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J. Phys. Chem. C 2010, 114, 5602–5610
Nonradiative Deactivation in Benzylidene Malononitriles† Chet Swalina and Mark Maroncelli* Department of Chemistry, The PennsylVania State UniVersity, UniVersity Park, PennsylVania 16802 ReceiVed: July 30, 2009; ReVised Manuscript ReceiVed: September 11, 2009
Electronic structure calculations are used to examine the nuclear motions responsible for ultrafast internal conversion in the benzylidene malononitriles DMN (4-N,N-dimethylaminobenzylidenemalononitrile) and JDMN (julolidinemalononitrile). Gas-phase B3LYP and RI-CC2 calculations using triple-ζ valence polarized basis sets reproduce the structural features measured in the crystalline state and the solution-phase dipole moments of these molecules in their ground states with reasonable accuracy. Most properties of the vertical S0 f S1 transition, which is well separated from other transitions, are also reasonably reproduced by both types of calculation. The large change in dipole moment (8-9 D) upon excitation is grossly underestimated by TDDFT calculations, despite the fact that such calculations predict the transition energies to within experimental uncertainties. Exploration of the S1 potential energy surface of DMN using DFT, RI-CC2, and CASSCF methods indicates that the internal conversion pathway is double-bond isomerization, not the TICT process often assumed. Preliminary classical molecular dynamics simulations of DMN in acetonitrile using the ab initio S1 surface support this assignment. 1. Introduction Benzylidine malononitriles such as DMN and JDMN (Figure 1) are weakly emissive push-pull chromophores which possess large nonlinear optical responses. The sensitivity of their emission quantum yields to solvent conditions has enabled use of these molecules as “solvent fluidity” probes in a range of environments, including conventional solvents,1-4 polymers,5-7 ionic liquids,8-10 and biological media.11-13 Recent work from our group shows that both DMN and JDMN undergo S1 f S0 internal conversion with time constants in the range of 1-5 ps in media of low viscosity.14 In slightly more viscous media, nonexponential decay kinetics and excitation-dependent quantum yields reflect heterogeneity in solvent friction on the time scale of this internal conversion.14,9 Despite their use as fluidity probes, there is only a vague understanding of what features of the local environment these molecules report, and even the identity of the large-amplitude motion responsible for their solvent sensitivity is uncertain. For example, some authors have assumed that a twisted intramolecular charge transfer (TICT) process, twisting about τa and/or τb in Figure 1,15,5,11 leads to emission quenching, some authors point to isomerization (τc) as being responsible,1 while others suggest cooperative motion of all three degrees of freedom is involved.16,2 In the present study we employ electronic structure calculations and molecular dynamics simulations in an effort to clarify the interpretation of the emission of these probes. Several groups have published computational studies of DMN and JDMN over the past few years.17,1,18-21 These studies all revealed S1 to be of charge-transfer (CT) character and to have high oscillator strength. Most recent studies17,19-21 have focused on modeling the solvent-dependent resonance Raman spectra of JDMN reported by Kelley and co-workers.22 Mennucci et al.19,21 and Guthmueller and Champange20 showed that TDDFT and CIS calculations in the presence of a continuum solvent †
Part of the “Barbara J. Garrison Festschrift”. * To whom correspondence should be addressed. E-mail: maroncelli@ psu.edu.
Figure 1. Molecular structures of DMN and JDMN and definition of the torsional angles considered in the deactivation of S1 DMN.
Figure 2. Neutral and zwitterionic resonance structures of the twostate model.
(PCM calculations23) could reasonably reproduce experimentally observed changes in the vibronic structure of both the absorption spectrum20 and the resonance Raman intensities19,20 with solvent. These changes are consistent with a simple picture of the S0 and S1 states being differently weighted mixtures of the neutral and zwiterionic resonance forms shown in Figure 2. Ferrighi et al.18 also computed the hyperpolarizabilities of DMN and homologues incorporating additional double bonds between the phenyl and malononitriles groups. They found that the large optical nonlinearities of these molecules were well reproduced by TDDFT calculations using the Coulomb-attenuated CAMB3LYP functional. All of the aforementioned computations concerned only the S1 state in the Franck-Condon (FC) region accessed by electronic absorption and resonance Raman spectroscopy. The sole study to explore S1 deactivation pathways
10.1021/jp907319n 2010 American Chemical Society Published on Web 11/05/2009
Nonradiative Deactivation in Benzylidene Malononitriles
J. Phys. Chem. C, Vol. 114, No. 12, 2010 5603
