Published: June 21, 2011 r2011 American Chemical Society 1849 dx.doi.org/10.1021/jz2005573 | J. Phys. Chem. Lett. 2011, 2, 1849–1854 LETTER pubs.acs.org/JPCL Modeling Coherent Anti-Stokes Raman Scattering with Time-Dependent Density Functional Theory: Vacuum and Surface Enhancement. John A. Parkhill,* Dmitrij Rappoport,* and Al  an Aspuru-Guzik* Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, Massachusetts 02138, United States b S Supporting Information C oherent anti-Stokes Raman Scattering (CARS) 1 is an in- creasingly popular four-wave mixing optical technique for spectroscopy and chemically specific microscopy. The advan- tages offered over simple spontaneous Raman spectroscopy are the coherent signal blue-shifted away from fluorescence and rapid acquisition from the collective response of many chromo- phores. Recent advances in the microscopic applications of this technique have improved signal collection through the use of tightly focused beams, 2 which relax the phase-matching condi- tion, and techniques for limiting the nonresonant (NR) signal. 3,4 Spectroscopic studies have separated the resonant from NR signals in the time domain 3 and designed more efficient 5,6 collection sequences. The enhancement of CARS by intense plasmon fields could potentially enhance the signal further and is the motivation for this work. To address this problem theo- retically, we have developed code to simulate CARS spectra of molecules bound to cluster models of metal surfaces, which is described below. The enhancement of spectroscopies by the intense fields of nearby collective excitations in metals or semiconductors has experienced a renaissance in recent years, especially surface- enhanced Raman scattering (SERS). 7 Given the nonlinear depen- dence of the CARS signal on input power (I CARS µ E 1 2 E 2 ), one might expect surface-enhanced CARS (SE-CARS). The first report of CARS occurring near a surface plasmon was published decades ago 8 and was followed by reports of CARS observed from single molecules 9 and on the tips of scanning-tunneling microscopes. 10 Despite these advances, the paucity of SE-CARS spectra and scattering cross sections available in the literature indicates that this remains a difficult experiment to perform and completely characterize. We will try to offer some indication of chemical enhancement effects of SE-CARS, and in the last section, we point out challenges facing application of the spectroscopy that should be given further attention. Past theory has focused 11,12 on understanding the classical electrodynamic features of CARS spectroscopy until Hartree Fock (HF) polarizability derivatives were combined with (static) density functional theory (DFT) vibrational frequencies to produce the first ab initio CARS spectra. 13,14 HF theory’s neglect of electronelectron interaction is especially unphysical for sys- tems with significant correlation, like metals. For this reason, we replace HF for the calculation of CARS on metal cluster models. In this work, we present the first CARS spectra calculated entirely with DFT. Prior to applying the method to metal clusters, we test the model on a few known experimental spectra from previous work to make some estimation of its usefulness. Theory. The CARS spectra in this paper are calculated in the double-harmonic approximation developed by the Aarhus group, 13 which follows from the much older double harmonic approxima- tion to Raman spectra, 15 which we briefly review. The typical CARS experiment applies two lasers of frequencies ω 1 and ω 2 , which scatter twice and once, respectively, off of the target material. Signal radiation collected at 2ω 1  ω 2 peaks when the Stokes shift, ω 1 ω 2 , coincides with a vibrational transition of the scatterer. On the scale of a single molecule, CARS is governed by the second hyperpolarizabiliity (χ (3) (2ω 1  ω 2 ;ω 1 ,  ω 2 ,ω 1 )). We include terms where the central resolution in the sum-over- states expression for χ (3) only includes excited vibrational states Received: April 26, 2011 Accepted: June 21, 2011 ABSTRACT: We present the first density functional simulations of coherent anti-Stokes Raman scattering (CARS) and an analysis of the chemical effects upon binding to a metal surface. Spectra are obtained from first-principles electronic structure calculations and are compared with available experiments and previously available theoretical results following from HartreeFock polarizability derivatives. A first approximation to the nonresonant portion of the CARS signal is also explored. We examine the silver pyridine cluster models of the surface chemical signal enhancement, previously introduced for surface-enhanced Raman scattering. Chemical resonant intensity enhancements of roughly 10 2 are found for several model clusters. The prospects of realizing further enhancement of CARS signal with metal surfaces is discussed in light of the predicted chemical enhancements. SECTION: Surfaces, Interfaces, Catalysis