Electrostatic Interaction Model for the Calculation of the Polarizability of Large Noble Metal Nanoclusters

In this work we have presented a capacitance-polarizability interaction model for describing the polarizability of large metal clusters. The model consists of interacting atomic capacitances and polarizabilities that are optimized to reproduce the full polarizability tensors of medium sized (N ≤ 68) gold and silver clusters. The reference polarizability tensors have been calculated using time-dependent density functional theory and shown good agreement with experimental results. We have shown that very good agreement between the model and the DFT results can be achieved both for the isotropic and anisotropic polarizability as a function of size, thus providing an accurate description of the polarizability of noble metal clusters. The model is computationally efficient and can easily handle cluster several nm in radius, thus, provides a natural bridge between the quantum mechanical methods and the macroscopic electrodynamic description. This allowed us to study the polarizability of silver and gold clusters having different shapes, i.e., spheres, rods, and disks, and sizes having diameters as large as 4.5 nm, thus, reaching the saturation of the polarizability. By partitioning the total polarizability into effective atomic polarizabilities that depend on the atomic position in the cluster, we provide a physical picture of the saturation of the polarizability of metal clusters as a function of size. This illustrates that the onset of the saturation occurs as the cluster starts to have a core of atoms showing bulk-like polarizabilities, surrounded by layers of atoms with surface-like polarizabilities. For larger clusters we see that the bulk core grows whereas the surface layers keep roughly the same thickness thus leading to a saturation of the polarizability as the size of the cluster increases

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

Understanding the Molecule−Surface Chemical Coupling in SERS

The enhancement mechanism due to the molecule-surface chemical coupling in surface-enhanced Raman scattering (SERS) has been characterized using time-dependent density functional theory. This has been achieved with a systematical study of the chemical enhancement of meta- and para-substituted pyridines interacting with a small silver cluster (Ag20). Changing the functional groups on pyridine enabled us to modulate the direct chemical interactions between the pyridine ring and the metal cluster. Surprisingly, we find that the enhancement does not increase as more charge is transferred from the pyridine ring to the cluster. Instead, we find that the magnitude of chemical enhancement is governed to a large extent by the energy difference between the highest occupied energy level (HOMO) of the metal and the lowest unoccupied energy level (LUMO) of the molecule. The enhancement scales roughly as (ωX/ω̅e)4, where ω̅e is an average excitation energy between the HOMO of the metal and the LUMO of the molecule and ωX is the HOMO−LUMO gap of the free molecule. The trend was verified by considering substituted benzenethiols, small molecules, and silver clusters of varying sizes. The results imply that molecules that show significant stabilization of the HOMO−LUMO gaps (such as those that readily accept π-backbonding) would be likely to have strong chemical enhancement. The findings presented here provide the framework for designing new molecules which exhibit high chemical enhancements. However, it remains a challenge to accurately describe the magnitude of the Raman enhancements using electronic structure methods, especially density functional theory, because they often underestimate the energy gap

Simulating Surface-Enhanced Raman Optical Activity Using Atomistic Electrodynamics-Quantum Mechanical Models

Raman optical activity has proven to be a powerful tool for probing the geometry of small organic and biomolecules. It has therefore been expected that the same mechanisms responsible for surface-enhanced Raman scattering may allow for similar enhancements in surface-enhanced Raman optical activity (SEROA). However, SEROA has proved to be an experimental challenge and mirror-image SEROA spectra of enantiomers have so far not been measured. There exists a handful of theories to simulate SEROA, all of which treat the perturbed molecule as a point-dipole object. To go beyond these approximations, we present two new methods to simulate SEROA: the first is a dressed-tensors model that treats the molecule as a point-dipole and point-quadrupole object; the second method is the discrete interaction model/quantum mechanical (DIM/QM) model, which considers the entire charge density of the molecule. We show that although the first method is acceptable for small molecules, it fails for a medium-sized one such as 2-bromohexahelicene. We also show that the SEROA mode intensities and signs are highly sensitive to the nature of the local electric field and gradient, the orientation of the molecule, and the surface plasmon frequency width. Our findings give some insight into why experimental SEROA, and in particular observing mirror-image SEROA for enantiomers, has been difficult

Orbital Renormalization Effects on the Coupling between Molecular Excitations and Plasmons

