries were considered to be most reliable and were used for calculations of the excited-state properties. The applicability of the two level model, reducing the general sum-over-states (SOS) expansion to only one term involving the ground state (g) and the lowest-lying (1)(pipi*) CT state (e), was checked by analysis of fluorescence and near UV absorption spectra. Measurements of the basic two-level model quantities ( Ege, microge and Deltamicro(eg)), by which the dominant components of alpha and beta tensors are expressed (alpha XX , beta XXX , X identical with long molecular axis), were designed to give approximate free-molecule values. It is proposed, in particular, an adjustment of the solvatochromic method for the determination of Deltamicro(eg), based on accurate measurements of absorption spectral shifts in n-hexane/diethyl ether mixtures with small diethyl ether volume fractions. Such an approach led to Mc1-4 beta XXX 's matching well in both value and n-dependence with EFISH data reported in the literature for similar merocyanines. For the fluorescent Mc4, the results were qualitatively well reproduced by an approach, which combines absorption and fluorescence solvent shifts. All the measured quantities were calculated for both trans and cis Mc1-4 by three semiempirical INDO-based approaches aiming at evaluating the performances of different integral parametrizations and CI extensions: ZINDO/S, CS INDO SCI, CS INDO SDCI. In all cases, alpha XX and beta XXX were found to rise proportionally to about n (1.3) and n (2), respectively, in qualitatively good agreement with the experimental values. As to the absolute values, however, experimental alpha XX 's and beta XXX 's were best reproduced by CS INDO SDCI combining Ohno-Klopman parametrization and CI including both single and double excitations. The validity of the two-level model was checked by comparison with converged SOS calculations for the longest chain merocyanine (Mc4) and finite field calculations of linear polarizabilities for all of the four dyes (Mc1-4).

Pyrrole-Based Hydrazone Organic Nonlinear Optical Crystals and Their Polymorphs

A series of new organic nonlinear optical nitrophenylhydrazone crystals based on pyrrole with various substituents (X: -H, -CH3, -CF3) on the hydrazone group (–CX═N–NH–) has been synthesized and their polymorphs have been investigated. The chromophore 2-((2-(4-nitrophenyl)hydrazono)methyl)-1H-pyrrole (HNPH) exhibits two polymorphs with large macroscopic nonlinearity, with a powder second harmonic generation activity of 420 times and 210 times that of urea at 1.9 μm for the anisotropic polar HNPH-I with Pn space group and the isotropic nonpolar HNPH-II polymorph with P212121 space group, respectively. The microscopic and macroscopic nonlinearities in the crystallographic system have been analyzed theoretically using finite field calculations.

Frequency and Solvent Dependence of Nonlinear Optical Properties of Molecules

Real-time, time-dependent density functional theory (RT-TDDFT) is used for the evaluation of the frequency dependence of the polarizability and hyperpolarizability of molecules intended for application in electro-optic devices. These first-principles computational methods are powerful but costly. Significantly easier calculations based on a simplified version of second-order time-dependent perturbation theory, the “two-state model” (TSM), are here used to provide another estimate of the frequency dependence. Furthermore, the TSM calculations can be done in the presence of a dielectric reaction field (the polarizable continuum model method) to provide estimates of the solvent dependent properties in addition to the frequency-dependent properties. Here we use RT-TDDFT to assess the accuracy of the frequency dependence of the TS, and a ground-state finite field calculation to assess the effect of additional states on the static hyperpolarizability. Both frequency and dielectric responses are important for evaluation of the suitability of molecules in nonlinear optical applications.

Static and Frequency‐Dependent Dipole–Dipole Polarizabilities of All Closed‐Shell Atoms up to Radium: A Four‐Component Relativistic DFT Study

We test the performance of four-component relativistic density functional theory by calculating the static and frequency-dependent electric dipole-dipole polarizabilities of all (ground-state) closed-shell atoms up to Ra. We consider 12 nonrelativistic functionals, including three asymptotically shape-corrected functionals, by using two smooth interpolation schemes introduced by the Baerends group: the gradient-regulated asymptotic connection (GRAC) procedure and the statistical averaging of (model) orbital potentials (SAOP). Basis sets of doubly augmented triple-zeta quality are used. The results are compared to experimental data or to accurate ab initio results. The reference static electric dipole polarizability of palladium has been obtained by finite-field calculations using the coupled-cluster singles, doubles, and perturbative triples method within this work. The best overall performance is obtained using hybrid functionals and their GRAC shape-corrected versions. The performance of SAOP is among the best for nonhybrid functionals for Group 18 atoms but its precision degrades when considering the full set of atoms. In general, we find that conclusions based on results obtained for the rare-gas atoms are not necessarily representative of the complete set of atoms. GRAC cannot be used with effective core potentials since the asymptotic correction is switched on in the core region.

