Temperature Transferability of Force Field Parameters for Dispersion Interactions.

The accuracy of force fields is a key to the successful prediction of the thermodynamic properties of materials. In simulations of organic molecules over large temperature ranges, atomistic force fields that are parametrized at, or near, ambient temperatures are found to systematically underestimate the intermolecular dispersion interactions at elevated temperatures. Analysis of the underestimates using diatomic molecules indicates that a minor part is due to the change in molecular polarizability, while the major part is due to the reduced dielectric constant of the bulk liquid as the density decreases with increasing temperature. By establishing the dispersion parameter as a linear function of temperature, we have successfully enhanced the temperature transferability of atomistic force fields. This approach is tested on 66 molecular liquids covering four functional groups - alkane, aromatic, ether, and ketone-aldehyde - over a broad range of temperatures by calculating liquid density, heat of vaporization, isobaric heat capacity, and shear viscosity.

Systematic Generation of Anisotropic Coarse-Grained Lennard-Jones Potentials and Their Application to Ordered Soft Matter.

We have developed an approach to coarse-grained (CG) modeling of the van der Waals (vdW) type of interactions among molecules by representing groups of atoms within those molecules in terms of ellipsoids (rather than spheres). Our approach systematically translates an arbitrary underlying all-atom (AA) representation of a molecular system to a multisite ellipsoidal potential within the family of Gay-Berne type potentials. As the method enables arbitrary levels of coarse-graining, or even multiple levels of coarse-graining within a single simulation, we describe the method as a Level of Detail (LoD) model. The LoD model, as integrated into our group's Metropolis Monte Carlo computational package, is also capable of reducing the complexity of the molecular electrostatics by means of a multipole expansion of charges obtained from an AA force field (or directly from electronic structure calculations) of the charges within each ellipsoid. Electronic polarizability may additionally be included. The present CG representation does not include transformation of bonded interactions; ellipsoids are connected at the fully atomistic bond sites by freely rotating links that are constrained to maintain a constant distance. The accuracy of the method is demonstrated for three distinct types of self-assembling or self-organizing molecular systems: (1) the interaction between benzene and perfluorobenzene (dispersion interactions), (2) linear hydrocarbon chains (a system with large conformational flexibility), and (3) the self-organization of ethylene carbonate (a highly polar liquid). Lastly, the method is applied to the interaction of large (∼100 atom) molecules, which are typical of organic nonlinear optical chromophores, to demonstrate the effect of different CG models on molecular assembly.

Relation of system dimensionality and order parameters.

Orientational order parameters are useful metrics for characterizing the probability distribution for vector-valued quantities such as the dipole moment or optical axis of molecules in materials such as liquid crystals and organic glasses. These parameters are the moments of the underlying orientational probability distribution. Many molecular systems can be characterized using a single centrosymmetric (even) moment. For dipolar systems, an applied electric or magnetic field can break the symmetry of the system, leading to nonzero acentric (odd) moments. For complex systems, it is difficult to characterize the nature of the bulk structures and to quantitatively understand the relationship between acentric and centrosymmetric moments. We have found that it is useful to relate the moments of the distribution in terms of an apparent dimensionality of the ordering process. Here we show that the idea of noninteger dimensionality, originally introduced by Stillinger, provides a useful method to characterize the relation between centrosymmetric and acentric orientational order parameters. Applying dimensional constraints is equivalent to removing rotational degrees of freedom or constraining rotation within a restricted volume. Simulations based on simple examples­using restoring potentials on arrays of independent dipoles­and on complex many-body Monte Carlo simulations of dipolar spheroids are described. An analysis of the results illustrates the utility of fractional dimensionality to describe ordering in materials.

An efficient method for calculating dynamical hyperpolarizabilities using real-time time-dependent density functional theory.

In this paper we present a time-domain time-dependent density functional theory (TDDFT) approach to calculate frequency-dependent polarizability and hyperpolarizabilities. In this approach, the electronic degrees of freedom are propagated within the density matrix based TDDFT framework using the efficient modified midpoint and unitary transformation algorithm. We use monochromatic waves as external perturbations and apply the finite field method to extract various orders of the time-dependent dipole moment. By fitting each order of time-dependent dipole to sinusoidal waves with harmonic frequencies, one can obtain the corresponding (hyper)polarizability tensors. This approach avoids explicit Fourier transform and therefore does not require long simulation time. The method is illustrated with application to the optically active organic molecule para-nitroaniline, of which the frequency-dependent polarizability α(-ω; ω), second-harmonic generation ß(-2ω; ω, ω), optical rectification ß(0; -ω, ω), third-harmonic generation γ(-3ω; ω, ω, ω), and degenerate four-wave mixing γ(-ω; ω, ω, -ω) are calculated.

