Structure, Dynamics, and Electronic Spectrum of N,N'-Diethyl-p

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J. Phys. Chem. B 1998, 102, 5145-5151

5145

Structure, Dynamics, and Electronic Spectrum of N,N′-Diethyl-p-nitroaniline at Water Interfaces. A Molecular Dynamics Study David Michael and Ilan Benjamin* Department of Chemistry, UniVersity of California, Santa Cruz, California 95064 ReceiVed: February 11, 1998

The adsorption of N,N′-diethyl-p-nitroaniline (DEPNA)sa common chromophore probe of liquid polaritysat the water liquid/vapor interface and at the water/1,2-dichloroethane (DCE) interface is studied using molecular dynamics computer simulations. The adsorption energetics, orientation, and reorientation dynamics are examined. The electronic absorption line shapes at the two interfaces, in bulk DCE, and in bulk water are calculated and are found to be in reasonable agreement with experimental results. Including many-body polarizable liquid potentials in the calculations at the water/DCE interface is found to improve the results. The role of surface roughness is examined by repeating the calculations for an artificially smooth water/DCE interface.

I. Introduction An important recent development in the study of liquid interfaces is the ability to measure microscopic properties of solute molecules that are adsorbed at the interface between a liquid and a second phase.1-4 Techniques such as second harmonic generation (SHG) and sum frequency generation (SFG) are able to provide a number of surface specific properties even when there is a substantial concentration of solute molecules in the bulk region.5 In addition to the ability of these techniques to obtain accurate concentrations, and thus adsorption isotherms and the corresponding free energies,6 they are also able to provide more microscopic-type data. This includes, for example, the orientation of adsorbates7-10 and vibrational spectra.4,11,12 An interesting new development, which has the potential to significantly improve our understanding of molecular interactions at liquid interfaces, is the ability to measure wavelengthdependent resonant surface nonlinear response. Although microemulsions, micelles, and oil/water interfaces have been investigated using UV-vis absorption spectroscopy,13,14 fluorescence spectroscopy,15 and attenuated total internal reflectance spectroscopy,16 the resonant SHG techniques allow for surfacespecific measurements. Using SHG, Girault and co-workers have determined the UV-vis spectra of p-nitrophenol, phenol, and p-propylphenol at the air/water interface,10 and Eisenthal and co-workers have used SHG to report the spectrum of the polarity indicator molecule N,N′-diethyl-p-nitroaniline (DEPNA) at the air/water interface.17 Teramae and co-workers have used picosecond time-resolved total internal reflection fluorescence to measure the fluorescence spectra of 8-anilino-1-naphthalenesulfonic at the water/heptane interface. The above studies are of major significance because one can use the extensive knowledge about the relationship between solvent effects on electronic spectra and solvent-solute interactions18,19 to gain insight into the microscopic environment at liquid interfaces. As a simple example, the shift in the peak spectrum at the interface relative to the spectrum in bulk liquids can provide information about the average polarity of the interface because changing the polarity of the medium will

change the relative stabilization of the ground and excited states. Thus, in the study by Wang et al.17 mentioned above, the DEPNA charge-transfer absorption band red-shifts from 329 nm in the gas phase to 359 nm in bulk hexane, to 429 nm in bulk water, and to 373 nm at the air/water interface, indicating that the interfacial environments have a polarity similar to that of a solvent such as CCl4 (in which the absorption spectrum peaks at 375 nm). The size and sign of the shift at a given condensed-phase environment will depend on the relative size of the solute dipole moment and the molecular polarizability in the ground (µg) and excited (µe) states. In particular, increasing the polarity of the solvent environment will lower the transition energy from the ground state to the excited state if the latter has a larger electric dipole moment. Thus, although pnitrophenol behaves like DEPNA (red-shifting from bulk hexane to the water/air interface to bulk water), phenol exhibits the opposite trend. This suggests that µe > µg for DEPNA and p-nitrophenol, but µg > µe for phenol (all of the transitions being of the π f π* type). Although assignment of an average polarity to the interface on the basis of a solvatochromic shift is a useful concept, it may be too simplistic. Unlike the bulk region in which the chromophore position and orientation is random, there is a specific orientation and a nonuniform position distribution of the probe at the interface. These can influence the spectral shift in addition to factors such as excited-state dipole moment. For example, in the experiments by Girault and co-workers mentioned above,10 it was found that the p-propylphenol peak spectrum at the water/air interface is blue-shifted compared with the peak spectrum in both bulk hexane and bulk water. This could be the result of the fact that a large portion of this hydrophobic molecule is only weakly hydrated at the interface, as suggested by the molecular dynamics simulation of a similar system.20 In addition, recent experimental21,22 and theoretical studies23,24 suggest that liquid interface roughness could play an important role in allowing a better than expected hydration of amphiphilic solutes adsorbed at the interface. We have recently examined the role of interface structure and probe location on the electronic spectrum of a generic dipolar solute at several liquid/liquid interfaces.24 In this paper,

