Daniel W. Silverstein

Theoretical Studies of Plasmonics using Electronic Structure Methods

3.1. Enhanced Electronic Excitations 3968 3.2. Surface-Enhanced Infrared Absorption 3970 4. Surface-Enhanced Fluorescence 3970 5. Surface-Enhanced Raman Scattering 3974 5.1. Early History of SERS 3974 5.2. The Electromagnetic Mechanism 3975 5.3. The Chemical Mechanism 3976 5.3.1. The Resonance Raman Mechanism 3976 5.3.2. The Charge-Transfer Mechanism 3977 5.3.3. The Nonresonant Chemical Mechanism 3977 5.4. Unifying the Description of SERS 3978 5.4.1. Combined Quantum and Classical Method for SERS 3979 6. Chiroptical Properties of Small Metal Clusters 3979 6.1. Circular Dichroism 3979 6.1.1. Chiral Core Model 3980 6.1.2. Dissymmetric Field Model 3981 6.1.3. Chiral Footprint Model 3981 6.2. Vibrational Raman Optical Activity 3983 7. Nonlinear Optical Properties 3984 7.1. Surface-Enhanced Hyper-Raman Scattering 3984 8. Conclusion 3986 Author Information 3987 Biographies 3987 Acknowledgment 3987 References 3988

Vibronic coupling simulations for linear and nonlinear optical processes: Theory

A comprehensive vibronic coupling model based on the time-dependent wavepacket approach is derived to simulate linear optical processes, such as one-photon absorbance and resonance Raman scattering, and nonlinear optical processes, such as two-photon absorbance and resonance hyper-Raman scattering. This approach is particularly well suited for combination with first-principles calculations. Expressions for the Franck-Condon terms, and non-Condon effects via the Herzberg-Teller coupling approach in the independent-mode displaced harmonic oscillator model are presented. The significance of each contribution to the different spectral types is discussed briefly.

Assessment of the accuracy of long-range corrected functionals for describing the electronic and optical properties of silver clusters.

The absorption spectra and ionization potentials of silver clusters Ag(n) (n=4-20) are examined in the framework of density-functional theory (DFT) using several different methods of representing the exchange-correlation functional. Three different types of exchange-correlation functionals are used: those including gradient corrections to the density in the generalized gradient approximation, global hybrid functionals mixing in a portion of the Hartree-Fock exchange, and long-range-corrected (LC-) functionals. Comparison of ionization potentials calculated using DFT with those derived from experiments demonstrates that LC-functionals more accurately represent the electronic structure of the silver clusters studied. Absorption spectra are compared with both experimental spectra and those derived using higher level theoretical calculations showing that the LC-functionals appear to correctly describe the optical transitions in the gas phase, particularly when a small redshift in the experimental spectrum is accounted for due to matrix effects. It is also demonstrated that the LC-hybrid functionals significantly reduce the occurrence of spurious states in the optical absorbance spectrum while maintaining the intensity of plasmon like features of the spectra for larger silver clusters.

Molecular logic gates using surface-enhanced Raman-scattered light.

A voltage-activated molecular-plasmonics device was created to demonstrate molecular logic based on resonant surface-enhanced Raman scattering (SERS). SERS output was achieved by a combination of chromophore-plasmon coupling and surface adsorption at the interface between a solution and a gold nanodisc array. The chromophore was created by the self-assembly of a supramolecular complex with a redox-active guest molecule. The guest was reversibly oxidized at the gold surface to the +1 and +2 oxidation states, revealing spectra that were reproduced by calculations. State-specific SERS features enabled the demonstration of a multigate logic device with electronic input and optical output.

Probing Two-Photon Properties of Molecules: Large Non-Condon Effects Dominate the Resonance Hyper-Raman Scattering of Rhodamine 6G

Experimentally measured resonance hyper-Raman (RHR) spectra spanning the S(1) ← S(0), S(2) ← S(0), and S(3) ← S(0) transitions in rhodamine 6G (R6G) have been recorded. These spectra are compared to the results of first-principles calculations of the RHR intensity that include both Franck-Condon (A-term) and non-Condon (B-term) scattering effects. Good agreement between the experimental and theoretical results is observed, demonstrating that first-principles calculations of hyper-Raman intensities are now possible for large molecules such as R6G. Such agreement indicates that RHR spectroscopy will now be a routine aid for probing multiphoton processes. This work further shows that optimization of molecular properties to enhance either A- or B-term scattering might yield molecules with significantly enhanced two-photon properties.