On the bond-length dependence of the static electric polarizability and hyperpolarizability of F 2

We have calculated accurate electric (hyper)polarizabilities for F 2. Relying on finite-field coupled-cluster calculations with very large, purpose-oriented basis sets we propose the following values (reference near-Hartree–Fock results in parentheses) for the mean ( α ¯ / e 2 a 0 2 E h - 1 ) and the anisotropy ( Δ α / e 2 a 0 2 E h - 1 ) of the dipole polarizability and the mean dipole hyperpolarizability ( γ ¯ / e 4 a 0 4 E h - 3 ): α ¯ = 8.4812 (8.5870), Δ α = 5.9446 (9.0719) and γ ¯ = 481 (268). For the derivatives of the dipole polarizability at R e we propose d α ¯ d R e = 3.11 and d Δ α d R e = 5.57 . Discrepancies between experimental estimates and theoretical predictions of the mean polarizability are noted and discussed.

Static dielectric response and Born effective charge of BN nanotubes fromab initiofinite electric field calculations

{\it Ab initio} investigations of the full static dielectric response and Born effective charge of BN nanotubes (BN-NTs) have been performed for the first time using finite electric field method. It is found that the ionic contribution to the static dielectric response of BN-NTs is substantial and also that a pronounced chirality-dependent oscillation is superimposed on the otherwise linear relation between the longitudinal electric polarizability and the tube diameter ($D$), as for a thin dielectric cylinderical shell. In contrast, the transverse dielectric response of the BN-NTs resemble the behavior of a thin (non-ideal) conducting cylindrical shell of a diameter of $D+4$\AA$ $, with a screening factor of 2 for the inner electric field. The medium principal component $Z_y^*$ of the Born effective charge corresponding to the transverse atomic displacement tangential to the BN-NT surface, has a pronounced $D$-dependence (but independent of chirality), while the large longitudinal component $Z_z^*$ exhibits a clear chirality dependence (but nearly $D$-independent), suggesting a powerful way to characterize the diameter and chirality of a BN-NT.

Pentacyanoiron(II) as an Electron Donor Group for Nonlinear Optics: Medium-Responsive Properties and Comparisons with Related Pentaammineruthenium(II) Complexes

In this article, we describe a series of complex salts in which electron-rich {Fe(II)(CN)(5)}(3)(-) centers are coordinated to pyridyl ligands with electron-accepting N-methyl/aryl-pyridinium substituents. These compounds have been characterized by using various techniques including electronic absorption spectroscopy and cyclic voltammetry. Molecular quadratic nonlinear optical (NLO) responses have been determined by using hyper-Rayleigh scattering (HRS) at 1064 nm, and also via Stark (electroabsorption) spectroscopic studies on the intense, visible d --> pi* metal-to-ligand charge-transfer (MLCT) bands. The relatively large static first hyperpolarizabilities, beta(0), increase markedly on moving from aqueous to methanol solutions, accompanied by large red-shifts in the MLCT transitions. Acidification of aqueous solutions allows reversible switching of the linear and NLO properties, as shown via both HRS and Stark experiments. Time-dependent density functional theory and finite field calculations using a polarizable continuum model yield relatively good agreement with the experimental results and confirm the large decrease in beta(0) on protonation. The Stark-derived beta(0) values are generally larger for related {Ru(II)(NH(3))(5)}(2+) complexes than for their {Fe(II)(CN)(5)}(3)(-) analogues, consistent with the HRS data in water. However, the HRS data in methanol show that the stronger solvatochromism of the Fe(II) complexes causes their NLO responses to surpass those of their Ru(II) counterparts upon changing the solvent medium.