S1089-5647(98)01106-7 CCC: $15.00 © 1998 American Chemical Society Published on Web 06/11/1998

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we examine in detail the electronic spectrum and several aspects of the structure and dynamics of DEPNA at the water liquid/ vapor interface and at the water/1,2-dichloroethane (ClCH2CH2Cl (DCE)) interface. We choose this system because its electronic absorption spectrum was recently measured at the air/water interface17 and at the water/DCE interface,25 and it was also measured in a number of bulk liquids. The structure and dynamics of the neat water liquid/vapor interface and the water/DCE interface have been previously characterized.26,27 The rest of the paper is organized as follows. In section II, we briefly describe the potential energy functions used and the method for calculating the electronic spectrum. In section III, we discuss the results and compare them with experimental data, when available. We conclude in section IV with a brief summary. II. Interaction Potentials and Methods A. Potential Energy Functions. The electronic absorption spectrum of DEPNA is calculated in bulk water, in bulk DCE, at the water liquid/vapor interface, and at the water/DCE interface. Details about the water, DCE, and water/DCE intermolecular and intramolecular potentials can be found elsewhere.26 Briefly, the water is described using a flexible SPC potential28 and the DCE using a four-center model in which each of the two CH2 groups is replaced by a united atom of mass 14. The interaction potentials are modeled using LennardJones plus Coulomb terms, where the Lennard-Jones parameters for the interactions between different atoms in different molecules are derived using the standard combination rule for mixtures.29 Some of the calculations at the water/DCE interface are carried out using polarizable water and DCE models. The polarizable water model is a flexible version of a model developed by Dang.30 In this model, the charges on the hydrogens (0.41 au) and the oxygen (-0.82 au) atoms are reduced to 0.365 and -0.73 au, respectively, which reproduces the water gas-phase electric dipole moment of 1.86 D. Atomic polarizabilities are assigned, RH ) 0.170 Å3 and RO ) 0.528 Å3, which give rise to induced dipoles that, together with the permanent dipole, approximately reproduce the total dipole moment of the nonpolarizable SPC model (2.3 D). It includes a multiparameter intramolecular potential31 selected to fit the vibrational spectrum of the water molecule. Similarly, the point charges on the CH2 and Cl atoms are reduced from (0.247 to (0.227 au, and the polarizabilities assigned are RCH2 ) 0.878 Å3 and RCl ) 1.910 Å3. The DEPNA structure is shown in Figure 1. We use an allatom model, except for the CH2 and CH3 groups, which are replaced by united atoms of mass 14 and 15, respectively (the hydrogens bonded to the aromatic carbons are treated explicitly). The intermolecular potentials for the interactions between DEPNA and each of the two liquids are also described by Lennard-Jones plus Coulomb terms, using the combination rules. The Lennard-Jones parameters for the DEPNA atoms are taken from the Amber force field32 and are given in Table 1. The point charges assigned to the DEPNA atoms are selected with the aid of recent ab initio calculations on nitrobenzene, which are then adjusted to reproduce the ground-state dipole moment of DEPNA. We assign a partial positive charge to the anilino nitrogen because an sp3 nitrogen without a formal charge attached to benzene is a strong ring activator. The ethyl groups attached to this nitrogen are given a zero charge because the basicity of amines is not greatly affected by the number of attached carbons. (The reduction in basicity observed with tertiary amines is thought to arise from steric and solvation

Figure 1. Schematic representation of the molecular structure of DEPNA. In parentheses are shown the point charges assigned to the different atoms (atomic units). The hydrogen atoms on the CH2 and CH3 groups are not treated explicitly.