Vibronic coupling simulations for linear and nonlinear optical processes: Simulation results

A vibronic coupling model based on time-dependent wavepacket approach is applied to simulate linear optical processes, such as one-photon absorbance and resonance Raman scattering, and nonlinear optical processes, such as two-photon absorbance and resonance hyper-Raman scattering, on a series of small molecules. Simulations employing both the long-range corrected approach in density functional theory and coupled cluster are compared and also examined based on available experimental data. Although many of the small molecules are prone to anharmonicity in their potential energy surfaces, the harmonic approach performs adequately. A detailed discussion of the non-Condon effects is illustrated by the molecules presented in this work. Linear and nonlinear Raman scattering simulations allow for the quantification of interference between the Franck-Condon and Herzberg-Teller terms for different molecules.

Probing One‐Photon Inaccessible Electronic States with High Sensitivity: Wavelength Scanned Surface Enhanced Hyper‐Raman Scattering

Electronic excited states play an essential role in a wide range of molecular processes from biology to molecular electronics. For example, charge separation and its subsequent transport in organic photovoltaics occurs through molecular excited states. Traditionally, experimental characterization of the topology of molecular excited states is achieved through spectroscopic techniques such as resonance Raman scattering. The sensitivity of resonance Raman to details of the excited state potential energy landscape is clearly elucidated in the theory of inelastic light scattering, although ab initio calculations of electronic excited states remain quite challenging. In some cases, one photon transitions to the electronic state of interest are either weak or forbidden and thus the methods available for probing these “dark” states are severely restricted. These dark states, however, are often coupled to the bright states and can play a major role in the electronic and nuclear dynamics. Indeed, a recent study of excited-state intermolecular proton transfer demonstrated that dark states can directly affect electronic relaxation kinetics, which subsequently alters the product branching ratios. Herein we report a method utilizing surface enhanced hyper-Raman scattering (SEHRS) to probe these one-photon inaccessible electronic states for analytes at low concentration (~10 10 m). We also demonstrate that a close coupling of time-dependent density functional theory (TDDFT) simulations of the two-photon absorption spectrum and off-resonance hyper-Raman spectra yield important insights into the nature of the probed electronic states. Hyper-Raman scattering is a type of nonlinear light scattering in which a photon at w= 2w0 wvib is incoherently scattered, where w0 is the laser frequency and wvib is a vibration characteristic of the material. Hyper-Raman scattering provides information that is complementary to that obtained from IR and Raman; further resonance hyper-Raman provides access to electronic states that are not one-photon allowed. While hyper-Raman scattering is an inherently weak process, the signal originating from molecules located near the surface of a plasmonic nanostructure can be enhanced by many orders of magnitude. SEHRS also contains unique information about surface symmetry and can be applied to biological imaging. SEHRS spectra of Rhodamine 6G (R6G) adsorbed on aggregated silver colloids were recorded for excitation wavelengths between 750–1045 nm in increments of ~15 nm. This range spans the two-photon absorption spectrum of R6G and selected (4 of 20) spectra are shown in Figure 1. All spectra are reported without baseline or background corrections and typical laser powers were ~5 mW (~63 pJ pulse ) at the sample. The concentration of R6G was 10 7 m for the wavelength scanned experiments but we have obtained spectra with [R6G] = 10 10 m. In order to systematically explore the changes in the SEHRS spectra as a function of excitation energy, we fit each spectrum to determine peak positions and areas (see the Supporting Information). The fitted areas were then used to plot ratios of the 771, 1316, 1535, and 1611 bands to the 1189 band as a function of excitation wavelength. Figure 2 compares the experimental and theoretical, oneand two-photon absorption spectrum of R6G with our peak area ratios as a function of excitation energy. The 1189 band was chosen as a reference because it remains mostly constant over the measured range and because the large signal difference between SEHRS and normal hyper-Raman scattering makes calibration to an internal standard difficult. The ratio 1316:1189 remains constant over the measured range, while the other ratios 771:1189, 1535:1189 and 1611:1189 correlate well with peaks in the two-photon absorption spectrum, suggesting that these bands experience a resonance enhancement. Further, 1535 peaks in a region where the one-photon absorption cross section is negligible. Our theoretically calculated absorption spectra (Figure 2) are in good agreement with experiment and yield insight into the nature of the responsible excited states. For excitation energies probed here, three excited states, S1, S2, and S3, contribute to the absorption spectra. However, excitation to S2 is not observed in the one-photon spectra. Figure 3 displays the frontier orbitals involved in the electronic transitions S1 !S0, S2 !S0, and S3 !S0. All three states are localized on the xanthene ring region of the R6G molecule and indeed the major modes observed are vibrations whose motion is concentrated in this area. To understand in more detail the observed SEHRS spectra we calculated the off-resonance hyper-Raman spectra by numerical differentiation of the static hyperpolarizability obtained from TDDFT. Calculations at this level of theory yield excellent agreement with experimental measurements of the absolute [a] C. B. Milojevich, Prof. J. P. Camden Department of Chemistry University of Tennessee Knoxville Knoxville, TN 37996-1600 (USA) Fax: (+ 1) 865-974-9332 E-mail : jcamden@utk.edu [b] D. W. Silverstein, Prof. L. Jensen Department of Chemistry Pennsylvania State University University Park, PA 16802 (USA) Fax: (+ 1) 814-865-3314 E-mail : jensen@chem.psu.edu Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201000868.