Synthesis, molecular structure, spectroscopic studies and second-order nonlinear optical behaviour of N, N′-(2-hydroxy-propane-1,3-diyl)-bis(5-nitrosalicylaldiminato- N, O)-copper(II)

N, N′-(2-Hydroxy-propane-1,3-diyl)-bis(5-nitrosalicylaldiminato- N, O)-copper(II) has been synthesized. The crystal structure has been determined by X-ray diffraction analysis, and linear optical characterization has been determined by UV–vis spectroscopy. It was found that the molecule under investigation has solvatochromic behaviour in the UV region, implying non-zero microscopic first hyperpolarizability. To reveal the microscopic nonlinear optical (NLO) properties, the static first hyperpolarizabilities ( β) and the electric dipole moments ( μ) were evaluated by using the ab initio finite field (FF) method. According to the results of the FF calculations, the synthesized compound exhibits non-zero β values, and it might have microscopic NLO behaviour.

The first hyperpolarizabilities of hemicyanine cationic derivatives studied by finite-field (FF) calculations

In this paper, we have designed 26 hemicyanine cationic derivatives by selecting π-conjugated bond and increasing alkyl chain length of electron donor (D) group and of electron acceptor (A) in order to describe their structure–property relationship. The geometries and molecular frontier orbitals are obtained from semi-empirical PM3 method. The finite-field (FF) method is performed to calculate molecular first hyperpolarizability ( β). It is concluded that hemicyanine molecular second-order nonlinear optical (NLO) properties are not dependent on σ-chain (abbreviation for the alkyl chain connected to cationic pyridinium ring) but determined by donor and acceptor. With the π-conjugation length increasing, the magnitudes of β increase and approach saturation, while the HOMO–LUMO energy gap Δ E HL values decrease resulting in red shift of absorption spectra peak. Moreover, it is interesting to note that the first hyperpolarizabilities of hemicyanine derivatives are linearly related to the HOMO–LUMO energy gap Δ E HL. It may be helpful to further understand the structure–property relationship of the organic NLO materials.

Quantum-chemical investigation of second-order nonlinear optical chromophores: Comparison of strong nitrile-based acceptor end groups and role of auxiliary donors and acceptors

We report a detailed quantum-chemical investigation of donor-acceptor substituted dipolar nonlinear optical chromophores incorporating the 4-(dimethylamino)phenyl donor end group and a variety of strong heterocyclic acceptor end groups, including tricyanofurans and tricyanopyrroles. In particular, we study the variation of the molecular second-order polarizability (beta) with the acceptor end group and when inserting auxiliary donors (thiophene) and acceptors (thiazole) into the pi bridge. Both finite-field calculations (in the context of local contributions) and sum-over-states calculations were carried out in order to probe the relationship between beta and the chemical structure of the various chromophores. The trends obtained with these two methods are fully consistent. The large beta values (up to 700 x 10(-30) esu) as well as the observed tunability of the optical absorption maximum (lambda(max)) make the chromophores investigated here interesting candidates for use in electro-optic applications at telecommunications wavelengths.

Comparison of frozen-density embedding and discrete reaction field solvent models for molecular properties

We investigate the performance of two discrete solvent models in connection with density functional theory (DFT) for the calculation of molecular properties. In our comparison we include the discrete reaction field (DRF) model, a combined quantum mechanics and molecular mechanics (QM/MM) model using a polarizable force field, and the frozen-density embedding (FDE) scheme. We employ these solvent models for ground state properties (dipole and quadrupole moments) and response properties (electronic excitation energies and frequency-dependent polarizabilities) of a water molecule in the liquid phase. It is found that both solvent models agree for ground state properties, while there are significant differences in the description of response properties. The origin of these differences is analyzed in detail and it is found that they are mainly caused by a different description of the ground state molecular orbitals of the solute. In addition, for the calculation of the polarizabilities, the inclusion of the response of the solvent to the polarization of the solute becomes important. This effect is included in the DRF model, but is missing in the FDE scheme. A way of including it in FDE calculations of the polarizabilities using finite field calculations is demonstrated.