TABLE 1: DEPNA Potential Energy Parameters a. Intermolecular Lennard-Jones Parameters atom or group

σ (Å)

 (kcal/mol)

CH2 CH3 aromatic carbon N (sp2) N (sp3) O H

3.98 3.86 3.296 3.118 3.118 2.851 2.744

0.1142 0.1811 0.12 0.16 0.08 0.20 0.01

b. Intramolecular Potential Parameters kC-N(sp2) 481 kcal mol-1 Å-2 rC-N(sp2) 1.486 Å kC-N(sp3) 481 kcal mol-1 Å-2 rC-N(sp3) 1.471 Å kO-N 525 kcal mol-1 Å-2 rO-N 1.223 Å kO-N-O 80 kcal mol-1 rad-2 θO-N-O 125.3° C-C-N-O 4.0 cos(2φ) kcal/mol

effects rather than from inductive effects.) The final charge assignments are given in Figure 1. Our DEPNA model is also fully flexible. The intramolecular potential energy function includes terms for bond stretching, angle bending, torsion, and improper torsion, as well as nonbonded interactions between atoms separated by three or more bonds. Interactions between atoms separated by exactly three bonds are scaled down by 50%. Nonbonded interactions are especially important for reproducing a reasonable torsion angle distribution about the bond between the nitro group and the benzene ring, since the oxygens are very close to the ring hydrogens (2.55 Å) in the planar configuration.33 The torsional energy barrier for rotation of the nitro group with respect to the benzene ring is set to 4 kcal/mol, a figure chosen as a compromise between estimated experimental results and ab initio calculations.34,35 All other bond lengths, as well as the stretching, bending, and torsional energy parameters, are taken from the Amber force field.32 For simplicity, ideal bond angles are used in the benzene ring (120°) and about sp3-hybridized

N,N′-Diethyl-p-nitroaniline

J. Phys. Chem. B, Vol. 102, No. 26, 1998 5147

atoms (109.5°). The nitro group uses bond angles and lengths taken from electron diffraction studies.36 All these parameters are summarized in Table 1. To determine the electronic absorption spectrum, we also need the DEPNA’s Born-Oppenheimer excited-state potential. Because there is not much information about this potential, we assume for simplicity that the excited-state intramolecular and nonelectrostatic potential is identical to that of the ground state, and the only difference is that in the excited state the charges are scaled by a factor that is selected to reproduce the position of the peak spectrum in bulk water. This is based on the reasonable assumption that most of the spectral shift is due to the difference in the charge distributions. This relatively crude model could be improved using ab initio calculations on the excited π* state, although these calculations are not very reliable. In principle, one may also use a polarizable DEPNA model with different atomic polarizabilities in the ground and excited states. It can be shown, however, that this has a much smaller effect on the spectrum compared with the other contributions discussed above, and thus, in the calculations reported below, our model DEPNA is nonpolarizable. B. Electronic Spectra Calculations. We use the FranckCondon approximation to calculate the electronic absorption spectrum assuming that the transition dipole moment is independent of solute and solvent positions. The absorption spectrum results from “vertical” transitions between the ground state and the Franck-Condon excited state of the solute. The Born-Oppenheimer potentials corresponding to these two states are given by

Vg ) Vbath + VLJ + Vgel + Ugpol Ve ) Vbath + VLJ + Veel + Uepol + ∆Egas

(1)

where ∆Egas is the fixed energy difference between the excited and ground electronic states of the solute in the gas phase and Vbath is the potential energy function for the bath modes (either one of the bulk liquids or the water liquid/vapor system or the water/DCE system), including the nonelectrostatic (LennardJones) and electrostatic interactions between the fixed point charges. VLJ is the total nonelectrostatic interaction between the solute’s atoms and the liquids’ atoms, and V gel and V eel are the electrostatic interactions between the fixed point charges on the solute and the solvent atoms in the ground and excited states, respectively. If the model liquids used are polarizable, then the additional terms Uνpol, ν ) g, e are the electrostatic interactions between the induced dipoles on the liquid molecules and other induced dipoles and fixed point charges for the solute in the electronic state ν. They are given by