Solvents level dipole moments.

The dipole moments of highly polar molecules measured in solution are usually smaller than the molecular dipole moments that are calculated with reaction field methods, whereas vacuum values are routinely calculated in good agreement with available vapor phase data. Whether from Onsager's theory (or variations thereof) or from quantum mechanical methods, the calculated molecular dipoles in solution are found to be larger than those measured. The reason, of course, is that experiments measure the net dipole moment of solute together with the polarized (perturbed) solvent "cloud" surrounding it. Here we show that the reaction field charges that are generated in the quantum mechanical self-consistent reaction field (SCRF) method give a good estimate of the net dipole moment of the solute molecule together with the moment arising from the reaction field charges. This net dipole is a better description of experimental data than the vacuum dipole moment and certainly better than the bare dipole moment of the polarized solute molecule.

Dielectric dependence of the first molecular hyperpolarizability for electro-optic chromophores.

Experimental and computational studies of the solvent dependence of the first molecular hyperpolarizability (ß) for two donor-bridge-acceptor chromophores (CLD-1 and YLD156) are presented. Hyper-Rayleigh scattering (HRS) measurements are performed with 1907 nm excitation in a series of solvents with dielectric constants ranging from ~2 (toluene) to ~36 (acetonitrile). For both chromophores an approximately 2-fold increase in ß is observed by HRS over this range of dielectric constants. Computational studies employing a polarized continuum model to represent the solvent are capable of reproducing this experimental result. The experimental and computational results are compared to the predictions of the widely employed two-state model (TSM) for ß. Surprisingly, for the chromophores studied here the TSM predicts that ß should decrease with increasing dielectric constant over the range investigated. The results presented here demonstrate that the TSM provides neither a quantitative nor qualitative description of the solvent dependence of ß for CLD-1 and YLD156. The enhancement of ß with increased dielectric constant suggests that modification of the dielectric surrounding the chromophore is one path by which the performance of nonlinear optical devices employing these chromophores may be significantly enhanced.

Measuring order in contact-poled organic electrooptic materials with variable-angle polarization-referenced absorption spectroscopy (VAPRAS).

Organic nonlinear electrooptical (ONLO) chromophores must be acentrically ordered for the ONLO material to have electrooptic (EO) activity. The magnitude of the order is characterized by the acentric order parameter, , where ß is the major Euler angle between the main axis of the chromophore and the poling field which imposes the acentric order. The acentric order parameter, which is difficult to measure directly, is related to the centrosymmetric order parameter, defined as = ½(3-1), through the underlying statistical distribution. We have developed a method to determine centrosymmetric order of the ONLO chromophores when the order is low (i.e., < 0.1). We have extended the method (begun by Graf et al. J. Appl. Phys. 1994, 75, 3335.) based on the absorption of light to determine the centrosymmetric order parameter induced by a poling field on a thin film sample of ONLO material. We find that the order parameters, analyzed by two different methods, are similar and also consistent with theoretical estimates from modeling of the system using coarse-grained Monte Carlo statistical mechanical methods.

Reduced dimensionality in organic electro-optic materials: theory and defined order.

Identification of electronic intermolecular electrostatic interactions that can significantly enhance poling-induced order is important to the advancement of the field of organic electro-optics. Here, we demonstrate an example of such improvement achieved through exploitation of the interaction of coumarin pendant groups in chromophore-containing macromolecules. Acentric order enhancement is explained in terms of lattice-symmetry effects, where constraint of orientational degrees of freedom alters the relationship between centrosymmetric and acentric order. We demonstrate both experimentally and theoretically that lattice dimensionality can be defined using the relationship between centrosymmetric order and acentric order. Experimentally: Acentric order is determined by attenuated total reflection measurement of electro-optic activity coupled with hyper-Rayleigh scattering measurement of molecular first hyperpolarizability, and centrosymmetric order is determined by the variable angle polarization referenced absorption spectroscopy method. Theoretically: Order is determined from statistical mechanical models that predict the properties of soft condensed matter.

Dielectric constants of simple liquids: stockmayer and ellipsoidal fluids.

Coarse-grained models of molecular interactions are of interest because they convey the essence of molecular interactions in simple and easy to understand form. However, coarse-grained models fail to adequately predict some material properties, such as the failure of the Stockmayer model to reproduce the dielectric behavior of highly polar liquids. We examine the behavior of the Stockmayer fluid over a range of dipole densities that covers known organic solvents, as well as that of an ellipsoidal Stockmayer-like fluid, using NVT rigid-body Monte Carlo simulations. Both fluids are examined under different electrostatic boundary conditions and ensemble sizes. While the Stockmayer model predicts that liquids of similar dipole density to acetonitrile would be ferroelectric and have a dielectric constant far higher than shown by experiment, the ellipsoidal model provides a better accounting of dielectric behavior. This result bodes well for the use of coarse-grained solvent models for large-scale simulations.