Polarization and polarizability in extended one-dimensional organic materials

The modern theory of polarization in extended insulators is applied to one-dimensional models for conjugated polymers and charge transfer salts. Closed expressions for the dependence of the polarization on the site and bond energy alternations are presented for uncorrelated models, and results from exact real-space diagonalization are obtained for correlated models. Changes in polarization induced by lattice phonons or molecular vibrations are directly related to the intensity of infrared bands in the far and mid-IR, respectively. We model intensities by introducing linear electron-vibration coupling and show that coupling to delocalized electrons generates a combination band consisting of a lattice phonon and a molecular vibration. The displaced dipole operator is defined on a real-space basis allowing for the finite field calculation of linear polarizability in finite size systems with periodic boundary conditions. Size-consistency arguments are used to demonstrate that the resulting polarizability becomes exact in the thermodynamic limit, and numerical calculations demonstrate that this approach leads to reliable results that converge rapidly to the thermodynamic limit.

Syntheses and Properties of Two-Dimensional Charged Nonlinear Optical Chromophores Incorporating Redox-Switchablecis-Tetraammineruthenium(II) Centers

In this article, we describe a series of new complex salts in which electron-donating cis-{Ru(II)(NH3)(4)}(2+) centers are connected to two electron-accepting N-methyl/aryl-pyridinium groups. These V-shaped complexes contain either monodentate 4,4'-bipyridyl-derived ligands or related chelates based on 2,2':4,4":4',4'''-quaterpyridyl and have been characterized by using various techniques including electronic absorption spectroscopy and cyclic voltammetry. Molecular quadratic nonlinear optical (NLO) responses beta have been determined by using hyper-Rayleigh scattering at 800 nm and also via Stark (electroabsorption) spectroscopic studies on the intense, visible d --> pi metal-to-ligand charge-transfer bands. These experiments reveal that these dipolar pseudo-C(2v)chromophores exhibit two substantial components of the beta tensor, beta(zzz)and beta(zyy), with the difference between them being most marked for the nonchelated systems. Time-dependent density-functional theory and finite field calculations serve to further illuminate the electronic structures and associated linear and NLO properties of the new chromophoric salts.

Polarizabilities and hyperpolarizabilities for the atoms Al, Si, P, S, Cl, and Ar: Coupled cluster calculations

Accurate static dipole polarizabilities and hyperpolarizabilities are calculated for the ground states of the Al, Si, P, S, Cl, and Ar atoms. The finite-field computations use energies obtained with various ab initio methods including Moller-Plesset perturbation theory and the coupled cluster approach. Excellent agreement with experiment is found for argon. The experimental alpha for Al is likely to be in error. Only limited comparisons are possible for the other atoms because hyperpolarizabilities have not been reported previously for most of these atoms. Our recommended values of the mean dipole polarizability (in the order Al-Ar) are alpha/e(2)a(0) (2)E(h) (-1)=57.74, 37.17, 24.93, 19.37, 14.57, and 11.085 with an error estimate of +/-0.5%. The recommended values of the mean second dipole hyperpolarizability (in the order Al-Ar) are gamma/e(4)a(0) (4)E(h) (-3)=2.02 x 10(5), 4.31 x 10(4), 1.14 x 10(4), 6.51 x 10(3), 2.73 x 10(3), and 1.18 x 10(3) with an error estimate of +/-2%. Our recommended polarizability anisotropy values are Deltaalpha/e(2)a(0) (2)E(h) (-1)=-25.60, 8.41, -3.63, and 1.71 for Al, Si, S, and Cl respectively, with an error estimate of +/-1%. The recommended hyperpolarizability anisotropies are Deltagamma/e(4)a(0) (4)E(h) (-3)=-3.88 x 10(5), 4.16 x 10(4), -7.00 x 10(3), and 1.65 x 10(3) for Al, Si, S, and Cl, respectively, with an error estimate of +/-4%.

A sequential Monte Carlo/Quantum Mechanics study of the dipole polarizability of liquid benzene

Metropolis Monte Carlo classical simulation and quantum mechanical calculations are performed to obtain the dipole polarizability of liquid benzene. Super-molecular configurations are sampled from NVT Monte Carlo simulation of liquid benzene at room temperature and are used for subsequent quantum mechanical calculations. The auto-correlation function of the energy is used to analyze the statistical correlation between the configurations. Finite-field INDO and DFT calculations are performed in the statistically uncorrelated super-molecular clusters obtained in the simulation. The quantum mechanical results are shown to represent statistically converged values. The final results corroborate the recent contention that the dipole polarizability of liquid benzene suffers only a small change in the condensed phase.