Uνpol

)-

1 2

∑k

µνk ‚Eνk

(2)

where µνk and Eνk are, respectively, the induced electric dipole and the electric field vector at atomic site k. The induced dipoles are calculated by iteratively solving at every step of the molecular dynamics the equation

µνk ) Rνk [Eνk -

Tkl‚µνl ] ∑ l*k

(3)

where T is the dipole-dipole tensor.37 If one uses nonpolarizable liquid models, the energy difference between the excited and ground states can be determined by molecular dynamics simulation on the ground state alone,

since immediately after the electronic transition all the atomic positions are identical to the positions just before the transition. If the polarizable nature of the solvents is taken into account, one must allow for instantaneous equilibration of the solvent electronic polarizabilities to the excited-state charge distribution (at fixed nuclear positions). This will generally lower the energy of the transition relative to the nonpolarizable model. This effect is usually small, especially for a polar solute in polar solvents, as was recently shown by Bader and Berne.38 The energy difference between the excited and ground states at a given atomic configuration (r) is given by

pΩ(r) ) Ve - Vg ) ∆Egas + Veel + Uepol - Vgel - Ugpol

(4)

The absorption line shape in the inhomogeneous limit is proportional to the equilibrium probability distribution of the transition frequencies:

∫δ[ω - Ω(r)] e-βV Iab(ω) ) 〈δ[ω - Ω(r)]〉g ) ∫e-βV dr

g

dr (5)

g

where β ) 1/(kT), δ is the Dirac delta function, and the ensemble average is calculated with the system in the ground state. According to eq 5, the spectrum can be determined by binning the energy difference pΩ(r). If one uses nonpolarizable liquid models, then pΩ(r) ) ∆Egas + V eel - V gel and the selection of DEPNA’s excited-state charges to fit the spectrum of DEPNA in bulk water can be accomplished by a single molecular dynamics run on the ground state system. One can simply record the electric potentials φi induced by the solvent at the location of each DEPNA atom i. This can then be used to compute the energy difference na

Veel - Vgel )

∑i φi(Qei - Qgi )

where na is the number of atoms in DEPNA and Qei and Qgi are the partial charges on atom i in the excited and ground states, respectively. Thus, one is able to calculate the spectrum for any choice of the excited-state charge distribution from the single MD run. In fact, because in our model the excited-state charges are related by the same scale factor κ to the groundstate charges (Qei ) κQgi ), one finds for the energy difference na

Veel - Vgel )

∑i φi(κQgi - Qgi ) ) (κ - 1)Vgel

Thus, it is sufficient to record only the values of V gel for the different configurations, and the search for the excited-state charge distribution is reduced to a trivial one-parameter fit. III. Results and Discussion DEPNA in Bulk Water and at the Water Liquid/Vapor Interface. The system includes 1016 water molecules and 1 DEPNA molecule in bulk water or at the water liquid/vapor interface. Each one of these two systems is simulated for 1 ns (after 100 ps equilibration) using a 1 fs integration time-step at T ) 300 K. The simulation in bulk water is used to fit the excited-state dipole moment of DEPNA as explained above. The value of the excited-state dipole found to best-fit the peak location of the bulk spectrum is µex ) 17 D. This value is subsequently used without modification in the calculation of

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Figure 2. Density profile of water in equilibrium (T ) 300 K) with its own vapor (solid line) and the probability distribution of the DEPNA center-of-mass location at the interface (dashed line) and in the bulk (dotted line).