Modeling the optical behavior of complex organic media: from molecules to materials.

For the past three decades, a full understanding of the electro-optic (EO) effect in amorphous organic media has remained elusive. Calculating a bulk material property from fundamental molecular properties, intermolecular electrostatic forces, and field-induced net acentric dipolar order has proven to be very challenging. Moreover, there has been a gap between ab initio quantum-mechanical (QM) predictions of molecular properties and their experimental verification at the level of bulk materials and devices. This report unifies QM-based estimates of molecular properties with the statistical mechanical interpretation of the order in solid phases of electric-field-poled, amorphous, organic dipolar chromophore-containing materials. By combining interdependent statistical and quantum mechanical methods, bulk material EO properties are predicted. Dipolar order in bulk, amorphous phases of EO materials can be understood in terms of simple coarse-grained force field models when the dielectric properties of the media are taken into account. Parameters used in the statistical mechanical modeling are not adjusted from the QM-based values, yet the agreement with the experimentally determined electro-optic coefficient is excellent.

Rational enhancement of second-order nonlinearity: bis-(4-methoxyphenyl)hetero-aryl-amino donor-based chromophores: design, synthesis, and electrooptic activity.

Two new highly hyperpolarizable chromophores, based on N,N- bis-(4-methoxyphenyl) aryl-amino donors and phenyl-trifluoromethyl-tricyanofuran (CF3-Ph-TCF) acceptor linked together via pi-conjugation through 2,5-divinylenethienyl moieties as the bridge, have been designed and synthesized successfully for the first time. The aryl moieties on the donor side of the chromophore molecules were varied as to be thiophene and 1-n-hexylpyrrole. The linear and nonlinear optical (NLO) properties of all compounds were evaluated in addition to recording relevant thermal and electrochemical data. The properties of the two new molecules were comparatively studied. These results are critically analyzed along with two other compounds, reported earlier from our laboratories and our collaborator's, that contain (i) aliphatic chain-bearing aniline and (ii) dianisylaniline as donors, keeping the bridge (2,5-divinylenethienyl-), and the acceptor (CF3-Ph-TCF), constant. Trends in theoretically (density functional theory, DFT) predicted, zero-frequency gas-phase hyperpolarizability [beta(0;0,0)] values are shown to be consistent with the trends in beta HRS(-2omega;omega,omega), as measured by Hyper-Rayleigh Scattering (HRS), when corrected to zero-frequency using the two-level model (TLM) approximation. Similarly, trends in poling efficiency data (r33/E(p)) and wavelength dispersion measured by reflection ellipsometry (using a Teng-Man apparatus) and attenuated total reflection (ATR) are found to fit the TLM and DFT predictions. A 3-fold enhancement in bulk nonlinearity (r33) is realized as the donor subunits are changed from alkylaniline to dianisylaminopyrrole donors. The results of these studies provide insight into the complicated effects on molecular hyperpolarizability of substituting heteroaromatic subunits into the donor group structures. These studies also demonstrate that, when frequency dependence and electric-field-induced ordering behavior are correctly accounted for, ab initio DFT generated beta(0;0,0) is effective as a predictor of changes in r33 behavior based on chromophore structure modification. Thus DFT can provide valuable insight into the electronic structure origin of complex optical phenomena in organic media.

Theory-guided design and synthesis of multichromophore dendrimers: an analysis of the electro-optic effect.

Extensive experimental and theoretical study suggests that interchromophore electrostatic interactions are among the most severe impediments to the induction and stability of large electro-optic coefficients in electric-field-poled organic materials. In this report, multichromophore-containing dendritic materials have been investigated as a means to minimize unwanted attenuation of nonlinear optical (electro-optic) activity at high chromophore loading. The dendritic molecular architectures employed were designed to provide optimized molecular scaffolding for electric-field-induced molecular reorientation. Design parameters were based upon past experimental results in conjunction with statistical and quantum mechanical modeling. The electro-optic behavior of these materials was evaluated through experimental and theoretical analysis. Experimental data collected from the dendrimer structures depict a reasonably linear relationship between chromophore number density (N) and electro-optic activity (r(33)) demonstrating a deviation from the dipolar frustration that typically limits r(33) in conventional chromophore/polymer composite materials. The observed linear dependence holds at higher chromophore densities than those that have been found to be practical in systems of organic NLO chromophores dispersed in polymer hosts. Theoretical analysis of these results using Monte Carlo modeling reproduces the experimentally observed trends confirming linear dependence of electro-optic activity on N in the dendrimer materials. These results provide new insight into the ordering behavior of EO dendrimers and demonstrate that the frequently observed asymptotic dependence of electro-optic activity on chromophore number density may be overcome through rational design.