Accurately describing the electronic structure of molecules on metal nanostructures is key to modeling their surface-enhanced properties. Particularly difficult is the modeling of the coupling between molecular excited states and plasmons. Here we present a computational efficient approach to study the renormalization effects on the molecular electronic structure and its optical properties due to the interactions with the metal surface. Accurate simulations of the renormalization effects are achieved by employing a hybrid atomistic electrodynamics and time-dependent density functional model. The coupling between the molecular absorption and the plasmon excitation depends strongly on the spectral overlap. Here we show that the renormalization effect for the benzene–tetracyano­ethylene donor–acceptor complex interacting with a metal nanoparticle causes a 0.6 eV shift in the absorption band. Furthermore, we show that the coupling between the molecular absorption and the plasmon excitation is caused by interference between the molecular absorption, the image field of the metal nanoparticle, and the near field due to the plasmon excitation. The results presented here illustrate the importance of using first-principles simulations to understand in detail the coupling between molecular absorption and plasmon excitation

Frozen Density Embedding with External Orthogonality in Delocalized Covalent Systems

Frozen density embedding (FDE) has become a popular subsystem density functional theory (DFT) method for systems with weakly overlapping charge densities. The failure of this method for strongly interacting and covalent systems is due to the approximate kinetic energy density functional (KEDF), although the need for approximate KEDFs may be eliminated if each subsystem’s Kohn–Sham (KS) orbitals are orthogonal to the other, termed external orthogonality (EO). We present an implementation of EO into the FDE framework within the Amsterdam density functional program package, using the level-shift projection operator method. We generalize this method to remove the need for orbital localization schemes and to include multiple subsystems, and we show that the exact KS-DFT energies and densities may be reproduced through iterative freeze-and-thaw cycles for a number of systems, including a charge delocalized benzene molecule starting from atomic subsystems. Finally, we examine the possibility of a truncated basis for systems with and without charge delocalization, and found that subsystems require a basis that allows them to correctly describe the supermolecular delocalized orbitals

Determining Molecular Orientation With Surface-Enhanced Raman Scattering Using Inhomogenous Electric Fields

The inhomogenous electric field near the metal surface of plasmonic nanoparticles allows molecular orientation to be determined from surface-enhanced Raman scattering (SERS). We illustrate this by simulating the effects of the field-gradient on the SERS spectrum of benzene and pyridine. To do this, we present an origin-independent formalism describing the effects of the local electric-field gradient in SERS. Using this formalism, we found that the field-gradient led to observation of Raman-inactive modes in benzene and allowed for extraction of orientation information from the SERS spectra of both benzene and pyridine. It was also observed that the SERS electromagnetic enhancement factor, when considering field-gradient effects, depends on the field-gradient magnitudes and is only approximately described by |<i>E</i>|⁴ for certain modes. The field-gradient mechanism may also lead to a weakening of intensities as compared to a homogeneous local field. Thus, inclusion of field-gradient effects are crucial in understanding relative intensity changes in SERS

Simulating Third-Order Nonlinear Optical Properties Using Damped Cubic Response Theory within Time-Dependent Density Functional Theory

A general implementation for damped cubic response properties is presented using time-dependent density functional theory (TDDFT) and Slater-type orbital basis sets. To directly calculate two-photon absorption (TPA) cross sections, we also present an implementation of a reduced damped cubic response approach. Validation of the implementations includes a detailed comparison between response theory and the sum-over-states approach for calculating the nonlinear optical properties of LiH, as well as a comparison between the simulated and experimental TPA and third-harmonic generation (THG) spectra for the dimethylamino-nitrostilbene (DANS) molecule. The study of LiH demonstrates the incorrect pole structure obtained in response theory due to the adiabatic approximation typically employed for the exchange-correlation kernel. For DANS, we find reasonable agreement between simulated and experimental TPA and THG spectra. Overall, this work shows that care must be taken when calculating higher-order response functions in the vicinity of one-photon poles due to the approximate kernels typically used in the simulations

Simulating Ensemble-Averaged Surface-Enhanced Raman Scattering

The ability to simulate surface-enhanced Raman scattering (SERS) is a vital tool in elucidating the chemistry of molecules near the vicinity of plasmonic metal nanoparticles. However, typical methods do not include the dynamics of the molecule(s) of interest and are often limited to a single or few molecules. In this work, we combine molecular dynamics simulations with the dressed-tensor formalism to simulate the SERS spectra of Ag nanoparticles coated with a full monolayer of pyridine molecules. This method allows us to simulate the ensemble-averaged SERS spectra of more realistic large scale systems, while accounting for the organization of molecules in the hotspots. Through these simulations, we find that the preferential binding location and orientation of the molecules, the choice of electrodynamics method, and the inclusion of field gradient effects influence both the enhancement distribution and the spectral signatures. We also show that both the translational and rotational motions of a pyridine molecule near a nanoparticle junction may be effectively tracked through its SERS spectrum