Figure 3. Calculated electronic spectral line shapes for DEPNA in bulk water (solid line) and at the water liquid/vapor interface (dashed line) from separated 1 ns trajectories.

the electronic spectra at the water liquid/vapor interface, in bulk DCE, and at the water/DCE interface. All the calculations of this section are done using a nonpolarizable water model. The experimental measurement of the electronic spectrum at the interface using SHG is done with a finite concentration of solute molecules, which are distributed throughout the system. The SHG technique picks out the signal from all the molecules in the region that is noncentrosymmetric. Since our calculations are done with a single solute, it is important to consider the location of this solute molecule. In Figure 2, we show the probability distribution of the DEPNA center of mass for the two cases we consider here (DEPNA in bulk water and at the water liquid/vapor interface), together with the water density profile. At the water liquid/vapor interface, the DEPNA position distribution sharply peaks near the Gibbs surface (which is approximately the plane where the water average density is 50% of the bulk value). This is consistent with a local free energy minimum at the interface. The solute distribution in the bulk has a broader peak, which also suggests a local minimum in the bulk. However, the 1 ns simulation time (in each case) is too short to map the full free energy profile, which is needed if one is to determine if DEPNA is surface-active. As far as the electronic spectrum is concerned, the calculated spectrum corresponds to “pure” surface and “pure” bulk values because during the 1 ns simulation of each case, there are no interconversions between the bulk and the surface, as is obvious from the distributions shown in Figure 2. Figure 3 shows the calculated electronic spectrum in bulk water (solid line) and at the water liquid/vapor interface (dashed line). Each line is well described by a Gaussian curve. This is consistent with a second-order cumulant39 expansion of the line shape expression given in eq 3. As discussed earlier, the excited-state dipole moment of DEPNA is chosen so that the peak position of its spectrum in bulk water agrees with the experimental value (429 nm). The width of the line shape (half width at half-height) is 34 nm, also in good agreement with the experimental value of 37 nm,17 suggesting that our assumptions,

Michael and Benjamin

Figure 4. Probability distribution for the angle between the normal to the water liquid/vapor interface and the following: (a) the main DEPNA symmetry axis (solid line); (b) the normal to the benzene ring (dashed line).

and in particular, the pure inhomogeneous broadening assumption, are quite acceptable. The calculated peak position of the spectrum at the water liquid/vapor interface is 382 nm, in reasonable agreement with the experimental value of 373 (4 nm, considering the experimental uncertainties and the very crude model we use for the excited-state charge distribution in DEPNA. The shift to the blue relative to bulk water reflects the relative destabilization of the excited state in the less polar water liquid/vapor interface environment. A comparison of the experimental and the calculated spectral widths at the interface is problematic. The experimental line width of the resonant SHG signal strongly depends on the component of the second-order susceptibility. The XZX component is broader than bulk water and the ZXX component much narrower. In contrast, we are essentially computing the linear absorption spectrum, and the calculated width is slightly narrower than in bulk water. In addition, we are looking at a single solute, and the experimental signal comes from a broader distribution. Important structural information that can be obtained under certain conditions5,6 from the SHG measurements is the orientational distribution of the probe molecule. This orientational distribution is also important in determining solvent accessibility to solvating the probe. For example, the polar end of the molecule is expected to point toward the bulk water, and thus, the shifts in the spectrum relative to bulk water may not be as big as one might expect on the basis of an average interface polarity. Figure 4 shows our results for the probability distribution function of two different angles. One is the angle between the main axis of DEPNA (the N-N vector) and the interface normal (solid line), and the other is the angle between the normal to the interface and the normal to the benzene ring. This plot shows that although there is a clear tendency for DEPNA to lie nearly flat at the interface, there is a substantial population at an orientation where the NO2 group points toward bulk water. The average value of the angle between the N-N vector and the interface normal is 73°, compared with the experimental value of 55°.17 Another interesting property that is also beginning to be amenable to experimental measurement is the reorientation time of the probe molecule, which gives additional information about the microenvironment at the interface. Figure 5 shows the reorientation-time correlation function defined as

C(t) ) 〈cos[eˆ(t + τ)‚eˆ (τ)]〉

(6)

where eˆ is a unit vector in some direction in the molecule frame and the angular brackets denote the equilibrium ensemble average over all the time origins t. The top panel of Figure 5 shows the time correlation for the reorientation of the main

N,N′-Diethyl-p-nitroaniline

Figure 5. Orientational time correlation functions for DEPNA at the water liquid/vapor interface: (top panel) reorientation of the main symmetry axis; (bottom panel) reorientation of the vector normal to the benzene ring. In each panel, the solid line is in bulk water and the dashed line at the water liquid/vapor interface.