Antiparallel-aligned neutral-ground-state and zwitterionic chromophores as a nonlinear optical material.

Efficient noncentrosymmetric arrangement of nonlinear optical (NLO) chromophores with high first-order hyperpolarizability (beta) for increased electro-optical (EO) efficiency has proven challenging as strong dipolar interactions between the chromophores encourage antiparallel alignment, attenuating the macroscopic EO effect. This work explores a novel approach to simultaneously achieve large beta values while providing an adjustable dipole moment by linking a strong neutral-ground-state (NGS) NLO chromophore with positive beta to a zwitterionic (ZWI) chromophore with negative beta in an antiparallel fashion. It is proposed that the overall beta of such a structure will be the sum of the absolute values of the two types of chromophores while the dipole moment will be the difference. Molecules 1-3 were synthesized to test the feasibility of this approach. Molecular dynamics calculations and NMR data supported that the NGS chromophore component and the ZWI chromophore component self-assemble to an antiparallel conformation in chloroform. Calculations showed that the dipole moment of 1 is close to the difference of the two component chromophores. Hyper-Rayleigh scattering (HRS) studies confirmed that the first hyperpolarizability of 1 is close to the sum of the two component chromophores. These results support the idea that an antiparallel-aligned neutral-ground-state chromophore and a zwitterionic chromophore can simultaneously achieve an increase in beta and a decrease of the dipole moment.

Linear and nonlinear optical properties of a macrocyclic trichromophore bundle with parallel-aligned dipole moments.

A macrocyclic trichromophore bundle 1 with parallel-aligned dipole moments has been synthesized to study the influence of aggregation and orientation of a nonlinear optical (NLO) chromophore on its optical properties. The linear and nonlinear optical properties of 1 and a single chromophore standard 2 have been studied by UV-vis absorption, fluorescence, solvatochromic spectrometry, and hyper-Rayleigh scattering (HRS). Reduced first-order hyperpolarizability beta, hypsochromic shift, enhanced solvatochromic shifts, and fluorescence quenching for individual chromophores were observed when 1 was compared with 2. Analysis of the data showed that the transition dipole moment changes only slightly when the chromophores are parallel aligned in the bundle architecture. However, the apparent hyperpolarizability of the individual chromophores decreased significantly by about 20%. The reduction in beta for the individual chromophores in 1 is largely due to the hypsochromic shift, i.e., excitation energy increase of the interband (charge-transfer) energy gap and the reduced difference between the ground-state and excited-state dipole moments. The hypsochromic shift and fluorescence quenching are consistent with exciton theory. Possible reasons for the enhanced solvatochromic shift are discussed.

Systematic study of the structure-property relationship of a series of ferrocenyl nonlinear optical chromophores.

A series of novel nonlinear optical (NLO) chromophores 1-4 incorporating the ferrocenyl (Fc) group as an electron donor and 2-dicyanomethylene-3-cyano-4-methyl-2,5-dihydrofuran (TCF) derivatives as electron acceptors are presented. The use of a constant Fc donor and varied acceptors and bridges makes it possible to systematically determine the contribution of the conjugated bridge and the acceptor strength to chromophore nonlinear optical activity. The X-ray crystal structures of all four chromophores allow for the systematic investigation of the structure-property relationship for this class of molecules. For example, the crystal structures reveal that both cyclopentadienyl groups in the ferrocenyl donor contribute to the electron donating ability. The first-order hyperpolarizabilities beta of these chromophores, measured by hyper-Rayleigh scattering (HRS) relative to p-nitroaniline are reported. These beta values are compared to those calculated by density functional theory (DFT). The excellent agreement between the theoretical and experimental beta values demonstrates that a linear relation exists between the hyperpolarizability and the bond length alternation. An electrooptic coefficient, r(33), of approximately 25 pm/V at 1300 nm, for compound 4, incorporated into a polymer matrix, is competitive with organic chromophores. Moreover, this r(33) is more than 30 times larger than the previously reported value for an organometallic chromophore in a poled polymer matrix. This work not only underscores the potential for Fc donor moieties, which have been underutilized, but also demonstrates that experimental characterization and theoretical simulations are now congruent, viable methods for assessing potential performance of NLO materials.