Multiscale Reactive Molecular Dynamics for Absolute pKa Predictions and Amino Acid Deprotonation

Accurately calculating a weak acid’s pKa from simulations remains a challenging task. We report a multiscale theoretical approach to calculate the free energy profile for acid ionization, resulting in accurate absolute pKa values in addition to insights into the underlying mechanism. Importantly, our approach minimizes empiricism by mapping electronic structure data (QM/MM forces) into a reactive molecular dynamics model capable of extensive sampling. Consequently, the bulk property of interest (the absolute pKa) is the natural consequence of the model, not a parameter used to fit it. This approach is applied to create reactive models of aspartic and glutamic acids. We show that these models predict the correct pKa values and provide ample statistics to probe the molecular mechanism of dissociation. This analysis shows changes in the solvation structure and Zundel-dominated transitions between the protonated acid, contact ion pair, and bulk solvated excess proton.

Simulating One-Photon Absorption and Resonance Raman Scattering Spectra Using Analytical Excited State Energy Gradients within Time-Dependent Density Functional Theory

A parallel implementation of analytical time-dependent density functional theory gradients is presented for the quantum chemistry program NWChem. The implementation is based on the Lagrangian approach developed by Furche and Ahlrichs. To validate our implementation, we first calculate the Stokes shifts for a range of organic dye molecules using a diverse set of exchange-correlation functionals (traditional density functionals, global hybrids, and range-separated hybrids) followed by simulations of the one-photon absorption and resonance Raman scattering spectrum of the phenoxyl radical, the well-studied dye molecule rhodamine 6G, and a molecular host-guest complex (TTF⊂CBPQT(4+)). The study of organic dye molecules illustrates that B3LYP and CAM-B3LYP generally give the best agreement with experimentally determined Stokes shifts unless the excited state is a charge transfer state. Absorption, resonance Raman, and fluorescence simulations for the phenoxyl radical indicate that explicit solvation may be required for accurate characterization. For the host-guest complex and rhodamine 6G, it is demonstrated that absorption spectra can be simulated in good agreement with experimental data for most exchange-correlation functionals. However, because one-photon absorption spectra generally lack well-resolved vibrational features, resonance Raman simulations are necessary to evaluate the accuracy of the exchange-correlation functional for describing a potential energy surface.

Understanding the Resonance Raman Scattering of Donor-Acceptor Complexes using Long-Range Corrected DFT.

The optical properties involving charge-transfer states of the donor-acceptor electron-transfer complexes carbazole/tetracyanoethylene (carbazole/TCNE) and hexamethylbenzene/tetracyanoethylene (HMB/TCNE) were investigated by utilizing the time-dependent theory of Heller to simulate absorbance and resonance Raman spectra. Excited-state properties were obtained using time-dependent density functional theory (TDDFT) using the global hybrid B3LYP and the long-range corrected LC- ωPBE functionals and compared with experimental results. It is shown that, while reasonable simulations of the absorbance spectra can be made using B3LYP, the resonance Raman spectra for both complexes are poorly described. The LC-ωPBE functional gives a more accurate representation of the excited-state potential energy surfaces in the Franck-Condon region for charge-transfer states, as indicated by the good agreement with the experimental resonance Raman spectrum. For the carbazole/TCNE complex, which includes contributions from two overlapping excited states on its absorbance spectrum, interference effects are discussed, and it is found that detuning from resonance with an excited state results in interference along with other factors. Total vibrational reorganization energy for both complexes is discussed, and it is found that both B3LYP and LC-ωPBE yield reasonable estimates of this quantity compared with experiment.