Figure 6. Density profile of the two liquids at the water/DCE interface (T ) 300 K) and the probability distribution of the DEPNA centerof-mass location: (A) the normal water/DCE interface; (B) the case of the artificially constrained “sharp” interface. The lines D1 and D2 correspond to the probability distribution of DEPNA’s location in two different simulations.

molecular axis, and the bottom panel shows the time correlation for the reorientation of the vector normal to the ring. One can clearly observe a faster reorientation at the interface (dashed line) than in the bulk (solid line) for both orientations. The slightly faster reorientation for the normal to the ring compared with that for the main molecular axis is consistent with the molecular geometry. Experimental data on the reorientation dynamics of DEPNA are not yet available. DEPNA in Bulk DCE at the Water/DCE Interface. The interfacial system includes 500 water molecules and 216 DCE molecules in addition to a single DEPNA molecule that is adsorbed at the liquid/liquid interface. This system is simulated for 1 ns (after a 100 ps equilibration), during which the DEPNA stays near the interface, as is demonstrated in panel A of Figure 6. To examine the contribution of surface roughness, we have carried out two additional 1 ns simulations while keeping the interface sharp by restricting the water center of mass to the region Z < 0 and the DCE center of mass to the region Z > 0. In these two different simulations, the DEPNA is located on

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Figure 7. Calculated electronic spectral line shapes for DEPNA in bulk DCE and at the water/DCE interface. In panel A, the spectra are calculated using the nonpolarizable liquid models, where the solid line is in bulk DCE and the dotted line at the water/DCE interface. In panel B, we use polarizable water and DCE potentials (solid line, bulk DCE; dotted line, interface). In panel C, we show the results for the two simulations at the “sharp” water/DCE interface, where the dotted and solid lines are for the locations D1 and D2 (of Figure 6), respectively.

average at two different positions near the interface on the DCE side, as depicted in panel B of Figure 6. The calculated electronic absorption spectra of DEPNA at the interface and in bulk DCE using nonpolarizable liquid models are shown in Figure 7A. The peak position at the interface is at 405 nm, compared with 429 nm in bulk water and 382 nm at the water liquid/vapor interface, suggesting that the water/DCE interface is significantly more polar than the free water surface. This is in agreement with recent results,25 which give for the peak spectrum at the water/DCE interface the value of 415 ( 15 nm. Our overestimation of the shift relative to that of bulk water (and thus our underestimation of the polarity) is due to the fact that our DCE model underestimates the shift in the energy of the DEPNA. Indeed, the calculated spectrum in bulk DCE also shown in Figure 7A does not agree very well with the experimental value (the experimental peak is at 398 nm compared with the calculated value of 370 nm). Since DCE is a weakly polar but quite polarizable liquid, the electronic polarizability could make a significant contribution. We show the results of the calculations using polarizable water and DCE models in Figure 7B. The spectrum of DEPNA in bulk DCE peaks at 385 nm, and the interfacial spectrum peak is now in excellent agreement with the experimental value. To better understand the contribution of the different terms in the potential energy to the observed shifts, we can make use of the pairwise additive nature of the nonpolarizable model. We may express the shift in the electronic spectrum at the water/ DCE interface relative to the gas phase, ∆ω(L/L), as a sum of contributions from the DCE (∆ω(L/L) DCE ) and the water (∆ωH(L/L) ): 2O

∆ω(L/L) ≡ ω(L/L) - ∆Egas/p ) ∆ωH(L/L) + ∆ω(L/L) DCE 2O

(7)

where ∆Egas is the transition energy in the gas phase and the superscript (L/L) refers to the fact that the corresponding quantities are determined at the liquid/liquid interface. We find that, as expected (because of the stronger interaction of DEPNA with water than with DCE), the water makes a larger contribu-