was a primarily experimental paper by Harriman and coworkers,1 who employed CIS/6-31G(d) calculations and concluded that torsional motion about τc is responsible for internal conversion of JDMN. In order to more definitively establish the motions responsible for nonradiative decay in the benzylidene malononitriles, we have applied higher-level electronic structure treatments such as an approximate second-order coupled cluster method (RICC2), the complete active space self-consistent field approach (CASSCF), and time-dependent density functional theory (TDDFT) augmented by classical molecular dynamics simulations. After briefly describing the methods employed, the results of this study are described in four sections. Section 3 compares the accuracy of various methods for reproducing observed properties of the ground states of DMN and JDMN. Similar comparisons for the S0 f S1 transition are described in Section 4. In Section 5 we discuss our exploration of the S1 potential energy surface of DMN, where we reach the same conclusion as did Allen et al.24 for JDMN, that isomerization about the double bond (τc) is the primary coordinate responsible for internal conversion in these molecules. Finally, the gas-phase τc torsional potential derived in Section 5 is used as input to preliminary classical molecular dynamics simulations of DMN in acetonitrile to show that motion along this coordinate is consistentwiththeinternalconversionratesobservedexperimentally. 2. Methods We have employed a variety of quantum chemical methods to study the molecular structure, S0 fS1 excitations, and S1 potential energy surface of DMN and JMN. Whereas TDDFT methods are the most economical choice for molecules of this size, the inherent defects in conventional TDDFT for chargetransfer systems such as these also necessitated exploration of additional methods such as the long-range corrected LC-TDBLYP approach, the second-order approximate coupled cluster (CC2)25 method, and the complete active space self-consistent field (CASSCF) method. Unless otherwise noted, all calculations employed the def-TZVP26 or def2-TZVP27 basis sets. In the LC-DFT approach, the Coulomb operator is divided into short- and long-range components:28
1 1 - erf(κr) erf(κr) ) + r r r
(1)
and full Hartree-Fock exchange is used for the long-range component (second term) of the operator. The physical motivation for this division arises from the observation that only pure Hartree-Fock (HF) exchange accounts for the donor-acceptor distance dependence of excitation energies in long-range charge transfer systems.29 Thus, the form of eq 1 ensures that DFT exchange is replaced asymptotically by HF exchange at large r in a fashion mediated by the so-called range separation parameter κ. Recent studies have shown that different values of κ are required to reproduce ground- versus excited-state properties,28 and we have therefore investigated how κ impacts the excitation energies, transition strengths, and dipole moments of malononitriles. All DFT and TDDFT calculations were performed with the GAMESS30 electronic structure program. The LC-DFT31 and LC-TDDFT approaches used were those of Tawada and coworkers.32 Except where otherwise noted, all DFT calculations employed the B3LYP functional.33 CC2 calculations under the resolution-of-the-identity approximation (RI-CC2)34 were used
to determine ground35 and excited states36 properties. Parallel RI-CC2 calculations37 were carried out with the Turbomole38 package. Geometries were optimized to within 10-4 Eh/a0. All CASSCF calculations were carried out using the GAMESS package30 using the 6-31G(d) basis set. Molecular dynamics (MD) simulations of DMN in acetonitrile solvent were performed using a modified version of the DLPOLY_2 code.39 Molecules were modeled as rigid collections of Lennard-Jones (12-6) plus Coulomb interaction sites. The three-site model developed by Edwards et al.40 was used to model acetonitrile. Lennard-Jones parameters for DMN were taken from the OPLS-AA force field.41 Charges and S1 torsional potentials of DMN were developed from electronic structure calculations as described in Sections 5 and 6. 3. Ground State Properties Ground state structural properties of DMN and JDMN are presented in Table 1. In the crystalline state both molecules are nearly planar with respect to the τa-c diherdral angles.42,43 There is a slight twist between the aromatic ring and malononitrile groups (τb > 0) due to repulsion between one CN group and the H atom on C3 of the ring (Figure 1). The amino nitrogen atom is also slightly pyramidalized, as indicated by τi in Table 1, which denotes the average of the three improper dihedral angles describing the deviation of the N11 center from the plane defined by C1, C12, and C13. The calculations generally reproduce these features observed in the crystalline state, but the DFT calculations overemphasize the planarity of the molecules. Calculated bond lengths and angles are also in good correspondence with those measured by X-ray diffraction. The comparisons in Table 1 show the hybrid DFT calculations B3LYP and PBE0 to provide the closest agreement with experiment (rmsd ) 0.02 Å) and RI-CC2 calculations the poorest agreement (rmsd ) 0.04-0.05 Å). The primary shortcoming of the RI-CC2 calculations with regard to structure is that they predict CN bonds that are up to 0.04 Å greater than experimental values. MP2 calculations (not shown) yield quite similar results, which suggests that the resolution-of-the-identity (RI) approximation is not the source of the error. A similar but much smaller overestimation of triple bond lengths was previously described by Ha¨ttig.35 To explore this shortcoming further, we optimized the geometries of the nonconjugated molecules acetonitrile and malononitrile, for which highly accurate gas-phase data are available for comparison (see Supporting Information, Table S-1). The experimental CN bond lengths in these nonconjugated molecules are comparable to the CN lengths in DMN and JDMN. In this case RI-CC2 and MP2 again overestimate these lengths but to a much smaller extent, ∼0.01 Å, and DFT and CCSD calculations provide somewhat better agreement with experiment. We also examined the “D1” diagnostic for the RI-CC2 calculations, which reports on the quality of the HF reference wave function44 (see Table S-2). We find that the values of D1 calculated for DMN and JDMN (∼0.1) are much above the threshold of 0.05 recommended for ground state work, whereas they fall in the acceptable range (