Non-linear ring currents: effect of strong magnetic fields on π-electron circulation

Finite-field calculations of non-linear induced current density in representative [4 n + 2] and [4 n] π systems, benzene and flat cyclooctatetraene (COT), show that a strong uniform perpendicular magnetic field enhances benzene π-diatropicity and decreases COT π-paratropicity. The non-linear current is stronger by two orders of magnitude in COT, but still small: at 1 a 0 height and in a field of 25 T, third-order effects contribute −5 ppm to the first-order π ring current. Classical arguments based on radial contraction of charge density rationalise the non-linear response of benzene, but that of COT depends on a specific orbital-rotation effect, characteristic of paratropic π systems.

Non-linear optical properties of TeO2-based glasses: ab initio static finite-field and time-dependent calculations

Ab initio calculations of the non-linear optical properties for the TeO4 and TeO3 structural units in TeO2-based glasses are presented. Time-dependent Hartree–Fock calculation below the frequency of ∼400THz (750nm) shows that the shorter wavelength of the light injected should lead to the higher non-linear optical responses in both TeO4 and TeO3 structural units. Static finite-field calculation with the localized molecular orbital analysis classifies the second hyperpolarizability by the electron pairs assigned to the chemical bonds. This analysis suggested that the lone pair of electrons on the Te atom is a key to the non-linear optical properties of the TeO2-based glasses and that the TeO4 structural unit is responsible for the higher non-linear optical properties rather than the TeO3.

Contrasting linear and quadratic nonlinear optical behavior of dipolar pyridinium chromophores with 4-(dimethylamino)phenyl or ruthenium(II) ammine electron donor groups.

In this article, we contrast the optical properties of dipolar chromophores having 4-(dimethylamino)phenyl electron donor (D) and pyridinium acceptor (A) groups with those of closely related cations having pyridyl-coordinated Ru(II) donors. A range of physical data, including that from Stark (electroabsorption) spectroscopy, permits unprecedented quantitative comparisons, most notably regarding the effects of extension of bridging polyene chains. The purely organic compounds display normal optical properties in that their intense, visible pi --> pi intramolecular charge-transfer (ICT) bands red-shift as the number of E-ethylene units (n) increases from 1 to 3 and the associated static first hyperpolarizabilities beta(0) increase steadily with n. The related Ru(II) complexes show intense, visible d --> pi metal-to-ligand charge-transfer (MLCT) bands, which are found to lower energy when compared with the ICT transitions of the corresponding organics. Abnormally, these MLCT bands blue-shift as n increases, and beta(0) maximizes at n = 2. Time-dependent density-functional theory and finite field calculations verify these empirical trends for both types of compound, which can be rationalized as arising from the differing orbital structures of the chromophores and the associated degrees of D-A electronic coupling.

Syntheses and spectroscopic and quadratic nonlinear optical properties of extended dipolar complexes with ruthenium(II) ammine electron donor and N-methylpyridinium acceptor groups.

In this paper, we describe the extremely unusual optical properties of Ru(II)-based electron donor-acceptor (D-A) polyene and some closely related chromophores. For three different polyene series, the intense, visible d-->pi* metal-to-ligand charge-transfer bands unexpectedly blue-shift as the number of E-ethylene units (n) increases from 1 to 3, and the static first hyperpolarizabilities beta(0) determined via hyper-Rayleigh scattering and Stark spectroscopy maximize at n = 2, in marked contrast to other known D-A polyenes in which beta(0) increases steadily with n. Time-dependent density-functional theory and finite field calculations verify these empirical trends, which arise from the orbital structures of the complexes. This study illustrates that transition metal-based nonlinear optical chromophores can show very different behavior when compared with their more thoroughly studied purely organic counterparts.

Some problems with the accuracy in ab initio calculations of the static dipole polarizability components: example of the OH − ion

The accuracy reachable in the finite-field ab initio calculations of the static polarizability components was analysed on the example of the hydroxide ion. Calculations were performed with the second-order Møller–Plesset theory, and the coupled-cluster method restricted to single, double, and approximate triple excitations. The choice of the control parameters, such as the energy convergence threshold and the associated field strength, were carefully examined. For several combinations of these parameters, we attempted to estimate the error introduced by the finite-field calculations of the polarizability components. The results obtained from parabolic and quartic polynomials fits were analysed and compared. Two levels of accuracy were considered: the best one, and a lower one which is able to give acceptable values.