5150 J. Phys. Chem. B, Vol. 102, No. 26, 1998

Michael and Benjamin

tion:

∆ωH(L/L) /∆ω(L/L) ) 0.64 2O (L/L) ) 0.36 ∆ω(L/L) DCE /∆ω

(8)

It is more informative to consider the interfacial contribution of each liquid to the spectral shift relative to the shift in the bulk phase. This can be used to quantify the degree of interaction of each liquid with the DEPNA at the interface by defining (Bulk) (L/L) (Bulk) sDCE ≡ ω(L/L) DCE /ωDCE , sH2O ≡ ∆ωH2O /∆ωH2O

(9)

(DCE) - ∆E /p is the shift in the peak where ∆ω(Bulk) gas DCE ) ω position of DEPNA in bulk DCE relative to that in the gas phase, and similarly, ∆ωH(Bulk) ) ω(H2O) - ∆Egas/p is the shift in bulk 2O water. We find that

sDCE ) 0.69, sH2O ) 0.50

(10)

so that even though the water contributes more than DCE to the shift, the contribution of DCE as a percentage of its “ability to contribute” is greater. Because of the many-body nature of the polarizable model, this simple analysis is not appropriate for this model. In addition to the electrostatic contribution (due to the interactions between the fixed charges on the liquid molecules and the DEPNA), the total shift now includes the polarization energy. The electrostatic contribution can still be partitioned as above. We find that the relative electrostatic contributions of the two liquids are almost exactly as in the nonpolarizable model. Next, we can use the following procedure to determine the total contribution of the polarization energy and the relative contribution of the two liquids. We compare the total average polarization energy 〈Uνpol〉, defined in eq 2 in each of the two electronic states, to the polarization energy computed with the same nuclear positions but without the charges on the DEPNA 〈UNC pol 〉. Because the latter number is independent of the electronic state, e the difference 〈δUν〉 ) 〈Uνpol〉 - 〈UNC pol 〉 obeys the relation 〈δU 〉 e g g - 〈δU 〉 ) 〈Upol〉 - 〈Upol〉 and thus gives the contribution of the polarization energy to the total shift. Furthermore, since eq 2 involves a sum over atomic sites, it can be partitioned to sum over water and DCE molecules. We find that at the water/ DCE interface for the ground-state DEPNA, 〈δUg〉H2O ) -1.1 kcal/mol, 〈δUg〉DCE ) -0.4 kcal/mol, and the total of 〈δUg〉 represents 10% of the total electrostatic interaction of DEPNA with the two liquids. In the excited state, 〈δUe〉H2O ) -3.2 kcal/mol, 〈δUe〉DCE ) -3.6 kcal/mol, and the total of 〈δUν〉 ) -6.8 kcal/mol represents 19% of the total electrostatic interaction of DEPNA with the two liquids. Thus, we conclude that the main contribution of the polarizable model to the red shift (relative to the nonpolarizable model) is in the much larger induced dipoles on the DCE molecules that are in the vicinity of the solute in its excited electronic state (which has larger charges). Figure 7C presents the spectra calculated for the two cases where the interface is forced to stay sharp, while the DEPNA occupies two different average locations. We note that when the DEPNA is located more into the DCE phase (dotted line), there is a large blue shift compared with the normal interface, reflecting a significantly less polar environment. There is a

Figure 8. Probability distribution for the angle between the normal to the water/DCE interface and the following: (a) the main DEPNA symmetry axis (panel A); (b) the normal to the benzene ring (panel B). In each panel, the solid line is for the normal interface and the dashed line for the “sharp” interface.

significantly smaller contribution of the water to the total shift:

∆ωH(L/L) /∆ω(L/L) ) 0.44 2O (L/L) ) 0.56 ∆ω(L/L) DCE /∆ω

(11)

(compare this with eq 8), and the ratios defined in eq 9 are now showing an even greater contribution of DCE:

sDCE ) 0.87, sH2O ) 0.28

(12)

