J. Phys. Chem. B 2006, 110, 8971-8977
8971
Molecular Dynamics Simulations Applied to Electric Field Induced Second Harmonic Generation in Dipolar Chromophore Solutions Yaoquan Tu, Yi Luo, and Hans A° gren* Theoretical Chemistry, Royal Institute of Technology, Alba NoVa UniVersity Center, S-10691 Stockholm, Sweden ReceiVed: January 18, 2006; In Final Form: March 1, 2006
Electric field induced second harmonic generation (EFISH) is an important experimental technique in extracting the first hyperpolarizability of an organic chromophore molecule. Such experiments are carried out in solutions with chromophore molecules dissolved in some common solvents. A known fact is that the first hyperpolarizabilities extracted from EFISH experiments are subject to the use of local field factors. In this work, we apply simulations to study the EFISH properties of chromophore solutions. By combining quantum chemistry calculations with the results derived from molecular dynamics simulations, we show how macroscopic EFISH properties can be modeled, using 4-(dimethylamino)-4′-nitroazobenzene dissolved in chloroform as a demonstration case. The focus of the study is on deriving accurate local field factors. We find that the local field approach applies very well to dipolar solutions, such as the one studied here, but that the local field factors derived are much smaller than the commonly used Onsager or Lorentz local field factors. Our study indicates that many of the reported first hyperpolarizabilities for dipolar molecules from EFISH experiments are most probably underestimated because the Onsager/Lorentz approach, commonly used in extracting the molecular first hyperpolarizability, neglects the effects of the shapes of dipolar chromophore molecules on the local field factors.
1. Introduction Organic molecules with large first hyperpolarizabilities are of great relevance in the contemporary search for effective nonlinear optical (NLO) materials to use in practical applications.1,2 Such molecules often display acentric symmetry with easily polarizable electrons. Among popular representatives of these, one finds conjugated dipolar molecules with π-electron bridges and donor-acceptor end groups to hold a special position as they show large first hyperpolarizabilities at the same time as they are accessible for flexible design by modern chemical synthetic techniques.1-6 These chromophores have accordingly been studied rather intensively by experimental methods, for instance, by hyper-Rayleigh scattering (HRS)7 or electric field induced second harmonic generation (EFISH).8 On the theoretical side, the first hyperpolarizabilities, generally denoted as β values, can be quite routinely modeled using contemporary electronic structure theory showing many rewarding applications, in particular, when the organic chromophore molecules are isolated. With the rapid development in computer technologies and modern quantum chemistry methods, such as time-dependent density functional theory (DFT), it is now possible to model the β values of such isolated organic chromophores with considerable accuracy. However, this situation is not directly met on the experimental side in that for most of the organic chromophore molecules it is difficult to assess the β values in their isolated form, as their often large dipole moments make them difficult to evaporate into the gas state. As a result, experimental measurements for organic chromophore molecules are often carried out in solutions with common organic solvents. To extract the β value of an isolated chromophore molecule from a measurement of a solution, local * Corresponding author. E-mail:
[email protected].
field approaches are often adopted. Due to the approximations made in such local field approaches, neglecting the detailed description of the interactions between the chromophore and its surrounding solvent structure, the experimentally derived β values for the isolated molecule can be associated with considerable uncertainties. The determination of molecular β values thus displays discrepancies between theoretical calculations and experimental measurements as a result of the fact that the theoretical calculations are carried out at the isolated chromophore level while the experimental measurements are made in solutions with inevitable intermolecular interactions. Many attempts have been made to close this gap in approach. One widely used way to estimate the nonlinearities of a chromophore in a solution is to augment the quantum chemistry methods with reaction field technology.9-11 This, in essence, still neglects the detailed description of the chromophore-solvent interactions and the solvent structure, and in particular, for polar or protic solutions, it may not suffice to obtain accurate properties of a chromophore solution. A further advance of the state of affairs in the current description of chromophore molecules in solutions calls for a detailed modeling of the intermolecular interactions. The significance of such detailed modeling can be dual: On one hand, one can anticipate a more accurate extraction of the β values of an isolated chromophore molecule from experimental measurements so that it is possible to compare them with those from theoretical calculations. Such comparisons should prove useful for the evaluation of the applicability of the theoretical calculations as well as for the development of new methods in modeling of molecular β values. On the other hand, with the knowledge of the detailed description of a chromophore molecule in a solvent, one can model directly the experimental
10.1021/jp0603583 CCC: $33.50 © 2006 American Chemical Society Published on Web 04/15/2006
8972 J. Phys. Chem. B, Vol. 110, No. 18, 2006
Tu et al. TABLE 1: Composition of the 5 Solutions Studieda
Figure 1. Structure of disperse red (DR) molecule.
HRS or EFISH values in solution. The comparison of the values from the theoretical side and those from the experiment can also provide us with important information about the quality of the theoretical modeling approaches, ranging from the calculation of molecular β values at the isolated chromophore level to the models describing the chromophore behavior in interacting systems. In this work, we aim to use quantum chemistry density functional theory (DFT) to model the β values of an isolated chromophore molecule and molecular dynamics (MD) computer simulation technology to describe in detail the properties of the chromophore molecules in organic solvents, in an attempt to close the discrepancy between the theoretical modeling and experimental measurements of molecular NLO properties. MD simulations have been widely used in the study of solutions, materials, biological systems, and chemical reactions as an important complementary tool to experiments. Applications of MD simulation techniques to the study of NLO molecules in organic solutions and polymeric materials have also been reported.12-16 The properties studied cover, for instance, first hyperpolarizabilities of azobenzene dendrimers in chloroform,14 the linear and nonlinear optical properties of liquid benzene,13 and the electric field poling effects of NLO molecules in polymers.12,15,16 In this paper, we report a study on EFISH properties of 4-(dimethylamino)-4′-nitroazobenzene, i.e., disperse red (DR; see Figure 1 for the structure), dissolved in chloroform (CHCl3) as a prototype guest-host system prone for molecular dynamics simulations. This contention follows from the assertion that DR serves as a typical dipolar chromophore molecule, while chloroform is a widely used organic solvent in which many measurements of organic chromophore molecules have been carried out. Furthermore, results from experimental EFISH measurements of DR chromophores in chloroform solvent are available,17,18 making the comparison of the experimental measurements and our theoretical study possible. In the following, we will, in some detail, describe the work using molecular dynamics simulations in the study of EFISH properties of DR molecules in chloroform, with the focus on how to derive more accurate local field factors from MD simulation results. 2. Computational Details The intra- and intermolecular interactions are modeled by a classical molecular mechanical force field having the following form:
E)
kr(r - req)2 + ∑ kθ(θ - θeq)2 + ∑ bonds angles Vn
∑ [1 + cos(nφ - γ)] + ∑ dihedrals 2 i