(compare this with eq 10). Although the DEPNA is on the DCE side of the interface, it is close enough to the water, resulting in the small but significant value of sH2O ) 0.28. Obviously, this behavior depends on the exact location of the probe. When the DEPNA is a little closer to the water (thin line labeled D2 in Figure 6B), the resulting spectrum (solid line in Figure 7C) is very close to the one calculated at the normal (rough) interface (Figure 7A). This suggests that the sensitivity of the spectrum shift to the probe location can be used to determine the roughness of the liquid/liquid interface. For example, this can be accomplished by varying the length of a long-chain hydrocarbon attached to the chromophore. We finally consider some structural and dynamical characterizations of DEPNA at the (nonpolarizable) water/DCE interface. Figure 8 shows the orientational probability distributions of the main axis (top panel) and the normal to the ring (bottom panel). Compared with the situation at the air/water interface, the DEPNA is clearly oriented perpendicular to the interface (both in the normal case and at the sharp interface), with the NO2 group toward the water phase. An examination of the detailed structure shows that, as expected, the oxygens of the NO2 group participate in hydrogen bonding with interfacial water molecules. On the other hand, there is no significant preference for the normal to the ring (bottom panel), which is in line with the cylindrical symmetry of the system. Figure 9 compares the reorientation time correlation function of DEPNA at the normal and sharp interface and in bulk DCE. Again, we see that the structure of the interface only mildly affects the dynamics of reorientation around both the main axis of DEPNA and the vector normal to the interface. However, both of these reorientation correlation functions are faster in bulk DCE than at the interface, reflecting a weaker coupling

N,N′-Diethyl-p-nitroaniline

J. Phys. Chem. B, Vol. 102, No. 26, 1998 5151 The calculations at the water/DCE interface are done using nonpolarizable and polarizable potentials for both of the solvents (but not the solute). The somewhat less accurate results obtained at the nonpolarizable water/DCE interface are shown to improve significantly when polarizable model potentials are used. This is mainly due to the additional stabilization of the more polar excited state due to the induced dipoles on neighboring DCE and water molecules. A more detailed examination of the effect of the water many-body polarizabilities on interfacial and bulk spectra has been presented elsewhere.40 Acknowledgment. This work has been supported by a grant from the National Science Foundation (CHE-9628072). References and Notes

Figure 9. Orientational time correlation functions for DEPNA at the water/DCE interface: (A) reorientation of the main symmetry axis; (B) reorientation of the vector normal to the benzene ring. In each panel, the solid line is in bulk DCE, the dashed line at the normal water/DCE interface, and the dotted line at the “sharp” water/DCE interface.

with the organic solvent than with water. A comparison with Figure 5 shows that the reorientation time at the interface is quite close to the reorientation time in bulk water. This may be the result of two competing effects: the lower interaction with interfacial water compared with that of bulk water (by about a factor of 2) should speed up the reorientation, but this is compensated for by the more restricted interfacial environment and stronger hydrogen bonding at the interface, which has been previously documented.26 IV. Concluding Remarks The adsorption of DEPNA at the water liquid/vapor interface and at the water/DCE interface has been described by molecular dynamics simulations. The calculated electronic absorption line shapes are in reasonable agreement with experimental data, allowing us to draw some conclusions about the chromophore microenvironment at these two interfacial systems. At the air/water interface, the molecules lie nearly flat. The electrostatic and dispersion interactions are significantly reduced at the interface relative to the bulk because there are fewer water molecules to interact with. This results in the significant destabilization of the (higher dipole) excited state relative to the ground state and the assignment of lower polarity to the interface region. Thus, the lower polarity is directly related to the lower density at the interface. At the water/DCE interface, the situation is more complicated because the water molecules are somewhat restricted in their possible arrangements because of the presence of the DCE molecules. Despite this, the liquid/liquid interface is more polar than the water liquid/vapor interface because (1) although the DCE is weakly polar, it does contribute to the shift and (2) interfacial roughness makes it possible for significantly more water molecules to interact with the chromophore than one would expect if the interface were sharp. Indeed, artificially removing the roughness by imposing external constraints, while keeping the solute on the organic side of the interface, significantly increases the shift to the blue, thus corresponding to a less polar environment quite close to that of the water liquid/ vapor interface.

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